WIRELESS SELF-CALIBRATION OF A PHASE-STACKED ARRANGE ANTENNA WITH DIRECTIONAL ANTENNA ELEMENTS

Abstract

A method for calibrating a phased array antenna is provided. The method comprises performing a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between a calibration line and the subset of antenna elements to obtain a calibrated subset of antenna elements;Acquiring a first OTA calibration measurement pair, the first OTA calibration measurement pair comprising a first OTA calibration measurement associated with a particular geometric relationship, determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement, acquiring a second OTA calibration measurement pair associated with the particular geometric relationship, and determining at least one of a phase correction factor and a gain correction factor between complex gains of a pair of uncalibrated antenna elements;

Description

FIELD OF TECHNOLOGY

[0001] The present disclosure relates to antenna devices for satellite communication systems and calibration architectures for antenna arrays. BACKGROUND

[0002] Satellite communications systems typically employ ground-based antennas that communicate with a constellation of satellites in orbit. Ground-based antennas are therefore exposed to weather and other environmental conditions. Therefore, antenna devices and their housing assemblies are described here that are rugged enough to protect the internal antenna components while enabling radio-frequency communication with a satellite communications system, such as a constellation of satellites.

[0003] Phased array antennas are used in a variety of wireless communication systems, such as satellite and cellular communication systems. Phased array antennas may contain a series of antenna elements arranged to behave like a larger directional antenna. In addition, a phased array antenna can be used to increase overall directivity and gain, control the angle of the array for greater gain and higher directivity, suppress interference from one or more directions, determine the direction of arrival of received signals, and improve the signal-to-interference ratio, among other things.Advantageously, a phased array antenna can be configured to implement beamforming techniques to transmit and / or receive signals in a preferred direction without the need to be physically repositioned or re-orientated.

[0004] In some cases, the performance characteristics of the antenna elements of a phased array antenna, such as gain, phase, delay, etc., may change due to weather and other environmental conditions. During operation of a phased array antenna, various calibration procedures can be performed to compensate for fluctuations in performance characteristics. SUMMARY

[0005] According to one embodiment of the present disclosure, a method for calibrating antenna elements is provided. The method comprises: performing a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between a calibration line and the subset of antenna elements to obtain a calibrated subset of antenna elements;Acquiring a first OTA calibration measurement pair, wherein the first OTA calibration measurement pair comprises a first OTA calibration measurement between a first uncalibrated antenna element of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements, wherein the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a particular geometric relationship; determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement;Acquiring a second OTA calibration measurement pair, the second OTA calibration measurement pair comprising a third OTA calibration measurement between a second uncalibrated antenna element of the antenna grid and the first uncalibrated antenna element and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element of the antenna grid, the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element being configured with the determined geometric relationship;and determining, based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement, at least one phase correction factor and / or a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element;

[0006] According to another embodiment of the present disclosure, an apparatus for calibrating antenna elements is provided. The apparatus comprises: a calibration line; an antenna grid; and one or more calibration components configured to: perform a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between the calibration line and the subset of antenna elements to achieve a calibrated subset of antenna elements;Acquiring a first OTA calibration measurement pair, wherein the first OTA calibration measurement pair comprises a first OTA calibration measurement between a first uncalibrated antenna element of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements, wherein the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a particular geometric relationship; determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement;Acquiring a second OTA calibration measurement pair, the second OTA calibration measurement pair comprising a third OTA calibration measurement between a second uncalibrated antenna element of the antenna grid and the first uncalibrated antenna element and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element of the antenna grid, the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element being configured with the determined geometric relationship;and determining, based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement, at least one phase correction factor and / or a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element;

[0007] In accordance with another embodiment of the present disclosure, a method for calibrating antenna elements is provided. The method includes: obtaining a first mutual coupling measurement associated with a first wireless (over-the-air = OTA) signal path between a first antenna element functional transmit (TX) port of a first antenna element and a second antenna element functional receive (RX) port of a second antenna element, wherein the first antenna element includes the first antenna element functional transmit (TX) port and a first antenna element functional receive (RX) port, and the second antenna element includes a second antenna element functional transmit (TX) port and the second antenna element functional receive (RX) port;Obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit port (TX port) of a third antenna element and the second antenna element functional receive port (RX port), wherein the third antenna element comprises the third antenna element functional transmit port (TX port) and a third antenna element functional receive port (RX port);Obtaining a third mutual coupling measurement associated with a third OTA signal path between a fourth antenna element functional transmit port (TX port) of a fourth antenna element and a fifth antenna element functional receive port (RX port) of a fifth antenna element, wherein the fourth antenna element comprises the fourth antenna element functional receive port (RX port) and a fourth antenna element functional transmit port (TX port), and the fifth antenna element comprises the fifth antenna element functional receive port (RX port) and a fifth antenna element functional transmit port (TX port);Obtaining a fourth mutual coupling measurement connected to a fourth OTA signal path between the functional transmit port (TX port) of the third antenna element and the functional receive port (RX port) of the fourth antenna element, wherein an antenna grid comprises a plurality of periodically spaced antenna elements including the first antenna element, the second antenna element, the third antenna element, the fourth antenna element, and the fifth antenna element; and determining, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement, and one or more redundancies, at least one of a phase correction factor and an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element.

[0008] According to another embodiment of the present disclosure, an apparatus for calibrating antenna elements is provided. The apparatus comprises: an antenna grid comprising a plurality of periodically spaced antenna elements, including a first antenna element, a second antenna element, a third antenna element, a fourth antenna element, and a fifth antenna element;and one or more calibration components configured to: obtain a first mutual coupling measurement connected to a first OTA signal path between a first antenna element functional transmit port (TX port) of the first antenna element and a second antenna element functional receive port (RX port) of the second antenna element, wherein the first antenna element comprises the first antenna element functional transmit port (TX) and a first antenna element functional receive port (RX), and the second antenna element comprises a second antenna element functional transmit port and the second antenna element functional receive port (RX);Obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit port (TX) of the third antenna element and the second antenna element functional receive port (RX), wherein the third antenna element comprises the third antenna element functional transmit port (TX) and a third antenna element functional receive port (RX);Obtaining a third mutual coupling measurement connected to a third OTA signal path between a fourth antenna element functional transmit port (TX) of the fourth antenna element and a fifth antenna element functional receive port (RX) of the fifth antenna element, wherein the fourth antenna element comprises the fourth antenna element functional receive port (RX) and a fourth antenna element functional transmit port (TX), and the fifth antenna element comprises the fifth antenna element functional receive port (RX) and a fifth antenna element functional transmit port (TX); Obtaining a fourth mutual coupling measurement connected to a fourth OTA signal path between the functional transmit port (TX) of the third antenna element and the functional receive port (RX) of the fourth antenna element;and determining, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement, and one or more redundancies, at least one phase correction factor and / or an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element; DESCRIPTION OF THE DRAWINGS

[0009] The foregoing aspects and many of the attendant advantages of this invention will be better appreciated as the following detailed description is taken in conjunction with the accompanying drawings: Fig. 1 is a diagram, not to scale, showing a simple example of communication in a satellite communication system according to some embodiments of the present disclosure; Fig. 2A is an example top view of a phased array antenna system according to some embodiments of the present disclosure; Fig. 2B is an exemplary illustration of a beamformer (BF) grating connected to a phased array antenna system in accordance with some embodiments of the present disclosure; Fig. 3 shows a radiation pattern illustrating an example main lobe and side lobes emanating from an example phased array antenna system in accordance with some embodiments of the present disclosure; Fig. 4A shows an example of a phased array antenna system in a transmit (TX) configuration according to some embodiments of the present disclosure; Fig. Figure 4B shows the example of the phased array antenna system of Fig. 4A in a receive configuration (RX), in accordance with some embodiments of the present disclosure; Fig. 4C and Fig. 4D illustrate exemplary over-the-air (OTA) calibration configurations for calibrating phased array antenna systems with dual-use antenna ports in accordance with some embodiments of the present disclosure; Fig. 4E illustrates an exemplary configuration for calibrating a TX antenna array with antenna elements having two antenna ports and using the functional TX port as a dual-use antenna port for calibration, in accordance with some embodiments of the present disclosure; Fig. 4F shows another example of a calibration configuration for calibrating a TX antenna array of antenna elements having a dual-use antenna port different from the functional TX port, in accordance with some embodiments of the present disclosure; Fig. 4G shows an exemplary configuration for calibration based on a transmit signal without requiring a coherent receive measurement (RX) port of BFs or front-end modules (FEMs), in accordance with some embodiments of the present disclosure; Fig. 5A shows an exemplary calibration configuration for calibrating antenna elements in a phased array antenna with antenna elements having dual-use ports for transmitted and received calibration signals, in accordance with some embodiments of the present disclosure; Fig. 5B shows another example of a calibration configuration for a phased array antenna with antenna elements having common calibration ports for transmitted and received calibration signals, in accordance with some embodiments of the present disclosure; Fig. 5C and Fig. 5D illustrate example calibration configurations for resolving ambiguities in calibration solutions based on OTA calibration measurements, in accordance with some embodiments of the present disclosure; Fig. 6 shows an exemplary configuration for a phased array antenna system having antenna elements with dedicated antenna ports for transmitting and receiving, in accordance with some embodiments of the present disclosure; Fig. 7 shows an exemplary calibration measurement configuration for a phased array antenna system including antenna elements with dedicated antenna ports for transmitting and receiving, in accordance with some embodiments of the present disclosure; Fig. 8A illustrates an exemplary calibration configuration with additional redundancy to supplement OTA measurements of mutual coupling for OTA calibration of a phased array antenna system in accordance with some embodiments of the present disclosure; Fig. Figure 8B shows a detailed view of a subsection of the antenna grid of the calibration training 800 of Fig. 8A, including a portion of a calibration line, in accordance with some embodiments of the present disclosure; Fig. 8C shows an example calibration result for calibrating antenna elements connected to a calibration line in accordance with some embodiments of the present disclosure; Fig. 8D and Fig. 8E illustrates an exemplary calibration configuration that may be used to perform OTA calibration of columns (rows) of antenna elements using a reference subset of self-calibrated antenna elements connected to a calibration line, in accordance with some embodiments of the present disclosure; Fig. 8F shows an example of a calibration configuration that may be used to perform OTA calibration of rows of antenna elements using a reference subset of self-calibrated antenna elements connected to a calibration line, in accordance with some embodiments of the present disclosure; Fig. 9A shows an exemplary configuration of a two-way FEM with dedicated transmit and receive ports connected to respective dual-port antenna elements of a sub-array of two antenna elements of an antenna grid, in accordance with some embodiments of the present disclosure; Fig. 9B shows an exemplary configuration of a three-way FEM with dedicated transmit and receive ports connected to respective dual-port antenna elements of a sub-array of three antenna elements of an antenna grid, in accordance with some embodiments of the present disclosure; Fig. 9C and Fig. 9D illustrate example configurations for sharing radio frequency input / output (RFIO) ports between pairs of two-way FEMs coupled to four antenna element sub-arrays arranged in a linear configuration, in accordance with some embodiments of the present disclosure; Fig. 9E to Fig. 9H illustrate example configurations for sharing RFIO ports between pairs of two-way FEMs arranged into four antenna element sub-arrays in a rectangular configuration, in accordance with some embodiments of the present disclosure; Fig. 9I shows an example calibration configuration for calibrating a rectangular array of antenna elements comprising four rows and four columns, in accordance with some embodiments of the present disclosure; Fig. 10A shows an exemplary calibration configuration for calibrating antenna elements in a two-dimensional (2D) phased array antenna in accordance with some embodiments of the present disclosure; Fig. 10B shows an exemplary calibration training for calibrating rows of antenna elements in the exemplary calibration training of Fig. 10A, in accordance with some embodiments of the present disclosure; Fig. 10C shows an example of a calibration result for calibrating rows of antenna elements using the exemplary calibration configuration of Fig. 10B, in accordance with some embodiments of the present disclosure; Fig. 10D shows an exemplary calibration training for the calibration of columns of antennas in the exemplary calibration training of Fig. 10A, in accordance with some embodiments of the present disclosure; Fig. 10E shows an example of a calibration result for the calibration of columns of antenna elements using the exemplary calibration configuration of Fig. 10D, in accordance with some embodiments of the present disclosure; Fig. 11A and Fig. 11B illustrates exemplary calibration configurations with four antenna element sub-arrays for calibrating a phased array antenna system using a single sub-array parameter, in accordance with some embodiments of the present disclosure; Fig. 12 shows an exemplary configuration for calibrating an edge antenna element in accordance with some embodiments of the present disclosure; Fig. 13A illustrates an exemplary antenna grid configuration for performing OTA calibration measurements for a phased array antenna system having antenna elements distributed on different printed circuit boards (PCBs), in accordance with some embodiments of the present disclosure; Fig. 13B shows an exemplary calibration configuration used to calibrate the antenna elements in the antenna grid configuration 1300 of Fig. 13A may be used in accordance with some embodiments of the present disclosure; Fig. Figure 13C shows an additional example of a calibration pattern that can be used to calibrate the antenna elements in the antenna grid pattern 1300 of Fig. 13A across two dimensions, in accordance with some embodiments of the present disclosure; Fig. 14 shows a cross-sectional view of a row of antenna elements along a calibration line extending between various PCBs of a phased array antenna system, in accordance with some embodiments of the present disclosure; Fig. 15A is a flowchart illustrating a process for OTA calibration of antenna elements for a phased array antenna system according to some embodiments of the present disclosure; Fig. 15B is a flowchart illustrating an additional method for OTA calibration of antenna elements for a phased array antenna system according to some embodiments of the present disclosure; Fig. 16 shows an example of a computer system in accordance with some embodiments of the present disclosure. DETAILED DESCRIPTION

[0010] Various embodiments of the disclosure are discussed in detail below. While the concepts of the present disclosure are susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are described in detail herein. It should be understood, however, that the intention is not to limit the concepts of the present disclosure to the particular forms disclosed; on the contrary, the intention is to cover all modifications, equivalents, and alternatives consistent with the present disclosure and the appended claims.

[0011] In the drawings, some structural or method features may be depicted in particular arrangements and / or orders. However, it should be appreciated that such specific arrangements and / or orders are not required. Rather, in some embodiments, such features may be arranged in a different manner and / or order than shown in the illustrative figures. Furthermore, the mention of a structural or method feature in a particular figure does not imply that that feature is required in all embodiments, and in some embodiments, it may not be included or may be combined with other features.

[0012] References in the specification to "a single embodiment," "an embodiment," "an illustrative embodiment," etc., indicate that the described embodiment may include a particular feature, structure, or feature, but not every embodiment necessarily includes that particular feature, structure, or feature. Furthermore, such terms do not necessarily refer to the same embodiment. Where a particular feature, structure, or feature is described in connection with one embodiment, it is understood that one skilled in the art will be able to apply that feature, structure, or feature in connection with other embodiments, whether or not explicitly described.Terms such as "top", "bottom", "upper", "lower", "vertical", "horizontal", "lateral" in this disclosure are intended to orient the reader with respect to the drawings and are not intended to represent the required orientation of the components or to impose orientation limitations on the claims.

[0013] The term "coupled with" refers to any component that is either directly or indirectly connected to another component and / or to any component that communicates with another component (e.g., via a wired or wireless connection, a capacitive or inductive RF coupling scheme, and / or any other suitable communication interface).

[0014] Embodiments of the present disclosure relate to antenna devices, including phased array antenna systems configured to transmit and / or receive radio frequency signals, as well as calibration systems and techniques for such antenna devices.

[0015] The phased array antenna systems of the present disclosure may be used in communication systems that provide high-bandwidth, low-latency network communications via a satellite constellation. Such a satellite constellation may be located in a non-geosynchronous Earth orbit (GEO), e.g., in a low Earth orbit (LEO).

[0016] The disclosed systems and techniques are described in the following disclosure as follows. The discussion begins with a description of exemplary systems and technologies for wireless communications and exemplary systems and circuits for phased array antennas, as described in Fig. 1, Fig. 2A and Fig. 2B. The following is an illustration of an exemplary main lobe and side lobes emanating from an exemplary antenna array of a phased array antenna system as shown in Fig. 3 shown.

[0017] This is followed by exemplary training for the operation of a phased antenna system in transmit (TX) and receive (RX) training, as in Fig. 4A and Fig. 4B. The following are examples of OTA calibration training for a phased array antenna system with antenna elements that have dual-use antenna connectors, as shown in Fig. 4C and Fig. 4D. The following are examples of calibration training for calibrating antenna arrays with antenna elements with two antenna ports, where one of the antenna ports is used as a dual-use port for transmitting and receiving signals during calibration, as shown in Fig. 4E and Fig. 4F. The following are examples of calibration configurations for a phased array antenna with antenna elements that have dual-use connectors for transmitted and received calibration signals, as shown in Fig. 5A and Fig. 5B.

[0018] The following are examples of calibration training to resolve ambiguities in calibration solutions based on OTA calibration measurements, as in Fig. 5C and Fig. 5D shown.

[0019] The following are examples of calibration training for a phased array antenna system with antenna elements with special antenna ports for transmitting and receiving (e.g. the transmit and receive ports of the FEM and / or beamforming components are each connected to a different port of a dual-polarized antenna element), as in Fig. 6. An example of calibration measurements for a phased array antenna system with antenna elements with dedicated antenna ports for transmitting and receiving, as shown in Fig. 7, then follows.

[0020] The following is an example of a calibration training with additional redundancy to complement OTA measurements of mutual coupling for the OTA calibration of a phased array antenna system, as described in Fig. 8A. The following is a detailed view of a subsection of the antenna grid of the calibration training 800 of Fig. 8A including a portion of a calibration line as shown in Fig. 8B. The following is an example of a calibration result for calibrating antenna elements connected to a calibration line as shown in Fig. 8C. The following is an example of a calibration training with which an OTA calibration of columns (rows) of antennas can be performed using a reference subset of self-calibrated antenna elements connected to a calibration line, as in Fig. 8D and Fig. 8E. The following is an example of a calibration setup that can be used for OTA calibration of rows of antenna elements, using a reference subset of self-calibrated antenna elements connected to a calibration line (see Fig. 8F).

[0021] This is followed by an exemplary design of two-way FEMs with dedicated transmit and receive ports coupled to corresponding dual-port antenna elements of a sub-array of two antenna elements of an antenna grid, as shown in Fig. 9A. The following is an exemplary embodiment of three-way FEMs with dedicated transmit and receive ports coupled to corresponding dual-port antenna elements of a sub-array of three antenna elements of an antenna grid, as shown in Fig. 9B. The following are exemplary configurations for sharing radio frequency input / output (RFIO) ports between pairs of two-way FEMs coupled to four antenna element sub-arrays arranged in a linear configuration, as shown in Fig. 9C and Fig. 9D. The following are exemplary configurations for sharing RFIO ports between pairs of two-way FEMs coupled to four antenna element sub-arrays arranged in a rectangular configuration, as shown in Fig. 9E to Fig. 9H. The following is an exemplary configuration for providing additional redundancy for OTA calibration using pairs of two-way coupling to four antenna element sub-arrays (see Fig. 9I).

[0022] The following is an example of a calibration configuration for calibrating antenna elements in a two-dimensional (2D) phased array antenna according to some embodiments of the present disclosure, as shown in Fig. 10A. The following is an example calibration training and a corresponding calibration result for the calibration of rows of antenna elements in the example calibration of Fig. 10A, as in Fig. 10B and Fig. 10C. The following is an example of a calibration pattern and a corresponding calibration result for the calibration of columns of antenna elements in the example calibration pattern of Fig. 10A, as in Fig. 10D and Fig. 10E shown.

[0023] The following are examples of calibration setups with four antenna element sub-arrays for calibrating a phased array antenna system using a single sub-array parameter, as in Fig. 11A and Fig. 11B.

[0024] The following is an example of the calibration of an edge antenna element, as in Fig. 12 shown.

[0025] The following is an example of an antenna grid configuration for performing OTA calibration measurements for a phased array antenna system with antenna elements distributed on different printed circuit boards (PCBs), as shown in Fig. 13A. The following is an example of a calibration pattern used to calibrate the antenna elements in the antenna grid pattern 1300 of Fig. 13A can be used as in Fig. 13B. The following is another example of a calibration pattern used to calibrate the antenna elements in the antenna grid pattern 1300 of Fig. 13A can be used over two dimensions, as in Fig. 13C.

[0026] The following is a cross-sectional view of a row of antenna elements along a calibration line extending between different PCBs of a phased array antenna system, as shown in Fig. 14. The following is a flowchart illustrating a method for OTA calibration of antenna elements for a phased array antenna system as described in Fig. 15A. The following is another flowchart illustrating a method for OTA calibration of antenna elements for a phased array antenna system as shown in Fig. 15B. The discussion concludes with a description of an exemplary computer system as shown in Fig. 16. The disclosure now addresses Fig. 1.

[0027] Fig. 1 shows a non-scale embodiment of an antenna and satellite communication system 100 in which embodiments of the present disclosure may be implemented. As shown in Fig. 1, a ground-based endpoint or user terminal (UT) 102 is installed at a location directly or indirectly on the Earth's surface, such as a house or other building, a tower, a vehicle, or other location where communication access via a satellite network is desired.

[0028] A communication path may be established between the UT 102 and a satellite (SAT) 104. In the illustrated embodiment, the first SAT 104, in turn, establishes a communication path with a gateway terminal 106. In another embodiment, the SAT 104 may establish a communication path with another satellite before communicating with a gateway terminal 106. The gateway terminal 106 may be physically connected to a ground network 108 via fiber optic, Ethernet, or another physical connection. The ground network 108 may be any type of network, including the Internet. Although one SAT 104 is illustrated, communication may be with and between a constellation of satellites. PHASE-CONTROLLED ARRAY ANTENNA SYSTEM

[0029] Fig. 2A and Fig. 2B are schematic representations of the electronic system of a phased array antenna system 200 in accordance with embodiments of the present disclosure. Referring to Fig. 2A, the phased array antenna system 200 is designed and configured to transmit and / or receive a combined beam of signals (also referred to as electromagnetic signals, wavefronts, or the like) in a preferred direction from or to an antenna aperture 212. Accordingly, the plurality of antenna elements simulates a large directional antenna. One advantage of the phased array antenna is its ability to transmit and / or receive signals in a preferred direction (i.e., the antenna's beamforming capability) without requiring the system to be physically repositioned or re-orientated.

[0030] According to one embodiment of the present disclosure, Fig. 2A illustrates a phased array antenna system 200 that may be configured to transmit and / or receive radio frequency (RF) signals. The phased array antenna system 200 includes a phased array antenna having a plurality of antenna elements 213, 214 defining an antenna aperture 212, e.g., antenna elements 213, 214 distributed in one or more rows and / or columns, and a plurality of phase shifters (not shown) configured to generate phase offsets between the antenna elements 213, 214. As a non-limiting example, a two-dimensional phased array antenna may be capable of two-dimensional electronically steered beam steering. In some cases, the range of available beam steering angles may depend on the configuration of the antenna elements in the two-dimensional phased array antenna.For example, a planar two-dimensional phased array antenna may be able to achieve the maximum possible range of scanning angles relative to a vector perpendicular to the plane of the array if the spacing of the antenna elements across the antenna grid 202 is appropriately chosen.

[0031] As in Fig. 2A, the plurality of antenna elements 213 in the antenna grid 202 are configured to transmit signals and / or receive signals. The antenna aperture 212 of the phased array antenna system 200 is the area through which power is radiated or received. A phased array antenna synthesizes a specific electric field (phase and amplitude) across an antenna aperture 212. As described in more detail below, the antenna grid 202 defining the antenna aperture 212 may include a plurality of antenna elements 213 arranged in a specific configuration that is physically and electronically supported by a printed circuit board (PCB).

[0032] As in Fig. As shown in Figure 2A, the antenna aperture 212 may be grouped into subgroups 204a and 204b of antenna elements. Each subgroup 204a, 204b of the plurality of antenna elements may include the M antenna elements 213, 214, which may each be associated with specific digital beamformer (DBF) chips 207, 208. The remaining antenna elements 217 of the plurality of antenna elements may similarly be associated with other DBF chips (not shown) in the DBF grid 206.

[0033] In some implementations, the system design objective may include performing OTA measurements of the mutual coupling between transmit and receive antennas, so that these measurements are sufficiently redundant to eliminate the need for an external reference (flying probe, near- or far-field source, etc.); the phased array system calibrates its RF paths itself. In some examples, OTA measurements alone may not provide sufficient redundancy and can be supplemented by performing mutual coupling measurements between a subset of TX or RX antennas and one or more calibration lines.

[0034] In some cases, the measurements from a calibration operation can be saved for later use. In some cases, the saved calibration measurements can be used to avoid repeated and / or redundant acquisition of measurements during operation of the phased array antenna. In some cases, the calibration process can be accelerated by reducing the number of measurements performed during calibration. As an illustrative example, the measurements from an initial self-calibration can be saved and reused in subsequent calibrations. In some cases, the calibration measurements can be performed from scratch during each calibration operation (e.g., without considering previous calibration measurements).For example, a phased array antenna system may be calibrated periodically during operation to align and / or calibrate the phased array antenna elements.

[0035] As in Fig. 2B, the phased array antenna system 200 may be a transmit phased array antenna system (TX), a receive phased array antenna system (RX), or a transmit and receive phased array antenna system (TX / RX). The illustrated phased array antenna system 200 includes an antenna grid 202 having a plurality of antenna elements 213, 214 and a DBF grid 206 having one or more DBF chips 207, 208 (which may be referred to herein as digital beamformers, DBFs, or DBF chips) for receiving signals from a modem 210 in the transmit (TX) direction and / or for transmitting signals to the modem 210 in the receive (RX) direction. The DBF chips 207 and 208 and antenna elements (213, 213, 217, etc.) may be configured to transmit and / or receive a combined beam of radio frequency signals with a radiation pattern from or to the antenna aperture 212.

[0036] The Fig. 2A and Fig. The configurations shown in FIG. 2B are illustrative and represent illustrative example configurations that may incorporate the calibration systems and techniques described herein. Other configurations may be used without departing from the scope of the present disclosure. For example, a phased array antenna system employing analog and / or hybrid beamforming schemes may be employed without departing from the scope of the present disclosure. MAIN LOBE AND SIDE LOBE OF A PHASE-STACKED ARRANGE ANTENNA

[0037] Fig. 3 shows a schematic 370 illustrating an exemplary main lobe 372 and side lobes 376 generated by an antenna group of an exemplary phased array antenna system (e.g., the phased array antenna system 200 of Fig. 2A). The diagram 370 may represent a polar diagram (radiation pattern), where the main lobe 372 and the various side lobes 376 represent a radiation pattern or effective isotropic radiation pattern (EIRP) of the phased array antenna system. As shown in Fig. 3, the main lobe 372 may have a greater field strength compared to other lobes (e.g., the side lobes 376) resulting from the transmission of the signal. The main lobe 372 may correspond to the steering direction 374 of the signal from a phased array antenna system to a satellite. In some examples, the main lobe 372 may correspond to the steering direction 374 of a signal from the phased array antenna system to a user terminal (e.g., UT 102 of Fig. 1) and / or gateway terminal (e.g. gateway terminal 106 of Fig. 1). The other sidelobes or sidelobes 376 may be the result of the size / shape of the array aperture (e.g., antenna aperture 212) and any type of excitation cone (e.g., amplitude cone) applied to the antenna array. These sidelobes may be worse and less predictable in the case of imperfect calibration, which leads to systematic and / or random errors in the individual antenna signals (magnitude and / or phase). Therefore, the overall EIRP mask and achievable sidelobe levels depend on the accuracy / quality of the calibration of the phased array antenna system. TRAINING OF PHASE-CONTROLLED ARRANGE ANTENNAS FOR TRANSMITTING AND RECEIVING

[0038] Fig. 4A and Fig. 4B show a transmit (TX) training (400) and a receive (RX) training (430) for a phased array antenna system. In the examples of Fig. 4A and Fig. 4B, the antenna elements 413, 415, 416, 414 are arranged in a row and evenly spaced in an antenna grid (e.g., the antenna grid 202 of Fig. 2B). In some cases (e.g., during nominal operation of a phased array antenna), the antenna elements 413, 415, 416, 414 may be configured to all transmit when the phased array antenna system is in a transmit (TX) mode, and they may be configured to all receive when the phased array antenna system is in a receive (RX) mode. As in Fig. As shown in Figure 4A, the front-end module (FEM) 420 can operate in a TX mode when the phased array antenna system is in TX mode. For example, in transmit mode, the power amplifier (PA) 421 is turned on and the low-noise amplifier (LNA) 423 is turned off. When the phased array antenna system is in RX mode, the FEM 422 is also in RX mode, as shown in Fig. 4B. For example, in RX mode, the PA 421 of each FEM 422 is turned off and the LNA 423 of each FEM 422 is turned on. CALIBRATION TRAINING FOR ANTENNAS WITH A DUAL-USE CONNECTOR

[0039] In some cases, the measurements required to perform the OTA calibration of a phased array antenna system (e.g., the phased array antenna system 200 of Fig. 2A) depend on the physical properties of the antenna system. An exemplary self-calibration approach described here can be applied to the calibration of a phased array antenna with a periodic antenna grid (e.g., antenna grid 202 of Fig. 2A), wherein at least one terminal of each antenna element (e.g., the antenna elements 213, 214, 217 of Fig. 2A) in the periodic antenna grid is "dual-use" capable during the self-calibration process. As used herein, a dual-use antenna port refers to a port of an antenna element that allows the same physical antenna port to be used for transmitting calibration signals and / or receiving calibration signals. For example, a dual-use antenna port may be used for both transmitting signals (e.g., in a TX mode) and receiving signals (e.g., in an RX mode) during nominal use of a phased array antenna system. In some examples, a dual-use antenna port may be used exclusively for transmitting signals (e.g., in a TX-only antenna array) or exclusively for receiving signals (e.g., in a RX-only antenna array) during nominal use of a phased array antenna system.

[0040] Fig. 4C and Fig. 4D show example calibration configurations 440 and 450, respectively, illustrating OTA calibration measurements for single-port antenna elements and dual-use antenna ports. In the examples of Fig. 4C and Fig. 4D, the antenna elements 413, 415, 416, 414 are arranged in a row and evenly spaced in an antenna grid (e.g., antenna grid 202 of Fig. 2B). Fig. Figure 4C includes an exemplary embodiment of calibration 440 showing OTA calibration measurements between RFIO ports 405 of a single beamformer (BF) 407. In contrast, Fig. 4D an additional exemplary calibration training 450 showing OTA calibration measurements between RFIO ports 405 of different BFs (e.g., BF 407 and additional BF 408).

[0041] In the examples shown by Fig. 4C and Fig. 4D, the FEMs 420 and the corresponding RFIO paths 433, 434 coupled to the RFIO ports 405 are configured in a TX mode. Furthermore, the FEMs 422 and the corresponding RFIO paths 435, 436 coupled to the RFIO ports 405 can be configured in an RX mode. In some cases, the antenna elements 413, 414 coupled to the RFIO paths 433, 434 configured in the TX mode can transmit RF signals OTA, and the antenna elements 415, 416 coupled to the RFIO paths 435, 436 configured in the RX mode can receive the transmitted signals. In some cases, the signals measured by antenna elements 415, 416 may be used to perform coherent complex measurements (e.g., phase and magnitude measurements) based on the mutual coupling between TX antenna elements 413, 414 and RX antenna elements 415, 416, as represented by OTA paths 424, 426, 428, 432.In some implementations, the FEMs 420, 422 may be implemented as FEM chips (e.g., integrated circuit (IC) chips) that include a single terminal (e.g., a package pin, a solder ball, or the like) connected to the corresponding antenna terminal of the antenna elements 413, 415, 416, 414. In the illustrated examples of . Fig. 4C and Fig. 4D, a switching mechanism (not shown) is located between PA 421 and LNA 423 within the FEM chip, and PA 421 and LNA 423 are connected to the same antenna port. However, in some implementations (not shown), PA 421 and LNA 423 may have dedicated ports (e.g., package pins, solder balls, or the like) on FEMs 420, 422, and the dedicated ports may be combined into a single port for connection to single-port antenna elements using a switching mechanism external to the FEM chips, without departing from the scope of the present disclosure. OTA CALIBRATION WITH NOMINAL ANTENNA PATHS

[0042] In many practical examples, a signal radiated by the TX antenna elements (e.g., antenna elements 413, 414) may be too strong for the RF paths of the RX antenna elements (e.g., antenna elements 415, 416), so that FEMs 422 configured in an RX mode and / or the corresponding RFIO port 405 operating in RX mode may be overloaded and / or saturated. Such saturation may be due to the RX paths (e.g., the RX RF paths) being very sensitive and capable of receiving extremely weak signals (e.g., below the thermal noise threshold). As a result, the maximum signal strength that the RX RF paths can tolerate may be many orders of magnitude lower than the signals output by the functional / nominal TX paths (e.g., TX RF paths) of the array.In some cases, the functional / nominal TX paths may not have sufficient dynamic range to reduce their RF path gain (and the signal strength from the antenna elements 413, 414) to avoid saturation of the RX paths. For example, the dynamic range of the TX paths may be limited to avoid performance degradation and / or over-design. As a result, the RFIO ports 405 and the FEMs 420 may be switched to a different mode to transmit at much lower signal levels, which are used only during the mutual coupling measurement, which may be referred to as the calibration measurement TX mode (“mTX mode”). Since performance metrics (e.g., efficiency, linearity, etc.) are not as critical for the mTX mode, it may be easier to transmit signals with a low power level (e.g.,comparable to or only a few orders of magnitude different from the target RX signals) to the output of the FEMs 420 of the TX antenna elements 413, 414 so that the RF paths of the RX antenna elements 415, 416 (e.g., FEMs 422 and RFIO ports 405 in a nominal RX configuration) can receive the transmitted signals without causing saturation.

[0043] Similarly, the problem of saturation of the RX RF paths of the RX antenna elements (e.g., antenna elements 415, 416) can be addressed during calibration of the nominal TX RF paths of the TX antenna elements (e.g., antenna elements 413, 414). In such an example, the goal may be to calibrate the functional TX array. Accordingly, changing the RF / analog settings of the nominal TX RF paths for the TX antenna elements to be calibrated (e.g., antenna elements 413, 414) may not be desirable. Instead, the RFIO ports 405 and FEMs 422, which are in RX mode when used for nominal RX operation, can be switched to a different configuration, which can be referred to as calibration measurement RX mode (e.g., mRX mode). In some cases, the RFIO ports 405 and FEMs 422 can be configured in mRX mode such that the RFIO ports 405 and / or FEMs 422 are much less sensitive.In some cases, by reducing the sensitivity of the RFIO ports 405 and / or FEMs 422 in mRX mode, the RX paths may be able to withstand nominal or near-nominal TX signals emanating from the TX antenna elements being calibrated. Such a reduction in the sensitivity of the RX paths in mRX mode may be acceptable, since mRX mode can only be used during calibration measurements. In some cases, the performance metrics of mRX mode are not as critical as the performance metrics of the nominal RX mode (e.g., for the functional RX paths). For simplicity, the TX and RX paths that perform mutual coupling measurements are referred to below as TX mode and RX mode, respectively. However, it can be assumed that the TX and RX paths are in a suitable operating mode for the transmission of calibration signals (e.g. mTX mode or TX mode) or the reception of calibration signals (e.g.mRX mode or RX mode) unless otherwise stated. ADDITIONAL CALIBRATION TRAINING WITH DUAL-USE CONNECTIONS

[0044] As mentioned above, the examples in Fig. 4C and Fig. 4D calibration configurations for antenna arrays with antenna elements that have a single connector that can function as a dual-use connector. However, in some cases, multi-connector antenna elements can be configured to provide a dual-use connector that can be used for TX and / or RX during OTA calibration.

[0045] Fig. 4E shows an exemplary calibration configuration 460 for calibrating a TX antenna array with antenna elements that have two antenna ports, using the functional TX port as a dual-use antenna port for calibration. As shown, the calibration configuration 460 includes antenna elements 463, 464, 465, 466, each with two antenna ports. In the example of Fig. 4E, the antenna elements 463, 464, 465, 466 are arranged in a row and evenly spaced in an antenna grid (e.g., the antenna grid 202 of Fig. 2B). In an illustrative example, antenna elements 463, 464, 465, 466 may be dual-linearly polarized antennas routed to a 3-decibel (3-dB) 90-degree hybrid 425 leading to a TX port 482 and a termination port 484. As shown, FEMs 467 include PAs 421 that may be coupled to the TX ports 482 of the respective antenna elements and are used to transmit signals from all antenna elements 463, 464, 465, 466 during nominal TX operation. In some cases, the FEMs 467 may include bypass switches 468 that may be configured to facilitate the measurement of the signals received via the TX port 482 to perform the OTA calibration. In some cases, the bypass switches 468 included in all FEMs 467 may be open during nominal operation. In the example of Fig. 4E, passive RX measurement paths (mRX) can be coupled to the TX ports 482 via a coupler 488. In some cases, the FEMs 467 can be configured to receive calibration signals by closing the bypass switches 468 and disabling the PA 421.

[0046] In the example of Fig. 4E, the antenna elements 463, 464 and the corresponding FEMs 467 are configured to transmit TX signals from the TX ports 482. As illustrated, the antenna elements 465, 466 and the corresponding FEMs 467 are configured to receive the TX signals output by the antenna elements 463, 464 via the TX ports 482 OTA. In some cases, the coupler 488 and its termination 489 may be located outside the FEMs 467 (e.g., on a circuit board). In some examples, the coupler 488 and / or its termination 489 may be physically located within the FEM 467 (e.g., in an IC chip) without departing from the scope of the present disclosure.

[0047] In some cases, the termination port 484 may be terminated by a termination 486. In some cases, by using a termination that is consistent across all antenna elements 463, 464, 465, 466, the periodicity of the antenna grid (e.g., the antenna grid 202 of Fig. 2B). For example, the termination port 484 may be terminated by another TX FEM chip (e.g., for operating a dual-polarized TX array). In another illustrative example, the termination port 484 may be terminated by an RX FEM chip that uses a calibration approach similar to the example in Fig. 4E. For example, an RX FEM may include a switchable TX path connected to the termination port 484 via a coupler. In some implementations, the termination port 484 may be terminated by a matched load without departing from the scope of the present disclosure. It should be noted that, compared to the implementation of Fig. 4C (e.g. based on switching the functional path between transmitting and receiving) the efficiency degradation of the functional path in the calibration training 460 of Fig. 4E can be much lower if one assumes that a weak coupler 488 (e.g. -20 dB coupling or less) potentially has a more limited link budget for mutual coupling measurements during calibration at the expense.

[0048] Fig. 4F shows an additional example of a calibration configuration 470 for calibrating a TX antenna array of two-port antenna elements that use a port different from the functional TX port as a dual-use antenna port for calibration. As shown, the additional example configuration 470 includes antenna elements 463, 464, 465, 466, each with two antenna ports. Similar to the configuration of Fig. 4E, the antenna elements 463, 464, 465, 466 may be dual-linear polarized antennas routed to a 3 dB 90-degree hybrid 475. In the example of Fig. 4F, the 3 dB 90-degree hybrid 457 can lead to a transmit port 472 and a calibration port 474. In the example of Fig. 4F assumes that a bidirectional calibration path is available as a separate pin 492 of the FEM 477 (e.g., a FEM IC chip) coupled to the calibration port 474.

[0049] As shown, the FEMs 477 can be trained for calibration by closing switch 491 and turning off PA 421. In some cases, the training of Fig. 4F can be used to measure the insertion loss of a coupler (e.g. coupler 488 in Fig. 4E) along the functional TX path. In some cases, providing a separate calibration path through calibration port 474 does not degrade the efficiency of the functional TX path (e.g., the TX RF path) coupled to TX port 472. In the example of Fig. 4F, the RFIO ports 405 can be selectively operated in a TX mode and / or an RX mode. Accordingly, the antenna elements 463, 464, 465, 466 can use the calibration port 474 to transmit and / or receive signals during calibration. In the example shown, the antenna elements 463, 464 are configured to transmit signals via the calibration port 474 with the corresponding FEMs 477 operating in the calibration mode. As shown, the antenna elements 465, 466 are configured to receive signals transmitted by the antenna elements 463, 464 via the calibration port 474 with the corresponding FEMs 477 operating in the calibration mode.

[0050] In some embodiments, the scattering / coupling parameters of the (passive) antenna array (e.g., the antenna elements 413, 414, 415, 416 of Fig. 4A to Fig. 4D, the antenna elements 463, 464, 465, 466 of Fig. 4E and Fig. 4F) be reciprocal (assuming no magnetic material is present within the antenna volume) and periodic (due to the periodic spacing of the antenna elements). In some cases, the combination of reciprocity and periodicity can result in some of the physically distinct OTA coupling paths exhibiting similar behavior (e.g., the same complex gain magnitude, mathematically expressed). Therefore, these redundancies (e.g., equivalence of physically distinct OTA coupling paths) can be used to calibrate a 2D antenna array without an external reference (e.g., far-field source, flying probe, etc.).

[0051] In the examples of Fig. 4C and Fig. 4D, the TX and RX calibration operations corresponding to the OTA path 424 are performed via the identical antenna ports of the antenna element 413 (TX) and the antenna element 415 (RX). In some cases, the operating mode of the FEMs 420, 422 can be reversed so that the antenna element 413 receives (RX) and the antenna element 415 transmits (TX), and the coupling behavior of the reversed OTA path (e.g., in the opposite direction of the OTA path 424) will be the same as the coupling behavior of the OTA path 424. Furthermore, due to the periodicity of the antenna grid, OTA path 432 can be considered a copy of the inverted OTA path shifted by two antenna elements (e.g., in the opposite direction of OTA path 424). As a result, OTA path 424 and OTA path 432 may exhibit identical coupling behavior. Furthermore, OTA path 426 and OTA path 428 may exhibit identical coupling behavior for the same reasons.In the exemplary training of . Fig. 4E, the same assumptions regarding the coupling behavior of rotated and / or inverted OTA paths can be applied, since an identical connector (e.g., the TX connector 482) is used for both TX and RX during calibration. In the example of Fig. 4F, the same assumptions regarding the coupling behavior of rotated and / or flipped OTA paths can be applied when the calibration port 474 is used for both TX and RX during the calibration process. WIRELESS (OVER−THE−AIR=OTA) SELF-CALIBRATION WITH DUAL-USE ANTENNA TERMINALS

[0052] Fig. 5A shows an exemplary calibration configuration 500 for calibrating antenna elements 502, 506, 508, 504 in a phased array antenna with antenna elements that have dual-use connectors. In the illustrated example, if the antenna elements 502, 504 are in transmit mode and the antenna elements 506, 508 are in receive mode, the linear four-element sub-array of the antenna elements 502, 506, 508, 504 may correspond to the configuration of the antenna elements 413, 415, 416, 416 shown in Fig. 4C and Fig. 4D. Accordingly, the complex OTA coupling parameters C1, C4, C2, C3 associated with the antenna ports of the antenna elements 502, 506, 508, 504 (e.g., without FEM or BF contributions) can be assigned to the OTA paths 424, 426, 428, 432 of Fig. 4C or Fig. 4D. As described above, the path similarities resulting from the reciprocity and periodicity of the antenna grid can lead to identical coupling for physically different OTA paths, such that C1 = C3 and C2 = C4.

[0053] When the antenna element 502 sends a calibration signal and the antenna element 506 receives the calibration signal and sends it to an RFIO port (e.g., RFIO port 405 of BF 407 of Fig. 4C, RFIO connector 405 of BF 407 or additional BF 408 of Fig. 4D), a complex number can be generated on the receiver side that represents the magnitude and phase of the received signal after traversing the RF path (a, 1) including the TX antenna element a (e.g., antenna element 502), RX antenna element 1 (e.g., antenna element 506), and the OTA path between antenna element a and antenna element 1 relative to a coherent reference signal. The generated complex number is the result of a single measurement and can be referred to as measured value M(1a). When antenna element 502 transmits a calibration signal and antenna element 508 receives it, the measured value can be referred to as measured value M(2a). Similarly, when antenna element 504 is transmitting and antenna element 506 is receiving, the measured value may be referred to as measured valueM(1b), and when antenna element 504 is transmitting and antenna element 508 is receiving, the measured value may be referred to as measured valueM(2b).

[0054] The complex measured values ​​M(1a), M(2a), M(1b), M(2b) can be expressed in terms of complex coupling parameters C1, C4, C2, C3 and complex gain of the RF paths of the antenna elements 1, 2, a, b (e.g., antenna elements 506, 508, 502, 504), as shown in equation (1) to equation (4) below: M(1a)=C1XaX1ej(θa)ej(θ1) M(1b)=C2XbX1ej(θb)ej(θ1) M(2a)=C4XaX2ej(θb)ej(θ2) M(2b)=C3XbX2ej(θb)ej(θ2)

[0055] X a , X b , X1, X2 are the contributions of the magnitude for the RF paths of the antenna elements a, b, 1 and 2 respectively and, θ a , θ b , θ1, θ2 are the phase contributions for the RF paths of the antenna elements a, b, 1 and 2 respectively. As shown in equation (5) to equation (7) below, the system of equations in equation (1) to equation (4) can be simplified to include the contributions of the complex coupling parameters C1, C2, C3, C4 and the contributions X a , X b , θ a, θ b of the TX paths of the antenna elements a, b, so that the remaining terms X1, X2, θ1, θ2 remain as unknowns in equation (7). M(1a)M(2a)=C1C4X1X2ej(θ1−θ2) M(1b)M(2b)=C2C3X1X2ej(θ1−θ2) M(1a)M(2a)M(1b)M(2b)=(C1C2C3C4)(X1X2)2e2j(θ1−θ2)=(X1X2)2e2j(θ1−θ2)

[0056] Referring to equation (7), the left side of the equation M(1a)M(2a)M(1b)M(2b) a known complex number X M e 2j(θM), which can be calculated from complex measured values ​​M(1a), M(2a), M(1b), M(2b). By taking the square root of both sides of equation (7), a pair of solutions is obtained, as shown in equation (8) below, which represents a magnitude and phase difference between the complex gain of RX path 1 and the complex gain of RF path 2. The magnitude and phase difference can then be used as a compensation factor to calibrate the RX antenna elements 506, 508 relative to each other: M(1a)M(2a)M(1b)M(2b)=(X1X2)2e−2j(θ1−θ2)=±X1X2e−j(θ1−θ2)

[0057] Equation (1) to equation (8) can also be used for calibration with antenna elements 506, 508 transmitting calibration signals and antenna elements 502, 504 receiving calibration signals to calibrate the TX antenna elements 506, 508 with respect to each other.

[0058] Fig. 5B shows another example of a calibration training 510. In the example of Fig. 5B is a sub-array with four antenna elements (e.g., antenna elements 512, 516, 518, 514) with a different geometry than in the exemplary calibration configuration 500 of Fig. 5A. In the example shown, the complex OTA coupling parameter between antenna element 512 and antenna element 516 may be denoted as C1, and the complex OTA coupling parameter between antenna element 514 and antenna element 516 may be denoted as C2. As mentioned above, OTA interaction paths may be flipped (e.g., due to reciprocity) and / or OTA interaction paths may be shifted along the x- and / or y-axis of the antenna grid by an integer number of antenna pitches (e.g., due to periodicity) without affecting the complex value of the complex coupling parameters C1, C2. Accordingly, the complex OTA coupling parameter C1 between antenna elements 512, 516 may be equal to the complex OTA coupling parameter C3 between antenna elements 514, 518.Similarly, the complex OTA coupling parameter C2 between the antenna elements 514, 516 may be equal to the complex OTA coupling parameter C4 between the antenna elements 512, 518. Therefore, Equation (1) through Equation (8) may be applied to measurements of the complex OTA coupling parameters C1, C2, C3, C4 between the antenna elements 512, 516, 518, 514 to calibrate the antenna elements 516, 518 with respect to the nominal receive operation and / or the nominal transmit operation.

[0059] Fig. 5B shows an additional sub-array with four antenna elements (e.g., antenna elements 522, 526, 528, 524). As illustrated, the OTA path between antenna element 522 and antenna element 528 can be viewed as a translation of the OTA path between antenna element 512 and antenna element 516 and may therefore have the same complex OTA coupling parameter C1. Similarly, the OTA path between antenna element 524 and antenna element 526 may have the OTA complex coupling parameter C3. The OTA path between antenna element 522 and antenna element 526 may have an OTA complex coupling parameter C5, and the OTA path between antenna element 524 and antenna element 526 may have an OTA complex coupling parameter C6. As described above, the complex OTA coupling parameter C5 and the complex OTA coupling parameter C6 may be equal due to the reciprocity and periodicity of the antenna grid.Therefore, equations (1) to (8) can also be applied to measurements of the complex OTA coupling parameters C1, C3, C5, C6 for the quad antenna array formed by the antenna elements 522, 526, 528, 524 to calibrate the antenna elements 526, 528 with respect to each other for nominal RX operation and / or nominal TX operation.

[0060] In another illustrative example in Fig. 5B, when antenna element 2 is receiving (e.g., the RF path of antenna element 2 is in RX mode) and all neighboring antenna elements are transmitting (e.g., the RF paths of antenna elements a, 1, b, c, d, e are all in TX mode), the complex measured values ​​M(2a), M(2b), M(2c), M(2d), M(2e), and / or M(2l) can be used in equations that do not require the square root operation of complex numbers, as shown in equation (8) above. As mentioned above, the complex value measured between the TX path of antenna element a and the RX path of antenna element 2 can be denoted as M(2a), and complex values ​​for other OTA measurement paths can follow a similar convention. In an illustrative example, the complex measured values ​​M(2a) and M(2c) can be used to directly determine a relative complex value (e.g., phase and amplitude) between the TX paths a and c without performing a square root operation, as shown in equation (9) below: M(2a)M(2c)=C4C2XaXcej(θa−θc)=XaXcej(θa−θc)

[0061] Therefore, using equation (9), the relative complex value (e.g., phase and amplitude) between TX paths of antenna elements a, c can be calculated without a ± pair of equally likely outcomes. Similarly, equation (10) below can be used to directly determine a relative complex value (e.g., phase and amplitude) between TX paths of antenna elements d, 1, and equation (11) can be used to directly determine a relative complex value (e.g., phase and magnitude) between TX paths of antenna elements e, b. M(2d)M(21)=C5C6XdX1ej(θd−θ1)=XdX1ej(θd−θ1) M(2e)M(2b)=C1C3XeXbej(θe−θb)=XeXbej(θe−θb)

[0062] In some cases, by using equation (9) to equation (11) and repeating the same measurement procedure over the antenna elements in the antenna grid (e.g., antenna grid 202 of Fig. 2B) that form the array aperture of the phased array antenna system, each RF path along axis 1, axis 2, axis 3 of the antenna grid can be calibrated with any other RF path that is two antenna elements away along axis 1, axis 2, or axis 3. As a result, four groups of antenna elements (represented by four different shades as in Fig. 5B) covering the entire antenna grid. After calibration, the antenna elements in a particular group can be uniquely calibrated relative to each other. For example, each of the antenna elements with horizontally striped shading can be part of a group of antenna elements that are calibrated with respect to each other. However, the antenna elements in different groups of antenna elements with different shading are not calibrated with respect to each other. For example, the group of antenna elements with horizontally striped shading is not calibrated relative to the group of antenna elements with vertically striped shading, the group of antenna elements with diagonally striped shading, or the group of antenna elements with white shading. However, the above equation (8) can also be used for calibration between antenna elements in different groups.For example, the antenna elements 512, 516, 538, 534 of . Fig. 5B the antenna elements 502, 506, 508, 504 of Fig. 5A. Accordingly, equation (8) can be used to perform a relative calibration between antenna elements in different groups. For example, the antenna element 516 with horizontal striped shading and the antenna element 538 with white shading in Fig. 5B with respect to each other, as described above with respect to the calibration of the antenna elements 506, 508 of Fig. 5A. However, it is not necessary to set up Equation (8) for all antenna pairs in the entire antenna grid. Instead, Equation (8) can be used to calibrate entire groups of antenna elements. For example, the relative calibration of antenna element 516 and antenna element 538 with respect to each other can be used to calibrate all antenna elements in the group of antenna elements with horizontal shading and all antenna elements in the group of antenna elements with white shading with respect to each other. In some cases, reducing the number of square root operations required to solve Equation (8) can, in a practical scenario, save computation time and / or improve accuracy during a calibration procedure. Eliminating Ambiguities in Calibration Solutions

[0063] As mentioned above, Equation (8) provides two mathematically valid solutions (with a phase difference of 180 degrees in sequence ±), while only one of the solutions provides a physically correct solution leading to a calibrated phased antenna. If the expected phase shift θ1 - θ2 is approximately known, the ambiguity in the solution of Equation (8) can be resolved by using the result that is closest to the (approximate) expected value (see Equation (8)). For example, if the actual phase shift θ1 - θ2 is known due to the reliability and repeatability of the design and / or the predictability of the electronic components of a phased antenna system, the solution to Equation (8) that is closest to the expected phase values ​​can be selected for calibrating the phased antenna system.In particular, the accuracy of the expected value of θ1 - θ2 should be better than 90 degrees (90°), so that the expected value can be used to distinguish between two solutions with the same magnitude and a 180-degree phase difference. If the accuracy of the expected value of θ1 - θ2 cannot be guaranteed across different designs, phased array temperature cycles, and / or long time periods, other redundancies can be used to select the correct solution to Equation (8).

[0064] Fig. 5C and Fig. 5D show exemplary calibration configurations 530, 560 with symmetries in a phased array antenna that can be used to resolve ambiguities in the solution of equation (8). In the examples of Fig. 5C and Fig. 5D, the antenna elements can be designed to have the properties of reciprocity and periodicity, as with respect to the antenna elements of Fig. 5A and Fig. 5B. However, it should be noted that the antenna elements in Fig. 5C and Fig. 5D properties that are not necessarily present in every type of antenna element that can be used in a phased array antenna. For example, the Fig. 5C are linearly polarized (LP) antenna elements, with one polarization running exactly along the y-axis. Another example is the Fig. 5D, which are right-handed circularly polarized (RHCP antenna elements).

[0065] Fig. 5C shows an exemplary configuration for calibration 530, in which each of the antenna elements 533 is a linearly polarized antenna element with a polarization along the y-axis. In the illustrated example, a TX antenna element 532 may transmit a calibration signal OTA. As illustrated, six RX antenna elements 534, 536, 538, 540, 542, 544 may receive the signal from the TX antenna element 532, and complex measurement values ​​M may be acquired for each measurement related to the antenna elements 534, 536, 538, 540, 542, 544. As shown, the antenna elements 534, 536 may have identical complex coupling parameters C1a, C1b, the antenna elements 538, 540 may have identical complex coupling parameters C2a, C2b, and the antenna elements 542, 544 may have identical complex coupling parameters C3a, C3b based on the grating periodicity and reciprocity.Furthermore, for the specific geometry of the calibration setup 530, which contains antenna elements polarized along the y-axis with high polarization purity, the complex coupling parameters C1a, C2b, C2a, C1b can be identical if each antenna element is physically symmetric along the x-axis. In some cases, when one cannot rely on the accuracy of the expected value of θ1 - θ2, the 180-degree ambiguity between two solutions of equation (8) can still be resolved using the additional boundary conditions C1a = C2b = C2a = C1b. In practice, it may happen that the antenna elements (532, 534, 536, 538, 540, 542, 544 in . Fig. 5C) do not exhibit high x-axis polarization isolation or perfect physical symmetry. In such examples, the complex coupling parameters C1a, C2b, C2a, C1b can still be approximately equal, with some phase error that can be much smaller than 90 degrees. In such cases, the complex coupling parameters C1a, C2b, C2a, C1b can still be used to resolve the ambiguity between two solutions of equation (8).

[0066] Fig. 5D shows an exemplary configuration for calibration 560, in which each of the antenna elements 563 is an RHCP-polarized antenna element with identical polarization. In the illustrated example, a TX antenna element 562 can transmit a calibration signal OTA. As illustrated, six RX antenna elements 564, 566, 568, 570, 572, 574 can receive the calibration signal from the TX antenna element 562, and complex measurement values ​​M can be acquired for each measurement related to the antenna elements 564, 566, 568, 570, 572, 574. As shown, the antenna elements 564, 566 may have identical complex coupling parameters C1a, C1b, the antenna elements 568, 570 may have identical complex coupling parameters C2a, C2b, and the antenna elements 572, 574 may have identical complex coupling parameters C3a, C3b based on the grating periodicity and reciprocity.Furthermore, for the specific geometry of the calibration formation 560, which includes RHCP polarized antenna elements with high polarization purity, rotational symmetry (physical symmetry), and a matched termination for the left-hand circularly polarized (LHCP) ports of the antenna elements, complex coupling parameters may exhibit a magnitude / phase relationship, as shown in equation (12) below:. C1a=C1b=C3ae−j(23π)=C2ae−j(43π)=C3be−j(23π)=C2be−j(43π)

[0067] In some examples, the ambiguity between two solutions of equation (8) that are 180 degrees out of phase can be resolved using the constraints presented in equation (12). In practice, it may happen that the antenna elements 562, 564, 566, 568, 570, 572, 574 do not have high polarization isolation, perfect physical symmetry, and / or identical termination for the LHCP ports of the antenna elements. In such examples, the phase relationships presented in equation (12) are not strictly true, but may still be accurate enough (e.g., with a phase error much less than 90 degrees) to be used to resolve the 180-degree ambiguity of equation (8). OTA CALIBRATION WITH DIFFERENT ANTENNA ELEMENT DESIGNS

[0068] In the above description of the OTA path similarities of Fig. 5A, the exemplary calibration training 440 of Fig. 4C and the additional exemplary calibration training 450 from Fig. 4D as examples. The calibration training 460 of Fig. However, the antenna elements 463, 465, 466, 464 shown in Figure 4E can also be assigned to the antenna elements of Fig. 5A, Fig. 5B and Fig. 5D as long as the TX port 482 is used when transmitting calibration signals (e.g., by TX antenna elements 463, 464) and when receiving calibration signals (e.g., by RX antenna elements 465, 466).

[0069] Similarly, the antenna elements 463, 465, 466, 464 may be those described in the additional exemplary calibration embodiment 470 of Fig. 4F, the antenna elements of Fig. 5A, Fig. 5B and Fig. 5D as long as the calibration port 474 is used when transmitting calibration signals (e.g., by the antenna elements 463, 464) and when receiving calibration signals (e.g., by the antenna elements 465, 466).

[0070] Fig. 5C refers to linearly polarized antennas and can therefore refer to designs that meet the requirements of Fig. 4C to Fig. 4F and were modified so that the polarization of the antenna elements should be changed to linear polarization. In the examples of Fig. 4E and Fig. 4F, this can be achieved by removing the 3 dB 90-degree hybrid 425. In addition, the references to the TX port 482 and the terminated port 484 of Fig. 4E can be replaced by references to dual linear connections of antenna elements 463, 465, 466, 464, which does not affect the calibration approaches described above. Similarly, the references to transmit port 472 and calibration port 474 in Fig. 4F may be replaced by references to dual linear connections of the antenna elements 463, 465, 466, 464. OTA calibration using a dual-purpose calibration port different from the functional port

[0071] As mentioned above, Fig. 4F an additional exemplary training 470, which differs from the training in Fig. 4C to Fig. 4E in that a calibration port 474 is used to both transmit and receive calibration signals during calibration. Consequently, performing the relative calibration using equation (1) through equation (8) alone or in combination with equation (9) through equation (11) provides calibration of antenna elements and their RF paths in a calibration mode (e.g., mRX mode) of FEMs 477 and / or RFIO ports 405. For example, for FEMs 477, switch 491 may be closed and PA 421 may be off or inactive. In some cases, additional measurements may be required to calibrate the functional RF paths (e.g., in TX mode of FEM 477, when PA 421 is on and switch 491 is open).

[0072] In an illustrative example, calibration of functional TX paths (e.g., functional TX RF paths) may begin by performing a relative calibration using Equation (1) through Equation (11) to calibrate the RF paths of each antenna when FEMs 477 and RFIO ports 405 are in a calibration mode (e.g., mRX mode may produce a fully calibrated RX antenna array).

[0073] In some implementations, a first calibration measurement may be performed using a TX antenna element selected from an arbitrary location of the antenna grid (e.g., from a location x m y n ), and an RX antenna element (e.g. a location, x m+k y n+l ) are carried out. In the illustrative example, the location, x m y n the location of an antenna element that transmits the m tealong the x-axis (e.g. along a row of antenna elements) and the n te along the y-axis (e.g., along a column of antenna elements) of the antenna grid 202, where m and n are integers. Furthermore, the location x m+k , y n+l the location of an antenna element that is offset by k antenna elements along the x-axis and l antenna elements along the y-axis from the antenna element at location (x m ,y n ), where k and l are integers. In some cases, the TX antenna element at the location, x m y nwith its RF path in functional TX mode. For example, in the FEM 477 corresponding to the TX antenna element, PA 421 may be turned on and switch 491 may be open. In some examples, the TX antenna element may transmit a calibration signal and the RX antenna element may receive the calibration signal, and a complex measurement value M[(x m+k , y n+l ) (x m , y n )] which represents the magnitude and phase of the received signal.

[0074] In some examples, a second calibration measurement may be performed by placing a TX antenna element at the location, x m+h1 y n+h2 (where h1 and h2 are integers) sends a calibration signal and a receiving antenna element at the location, x m+h1+k y n+h2+l receives the calibration signal. In some cases, a complex measurement value M[(x m+h1+k, y n+h2+l ) (x m+h1, y n+h2)], which represents the magnitude and phase of the received signal. The relationship between the first calibration measurement and the second calibration is shown in equation (13) below: M[(xm+k,yn+l)(xm,yn)]M[(xm+h1+k,yn+h2+l)(xm+h1,yn+h2)]=C(xm+k,yn+l)(xm,yn)C(xm+h1+k,yn+h2+l)(xm+h1,yn+h2)Xm+k, n+lXm+h1+k,n+h2+lXm,nXm+h1,n+h2ej(θm+k,n+l+θm,n)ej(θm+h 1+k,n+h2+i+θm+h1,n+h2)=Xm,nXm+h1,n+h2ej(θm,n−θm+h1,n+h2)

[0075] As already mentioned, the pairs of antenna elements used to measure the complex OTA coupling parameters C (xm+k, yn+l) (xm, yn ) and C (xm+h1+k, yn+h2+l) (xm+h1, yn+h2 ) are used to create shifted copies of each other (along the antenna rows or columns), and the grating periodicity ensures that the complex OTA coupling parameters have the same numerical value, so that they cancel each other out. In addition, X m+k,n+l e j(θm+k,n+l) and X m+h1+k,n+h2+l e j(θm+h1+k,n+h2+l)Magnitude and phase components of the mRX paths of the antenna elements at the location, x m+k y n+l and at location, x m+h1+k y n+h2+l , which were originally calibrated using equations (1) to (11) to be equal in amplitude and phase and therefore cancel each other out. Therefore, equation (13) can be simplified as shown above. In some cases, equation (13) can provide a direct relationship between the functional TX RF paths of antenna elements at the site, x m , y n and at location, x m+h1 y n+h2 ,. Accordingly, equation (13) can calibrate any two RF paths (e.g., functional TX paths) with respect to each other, since h1, h2 can have any integer value without affecting equation (13).

[0076] It should be understood that Equation (1) through Equation (13) and the calibration configurations to which they refer have been described as if local measurements are acquired and then Equation (1) through Equation (13) are solved for those measurements to calibrate two antenna elements at a time, and then the process is repeated sequentially to calibrate the entire 2D antenna array. However, the calibration examples above are intended to illustrate the process of measuring complex OTA coupling parameters and the physical redundancies used for calibration. In some cases, calibration configurations different from the examples described here may be used without exceeding the scope of the present disclosure.For example, all possible measurements between any pair of antenna elements that could be used in a sequential approach and the calculations presented in equation (1) through equation (13) can be organized as a set of linear equations to be solved using a suitable mathematical approach (e.g., least squares). In some examples, hundreds or thousands of linear equations may be solved simultaneously. The exact manner of solving this larger set of equations may depend on the required accuracy and the computational resources and / or time available during functional phased array operation and is outside the scope of the present disclosure. SELF-CALIBRATION WITH PURE VALUE MEASUREMENTS

[0077] The Fig. 5A to Fig. The examples shown in Figure 5D and Equations (1) to (13) assume that coherent RF measurements between TX / RX antenna element pairs can be performed during a calibration process. Although performing coherent RF measurements between TX / RX antenna element pairs may help speed up the calibration process and / or achieve better accuracy in some practical scenarios, coherent RF measurements between TX / RX antenna element pairs are not a fundamental part of the OTA self-calibration approach described here.

[0078] Fig. 4G shows a calibration training 480 that does not require coherent measurements to perform the calibration. In some aspects, the calibration training 480 may be Fig. 4G of Calibration Training 460 from Fig. 4E, except that the path through bypass switches 468 is replaced by a detector 496. In some implementations, detector 496 may be a voltage detector, a current detector, a power detector, and / or any combination thereof. In one example, detector 496 may include an RMS voltage detector (or peak voltage detector) that produces a real number output corresponding to the RMS voltage magnitude of a signal from TX terminal 482 and coupled to the input of detector 496 via coupler 488.

[0079] In some examples, the magnitude output by detector 496 may be sent to a processor via digital / data paths 497 during calibration mode. In some cases, the processor may be included in a BF (e.g., in BF 407, in additional BF 408 of Fig. 4A to Fig. 4D). In some examples, the processor may be included in a modem (e.g., in the modem 210 in Fig. 2B). In some cases, the processor may be the processor 1610 of the computer system 1600 of Fig. 16 correspond.

[0080] In some implementations, the measurements acquired by detector 496 may only be magnitude. In some cases, multiple measurements may be taken while adjusting the gain and phase of the transmit paths to generate complex data related to the magnitude-phase relationship (e.g., a complex ratio) of the transmit paths from two different TX antenna elements (e.g., antenna element 463 and antenna element 464). For example, if antenna elements 463 and 464 are simultaneously transmitting the same waveform and antenna element 465 is receiving the transmitted signals, the signal flowing from TX port 482 of antenna element 465 toward FEM 487 is a vector sum of the signal coming from antenna element 463 and antenna element 464.In particular, the magnitude detected by the detector 496 of the antenna element 465 when the TX antenna elements 463, 464 transmit simultaneously is proportional to the magnitude of a complex sum shown in equation (14) below:. V465,(463,464)=|C424X463ej(θ463)+C428X464ej(θ464)|

[0081] Where C 424 and C 428 denote the complex coupling parameters through the OTA paths 424 and 428, X 463 and X 464 denote the amounts of the complex gain of the respective RF paths for the antenna elements 463, 464, and θ 463 , θ 464 denotes the phase of the complex gain of the respective RF paths for the antenna elements 463, 464 and | | represents the magnitude of the complex value within the brackets. In some implementations, the value V detected by the detector 496 may 465,(463,464) be measured repeatedly, while the amount X 463 and the phase θ 463of the RF path of the antenna element 463 so that the value of V 465,(463,464) is minimized. The minimum value of V 465,(463,464) occurs when the complex gain factor of the RF path of the antenna element 463 is chosen so that |C424X463'ej(θ463')+C428X464ej(θ464)|=0, ie C424X463'ej(θ463')=−C428X464ej(θ464) or C424X463'ej(θ463')C428X464ej(θ464)=−1. As used here, the amount X463' and the phase θ463' to the specific magnitude and phase settings along the RF path of the antenna element 463 (e.g., from phase shifters, from PAs 421 or the like), so that V 465,(463,464) = 0. In some cases, knowledge of the values ​​of X463',θ463' equivalent to knowing the complex value M(1a)M(1b) or the ratio of equation (1) to equation (2).

[0082] In some implementations, the same search procedure may be used to minimize the voltage value V 466,(463,464) be used when the antenna element 466 is the receiving antenna element to find the magnitude and phase settings of the RF path for the antenna element 466, the C424X463''ej(θ463'')C428X464ej(θ464)=−1 fulfill what the knowledge of M(2a)M(2b) or the ratio of equation (3) to equation (4). As used here, the amount X463'' and the Phaseθ463'' to the specific magnitude and phase settings along the RF path of the antenna element 463 (e.g., from phase shifters, from PAs 421 or the like), so that V 466,(463,464) = 0. Therefore, the procedure described in equation (5) to equation (8) can be modified to M(1a)M(1b)M(2a)M(2b) and then obtain the relative ratio of the complex gain (e.g., magnitude and phase) between the RF path of the TX antenna element 463 and the RF path of the TX antenna element 464. In such an example, there is still a 180-degree ambiguity similar to the ambiguity in the solution of equation (8) and can be resolved by similar methods described above with respect to the Fig. 4C to Fig. 4F shown trainings are dissolved. OTA SELF-CALIBRATION WITH SPECIAL ANTENNA CONNECTORS (TX ONLY OR RX ONLY) AND CALIBRATION LINES

[0083] In some cases, phased array antennas may have antenna elements with special antenna connectors that can be operated as pure transmit or receive antennas during calibration, so that some of the Fig. 5A to Fig. 5D do not apply. For example, if the assumptions that C2 = C4, C1 = C3 or C5 = C6 in Fig. 5A and Fig. 5B no longer apply, equations (1) to (4) cannot be simplified to equation (8). In such a case, more redundancies within the phased array antenna may be required to calibrate the functional RF paths to each other without using an external reference (e.g., a far-field source, a flying probe, etc.).

[0084] Fig. 6 shows an exemplary calibration configuration 600 with antenna elements 613, 614, 615, 616 that have dedicated TX-only and RX-only antenna ports. For example, antenna elements 613 may be dual-linearly polarized antennas routed to a 3 dB 90-degree hybrid 625, which results in an RX port 684 and a TX port 682. As shown, the RX port 684 and the TX port 682 may be coupled to the corresponding ports of the FEMs 620, 622. As shown, the FEMs 620, 622 may each include a PA 621 and an LNA 623. In the illustrated example, FEMs 620 are configured in a TX configuration, and FEMs 622 are configured in an RX configuration. In some cases, FEMs 620, 620 may have a dedicated RX port coupled to the input of LNA 623 and a dedicated TX port coupled to the output of PA 621.In some cases, each FEM 620, 622 may include a combined IO port 626 connected to the output of the LNA 623 and the input of the PA 621. In some implementations, the output of the LNA 623 and the input of the PA 621 may be combined using a passive or active combiner included in each FEM 620, 622. In some examples, the combined IO port 626 of each FEM 620, 622 may be routed to an RFIO port 605 of the BF 607. The specific RFIO paths shown are referred to as RFIO 653, RFIO 655, RFIO 656, RFIO 654, which correspond to the antenna elements 613, 615, 616, 614, respectively.

[0085] In some examples, when a particular FEM 622 is in RX mode, the LNA 623 is active, the PA 621 is off (or inactive), and the RFIO port 605 routed to the FEM 622 is in an RX configuration. When an FEM 620 is in TX mode, the LNA 623 is off (or inactive), the PA 621 is active, and the RFIO port 605 routed to the FEM 620 is in a TX configuration. In an illustrative example, a complex coupling parameter (e.g., complex coupling parameter S (684,615), (682,613) ) for the OTA path 632 from the TX port 682 of the antenna element 613 to the RX port 684 of the antenna element 615 when RFIO 653 is in TX mode and RFIO 655 is in RX mode (as in Fig. 6). Similarly, a complex coupling parameter (e.g., complex coupling parameter S (684,613), (682,615) for a reverse OTA path (not shown) in the opposite direction of the OTA path 632 from the TX port 682 of the antenna element 615 to the RX port 684 of the antenna element 613 when RFIO 655 is in TX mode and RFIO 653 is in RX mode (not in Fig. 6). In the exemplary calibration training 600 of Fig. 6, the antenna array is not assumed to have a particular physical symmetry between the antenna element 613 and the antenna element 615, and the complex coupling parameters for the OTA path 632 and the reverse OTA path in the opposite direction of the OTA path 632 are not assumed to be equal, so that S (684,613), (682,615) ≠ S (684,615), (682,613) .

[0086] Fig. Figure 7 shows an example of a calibration measurement setup 700 for a phased array antenna system with antenna elements having dedicated antenna ports for transmitting and receiving. As shown in Fig. 7, the calibration measurement configuration 700 comprises a group of four antenna elements 702, 706, 708, 704 in a linear arrangement with corresponding OTA paths similar to the linear arrangement of the antenna elements 502, 506, 508, 504 of Fig. 5A and the corresponding OTA paths in Fig. 5A. In the example of Fig. 7, the antenna elements 702, 706, 708, 704 may, however, Fig. 6. Therefore, when calibrating the antenna elements 702, 706, 708, 704, it is not assumed that mirrored and / or shifted OTA paths behave identically, and therefore it is not assumed that the complex coupling parameter C1 is equal to the complex parameter C3 (e.g., C1 ≠ C3) and that the complex coupling parameter C2 is equal to the complex parameter C4 (e.g., C2 ≠ C4). Accordingly, equations (1) to (4) for the complex measured values ​​M(1a), M(2a), M(1b), M(2b) using the antenna elements 702, 706, 708, 704 cannot be simplified in the same way as shown in equation (8) above.

[0087] Fig. Figure 8A shows an exemplary calibration setup 800 with additional redundancy to complement OTA measurements of mutual coupling for OTA calibration of a phased array antenna system. As shown in Fig. 8A, one or more calibration lines (e.g., calibration lines 802, 804, 806) may be coupled to a subset of the antenna elements of the antenna array (e.g., antenna elements 812, 814, 816, 818, 808). For example, calibration line 802 may be coupled to antenna elements 808, 816, 818, calibration line 804 may be coupled to antenna elements 812, 816, and calibration line 806 may be coupled to antenna elements 814, 818. As illustrated, calibration formation 800 may also include antenna elements 813 that are not connected to any of calibration lines 802, 804, 806.

[0088] In some cases, the one or more calibration lines 802, 804, 806 can be used to calibrate the corresponding antenna elements. For example, the antenna elements 812 connected to the calibration line 804 can be calibrated relative to each other using the mRX / mTX measurement ports at both ends of the calibration line 804. Similarly, the antenna elements 808 can be calibrated relative to each other using the mRX / mTX measurement ports at both ends of the calibration line 802, and the antenna elements 814 can be calibrated using the mRX / mTX measurement ports at both ends of the calibration line 806. In some implementations, after calibrating the antenna elements 808, 812, 814 using the calibration lines 802, 804, 806, the fact that the functional RF path of the calibrated antenna elements is already calibrated relative to each other (e.g.identical phase and magnitude behavior) can be used to estimate the previously unknown complex ratios C1 / C3 and C2 / C4 in equation (1) to equation (4). In some implementations, the estimated ratios C1 / C3 and C2 / C4 can then be used in other parts of the antenna array where there are no calibration lines to simplify equations (1) to equation (4) into a form similar to equation (8) and to align the entire 2D antenna array.

[0089] Fig. Figure 8B shows a detailed view of a subsection 810 of the antenna grid (e.g., the antenna grid 202 of Fig. 2B) Calibration Training 800 of Fig. 8A including a section of the calibration line 802. As shown, the section of the calibration line 802 in subsection 810 runs along and is coupled to three antenna elements 808. As shown, the subsection 810 may also include antenna elements 813 of the antenna grid that are not coupled to the calibration line 802. Each section of the calibration line 802 between the antenna elements 808 may repeat periodically with an effective length L between the antenna elements 808 (individually referred to as antenna elements 1, 2, 3). In some cases, the effective length of the individual sections of the calibration line 802 may not be the same, but the sections of the calibration line 802 may instead have known ratios of the effective lengths. In some implementations, the calibration line 802 may be consistent (e.g.,Each antenna element 808 may be coupled to the transmit / receive RF path of each antenna element 808 by a weak coupler (e.g., with a coupling factor of less than -20 dB to prevent degradation of antenna efficiency). In some cases, a calibration signal may be transmitted (or received) from port A or port B and received (or transmitted) by the RF paths of antenna elements 1, 2, and 3. In some examples, the measurements obtained from the measurement pairs (A,1), (A,2), (A,3), (B,1), (B,2), (B,3) can produce sufficient redundancy using assumptions about the calibration line sections (e.g., equal effective lengths or known effective length ratios) and the consistent coupling levels to the antennas so that RF paths for antenna elements 1, 2, 3 can be calibrated.In some examples, a similar technique can be used to calibrate more than three antenna elements along a calibration line. A more detailed explanation of the method for performing calibration using the calibration techniques described in . Fig. 8A and / or subsection 810 of Fig. 8B is outside the scope of the present disclosure and can be found in U.S. Patent Application No. 18 / 132,108, entitled "ANTENNA APPARATUS AND IN-LINE CALIBRATION SYSTEM FOR SAME," which is hereby incorporated herein in its entirety and for all purposes.

[0090] Fig. 8C shows a calibration result 830 of a calibration performed on the antenna elements 812 using the calibration line 804. As shown, the RF paths (RX and / or TX) for the antenna elements 819 (including the individually labeled antenna elements a, b, c, d, e, f) can be aligned in magnitude and phase through the calibration line 804 prior to performing OTA coupling measurements. Fig. 8C also shows OTA calibration measurements that can be used to calibrate the antenna elements 819 (including the individually labeled antenna elements 1, 2, 3) using the calibrated antenna elements 812 as a reference. In the illustrated example, the antenna elements 819 are configured in TX mode, and the antenna elements 819 transmit calibration signals from a TX port (e.g., TX port 682 of Fig. 6), while the antenna elements 812 transmit the calibration signals OTA via an RX port (e.g. RX port 684 of Fig. 6). In an illustrative example, antenna element 1 is configured to transmit calibration signals that are received by antenna elements a and b OTA. As illustrated, the OTA path between antenna element 1 and antenna element a may have complex coupling parameters S1, and the OTA path between antenna element 1 and antenna element b may have a complex coupling parameter S2. In some examples, a measurement between the RF path of antenna element 1 and the RF path of antenna element a may be referred to as a complex measurement value M(a1). Similarly, a measurement value between the RF path of antenna element 1 and the RF path of antenna element b may be referred to as a complex measurement value M(b1). In some aspects, the complex measured values ​​M(a1), M(b1) can be used to determine a relationship between the complex coupling parameters S1, S2, as shown in equation (15) to equation (17) below: M(a1)=S1XaX1ej(θa)ej(θ1) M(b1)=S2XbX1ej(θb)ej(θ1) M(a1)M(b1)=S1S2XaXbej(θa−θb)=S1S2

[0091] X a ,X b , the contributions of the magnitude for the RF paths of the antenna elements a and b and θ a , θ b the phase contributions for the RF paths of antenna elements a and b, respectively. The simplification of equation (17) is possible because the RF path for antenna element a and the RF path for antenna element b were previously calibrated using the calibration line 804 such that X a = X b and θ a = θ b. Therefore, two acquired OTA measurements (e.g., M(a1), M(b1)) can be used to calculate a value for the ratio S1 / S2. However, a value for the ratio S1 / S2 calculated based on two acquired OTA measurements may not be accurate because the calibration accuracy of the antenna elements 812 by the calibration line 804 may contain a phase error and / or a magnitude error. However, additional OTA measurements with different antenna elements 812 at different locations along the calibration line can be used to calculate additional values ​​for the ratio S1 / S2 using Equation (15) to Equation (17). For example, an additional value for the ratio S1 / S2 can be calculated based on the measurement of a calibration signal transmitted by antenna element 2, which is received by both antenna element c (e.g., complex measurement value M(c2)) and antenna element d (e.g.,complex measurement value M(d2)). In another example, an additional estimate for the ratio S1 / S2 may be calculated based on the measurement of a calibration signal transmitted by antenna element 3, which is received by both antenna element e (e.g., complex measurement value M(e3)) and antenna element f (e.g., complex measurement value M(f3)). In some cases, the values ​​for the ratio S1 / S2 obtained from multiple pairs of OTA calibration measurements may be combined (e.g., averaged) to provide a numerical estimate of the ratio S1 / S2.

[0092] Fig. 8D shows a calibration training 840 that includes the calibration of antenna elements based on OTA calibration measurements and the estimation of the ratio S1 / S2 as in Fig. 8C described above. As illustrated, the estimated ratio S1 / S2 can be used to calibrate columns of antenna elements (e.g., columns 844, 845) that are not connected to the calibration line 804. For example, an antenna element 1 in column 844 can be calibrated based on a pair of OTA measurements of a calibration signal transmitted by antenna element 1 and received by a neighboring pair of antenna elements a, b in column 843. In some cases, the two complex measured values ​​M(a1) / M(b1) can be substituted into the left-hand side of equation (15) and equation (16). However, the ratio of the two measured complex values ​​(e.g., M(a1) / M(b1) of equation (15) and equation (16)) does not simplify equation (17) because the values, X a , X b , θ a , θ bare unknown when the antenna elements a, b are selected from column 843 that have not been calibrated with the calibration line 804. However, equation (15) and equation (16) can be rewritten using the numerical estimation of the ratio S1 / S2 as shown in equation (18) below: M(a1)M(b1)S1S2=XaXbej(θa−θb)

[0093] In some cases, the terms on the left side of equation (18) may have numerical values. For example, complex measured values ​​M(a1), M(b1) may have known numerical values ​​derived from OTA measurements, and the ratio S1 / S2 may have an estimated numerical value, as discussed above with respect to Fig. 8C. Furthermore, the terms on the right-hand side of equation (18) can represent the relative values ​​of magnitude and phase of the RF path for antenna element a and the RF path for antenna element b. In some cases, a calibrated pair of antenna elements can have the same magnitude, so that X a = X b , and for the same phase, so that θ a = θ b . Accordingly, the RF paths of the antenna elements a, b can be calibrated with respect to each other using a complex compensation factor determined from equation (18).

[0094] As described in Calibration Training 850 of Fig. 8E, a similar calibration procedure may be applied to each adjacent pair of antenna elements in column 843, such that the RF paths of all antenna elements in column 843 are calibrated with respect to each other. Furthermore, a similar calibration process may be used to calibrate the antenna elements in all columns (e.g., columns 844, 845, 851, 852, 853, 854, 855, 856, 857, 858, 859, 861) of the antenna array, such that in each column, all antennas are calibrated with each other, as illustrated by antenna elements with a particular shading. As shown, although the individual antenna elements of each column (e.g., columns 844, 845, 856, 857, 858, 859, 861) of the antenna array may be calibrated, calibration training 850 shows that the columns cannot be calibrated relative to each other.

[0095] Fig. 8F shows a calibration setup 860 that can be used to perform OTA calibration of rows of antenna elements using a reference subset of self-calibrated antenna elements 808 connected to a calibration line 802. In the illustrated example of Fig. 8F, it is assumed that the antenna elements 808 are calibrated by the calibration line, as indicated by the black shading. In some implementations, a pair of adjacent antenna elements 862 in the same row 871 of antenna elements may send calibration signals to a single receive antenna element 808 to estimate the ratio of the complex OTA coupling parameters S3 / S4 using Equation (15) through Equation (17). In some cases, the estimated S3 / S4 ratio and an equation similar to Equation (18) may be used to calibrate rows of antenna elements in each row of antenna elements (e.g., rows 871, 872, 873, 874, 875, 876, 877, 878) relative to each other, as indicated by antenna elements sharing a particular shading. In some cases, the calibration of columns of antenna elements, as in Fig. 8E, and the calibration of rows of antenna elements as shown in Fig. 8F, can be used to perform a full 2D calibration of the antenna elements of the antenna array.

[0096] In some implementations, one or more calibration lines may be configured to couple to antenna elements in multiple rows and multiple columns of an antenna array. In some cases, antenna elements in multiple rows and columns of an antenna array may be calibrated with respect to one another. In some examples, OTA calibration measurements may be acquired between pairs of antenna elements and a single calibrated antenna element to estimate a complex coupling parameter relationship (e.g., S1 / S2, S3 / S4, S5 / S6). In some cases, an equation similar to equation (18) above may be used to calibrate groups of antenna elements relative to one another based on OTA calibration measurements. In some implementations, groups of antenna elements relative to one another based on OTA calibration measurements may be referred to as calibration groups.In some examples, the antenna elements calibrated relative to each other based on measurements using the one or more calibration lines may also be referred to as calibration groups. In some cases, the geometry of the calibration groups may vary based on the geometry of the one or more calibration lines. In some cases, a full 2D calibration of the antenna elements of the antenna group may be performed based on antenna elements included in multiple calibration groups.One or more calibration lines configured to couple to antenna elements in multiple rows and multiple columns of an antenna array (not shown) may include, for example, a curved calibration line, a zigzag calibration line, a meandering calibration line, a piecewise linear calibration line, and / or any combination thereof.

[0097] It should be understood that Equation (15) to Equation (18) and the measurement configurations to which they refer have been described as if local measurements are acquired and then Equation (15) to Equation (18) are solved for these measurements to calibrate two antenna elements at a time, and then the process is repeated sequentially to calibrate the entire 2D antenna array. However, the above calibration examples serve to clarify the process of measuring the complex OTA coupling parameters and the physical redundancies (e.g., estimated ratio S1 / S2, estimated ratio S3 / S4) used for calibration. In some cases, calibration configurations different from the examples described here may be used without exceeding the scope of the present disclosure.For example, all possible measurements between any pair of antenna elements and / or between an antenna element and a calibration line that could be used in a sequential calculation, and the calculations presented in equation (15) through equation (18), can be organized as a set of linear equations to be solved using a suitable mathematical approach (e.g., least squares). In some examples, hundreds or thousands of linear equations may be solved simultaneously. The exact manner of solving this larger set of equations may depend on the required accuracy and the computational resources and / or time available during functional phased array operation and is outside the scope of the present disclosure. SELF-CALIBRATION WITH SUB-ARRAYS OF AN ANTENNA AND A FRONT-END MODULE

[0098] The systems and techniques described here for performing OTA self-calibration can also be applied to antenna elements that lack dual-use connectors, as in the examples of Fig. 4A to Fig. 4G and Fig. 5A to Fig. 5D, so that equations (1) to (14) cannot be applied without additional redundancies to achieve a complete calibration. Furthermore, the systems and techniques described here for performing OTA self-calibration in a system without calibration lines to provide additional redundancy, as in Fig. 8A to Fig. 8F, so equations (15) through equation (18) are not applicable. In some implementations, groups of antenna elements (also referred to herein as antenna element sub-arrays) formed from antenna elements routed to the same FEM chip and / or RFIO path can be used as internal reference points for determining the relative calibration between the antenna elements of an antenna array. In some aspects, the systems and techniques assume predictable routing of RF transmission lines (e.g., the routing of traces on a printed circuit board and / or a waveguide distribution network) and / or predictable FEM chip characteristics (e.g., relative gain levels of different paths in a given FEM).

[0099] Fig. 9A to Fig. 9H show various exemplary configurations of antenna sub-arrays and configurations (e.g., combinations and / or orientations) of corresponding FEMs and / or RFIO lines routed to a BF. For example, Fig. 9A shows a calibration training with a two-way FEM 922 (e.g., an FEM with two TX / RX port pairs TX1 / RX1, TX2 / RX2) that can control two dual-port antenna elements 913 and has a single bidirectional RFIO port 925 that can be routed to a BF RFIO 905 or a passive power combiner / splitter (e.g., a Wilkinson combiner / splitter). In the exemplary calibration training 900 of Fig. 9A, the two antennas connected to the FEM 922 are aligned along the x-axis of the antenna grid. Fig. 9B shows an additional calibration configuration 910 with a three-way FEM 924 (e.g., an FEM with three TX / RX port pairs TX1 / RX1, TX2 / RX2, TX3 / RX3) that can control three dual-port antenna elements 913.

[0100] In both exemplary training courses of Fig. 9A and Fig. 9B, the inclusion of a single RFIO port 925 for the two-way FEM 922 and the three-way FEM 924 indicates that the FEMs 922, 924 have internal RF phase and / or gain shifters to control the relative complex RF gain (e.g., phase and / or magnitude) of the RF path between RFIO port 925 and TX1, the RF path between RFIO port 925 and TX2, and / or the RF path between RFIO port 925 and TX3. Similarly, the specification of a single RFIO port 925 indicates that the FEMs 922, 924 have internal RF phase shifters and / or amplifiers to control the relative phase and / or magnitude of the complex RF gain for the RF path between RX1 and RFIO port 925, the RF path between RX2 and RFIO port 925, and / or the RF path between RX3 and RFIO port 925. In some cases, the FEMs 922, 924 may include passive power combiners / dividers (e.g.,a Wilkinson combiner / divider) for sharing the single RFIO port 925 between the TX / RX pairs of each FEM. In some cases, the internal circuitry 926 may include phase shifters, amplifiers, filters, combiners / dividers, other electrical components, and / or any combination thereof. For illustrative purposes, each of the circuits shown in . Fig. 9C to Fig. 9I, Fig. 10A to Fig. 10E, Fig. 11A, Fig. 11B and Fig. 12 described FEMs can optionally contain internal circuits 926.

[0101] Fig. Figure 9C shows a linear configuration 920 in which the RFIO ports 925 of a first FEM 922 and a second FEM 933 are combined with a power combiner / divider 928 (e.g., a -3 dB Wilkinson combiner / divider) to form a four-element subarray. As shown in the figure, the antenna elements 913 in the four-element subarray are arranged in a row of four antenna elements (e.g., a 1×4 array of antenna elements) aligned along the x-axis. Fig. 9D shows a rotated linear calibration formation 930. As shown, the rotated linear calibration formation 930 can be the linear formation 920 of Fig. 9C, except that the antenna elements 913 of the four-element sub-array are arranged in a 1x4 array of antenna elements aligned along the y-axis. In some examples, the x-axis and y-axis may represent orthogonal directions in the plane of a 2D antenna grid (e.g., the antenna grid 202 of Fig. 2B).

[0102] Fig. Figure 9E shows a rectangular configuration 940 in which the RFIO ports 925 of a first FEM 922 and a second FEM 933 are combined with a power combiner / splitter 928 (e.g., a -3 dB Wilkinson combiner / splitter) to form a rectangular four-element subarray (e.g., a 2x2 array of antenna elements). As shown, the two dual-port antenna elements 913 routed to FEM 922 are aligned along the x-axis, and the two dual-port antenna elements 913 routed to FEM 933 are aligned along the x-axis with a different x-coordinate. In addition, the two dual-port antenna elements 913 coupled to the TX1 / RX1 ports of the FEMs 922, 933 are aligned along the y-axis, and the two antenna elements coupled to the TX2 / RX2 ports of the FEMs 922, 933 are aligned along the y-axis with a different y-coordinate. Fig. 9E also includes information on xy positions (e.g., x1, y1) for each of the dual-port antenna elements 913.

[0103] Fig. 9F shows an additional rectangular configuration 950 in which RFIO ports 925 of a first FEM 922 and a second FEM 933 are combined with a power combiner / splitter 928 (e.g., a -3 dB Wilkinson combiner / splitter) to form a rectangular four-element subarray (e.g., a 2x2 array of antenna elements). As shown, the two dual-port antenna elements 913 routed to FEM 922 are aligned along the x-axis, and the two dual-port antenna elements 913 routed to FEM 933 are aligned along the x-axis with a different y-coordinate. As shown, the dual-port antenna element 913 coupled to the TX1 / RX1 port of the FEM 922 is aligned along the y-axis with the antenna element coupled to the TX2 / RX2 port of the FEM 933.Furthermore, the dual-port antenna element 913 coupled to the TX2 / RX2 port of the FEM 922 is aligned along the y-axis with the antenna element coupled to the TX1 / RX1 port of the FEM 933 with a different x-coordinate. Fig. 9F also includes information on xy positions (e.g., x1, y1) for each of the dual-port antenna elements 913.

[0104] Fig. 9G shows a rotated rectangular formation 960 corresponding to the calibration formation of Fig. 9E, except that the arrangement of the Fig. 9E is rotated 90 degrees relative to the xy-axis of the antenna grid. Similarly, Fig. 9H an additional rotated calibration training 970, which corresponds to the calibration training of Fig. 9F, except that the arrangement of the Fig. 9F is rotated 90 degrees relative to the xy axis of the antenna grid.

[0105] Fig. 9I shows an exemplary calibration configuration 980 for calibrating a rectangular group of antenna elements comprising four rows and four columns (e.g., a 4x4 array of antenna elements). In the Fig. 9I, the 4x4 array of antenna elements may include a first 2x2 array of antenna elements 982, a second 2x2 array of antenna elements 984, a third 2x2 array of antenna elements 986, and a fourth 2x2 array of antenna elements 988. In the example shown in Fig. 9I, the 2x2 sub-arrays of antenna elements 982, 984 resemble the topology used in the rectangular configuration 940 of Fig. 9E, and the 2x2 sub-arrays of antenna elements 986, 988 are similar to the topology of Fig. 9E with a rotation of 180 degrees around the xy-axis of the antenna grid. The calibration training 980 of Fig. 9I is for illustrative purposes, and other configurations may be used without departing from the scope of the present disclosure. In some implementations, the exemplary calibration configuration 980 of Fig. 9I may provide a variation in the design of the antenna elements in a region of interest, so that internal symmetries in the FEMs 922, 933 and the power combiners / splitters 928 may provide additional redundancies to achieve a full 2D calibration of the antenna elements in a phased array antenna.

[0106] As in Fig. 9I, a parameter D1 can be defined as the expected value of the ratio of the complex RF gain of the TX1 port of FEM 922 and the TX1 port of FEM 933. Similarly, a parameter D2 can be defined as the expected value of the ratio of the complex RF gain of the TX2 port of FEM 922 and the TX2 port of FEM 933. Here, the complex RF gain of a TX port is defined as the RF gain between the combiner / divider 928 and the output of the respective TX port (e.g., the output of a PA coupled to the TX port).

[0107] In some implementations, the combiner / splitter 928 may be symmetric and provided with phase-matched routing from the combiner / splitter 928 to the RFIO port 925 of both the FEM 922 and the FEM 933. In such an example, D1 ≈1 and D2 ≈1 assume that the FEMs 922, 933 are contained in FEM chips with the same physical architecture. In some cases, the approximate equalities D1 ≈1 and D2 ≈1 may result from complex gain variations of a given FEM design from one physical FEM chip / sample to another.

[0108] With reference to Fig. 9I can be a parameter Δ 12 be defined as the expected value of the ratio of the complex RF gain of the TX1 port to the RF gain of the TX2 port of a particular FEM 922, 933. In some implementations, the expected value of Δ 12deviate from one due to an inherent asymmetry of the RF path of the TX1 port and the RF path of the TX2 port within the FEMs 922, 933 (e.g., an asymmetry in the physical design of the FEM chip) (e.g., Δ 12 ≠ 1). Although the parameters D1, D2, Δ 12 described above for the RF paths of the TX ports, the parameters D1, D2, Δ 12 can also be defined for the RF paths of the RX ports without loss of generality. Equations (19) to (21) below contain mathematical descriptions of the parameters Δ 12 , D1 and D2, respectively: Δ12≈G(IO1,a1)G(IO1,a2)≈G(IO1,b1)G(IO1,b2)≈G(IO2,a1)G(IO2,a2)≈G(IO3,b1)G(IO3,b2)≈⋯ D1≈G(IO1,a1)G(IO1,b1)≈G(IO2,a1)G(IO2,b1)≈G(IO3,a1)G(IO3,b1)≈G(IO4,a1)G(IO4,b1)≈1 D2≈G(IO1,a2)G(IO1,b2)≈G(IO2,a2)G(IO2,b2)≈G(IO3,a2)G(IO3,b2)≈G(IO4,a2)G(IO4,b2)≈1

[0109] IO refers to mto the specific RFIO number of a particular BF RFIO 905 (e.g. RFIO-1, RFIO-2, RFIO-3, RFIO-4), a i is the identifier of the i ten TX (or RX) port of FEM 922, and b j is the identifier of the j ten TX (or RX) port of FEM 933. The parameter D1 can have a standard deviation σ D1 the parameter D2 can have a standard deviation σ D2 and the parameter Δ 12 can be a standard deviation σ Δ12 In some cases, the standard deviation for each parameter D1, D2, Δ 12 depend on the complexity (e.g. number of stages, filters, phase shifters, etc.) of the RF signal path within the chip of FEM 922, 933, on manufacturing variations and / or variations of the assembly process.

[0110] In some cases, the parameters D1,D2 , and / or Δ 12used as internal references and therefore provide additional redundancy for OTA measurements during calibration. In some cases, the relative standard deviation of the parameters D1, D2 and / or Δ 12 be used to determine which parameter to use during the calibration of a particular phased array antenna. For example, the use of the parameter D1, D2 and / or Δ 12 with the smallest standard deviation after completion of a calibration procedure will result in the most reliable calibration possible.

[0111] Fig. Figure 10A shows an example calibration configuration 1000 for calibrating antenna elements in a 2D phased array. To simplify the illustration, the two separate paths connecting the TX port and the RX port of an FEM to two separate ports of an antenna element are combined into a single TX / RX port. Fig. 10A to Fig. 10E, Fig. 11A, Fig. 11B and Fig. 12 are to be understood as referring to the type of FEMs (e.g. FEMs 922, 933), the antenna elements (e.g. antenna elements 913) and the connections between FEMs and antenna elements that are used in the exemplary calibration embodiments in Fig. 9A to Fig. 9I. In the example of Fig. 10A, the antenna elements 1013 connected to a particular FEM 1022, 1033 are aligned along the y-axis. In addition, the FEMs 1022, 1033 connected to the same power combiner / divider (e.g., combiner / divider 928 of Fig. 9C to Fig. 9I) and BF RFIO 1005 are aligned along the x-axis.

[0112] Fig. 10B shows a calibration training 1020 for calibrating rows of antenna elements in the calibration training 1000 of Fig. 10A. As in Fig. 10B, antenna elements 1013 (e.g., antenna elements a, b, c, d, e, f, g, h) transmit calibration signals (e.g., in a TX / mTX mode), and antenna elements 1014 (e.g., antenna elements 1, 2, 3, 4, 5, 6, 7, 8) receive the calibration signals (e.g., in an RX / mRX mode). As shown, the OTA path from antenna element a to antenna element 1 has a complex coupling parameter S2, and the OTA path from antenna element b to antenna element 1 has a complex coupling parameter S1. In some cases, the complex coupling parameters S1,S2 may be identical for pairs of adjacent antenna elements with a shift along the x-axis of the antenna grid by an integer multiple of the x-axis spacing of the antenna elements. For example, the OTA path from antenna element c to antenna element 3 has a complex coupling parameter S2, and the OTA path from antenna element d to antenna element 3 has a complex coupling parameter S1.A similar relationship between the complex coupling parameters S1, S2 can be expected for any triad of antennas (e.g., antenna elements e, f, 5) with the same relative geometry. In some cases, the complex measurements M(1a) and M(1b) can be obtained from measurements of the mutual coupling between the transmitting antenna elements a, b and the receiving antenna element 1. Equation (22) illustrates the relationship between the complex measurements M(1a) and M(1b) as shown below:. M(1a)M(1b)=S2S1XaejθaXbejθb≈S2S1 D1≈S2S1

[0113] Similarly, complex measurements can be generated from mutual coupling measurements taken for corresponding antenna elements in the other 2x2 antenna element arrays in Fig. 10B, resulting in a similar relationship as shown in equation (22) below: M(1a)M(1b)≈M(3c)M(3d)≈M(5e)M(5f)≈M(7g)M(7h)≈S2S1

[0114] Equation (23) illustrates that in the calibration training 1020, multiple mutual coupling measurements can be performed and an estimate (e.g., a best fit, least squares, etc.) for the ratio S2 / S1 can be determined. In some cases, the estimate of the ratio S2 / S1 can be used directly to align all antenna elements that are adjacent along the x-axis (e.g., antenna elements b, c), including those used for the mutual coupling measurements (e.g., antenna elements a, b), as shown in Equation (24): M(2b)M(2c)=S2S1XbejθbXcejθc⇒M(2b)S1M(2c)S2=XbejθbXcejθc

[0115] It should be clear that the left-hand side of equation (24) represents a complex numerical value, since the mutual coupling measurements can be captured as complex numerical values, and the estimated ratio S1 / S2 can be determined as a complex numerical value. Accordingly, the right-hand side of equation (24) can provide a complex compensation factor to calibrate antenna b and antenna c relative to each other. As mentioned above, the estimated ratio S1 / S2 can be determined from a best fit to multiple measurement pairs from equation (23), which can provide a more accurate value for the ratio S1 / S2 than a single measurement pair. Consequently, equation (24) can also be used to calibrate pairs of antenna elements that are already assumed to be calibrated due to similarity in FEMs (e.g., antenna element pair (a, b), (c, d), (e, f), or (g, h)).Accordingly, all antenna elements in a row of antenna elements (e.g., antenna elements a, b, c, d, e, f, g, h) can be calibrated relative to each other using equation (24).

[0116] Fig. 10C shows a calibration result 1040, which corresponds to Fig. 10B and Equations (23) to (24). As shown, each row of antenna elements in the calibration result may contain 1040 antenna elements that are calibrated with respect to each other, as indicated by antenna elements with the same shading. As shown in Fig. As shown in Figure 9C, although the antenna elements in each individual row are calibrated relative to each other, the antenna elements in different rows may not be calibrated relative to each other.

[0117] Fig. 10D shows a calibration pattern 1060 for calibrated columns of antenna elements in the exemplary calibration pattern of Fig. 10A. As in Fig. As shown in Figure 10D, the calibration training 1060 uses the parameter Δ 12to calibrate columns of antenna elements relative to each other. As shown, OTA target paths to be estimated are shown between the antenna elements q, r, s, t, u, v, x, which transmit calibration signals (e.g., in a TX / mTX mode), and the antenna elements 9, 10, 11, 12, 13, 14, 15, 16, which receive calibration signals (e.g., in an RX / mRX mode). As shown, an antenna element r can transmit calibration signals, which are received by the antenna elements 9, 10 via OTA paths having complex coupling parameters S4 and S3, respectively. In some cases, complex measurements, e.g., (M(9r) and M(10r)), can be generated from measurements of the mutual coupling between the transmitting antenna elements r and the receiving antenna elements 9, 10, as shown in equation (25): M(9r)M(10r)=S4S3X9ejθ9X10ejθ10≈S4S3Δ12

[0118] In addition, an antenna t can transmit calibration signals that are received by antenna elements 11 and 12 via OTA links having complex coupling parameters S4 and S3, respectively. Note that the FEMs coupled to antenna elements t, 11, and 12 can be rotated 180 degrees relative to antenna elements r, 9, and 10. As a result of the 180-degree rotation, the relationship between the complex coupling parameters S4 and S3 and the parameter Δ 12 be inverted as shown in equation (26) below: M(11t)M(12t)=S4S3X11ejθ11X12ejθ12≈S4S31Δ12

[0119] The following equation (27) illustrates an estimate for the ratio S4S3, which can be determined by combining equation (25) and equation (26): M(9r)M(10r)M(11t)M(12t)=M(13v)M(14v)M(15x)M(16x)≈±S4S3

[0120] As shown, Equation (27) provides an estimate for S4 / S3 that contains a ± ambiguity. In some cases, the ± ambiguity can be resolved using the same or similar procedures as those used to resolve the ± ambiguity in Equation (8), as described in the section "RESOLVING AMBIGUINESS IN CALIBRATION SOLUTIONS."

[0121] Fig. 10E shows a calibration result 1080, which corresponds to Fig. 10D and Equations (25) to (27). As shown, each column of antenna elements in the calibration result may contain 1080 antenna elements calibrated with respect to each other, as indicated by antenna elements with the same shading.

[0122] In some cases, once the ambiguity is resolved, each adjacent antenna pair along a column (e.g., along the y-axis of Fig. 10E) are calibrated relative to each other to obtain calibrated antenna columns. In some cases, the calibration of columns of antenna elements can be compared with the calibration of rows of antennas, as shown in Fig. 10C to obtain a fully calibrated 2D antenna array.

[0123] In some implementations, the parameters D1 and / or D2 can be used to obtain direct estimates of the ratio S4 / S3. Fig. For example, Figure 11A shows another exemplary embodiment 1100 for calibrating antenna elements in a 2D phased array. In the example of Fig. 11A, a first 4x4 sub-array of antenna elements 1182 comprises four identical 2x2 sub-arrays of antenna elements. In the 4x4 sub-array of antenna elements 1182, four antenna elements located at the xy positions (x1, y7), (x2, y7), (x1, y8), and (x2, y8) may correspond to a rectangular 2x2 antenna formed in the rotated rectangular configuration 960 of Fig. 9G. Similarly, four antenna elements located at the xy positions (x3, y7), (x4, y7), (x3, y8), and (x4, y8) may correspond to a 2x2 rectangular antenna element group formed in the rotated rectangular configuration 960 of Fig. 9G. As shown, the 4x4 sub-array of antenna elements 1182 also includes four antenna elements located at the xy positions (x1, y5), (x2, y5), (x1, y6), and (x2, y6), which may correspond to a 2x2 rectangular antenna element group formed in the rotated rectangular configuration 960 of Fig. 9G is shown mirrored across the x-axis. Similarly, four antenna elements located at the xy positions (x3, y5), (x4, y5), (x3, y6) and (x4, y6) may correspond to a 2x2 rectangular antenna element array, which in the rotated rectangular configuration 960 of Fig. 9G is mirrored on the x-axis. As shown, the 4x4 sub-array of antenna elements 1188 can be formed with an identical geometry as the 4x4 sub-array of antenna elements 1182. As shown in Fig. 11A, however, the 4x4 arrays of antenna elements 1184, 1186 and the corresponding FEMs and / or power dividers are rotated 90 degrees relative to the 4x4 arrays of antenna elements 1182, 1188.

[0124] As above with regard to Fig. 10A, the exact orientation of the FEMs and / or power dividers can be varied without exceeding the scope of the present disclosure. For example, the arrangement of the FEMs and / or power dividers can be varied as long as the method for estimating the ratios of the complex OTA coupling parameters (e.g., S4 / S3 or S2 / S1) is dependent on the parameter Δ 12 and either the parameter D1 or the parameter D2. In some cases, the detection of complex OTA coupling patterns in an antenna array designed to allow measurements of physically interchangeable OTA paths (e.g., translated by an integer multiple of the antenna spacing) can be dependent on two different parameters Δ 12 and D1 or D2, ensure that both the ratio S4 / S3 and the ratio S2 / S1 can be estimated by using D1 (or D2) without any ambiguity and further by using the parameter Δ 12is valued without any ambiguity.

[0125] Fig. 11B shows an exemplary calibration training 1150 that uses a calibration approach that depends on two parameters as described in Fig. 11A. As described in Fig. 11B, measurements within the 4x4 sub-array of antenna elements 1182 of signals transmitted by antenna elements 1113 with y-position y8 and received at antenna elements 1114 with y-position y6 can be used to estimate the ratio S2 / S1 based on the parameter D1 and to calibrate the antenna elements with y-position y8 in the 4x4 sub-array of antenna elements 1182 relative to each other. As shown, measurements within the 4x4 sub-array of antenna elements 1186 of signals transmitted by antenna elements with x-position x4 and received by antenna elements 1124 with x-position x2 can be used to estimate the ratio S4 / S3 based on the parameter D1 and to calibrate the antenna elements 1123 with x-position x4 in the 4x4 sub-array of antenna elements 1186 relative to each other.Therefore, both the ratio S4 / S3 and the ratio S2 / S1 can be estimated using only the parameter D1 and an expression similar to equation (23).

[0126] In some cases, the ratio S4 / S3 and the ratio S2 / S1 can both be calculated based on the parameter Δ 12 be estimated. For example, additional measurements within the 4x4 sub-array of antenna elements 1182 of signals transmitted by antenna elements with x-position x3 and received at antenna elements with x-position x2 can be used to determine the ratio S4 / S3 based on the parameter Δ 12and to calibrate the antenna elements 1123 with x-position x3 in the 4x4 sub-array of antenna elements 1182 relative to each other. Similarly, additional measurements within the 4x4 sub-array of antenna elements 1186 of signals transmitted by antenna elements with y-position y3 and received at antenna elements with y-position y2 can be used to determine the ratio S2 / S1 based on the parameter Δ 12 and to calibrate the antenna elements with y-position y3 in the 4x4 sub-array of antenna elements 1186 relative to each other. In some cases, the additional measurements for estimating the ratio S2 / S1 and the ratio S4 / S3 can be used to improve the accuracy of the estimates for the ratio S2 / S1 and the ratio S4 / S3.

[0127] The example in Fig. Figure 11B describes the calibration of antennas along rows and / or columns of antenna elements in the antenna grid of a phased array antenna using Δ 12 and D1 (or D2). It is understood that when determining the estimates for the ratio S2 / S1 and the ratio S4 / S3, one parameter may be preferred over another. For example, the estimates for the ratio S2 / S1 and the ratio S4 / S3 that result in a 2D array calibration may depend more heavily on a preferred parameter. For example, the parameter Δ 12 depends on the RF paths located within a single physical FEM chip, while the parameters D1 or D2 depend on the similarity between two physically different FEM chips with identical designs. In an illustrative example, the parameter Δ 12to be preferred if the differences in the manufacturing process (e.g. typical compared to a fast corner case) from FEM chip to FEM chip are so large that σ Δ12 « s D1 and σ Δ12 « s D2 may be preferred. In some cases, a non-preferred parameter, such as D1 or D2 in the example above, may be used to resolve a 180-degree ambiguity in solutions determined using the preferred parameter.

[0128] It should be understood that Equation (23) through Equation (27) and the calibration configurations they refer to have been described as if local measurements are acquired and then Equation (23) through Equation (27) are solved for those measurements to calibrate two antenna elements at a time, and then the process is repeated sequentially to calibrate the entire 2D antenna array. However, the calibration examples above are intended to illustrate the process of measuring complex OTA coupling parameters and the physical redundancies used for calibration. In some cases, calibration configurations different from the examples described here may be used without exceeding the scope of the present disclosure.For example, all possible measurements between any pair of antenna elements that could be used in a sequential approach and the calculations presented in equation (1) through equation (13) can be organized as a set of linear equations to be solved using a suitable mathematical approach (e.g., least squares). In some examples, hundreds or thousands of linear equations may be solved simultaneously. The exact manner of solving this larger set of equations may depend on the required accuracy and the computational resources and / or time available during functional phased array operation and is outside the scope of the present disclosure. CALIBRATION OF ANTENNA ELEMENTS AT THE EDGE OF THE ANTENNA GRID

[0129] In the examples of Fig. 4A to Fig. 11B, the periodic repeatability of the relationship between the OTA paths across the antenna grid (e.g., the antenna grid 202 of Fig. 2A) to create and / or simplify equations for calibrating the antenna elements of the antenna grid. For example, the measured ratio S2 / S1 (subject to limitations resulting from the finite size of the array and / or manufacturing accuracy) should be identical at a given location (x, y) and at any other location (x+N(x0), y+M(y0)), where M and N are integers and x0 and y0 are the distances between periodic antenna elements along the x-axis and the y-axis, respectively. In some cases, antenna elements (e.g., the antenna elements 213 in Fig. 2A) which are arranged around the edge of the antenna grid (e.g. the antenna grid 202 in Fig. 2A) may not exhibit the same repeatability of the relationship between the OTA paths. For example, the repeatability of the relationship between the OTA paths may be interrupted at the edges of an antenna grid if there are no additional or dummy antenna elements (with the same connectors as the functional antenna elements) around the active antenna grid to prevent abrupt changes in the mutual coupling environment for the functional antennas.

[0130] In some cases, the omission of additional antenna elements may be intentional to save space and weight of the antenna system, but this may compromise the calibration accuracy of the antenna elements at the edge of the system. Accordingly, systems and techniques are needed to improve the calibration accuracy of edge antenna elements. The systems and techniques described here may contain internal redundancies (e.g., the parameters D1, D2, and / or Δ 12 ) of sub-arrays of antenna elements (e.g. as in Fig. 9A to Fig. 9I) without relying on the OTA measurements of mutual coupling at the edge of the antenna grid.

[0131] Fig. 12 shows an example of an edge antenna element calibration training 1200. In the illustrative example of Fig. 12, sub-arrays of antenna elements formed by power dividers 1228 and FEMs (e.g., FEM 1212, FEM 1214, FEM 1222) with common BF RFIOs 1205 have different orientations at the array edge (e.g., sub-arrays of antenna elements 1210) compared to the orientation of sub-arrays of antenna elements across the rest of the antenna grid (e.g., sub-arrays of antenna elements 1220). As in Fig. As shown in Figure 12, the ratio of the complex coupling parameters S5 / S6 can be estimated using antenna elements that are at least N antenna elements away from the edge of the antenna array, where N is an integer. As used herein, the term "edge antenna elements" refers to antenna elements that are N or fewer antenna elements away from the edge of the antenna array. As shown in Fig. 12, a value of N = 4 is used, so that the first four edge antenna elements 1213 (e.g., edge antenna elements 1232, 1234, 1236, 1238) located away from the antenna grid edge 1250 are excluded from the measurements for estimating the complex coupling parameter ratio S5 / S6. As shown, the ratio S5 / S6 can then be used to calibrate the edge antenna element 1232 (also referred to as edge antenna element 1) relative to the non-edge antenna elements 2, 3, 4, 5 using calibration methods similar to those described in Fig. 10A to Fig. 10E and the procedures described in equation (23) to equation (27) are similar.

[0132] In some cases, after the edge antenna element 1 has been calibrated relative to the non-edge antenna elements 1240 (also referred to as non-edge antenna elements 2, 3, 4, 5), the edge antenna element 1234 (also referred to as edge antenna element 0) can be calibrated relative to the edge antenna element 1 by directly obtaining an estimate of the parameter Δ 12 As mentioned above, the parameter Δ 12represent a complex gain relationship between an antenna element coupled to a TX / RX 1 port of a FEM and an antenna element coupled to a TX / RX 2 port of the same FEM. In some cases, after calibrating antenna element 0 and antenna element 1, it can be directly assumed that edge antenna element 1238 (also referred to as edge antenna element -2) and edge antenna element 1236 (also referred to as edge antenna element -1) have the same magnitude and phase as antenna 0 and 1, respectively, since D1 ≈ 1 and D2 ≈ 1. In some cases, the parameter Δ 12 be estimated by dividing equation (25) by equation (26) and taking a square root (e.g. instead of multiplying to obtain equation (27). In some cases, the square root term may in turn contain measured estimates of ±Δ 12 deliver to several locations. As in Fig. 12, antenna elements 1223 (also referred to as antenna elements a, b, c, d) that are not used for edge measurements can be used during OTA measurements of mutual coupling. While the example in Fig. 12 uses a value of N = 4, it should be understood that other values ​​for N such as N = 2, N = 3, or N > 4 may be used without exceeding the scope of the present disclosure. In some cases, a value for N may be selected based on the antenna elements used and / or the sensitivity of the antenna elements to array edge effects.

[0133] In some cases, the exemplary edge antenna element calibration training 1200 of Fig. 12, as long as the measurements of the mutual OTA coupling are limited to antennas that are N elements away from the antenna grid edge 1250. It should be understood that when using the method described in Fig. 12, if a standard deviation of one or more of the parameters D1, D2 and Δ 12 is greater than the variation in the coupling of OTA coupling paths in different parts of the antenna grid (e.g. variation of S 5I S6) around the active antenna grid edge, which is Fig. 12 may not be able to improve the relative calibration of the edge antenna elements. In such an example, the calibration method described in Fig. 10A to Fig. 10E and equations (23) to (27) are followed uniformly for the entire group of antenna elements, without making exceptions for edge antenna elements, as in Fig. 12 shown. CALIBRATION OF ANTENNA ELEMENTS ON DIFFERENT PRINTED BOARDS

[0134] In some cases, antenna grids for phased array antenna systems can be so large that the antenna elements of the antenna grid (e.g., the antenna grid 202 of Fig. 2A) must be distributed across multiple structures (e.g., multiple standard-sized PCBs), each accommodating a subset of the antenna elements of the antenna grid. In some implementations, the discontinuities in the antenna grid across the multiple PCBs may be so large that self-calibration approaches relying on OTA coupling path similarities become unusable. Accordingly, systems and techniques are needed that enable self-calibration in phased array antenna systems with antenna elements of an antenna grid distributed across multiple PCBs. Fig. 13A to Fig. 13C show calibration configurations that use one or more calibration lines across different PCBs (e.g., PCB boards) of a phased array antenna system. In some cases, the one or more calibration lines can be used to calibrate the antenna elements on the different PCB boards with respect to each other without relying on OTA paths between the PCB boards.

[0135] Fig. 13A shows an exemplary antenna grid configuration 1300 for performing OTA calibration measurements for a phased array antenna system with antenna elements distributed on different PCBs. In the exemplary antenna grid configuration 1300 of Fig. 13A, three different PCB plates 1311, 1312, 1313 containing antenna elements of the antenna grid are separated by gaps 1325. As in Fig. 13A, the PCB board 1311 houses the antenna elements 1301, the PCB board 1312 houses the antenna elements 1302, and the PCB board 1313 houses the antenna elements 1303. As shown, all of the antenna elements 1301, 1302, 1303 may be part of the same antenna grid (e.g., the antenna grid 202 of Fig. 2A) such that their xy positions match a periodic antenna grid. In some implementations, the antenna elements on a particular circuit board can be calibrated relative to each other using equation (1) through equation (14) and / or equation (15) through equation (27). For example, antenna elements with dual-use antenna connectors can be calibrated using equation (1) through equation (14). In some cases, antenna elements without dual-use antenna connectors (e.g., dedicated connectors for transmit and receive mode) can be calibrated using equation (15) through equation (27).After calibration has been performed for the antenna elements on each circuit board, antenna elements 1301 can be calibrated relative to each other, antenna elements 1302 relative to each other, and antenna elements 1303 relative to each other, as indicated by common shading of all antenna elements on a particular circuit board. As shown in FIG. Fig. However, as shown in Figure 13B, the individual PCB boards 1311, 1312, 1313 and the corresponding antenna elements may have different relative calibrations.

[0136] As previously mentioned, the OTA coupling paths that extend across the gap 1325 may not be suitable for resolving the relative calibration differences between antenna elements on different PCB boards 1311, 1312, 1313. For example, the complex coupling parameters relating to the OTA paths between a group of four antenna elements, all located on a single PCB board 1311, 1312, 1313, may include the complex coupling parameters C1, C2, C3, C4, as shown in Fig. 13A and Fig. 13B. In some cases, antenna elements located at xy positions of the antenna grid near the PCB edges may form four antenna element groups that include OTA paths that cross a gap 1325 between two PCB boards. For example, antenna element 1321 may be part of a group of four antenna elements with antenna elements 1322 that include OTA paths that cross the gap 1325 between PCB board 1311 and PCB board 1312. As shown, the complex coupling parameters related to the two OTA paths across the gap 1325 may be the complex coupling parameters C e1 , C e2 that have an identical geometry to the complex coupling parameters C1, C2. If the gap 1325 is large enough to change the values ​​of the mutual coupling, the complex coupling parameters can in some cases be changed so that C1 ≠ C e1and C2 ≠ C e2 . To the extent that a self-calibration method relies on OTA coupling path similarities, the discontinuity introduced by the gaps 1325 may prevent accurate calibration results across the PCB plates 1311, 1312, 1313.

[0137] Fig. 13B shows an exemplary calibration configuration 1320 used to calibrate the antenna elements in the antenna grid configuration 1300 of Fig. 13A across the PCB boards 1311, 1312, 1313. As illustrated, one or more calibration lines 1334 may be formed across all PCB boards by internal (e.g., to the PCB structure) transmission lines (TLs) 1345 and bridge transmission lines (jumper transmission lines) 1338. In some examples, the bridge transmission lines 1338 may be external to the PCB boards 1311, 1312, 1313. In the illustrated example of Fig. 13B, the connection points 1335, 1336 of the internal TLs 1345 can be coupled to measurement ports (e.g., mRX / mTX). Furthermore, the internal TLs 1345 can be coupled (e.g., through a weak coupler) to antenna elements, and the measurement ports can be used to calibrate the antenna elements along the calibration line. For example, all antenna elements 1351, 1352, 1353 on the PCB boards 1311, 1312, 1313 can be measured through some or all of the measurement ports coupled to the connection points 1335, 1336. In some cases, the measurements performed using the one or more calibration lines 1334 can be used to calibrate the antenna elements 1351, 1352, 1353 relative to each other.After calibration using the one or more calibration lines 1334, a magnitude / phase relationship between the antenna elements across all PCB boards can be established and a complete calibration of the antenna elements of the antenna grid can be achieved.

[0138] As mentioned above, all antenna elements 1351 may have been previously calibrated relative to the remaining antenna elements 1301 on the PCB board 1311. Similarly, the antenna elements 1352, 1302 may have been calibrated relative to each other and / or the antenna elements 1353, 1303 may have been calibrated relative to each other. Therefore, the calibration provided by the calibration lines does not need to be very precise on an antenna element-by-antenna element basis. For example, the calibration lines 1334 may be used to align antenna elements on different PCB boards (e.g., antenna elements 1351, 1352, antenna elements 1352, 1353, and / or antenna elements 1351, 1353) relative to each other in an "average" sense. In some examples, calibration of antenna element groups on different PCB boards can be used to calibrate the circuit board.In some cases, calibration on an average direction between groups of antenna elements on PCBs can compensate for the reduction in the accuracy of the calibration measurements that may result from the interruption of the periodic calibration line sections by bridging transmission lines 1338, 1339.

[0139] Fig. Figure 13C shows another example of a calibration pattern 1340 for the 2D calibration of an antenna grid distributed across six PCB boards in a 2x3 board arrangement. As shown in the figure, separate calibration lines 1334 and bridge transmission lines 1338 extending horizontally, as well as calibration lines 1337 and bridge transmission lines 1339 extending vertically, can be used to calibrate the antenna elements of the PCB boards relative to each other to obtain complete 2D alignment between all antenna elements of the antenna grid.

[0140] Fig. Figure 14 shows a cross section 1400 of a row of antenna elements 1451, 1452 along a calibration line 1434 (e.g. calibration line 1334 of Fig. 13B) between different PCBs of a phased array antenna system. As shown in Fig. 14, the FEM and / or beamformer chips 1422, 1423 on different PCB boards 1411, 1412 are connected to the calibration line 1434 via couplers 1424. In the example shown, the calibration line 1434 is formed by internal TLs 1445, a connector 1442, and an RF cable 1438. In some implementations, the FEM and / or beamformer chips 1422, 1423 can perform measurements on the antenna elements 1451 of the PCB board 1411 and the antenna elements 1452 of the PCB board 1412 and determine relative phase / magnitude relationships between all antenna elements 1451, 1452. The determined phase / magnitude relationships can in turn be used to calibrate the antenna elements 1451 as a group against the antenna elements 1452 as a group, which in turn can be used to obtain a relative calibration between all antenna elements on the PCB board 1411 and all antenna elements on the PCB board 1412.

[0141] Fig. 15A is a flowchart illustrating a process 1500 for over-the-air (OTA) calibration of antenna elements for a phased array antenna system.

[0142] In block 1502, the method 1500 includes performing a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on inline calibration measurements between a calibration line (e.g., calibration line 802, calibration line 804, calibration lines 806 of Fig. 8A, calibration line 804 from Fig. 8C) and the subset of antenna elements to form a calibrated subset of antenna elements (e.g., antenna elements 812 of Fig. 8C).

[0143] In block 1504, the process 1500 includes acquiring a first OTA calibration measurement pair. In some examples, the first OTA calibration measurement pair includes a first OTA calibration measurement between a first uncalibrated antenna element (e.g., antenna elements 819 of Fig. 8C) of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements. In some cases, the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a specific geometric relationship.

[0144] In block 1506, the process 1500 includes determining a complex coupling ratio (e.g. S1S2 of equation (17)), which is associated with the special geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement.

[0145] In block 1508, the method 1500 includes acquiring a second OTA calibration measurement pair, wherein the second OTA calibration measurement pair includes a third OTA calibration measurement between a second uncalibrated antenna element (e.g., an antenna element in column 844 of Fig. 8D) of the antenna grid and the first uncalibrated antenna element (e.g. antenna element a of Fig. 8D) and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element (e.g. antenna element b of Fig. 8D) of the antenna grid. In some implementations, the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element are configured with the particular geometric relationship.

[0146] In block 1510, the method 1500 includes determining a phase correction factor and / or a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement.

[0147] In some cases, determining the complex coupling ratio associated with the particular geometric relationship comprises acquiring a plurality of OTA calibration measurement pairs, each respective calibration measurement pair of the plurality of OTA calibration measurement pairs associated with a respective uncalibrated antenna element and a respective pair of antenna elements of the calibrated subset of antenna elements having the particular geometric relationship; determining a respective complex coupling ratio value for each respective OTA calibration measurement pair of the plurality of OTA calibration measurement pairs to obtain a plurality of complex coupling ratio values; and determining the complex coupling ratio based on the plurality of complex coupling ratio values.

[0148] In some examples, determining the complex coupling ratio based on the plurality of complex coupling ratio values ​​comprises averaging the plurality of complex coupling ratio values ​​to obtain the complex coupling ratio.

[0149] In some implementations, method 1500 includes calibrating a first group of antenna elements relative to each other based on a plurality of OTA calibration measurement pairs, wherein each OTA calibration measurement pair of the plurality of OTA calibration measurement pairs includes a respective pair of measurements between a respective antenna element of a second group of antenna elements and a respective pair of antenna elements of the first group of antenna elements formed with the particular geometric relationship.

[0150] In some cases, the first group of antenna elements includes the first uncalibrated antenna element and the third uncalibrated antenna element, and the second group of antenna elements includes the second uncalibrated antenna element.

[0151] In some examples, method 1500 includes calibrating antenna elements of the antenna grid based on the complex coupling ratio to obtain a plurality of calibrated antenna element groups, wherein different calibrated antenna element groups of the plurality of calibrated antenna element groups are not calibrated relative to each other. In some embodiments, method 1500 includes calibrating the different calibrated antenna element groups of the plurality of calibrated antenna element groups based on in-line calibration measurements between an additional calibration line and at least one antenna element of each respective different calibrated antenna element group of the plurality of calibrated antenna element groups.

[0152] Fig. 15B is a flowchart illustrating a process 1520 for over-the-air (OTA) calibration of antenna elements for a phased array antenna system.

[0153] In block 1522, the process 1520 includes obtaining a first mutual coupling measurement associated with a first over-the-air (OTA) signal path between a first antenna element functional transmit (TX) port of a first antenna element (e.g., antenna element a of Fig. 10B) and a second antenna element function receive (RX) terminal of a second antenna element (e.g. antenna element 1 of Fig. 10B). In some cases, the first antenna element comprises the first antenna element functional transmit port (TX) and a first antenna element functional receive port (RX), and the second antenna element comprises a second antenna element functional transmit port and a second antenna element functional receive port (RX).

[0154] In block 1524, the process 1520 includes obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit (TX) port of a third antenna element (e.g., antenna element b of Fig. 10B) and the second antenna element functional receive port (RX). In some examples, the third antenna element includes a third antenna element functional transmit port (TX) and a third antenna element functional receive port (RX).

[0155] In block 1526, the process 1520 includes obtaining a third mutual coupling measurement associated with a third OTA signal path between a fourth antenna element functional transmit (TX) port of a fourth antenna element (e.g., antenna element c of Fig. 10B) and an antenna element function receiving terminal (RX) of a fifth antenna element (e.g. antenna element 2 of Fig. 10B). In some embodiments, the fourth antenna element comprises a fourth antenna element functional receive port (RX) and a fourth antenna element functional transmit port (TX), and the fifth antenna element comprises the antenna element functional receive port (RX) and a fifth antenna element functional transmit port (TX).

[0156] At block 1528, process 1520 includes obtaining a fourth mutual coupling measurement associated with a fourth OTA signal path between the third antenna element functional transmit (TX) port of the third antenna element and the fourth antenna element functional receive (RX) port of the fourth antenna element. In some examples, an antenna grid includes a plurality of periodically spaced antenna elements, including the first antenna element, the second antenna element, the third antenna element, the fourth antenna element, and the fifth antenna element.

[0157] In block 1530, the process 1520 includes determining a phase correction factor and / or an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement, and one or more redundancies.

[0158] In some cases, the third OTA signal path is associated with a first complex OTA signal path coupling coefficient; the fourth OTA signal path is associated with a second complex OTA signal path coupling coefficient; and the one or more redundancies are a parameter (e.g., D1, D2, Δ 12from equation (19) to equation (21)) of the antenna grid. In some examples, the antenna grid parameter comprises a first plurality of complex gain relationships between nominally identical transmit (TX) ports (e.g., TX1, TX2 of Fig. 10B) and / or receive (RX) ports (e.g. RX1, RX2 of Fig. 10B) of a pair of front-end modules (FEMs) (e.g., FEMs 1022 of Fig. 10B), wherein an input / output IO port of each respective FEM of the pair of FEMs is coupled to a power combiner / divider; or a second plurality of complex gain relationships between pairs of transmit (TX) and / or receive (RX) ports of individual FEMs.

[0159] In some examples, process 1520 includes calibrating a plurality of edge elements of the antenna grid, wherein a first edge element (e.g., antenna element 1 of Fig. 12) of the antenna grid relative to a non-edge element (e.g. the antenna element 2 and / or the antenna element a of Fig. 12) of the antenna grid is calibrated based on the parameter of the antenna grid (e.g., D1 of equation (20)). In some cases, a second edge element of the antenna grid is calibrated relative to the first edge element of the antenna grid based on an additional parameter of the antenna grid (e.g., D2, Δ 12 of equation (19) and equation (21)).

[0160] In some cases, a first subset of antenna elements of the antenna grid is arranged such that OTA calibration measurements between antenna elements of the first subset of antenna elements associated with a particular geometry of antenna elements are associated with a first parameter of the antenna grid; and a second subset of antenna elements of the antenna grid is arranged such that OTA calibration measurements between antenna elements of the second subset of antenna elements associated with a particular geometry of antenna elements are associated with a second parameter of the antenna grid, wherein the second parameter of the antenna grid is different from the first parameter of the antenna grid.

[0161] In some embodiments, the third OTA signal path corresponds to a first geometric relationship between the first antenna element function transmit port (TX) and the fourth antenna element function receive port (RX); and the second OTA signal path corresponds to a second geometric relationship between the third antenna element function transmit port (TX) and the second antenna element function receive port (RX), wherein the second geometric relationship is different from the first geometric relationship.

[0162] In some examples, the one or more redundancies include in-line calibration measurements between a calibration line and a subset of antenna elements of the antenna grid.

[0163] In some examples, one or more processes, such as acquiring calibration measurements, calculating calibration adjustments, calculating phased array antenna parameters, and / or any combination thereof, may be performed by one or more computing devices or devices. In some examples, the phased array antenna systems, FEMs, BF modules, RFIO circuits, and / or other components described herein may be implemented by a Fig. 1 shown UT or SAT and / or one or more computing devices with the Fig. 16. In some cases, such a computing device or device may include a processor, microprocessor, microcomputer, or other component of a device configured to perform one or more operations described herein. In some examples, such a computing device or device may include one or more antennas for transmitting and receiving RF signals. In some examples, such a computing device or device may include a modem for transmitting, receiving, modulating, and demodulating RF signals.

[0164] The components of the computing device may be implemented in circuits. For example, the components may include electronic circuits or other electronic hardware and / or may be implemented using electronic circuits that may include one or more programmable electronic circuits (e.g., microprocessors, graphics processing units (GPUs), digital signal processors (DSPs), central processing units (CPUs), and / or other suitable electronic circuits) and / or may be implemented using computer software, firmware, or any combination thereof to perform the various operations described herein.The computing device may further include a display (as an example of the output device or in addition to the output device), a network interface configured to communicate and / or receive the data, any combination thereof, and / or other component(s). The network interface may be configured to transmit and / or receive Internet Protocol (IP)-based data or other types of data.

[0165] In some cases, one or more operations described herein may be implemented in hardware, computer instructions, or a combination thereof. In the context of computer instructions, the operations represent computer-executable instructions stored on one or more computer-readable storage media that, when executed by one or more processors, perform the recited operations. Computer-executable instructions generally include routines, programs, objects, components, data structures, and the like that perform particular functions or implement particular data types. The order in which the operations are described is not limiting, and any number of the described operations may be combined in any order and / or in parallel to implement the processes.

[0166] Fig. 16 shows an exemplary computing device architecture 1600 that can implement various techniques and / or operations described herein. For example, the computing device architecture 1600 can be used to implement at least some portions of the Fig. 1 illustrated UTs 102, SATs 104 and / or gateway terminals 106, of the phased array antenna system 200 of Fig. 2A and Fig. 2B, the calibration training 440 of Fig. 4C, the calibration training 450 of Fig. 4D, the calibration training 460 of Fig. 4E, the calibration training 470 of Fig. 4F and / or the calibration training 480 from Fig.4G and perform at least some of the operations described herein. The components of the computing device architecture 1600 are shown in electrical communication with one another using an interconnect 1605, such as a bus. The example computing device architecture 1600 includes a processing unit (CPU or processor) 1610 and a computing device interconnect 1605 that connects various computing device components, including the computing device memory 1615, such as read-only memory (ROM) 1620 and random access memory (RAM) 1625, to the processor 1610.

[0167] Computing device architecture 1600 may include a cache of high-speed memory directly connected to, located in close proximity to, or integrated as part of, the processor 1610. Computing device architecture 1600 may copy data from memory 1615 and / or storage device 1630 to cache 1612 for rapid access by the processor 1610. In this way, the cache may provide a performance boost that eliminates processor 1610 delays while waiting for data. These and other modules may control the processor 1610 or be configured to perform various actions. A different memory 1615 may also be used for the computing device. Memory 1615 may include several different memory types with different performance characteristics.Processor 1610 may include any general-purpose processor and a hardware or software service stored in memory device 1630 and configured to control processor 1610, as well as a special-purpose processor in which software instructions are integrated into the processor design. Processor 1610 may be a self-contained system that includes multiple cores or processors, a bus, a memory controller, a cache, etc. A multi-core processor may be symmetric or asymmetric.

[0168] To enable user interaction with computing device architecture 1600, an input device 1645 may represent any number of input mechanisms, such as a microphone for voice, a touchscreen for gesture or graphical input, keyboard, mouse, motion input, speech, etc. An output device 1635 may also be one or more of a variety of output mechanisms known to those skilled in the art, such as a display, a projector, a television, a speaker system. In some cases, multimodal computing devices may allow a user to provide multiple types of input to communicate with computing device architecture 1600. Communication interface 1640 may generally control and manage user input and output of the computing device.There is no restriction for operation on a particular hardware arrangement and therefore the basic features here can be easily replaced by improved hardware or firmware arrangements as they are developed.

[0169] The storage device 1630 is a non-volatile memory and may be a hard disk or other type of computer-readable media capable of storing data accessible by a computer, such as magnetic cassettes, flash memory cards, solid-state storage devices, digital versatile disks, cartridges, RAMs (Random Access Memories) 1625, ROMs (Read Only Memory) 1620, and hybrids thereof. The storage device 1630 may include software, code, firmware, etc., for controlling the processor 1610. Other hardware or software modules are also contemplated. The storage device 1630 may be connected to the port of the computing device 1605. In one aspect, a hardware module that performs a particular function may include the software component stored in a computer-readable medium in conjunction with the necessary hardware components, such as the processor 1610, the port 1605, the output device 1635, etc., to perform the function.

[0170] The term "computer-readable medium" includes, but is not limited to, portable or non-portable storage devices, optical storage devices, and various other media capable of storing, containing, or transmitting instructions and / or data. A computer-readable medium may be a non-transitory medium capable of storing data and which does not contain carrier waves and / or transient electronic signals that propagate wirelessly or over wired connections. Examples of a non-transitory medium may include, but are not limited to, a magnetic disk or tape, optical storage media such as a compact disc (CD) or digital versatile disk (DVD), flash memory, storage, or memory devices.A computer-readable medium may store code and / or machine-executable instructions that may represent a procedure, function, subroutine, program, routine, subprogram, module, software package, class, or any combination of instructions, data structures, or program instructions. A code segment may be coupled to another code segment or hardware circuit by passing and / or receiving information, data, arguments, parameters, or memory contents. Information, arguments, parameters, data, etc., may be passed, relayed, or transmitted in any manner, e.g., by sharing memory, passing messages, passing tokens, transmitting over the network, or the like.

[0171] In some examples, the computer-readable storage devices, media, and memories may include a wired or wireless signal containing a bit stream and the like. However, non-transitory computer-readable storage media expressly exclude media such as energy, carrier signals, electromagnetic waves, and signals per se.

[0172] In the above description, specific details are set forth to provide a thorough understanding of the embodiments and examples described herein. However, one skilled in the art will appreciate that the embodiments may be practiced without these specific details. For clarity, in some cases, the present technology may be illustrated as including individual functional blocks, including devices, device components, steps or routines in a method embodied in software, or combinations of hardware and software. Components other than those shown in the figures and / or described herein may be used. For example, circuits, systems, networks, processes, and other components may be illustrated as components in block diagram form so as not to obscure the embodiments with unnecessary detail.In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order not to obscure the embodiments.

[0173] Individual embodiments may be described above as a process or method, represented as a sequence diagram, flowchart, data flow diagram, structure diagram, or block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations may be performed in parallel or concurrently. Furthermore, the order of operations may be rearranged. A process terminates when its operations are complete, but may contain further steps not included in a diagram. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. If a process corresponds to a function, its termination may correspond to a return of the function to the calling function or to the main function.

[0174] Methods and techniques according to the examples described above may be implemented using signals and / or computer-executable instructions stored on or otherwise available from computer-readable media. Such instructions may include, for example, instructions and data that cause or otherwise cause a general-purpose computer, a special-purpose computer, or a processing device to perform a particular function or set of functions. Portions of the computing resources used may be accessible over a network. The computer-executable instructions may be, for example, binary files, instructions in intermediate formats such as assembly language, firmware, or source code.Examples of computer-readable media that can be used to store instructions, information used, and / or information created during the methods according to the described examples include magnetic or optical disks, flash memory, USB devices with non-volatile memory, networked storage devices, etc.

[0175] Devices implementing methods and techniques according to these disclosures may include hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof, and may have a variety of form factors. When implemented in software, firmware, middleware, or microcode, the program code or code segments for performing the required tasks (e.g., a computer program product) may be stored in a computer-readable or machine-readable medium. The required tasks may be performed by one or more processors. Typical examples of form factors include laptops, smartphones, mobile phones, tablet devices or other small form factor personal computers, personal digital assistants, rackmount devices, standalone devices, and so on. The functionality described herein may also be embodied in peripheral devices or add-in cards.Such functionality can also be implemented on a circuit board between different chips or different processes running in a single device, to give another example.

[0176] The instructions, the media for conveying such instructions, the computing resources for executing them, and other structures for supporting such computing resources are exemplary means for providing the functionality described in the disclosure.

[0177] In the foregoing description, aspects of the application are described with reference to particular embodiments, but those skilled in the art will recognize that the application is not so limited. Therefore, while illustrative embodiments of the application have been described in detail herein, it is to be understood that the inventive concepts may be embodied and used in other ways, and the appended claims are intended to be construed to include such variations unless limited by the prior art. Various features and aspects of the application described above may be used individually or together. Furthermore, embodiments may be used in any number of environments and applications beyond those described herein without departing from the broader spirit and scope of the specification.The description and drawings are accordingly to be considered as illustrative rather than restrictive. For purposes of illustration, the methods have been described in a particular order. It should be understood that in alternative embodiments, the methods may be performed in a different order than that described.

[0178] One skilled in the art will understand that the symbols or terms used herein that are less than ("<") and greater than (">") may be replaced by symbols that are less than or equal to ("≤") or greater than or equal to ("≥"), respectively, without exceeding the scope of this description.

[0179] When components are described as being "designed" to perform particular operations, such design may be achieved, for example, by designing electronic circuits or other hardware to perform the operation, by programming programmable electronic circuits (e.g., microprocessors or other suitable electronic circuits) to perform the operation, or by any combination thereof.

[0180] Claim language or other language in the disclosure that refers to "at least one" of a group and / or "one or more" of a group means that one or more members of the group (in any combination) satisfy the claim. For example, the language "at least one of A and B" or "at least one of A or B" means A, B, or A and B. In another example, the language "at least one of A, B, and C" or "at least one of A, B, or C" means A, B, C, or A and B, or A and C, or B and C, or A and B and C. The language "at least one" of a set and / or "one or more" of a set does not limit the set to the items listed in the set.For example, the phrase “at least one of A and B” or “at least one of A or B” may mean A, B or A and B and may additionally include items not listed in the set of A and B.

[0181] The various logical blocks, modules, circuits, and algorithm steps described in connection with the examples disclosed herein may be implemented as electronic hardware, computer software, firmware, or combinations thereof. To clarify this interchangeability of hardware and software, various components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the particular application and the design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in different ways for each specific application, but such implementation choices should not be interpreted as a departure from the scope of the application at hand.

[0182] The techniques described herein may also be implemented in electronic hardware, computer software, firmware, or a combination thereof. Such techniques may be implemented in a variety of devices, e.g., general purpose computers, wireless communications devices, or integrated circuits capable of multiple uses, including application in wireless communications and other devices. Any features described as modules or components may be implemented together in an integrated logic device or separately as discrete but interoperable logic devices. When implemented in software, the techniques may be realized, at least in part, by a computer-readable data storage medium containing program code including instructions that, when executed, performs one or more of the methods, algorithms, and / or operations described above.The computer-readable data storage medium may be part of a computer program product, which may include packaging materials. The computer-readable medium may comprise a memory or data storage medium, such as random access memory (RAM), such as synchronous dynamic random access memory (SDRAM), read-only memory (ROM), non-volatile random access memory (NVRAM), electrically erasable programmable read-only memory (EEPROM), FLASH memory, a magnetic or optical data storage medium, and the like. The techniques may additionally or alternatively be implemented at least in part by a computer-readable communications medium carrying or conveying program code in the form of instructions or data structures that a computer can access, read, and / or execute, such as transmitted signals or waves.

[0183] The program code may be executed by a processor, which may include one or more processors, such as one or more digital signal processors (DSPs), general-purpose microprocessors, application-specific integrated circuits (ASICs), field-programmable logic arrays (FPGAs), or other equivalent integrated or discrete logic circuits. Such a processor may be configured to perform any of the techniques described in this disclosure. A general-purpose processor may be a microprocessor; alternatively, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing units, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or other such configuration.Accordingly, as used herein, the term "processor" may refer to any of the foregoing structures, any combination of the foregoing structures, or any other structure or device suitable for implementing the techniques described herein.

[0184] Illustrative aspects of disclosure include: Aspect 1: A method for calibrating antenna elements, the method comprising: performing a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between a calibration line and the subset of antenna elements to achieve a calibrated subset of antenna elements;Acquiring a first OTA calibration measurement pair, wherein the first OTA calibration measurement pair comprises a first OTA calibration measurement between a first uncalibrated antenna element of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements, wherein the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a particular geometric relationship; determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement;Acquiring a second OTA calibration measurement pair, the second OTA calibration measurement pair comprising a third OTA calibration measurement between a second uncalibrated antenna element of the antenna grid and the first uncalibrated antenna element and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element of the antenna grid, the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element being configured with the determined geometric relationship;and determining, based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement, at least one phase correction factor and / or a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element; Aspect 2: The method of aspect 1, wherein determining the complex coupling ratio associated with the particular geometric relationship comprises: acquiring a plurality of OTA calibration measurement pairs, each respective calibration measurement pair of the plurality of OTA calibration measurement pairs associated with a respective uncalibrated antenna element and a respective pair of antenna elements of the calibrated subset of antenna elements having the particular geometric relationship; determining a respective complex coupling ratio value for each respective OTA calibration measurement pair of the plurality of OTA calibration measurement pairs to obtain a plurality of complex coupling ratio values; and determining the complex coupling ratio based on the plurality of complex coupling ratio values. Aspect 3: The method of aspect 2, wherein determining the complex coupling ratio based on the plurality of complex coupling ratio values ​​comprises averaging the plurality of complex coupling ratio values ​​to obtain the complex coupling ratio. Aspect 4: The method of any one of aspects 1 to 3, further comprising calibrating a first group of antenna elements relative to each other based on a plurality of OTA calibration measurement pairs, wherein each OTA calibration measurement pair of the plurality of OTA calibration measurement pairs comprises a respective pair of measurements between a respective antenna element of a second group of antenna elements and a respective pair of antenna elements of the first group of antenna elements formed with the particular geometric relationship. Aspect 5: The method of aspect 4, wherein the first group of antenna elements comprises the first uncalibrated antenna element and the third uncalibrated antenna element, and the second group of antenna elements comprises the second uncalibrated antenna element. Aspect 6: The method of any one of aspects 1 to 5, further comprising calibrating antenna elements of the antenna grid based on the complex coupling ratio to achieve a plurality of calibrated antenna element groups, wherein different calibrated antenna element groups of the plurality of calibrated antenna element groups are not calibrated relative to each other. Aspect 7: The method of aspect 6 further comprising calibrating the different calibrated antenna element groups of the plurality of calibrated antenna element groups based on in-line calibration measurements between an additional calibration line and at least one antenna element of each respective different calibrated antenna element group of the plurality of calibrated antenna element groups. Aspect 8: An apparatus for calibrating antenna elements, the apparatus comprising: a calibration line; an antenna grid; and one or more calibration components configured to: perform a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between the calibration line and the subset of antenna elements to obtain a calibrated subset of antenna elements;Acquiring a first OTA calibration measurement pair, wherein the first OTA calibration measurement pair comprises a first OTA calibration measurement between a first uncalibrated antenna element of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements, wherein the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a particular geometric relationship; determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement;Acquiring a second OTA calibration measurement pair, the second OTA calibration measurement pair comprising a third OTA calibration measurement between a second uncalibrated antenna element of the antenna grid and the first uncalibrated antenna element and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element of the antenna grid, the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element being configured with the determined geometric relationship;and determining, based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement, at least one phase correction factor and / or a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element; Aspect 9: The apparatus of aspect 8, wherein, to determine the complex coupling ratio associated with the determined geometric relationship, the one or more calibration components are configured to: acquire a plurality of OTA calibration measurement pairs, each respective calibration measurement pair of the plurality of OTA calibration measurement pairs being associated with a respective uncalibrated antenna element and a respective pair of antenna elements of the calibrated subset of antenna elements having the determined geometric relationship; determine a respective complex coupling ratio value for each respective OTA calibration measurement pair of the plurality of OTA calibration measurement pairs to obtain a plurality of complex coupling ratio values; and determine the complex coupling ratio based on the plurality of complex coupling ratio values. Aspect 10: The apparatus of aspect 9, wherein determining the complex coupling ratio based on the plurality of complex coupling ratio values ​​comprises averaging the plurality of complex coupling ratio values ​​to obtain the complex coupling ratio. Aspect 11: The apparatus of any one of aspects 8 to 10, wherein the one or more calibration components are configured to calibrate a first group of antenna elements relative to each other based on a plurality of OTA calibration measurement pairs, wherein each OTA calibration measurement pair of the plurality of OTA calibration measurement pairs comprises a respective pair of measurements between a respective antenna element of a second group of antenna elements and a respective pair of antenna elements of the first group of antenna elements configured with the particular geometric relationship. Aspect 12: The apparatus of aspect 11, wherein the first group of antenna elements comprises the first uncalibrated antenna element and the third uncalibrated antenna element, and the second group of antenna elements comprises the second uncalibrated antenna element. Aspect 13: The apparatus of any one of aspects 8 to 12, wherein the one or more calibration components are configured to calibrate the antenna elements of the antenna grid based on the complex coupling ratio to achieve a plurality of calibrated antenna element groups, wherein different calibrated antenna element groups of the plurality of calibrated antenna element groups are not calibrated relative to each other. Aspect 14: The apparatus of aspect 13, wherein the one or more calibration components are configured to calibrate the different calibrated antenna element groups of the plurality of calibrated antenna element groups based on in-line calibration measurements between an additional calibration line and at least one antenna element of each respective different calibrated antenna element group of the plurality of calibrated antenna element groups. Aspect 15: A method for calibrating antenna elements, the method comprising: obtaining a first mutual coupling measurement associated with a first wireless (over-the-air = OTA) signal path between a first antenna element functional transmit (TX) port of a first antenna element and a second antenna element functional receive (RX) port of a second antenna element, wherein the first antenna element comprises the first antenna element functional transmit (TX) port and a first antenna element functional receive (RX) port, and the second antenna element comprises a second antenna element functional transmit (TX) port and the second antenna element functional receive (RX) port;Obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit port (TX port) of a third antenna element and the second antenna element functional receive port (RX port), wherein the third antenna element comprises the third antenna element functional transmit port (TX port) and a third antenna element functional receive port (RX port);Obtaining a third mutual coupling measurement associated with a third OTA signal path between a fourth antenna element functional transmit port (TX port) of a fourth antenna element and a fifth antenna element functional receive port (RX) of a fifth antenna element, wherein the fourth antenna element comprises a fourth antenna element functional receive port (RX port) and the fourth antenna element functional transmit port (TX port), and the fifth antenna element comprises the fifth antenna element functional receive port (RX port) and a fifth antenna element functional transmit port (TX port);Obtaining a fourth mutual coupling measurement associated with a fourth OTA signal path between the third antenna element functional transmit port (TX port) of the third antenna element and the fourth antenna element functional receive port (RX port) of the fourth antenna element, wherein an antenna grid comprises a plurality of periodically spaced antenna elements including the first antenna element, the second antenna element, the third antenna element, the fourth antenna element, and the fifth antenna element;and determining, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement, and one or more redundancies, at least one phase correction factor and / or an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element; Aspect 16: The method of aspect 15, wherein: the third OTA signal path is associated with a first complex OTA signal path coupling coefficient; the fourth OTA signal path is associated with a second complex OTA signal path coupling coefficient; and the one or more redundancies comprise a parameter of the antenna grid. Aspect 17: The method of aspect 16, wherein the antenna grid parameter comprises at least one of: a first plurality of complex gain relationships between nominally identical transmit (TX) and / or receive (RX) ports of a pair of front-end modules (FEMs), wherein an input / output (IO) port of each respective FEM of the pair of FEMs is coupled to a power combiner / splitter; or a second plurality of complex gain relationships between pairs of transmit (TX) and / or receive (RX) ports of individual FEMs. Aspect 18: The method of aspect 16 further comprising calibrating a plurality of edge elements of the antenna grid, wherein a first edge element of the antenna grid is calibrated relative to a non-edge element of the antenna grid based on the parameter of the antenna grid. Aspect 19: The method of aspect 18, wherein a second edge element of the antenna grid is calibrated relative to the first edge element of the antenna grid based on an additional parameter of the antenna grid. Aspect 20: The method of any one of aspects 15 to 19, wherein: a first subset of antenna elements of the antenna grid is arranged such that OTA calibration measurements between antenna elements of the first subset of antenna elements associated with a particular geometry of antenna elements are associated with a first parameter of the antenna grid; and a second subset of antenna elements of the antenna grid is arranged such that OTA calibration measurements between antenna elements of the second subset of antenna elements associated with a particular geometry of antenna elements are associated with a second parameter of the antenna grid, wherein the second parameter of the antenna grid is different from the first parameter of the antenna grid. Aspect 21: The method of any one of aspects 15 to 20, wherein: the third OTA signal path corresponds to a first geometric relationship between the first antenna element functional transmit port (TX port) of the first antenna element and the fourth antenna element functional receive port (RX port) of the fourth antenna element; and the second OTA signal path corresponds to a second geometric relationship between the third antenna element functional transmit terminal (TX terminal) of the third antenna element and the second antenna element functional receive terminal (RX terminal) of the second antenna element, wherein the second geometric relationship differs from the first geometric relationship. Aspect 22: The method of any of aspects 15 to 21, wherein the one or more redundancies comprise inline calibration measurements between a calibration line and a subset of antenna elements of the antenna grid. Aspect 23: An apparatus for calibrating antenna elements, the apparatus comprising: an antenna grid comprising a plurality of periodically spaced antenna elements including a first antenna element, a second antenna element, a third antenna element, a fourth antenna element, and a fifth antenna element;and one or more calibration components configured to: obtain a first mutual coupling measurement connected to a first OTA signal path between a first antenna element functional transmit port (TX port) of the first antenna element and a second antenna element functional receive port (RX port) of the second antenna element, wherein the first antenna element comprises the first antenna element functional transmit port (TX port) and a first antenna element functional receive port (RX port), and the second antenna element comprises a second antenna element functional transmit port and the second antenna element functional receive port (RX port);Obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit port (TX port) of the third antenna element and the second antenna element functional receive port (RX port), wherein the third antenna element comprises the third antenna element functional transmit port (TX port) and a third antenna element functional receive port (RX port);Obtaining a third mutual coupling measurement associated with a third OTA signal path between a fourth antenna element functional transmit port (TX port) of the fourth antenna element and a fifth antenna element functional receive port (RX port) of the fifth antenna element, wherein the fourth antenna element comprises a fourth antenna element functional receive port (RX port) and the fourth antenna element functional transmit port (TX port), and the fifth antenna element comprises the fifth antenna element functional receive port (RX port) and a fifth antenna element functional transmit port (TX port); Obtaining a fourth mutual coupling measurement associated with a fourth OTA signal path between the third antenna element functional transmit port (TX port) of the third antenna element and the fourth antenna element functional receive port (RX port) of the fourth antenna element;and determining, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement, and one or more redundancies, at least one phase correction factor and / or an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element; Aspect 24: A non-transitory, computer-readable storage medium having stored thereon instructions that, when executed by one or more processors, cause the one or more processors to perform any of the operations of aspects 1 to 22. Aspect 25: An apparatus having means for performing any of the operations described in aspects 1 to 22. Aspect 26: A method comprising operations according to any of aspects 1-22 and aspect 23. Aspect 27: An apparatus for calibrating antenna elements. The apparatus comprises a memory (e.g., implemented in a circuit) configured to store one or more frames, and one or more processors (e.g., one or more processors) connected to the memory. The one or more processors are configured to perform operations according to any of aspects 1-32 and aspect 33. Aspect 28: A computer-readable storage medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform operations according to any of aspects 1-22 and aspect 23. Aspect 29: An apparatus having means for performing operations according to any one of aspects 1-22 and aspect 23. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 18 / 132,108

[0089]

Claims

[] The embodiments of the invention for which exclusive property or privilege is claimed are defined as follows: [1] A method for calibrating antenna elements, the method comprising: Performing a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between a calibration line and the subset of antenna elements to achieve a calibrated subset of antenna elements; Acquiring a first OTA calibration measurement pair, wherein the first OTA calibration measurement pair comprises a first OTA calibration measurement between a first uncalibrated antenna element of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements, wherein the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a specific geometric relationship; Determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement; Acquiring a second OTA calibration measurement pair, wherein the second OTA calibration measurement pair comprises a third OTA calibration measurement between a second uncalibrated antenna element of the antenna grid and the first uncalibrated antenna element and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element of the antenna grid, wherein the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element are configured with the particular geometric relationship; and Determining, based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement, at least one of a phase correction factor and a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element. [2] The method of claim 1, wherein determining the complex coupling ratio associated with the particular geometric relationship comprises: Acquiring a plurality of OTA calibration measurement pairs, each respective calibration measurement pair of the plurality of OTA calibration measurement pairs being associated with a respective uncalibrated antenna element and a respective pair of antenna elements of the calibrated subset of antenna elements having the particular geometric relationship; Determining a respective complex coupling ratio value for each respective OTA calibration measurement pair from the plurality of OTA calibration measurement pairs to obtain a plurality of complex coupling ratio values; and Determine the complex coupling ratio based on the multiple complex coupling ratio values. [3] The method of claim 2, wherein determining the complex coupling ratio based on the plurality of complex coupling ratio values ​​comprises averaging the plurality of complex coupling ratio values ​​to obtain the complex coupling ratio. [4] The method of any one of claims 1 to 3, further comprising calibrating a first group of antenna elements relative to each other based on a plurality of OTA calibration measurement pairs, wherein each OTA calibration measurement pair of the plurality of OTA calibration measurement pairs comprises a respective pair of measurements between a respective antenna element of a second group of antenna elements and a respective pair of antenna elements of the first group of antenna elements formed with the particular geometric relationship. [5] The method of claim 4, wherein the first group of antenna elements comprises the first uncalibrated antenna element and the third uncalibrated antenna element, and the second group of antenna elements comprises the second uncalibrated antenna element. [6] The method of any one of claims 1 to 5, further comprising calibrating antenna elements of the antenna grid based on the complex coupling ratio to obtain a plurality of calibrated antenna element groups, wherein different calibrated antenna element groups of the plurality of calibrated antenna element groups are not calibrated relative to each other. [7] The method of claim 6 further comprising calibrating the different calibrated antenna element groups of the plurality of calibrated antenna element groups based on in-line calibration measurements between an additional calibration line and at least one antenna element of each respective different calibrated antenna element group of the plurality of calibrated antenna element groups. [8] An apparatus for calibrating antenna elements, the apparatus comprising: a calibration line; an antenna grid; and one or more calibration components designed to: performing a relative calibration of a subset of antenna elements of an antenna grid relative to each other based on in-line calibration measurements between the calibration line and the subset of antenna elements to achieve a calibrated subset of antenna elements; Acquiring a first OTA calibration measurement pair, wherein the first OTA calibration measurement pair comprises a first OTA calibration measurement between a first uncalibrated antenna element of the antenna grid and a first antenna element of the calibrated subset of antenna elements, and a second OTA calibration measurement between the first uncalibrated antenna element of the antenna grid and a second antenna element of the calibrated subset of antenna elements, wherein the first uncalibrated antenna element, the first antenna element of the calibrated subset of antenna elements, and the second antenna element of the calibrated subset of antenna elements are configured with a specific geometric relationship; Determining a complex coupling ratio associated with the particular geometric relationship based on the first OTA calibration measurement and the second OTA calibration measurement; Acquiring a second OTA calibration measurement pair, wherein the second OTA calibration measurement pair comprises a third OTA calibration measurement between a second uncalibrated antenna element of the antenna grid and the first uncalibrated antenna element and a fourth OTA calibration measurement between the second uncalibrated antenna element and a third uncalibrated antenna element of the antenna grid, wherein the second uncalibrated antenna element, the first uncalibrated antenna element, and the third uncalibrated antenna element are configured with the particular geometric relationship; and Determining, based on the complex coupling ratio and a ratio between the third OTA calibration measurement and the fourth OTA calibration measurement, at least one phase correction factor and / or a gain correction factor between a complex gain of the first uncalibrated antenna element and a complex gain of the third uncalibrated antenna element. [9] The apparatus of claim 8, wherein, for determining the complex coupling ratio associated with the particular geometric relationship, the one or more calibration components are configured to: Acquiring a plurality of OTA calibration measurement pairs, each respective calibration measurement pair of the plurality of OTA calibration measurement pairs being associated with a respective uncalibrated antenna element and a respective pair of antenna elements of the calibrated subset of antenna elements having the particular geometric relationship; Determining a respective complex coupling ratio value for each respective OTA calibration measurement pair from the plurality of OTA calibration measurement pairs to obtain a plurality of complex coupling ratio values; and Determine the complex coupling ratio based on the multiple complex coupling ratio values. [10] The apparatus of claim 9, wherein determining the complex coupling ratio based on the plurality of complex coupling ratio values ​​comprises averaging the plurality of complex coupling ratio values ​​to obtain the complex coupling ratio. [11] The apparatus of any one of claims 8 to 10, wherein the one or more calibration components are configured to calibrate a first group of antenna elements relative to each other based on a plurality of OTA calibration measurement pairs, each OTA calibration measurement pair of the plurality of OTA calibration measurement pairs comprising a respective pair of measurements between a respective antenna element of a second group of antenna elements and a respective pair of antenna elements of the first group of antenna elements configured with the particular geometric relationship. [12] The apparatus of claim 11, wherein the first group of antenna elements comprises the first uncalibrated antenna element and the third uncalibrated antenna element, and the second group of antenna elements comprises the second uncalibrated antenna element. [13] The apparatus of any one of claims 8 to 12, wherein the one or more calibration components are configured to calibrate antenna elements of the antenna grid based on the complex coupling ratio to achieve a plurality of calibrated antenna element groups, wherein different calibrated antenna element groups of the plurality of calibrated antenna element groups are not calibrated relative to each other. [14] The apparatus of claim 13, wherein the one or more calibration components are configured to calibrate the different calibrated antenna element groups of the plurality of calibrated antenna element groups based on in-line calibration measurements between an additional calibration line and at least one antenna element of each respective different calibrated antenna element group of the plurality of calibrated antenna element groups. [15] A method for calibrating antenna elements, the method comprising: Obtaining a first mutual coupling measurement associated with a first over-the-air (OTA) signal path between a first antenna element functional transmit port (-TX port) of a first antenna element and a second antenna element functional receive port (-RX port) of a second antenna element, wherein the first antenna element comprises the first antenna element functional transmit port (-TX port) and a first antenna element functional receive port (-RX port), and the second antenna element comprises a second antenna element functional transmit port and the second antenna element functional receive port (-RX port); Obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit port (-TX port) of a third antenna element and the second antenna element functional receive port (-RX port), wherein the third antenna element comprises the third antenna element functional transmit port (-TX port) and a third antenna element functional receive port (-RX port); Obtaining a third mutual coupling measurement associated with a third OTA signal path between a fourth antenna element functional transmit port (-TX port) of a fourth antenna element and a fifth antenna element functional receive port (-RX port) of a fifth antenna element, wherein the fourth antenna element comprises a fourth antenna element functional receive port (-RX port) and the fourth antenna element functional transmit port (-TX port), and the fifth antenna element comprises the fifth antenna element functional receive port (-RX port) and a fifth antenna element functional transmit port (-TX port); Obtaining a fourth mutual coupling measurement associated with a fourth OTA signal path between the third antenna element functional transmit port (-TX port) of the third antenna element and the fourth antenna element functional receive port (-RX port) of the fourth antenna element, wherein an antenna grid comprises a plurality of periodically spaced antenna elements including the first antenna element, the second antenna element, the third antenna element, the fourth antenna element, and the fifth antenna element; and Determining, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement and one or more redundancies, at least one phase correction factor and / or an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element. [16] The method of claim 15, wherein: the third OTA signal path is connected to a first complex coupling coefficient of the OTA signal path; the fourth OTA signal path is connected to a second complex coupling coefficient of the OTA signal path; and one or more redundancies comprise a parameter of the antenna grid. [17] The method of claim 16, wherein the antenna grid parameter comprises at least one of the following elements: a first plurality of complex gain relationships between nominally identical transmit (TX) and / or receive (RX) ports of a pair of front-end modules (FEMs), wherein an input / output (IO) port of each respective FEM of the pair of FEMs is coupled to a power combiner / divider; or a second plurality of complex gain relationships between pairs of transmit (TX) and / or receive (RX) ports of individual FEMs. [18] The method of claim 16 or 17 further comprising calibrating a plurality of edge elements of the antenna grid, wherein a first edge element of the antenna grid is calibrated relative to a non-edge element of the antenna grid based on the parameter of the antenna grid. [19] The method of claim 18, wherein a second edge element of the antenna grid is calibrated relative to the first edge element of the antenna grid based on an additional parameter of the antenna grid. [20] The method according to any one of claims 15 to 19, wherein: a first subgroup of antenna elements of the antenna grid is arranged such that OTA calibration measurements between antenna elements of the first subgroup of antenna elements associated with a specific geometry of antenna elements are associated with a first parameter of the antenna grid; and a second subgroup of antenna elements of the antenna grid is arranged such that OTA calibration measurements between antenna elements of the second subgroup of antenna elements associated with the particular geometry of antenna elements are associated with a second parameter of the antenna grid, wherein the second parameter of the antenna grid differs from the first parameter of the antenna grid. [21] The method according to any one of claims 15 to 20, wherein: the third OTA signal path corresponds to a first geometric relationship between the first antenna element functional transmit terminal (TX terminal) of the first antenna element and the fourth antenna element functional receive terminal (RX terminal) of the fourth antenna element; and the second OTA signal path corresponds to a second geometric relationship between the third antenna element functional transmit terminal (TX terminal) of the third antenna element and the second antenna element functional receive terminal (RX terminal) of the second antenna element, wherein the second geometric relationship differs from the first geometric relationship. [22] The method of any one of claims 15 to 21, wherein the one or more redundancies comprise in-line calibration measurements between a calibration line and a subset of antenna elements of the antenna grid. [23] An apparatus for calibrating antenna elements, the apparatus comprising: an antenna grid having a plurality of periodically spaced antenna elements, including a first antenna element, a second antenna element, a third antenna element, a fourth antenna element, and a fifth antenna element; and one or more calibration components designed to: Obtaining a first mutual coupling measurement associated with a first OTA signal path between a first antenna element functional transmit port (-TX port) of the first antenna element and a second antenna element functional receive port (-RX port) of the second antenna element, wherein the first antenna element comprises the first antenna element functional transmit port (-TX port) and a first antenna element functional receive port (-RX port), and the second antenna element comprises a second antenna element functional transmit port and the second antenna element functional receive port (-RX port); Obtaining a second mutual coupling measurement associated with a second OTA signal path between a third antenna element functional transmit port (-TX port) of the third antenna element and the second antenna element functional receive port (-RX port), wherein the third antenna element comprises the third antenna element functional transmit port (-TX port) and a third antenna element functional receive port (-RX port); Obtaining a third mutual coupling measurement associated with a third OTA signal path between a fourth antenna element functional transmit port (-TX port) of the fourth antenna element and a fifth antenna element functional receive port (-RX port) of the fifth antenna element, wherein the fourth antenna element comprises a fourth antenna element functional receive port (-RX port) and the fourth antenna element functional transmit port (-TX port), and the fifth antenna element comprises the fifth antenna element functional receive port (-RX port) and a fifth antenna element functional transmit port (-TX port); Obtaining a fourth mutual coupling measurement associated with a fourth OTA signal path between the third antenna element functional transmit port (-TX port) of the third antenna element and the fourth antenna element functional receive port (-RX port) of the fourth antenna element; and Determining, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, the fourth mutual coupling measurement and one or more redundancies, at least one phase correction factor and / or an amplitude correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element.

Images