Antenna arrays pattern search systems and methods

Abstract

Systems and methods for implementing phase control of an antenna array are provided. In one example, a method includes determining first sets of phase values based on a predetermined direction. Each first set of phase values is associated with a respective resolution index. Each set of phase values includes a respective phase value for each antenna element. The method further includes determining second sets of phase values based on the first sets of phase values and a phase control parameter. The method further includes determining gain values based on the second sets of phase values and the predetermined direction. The method further includes, for each constellation point of a digital modulation scheme, determining a respective resolution index based on the gain values and determining a channel phase for each antenna element based on the respective resolution index for the constellation point. Related systems are also provided.

Description

Docket No. 61658.154WO01 Client Ref. No. PER-577-PCTANTENNA ARRAYS PATTERN SEARCH SYSTEMS AND METHODSMark Magdaleno and Farshid AryanfarCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of U. S. Provisional Patent Application No. 63 / 742,391 filed January 6, 2025 and entitled “ANTENNA ARRAYS PATTERN SEARCH SYSTEMS AND METHODS," which is incorporated herein by reference in its entirety.TECHNICAL FIELD

[0002] The present disclosure relates generally to antenna systems and methods, and more particularly, for example, to systems and methods for efficiently implementing phase control of antenna arrays.BACKGROUND

[0003] Modem antenna arrays, which are used in various systems including radar systems, cellular networks, satellite communications, broadcasting systems, and the like, generally operate through the transmission and / or reception of signals across one or more radio frequency (RF) bands and / or protocols. During operation, it is common to adjust the phase and / or amplitude of radio signals transmitted through different antenna elements to direct a focused beam of radio signals in a particular target direction. Beamforming through an antenna array is commonly controlled through RF front end circuitry, which may be physically located, for example, in a front end module.SUMMARY

[0004] Embodiments of the present disclosure include systems and methods for implementing phase control of an antenna array. In various embodiments, a method includes determining a first plurality of sets of phase values based on a predetermined direction. Each set of phase values is associated with a respective resolution index of a plurality of resolution indices. Each set of phase values includes a respective phase value for each antenna element of a plurality of antenna elements of an antenna array. The method further includes determining a second plurality of sets of phase values based on the first plurality of sets of phase values and a phase control parameter. The method further includes determining a plurality of gain values based on the second plurality of sets of phase values and theDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTpredetermined direction. The method further includes, for each constellation point of a digital modulation scheme, determining a respective resolution index of the plurality of resolution indices based on the plurality of gain values. The method further includes, for each constellation point of the digital modulation scheme, determining a channel phase for each antenna element of the plurality of antenna elements based on the respective resolution index for the constellation point.

[0005] In various embodiments, a system includes a radio frequency (RF) front end circuit coupled to an antenna array including a plurality of antenna elements. The RF front end circuit includes a plurality of channels, where each channel includes channel circuitry configured to adjust a phase of an RF signal for output to a corresponding antenna element of the plurality of antenna elements. The system further includes control circuitry configured to control the channel circuitry corresponding to each channel. The control circuitry is configured to control the channel circuitry by determining a first plurality of sets of phase values based on a predetermined direction, where each set of phase values is associated with a respective resolution index of a plurality of resolution indices and each set of phase values includes a respective phase value for each antenna element of the plurality of antenna elements. The control circuitry is configured to control the channel circuitry further by determining a second plurality of set of phase values based on the first plurality of sets of phase values and a phase control parameter. The control circuitry' is configured to control the channel circuitry further by determining a plurality' of gain values based on the second plurality of sets of phase values and the predetermined direction. The control circuitry is configured to control the channel circuitry further by, for each constellation point of a digital modulation scheme, determining a respective resolution index of the plurality of resolution indices based on the plurality' of gain values and determining a channel phase for each antenna element of the plurality of antenna elements based on the respective resolution index for the constellation point.

[0006] The scope of the disclosure is defined by the claims, which are incorporated into this section by reference. A more complete understanding of embodiments of the present disclosure will be afforded to those skilled in the art, as well as a realization of additional advantages thereof, by a consideration of the following detailed description of one or more embodiments. Reference will be made to the appended sheets of drawings that will first be described briefly.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCTBRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIG. 1 illustrates an example wireless communications system, in accordance with one or more embodiments of the present disclosure.

[0008] FIG. 2 illustrates an example plot for a 4-channel array with 2-bits of phase control per channel, in accordance with one or more embodiments of the present disclosure.

[0009] FIG. 3 illustrates aspects of an example digital control system and process four antenna elements of an antenna array, in accordance with one or more embodiments of the present disclosure.

[0010] FIG. 4 illustrates an encoding example for four antenna elements, in accordance with embodiments of the present disclosure

[0011] FIG. 5 illustrates an example implementation of digital beamforming using an N-channel array, in accordance with one or more embodiments of the present disclosure.

[0012] FIG. 6 illustrates an example array plot showing beam steering in an 8-element array with 2-bit phase control, in accordance with one or more embodiments of the present disclosure.

[0013] FIG. 7 illustrates an example digital phase shift keying process, in accordance with one or more embodiments of the present disclosure.

[0014] FIG. 8 illustrates another example of a digital phase shift keying process, in accordance with one or more embodiments of the present disclosure.

[0015] FIG. 9 illustrates an example 2-bit phase state algorithm, in accordance with one or more embodiments of the present disclosure.

[0016] FIG. 10 illustrates aspects of an example 2-bit phase state algorithm, in accordance with one or more embodiments of the present disclosure.

[0017] FIG. 11 illustrates an example phase shifter, in accordance with one or more embodiments of the present disclosure.

[0018] FIGs. 12A and 12B illustrate example die implementations of a 2-bit control system and antenna array, in accordance with one or more embodiments of the present disclosure.

[0019] FIG. 13 illustrates an algorithm for determining sequences associated with a desired constellation point based on 2-bit control, in accordance with one or more embodiments of the present disclosure.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0020] FIG. 14 illustrates additional aspects of the algorithm of FIG. 13, in accordance with one or more embodiments of the present disclosure.

[0021] FIGs. 15 and 16 illustrate flow diagrams of example processes for performing pattern searching to determine phase states of antennas of an antenna array based on constellation points of a predetermined digital modulation scheme in accordance with one or more embodiments of the present disclosure.

[0022] FIG. 17A illustrates an example plot showing realizable / available channel phase state for a phase sweep search space implemented by pattern searching in accordance with one or more embodiments of the present disclosure.

[0023] FIG. 17B illustrates an example plot showing realizable / available channel gain state, respectively, for a phase sweep search space implemented by pattern searching in accordance with one or more embodiments of the present disclosure.

[0024] FIG. 18A illustrates an example plot showing realizable / available channel phase state for a phase sweep search space implemented by pattern searching when a resolution parameter is too small.

[0025] FIG. 18B illustrates an example plot showing realizable / available channel gain state for a phase sweep search space implemented by pattern searching when a resolution parameter is too small.

[0026] FIG. 19A illustrates an example result of pattern searching in accordance with one or more embodiments of the present disclosure.

[0027] FIG. 19B illustrates an example plot showing a phase error relative to symbols of a digital modulation scheme for the pattern searching associated with the result shown in FIG.19A in accordance with one or more embodiments of the present disclosure.

[0028] FIG. 19C illustrates an example plot showing a gain for each symbol of a digital modulation scheme for the pattern searching associated with the result shown in FIG. 19A in accordance with one or more embodiments of the present disclosure.

[0029] FIG. 20 illustrates an example plot showing results of pattern searching in accordance with one or more embodiments of the present disclosure.

[0030] FIG. 21 A illustrates a phase population of all possible combinations associated with 2-bit phase control of an antenna array with no phase dithering implemented in accordance with one or more embodiments of the present disclosure.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0031] FIG. 21B illustrates a phase population of all possible combinations associated with 2-bit phase control of an antenna array with phase dithering implemented in accordance with one or more embodiments of the present disclosure.

[0032] Embodiments of the present disclosure and their advantages are best understood by referring to the detailed description that follows. It is noted that sizes of various components and distances between these components are not drawn to scale in the figures. It should be appreciated that like reference numerals are used to identify like elements illustrated in one or more of the figures.DETAILED DESCRIPTION

[0033] The present disclosure describes improved systems and methods for controlling antenna arrays, including large-scale antenna arrays. For example, in various implementations disclosed herein, efficient and scalable control systems and methods are provided for antenna arrays having millimeter-wave apertures suitable for communications above 100 GHz that use beamforming with 100s of elements per square centimeter. Such antenna arrays may employ advanced beamforming techniques with hundreds of radiating elements per square centimeter, enabling highly directional communication capabilities. The disclosed systems are designed to optimize power efficiency and signal fidelity while accommodating the high spatial resolution required for modem communication applications.

[0034] In some embodiments, such systems and methods may provide efficient antenna array and RF front end systems that are scalable to facilitate control / handling of antenna arrays, such as in a millimeter wave antenna array. The control of each antenna element in an array is inherently complex, especially as the number of antenna elements increases, often resulting in digital control schemes with inefficient power consumption and signal processing demands. For example, an RF distribution network may receive an input signal and distribute it to N-antenna elements in the antenna array. A phase shift may be imposed on the signal going to each antenna element, enabling precise steering of the phase front in a desired direction. In some systems, in addition to phase control per antenna element, there may also be amplitude control the signal going to each antenna element to suppress unwanted side lobes and / or optimize beam patterns.

[0035] In operation, the systems and methods disclosed herein provide independent control of the phase and the gain of the signal generated by each antenna element. In some cases, the phase and gain adjustments may occur over picosecond time scales to allow dynamic beamDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTsteering across wide angular ranges. In conventional systems by contrast, a phased antenna array system may implement high resolution control, requiring a communication bandwidth of 10 bits per channel, for example, for each antenna element and operate over microsecond time scales. This translates to significant data throughput requirements in arrays containing thousands of elements, necessitating efficient digital processing architectures to minimize latency and power consumption.

[0036] The disclosed systems and methods address these challenges and other challenges by leveraging innovations in integrated circuit design, such as highly efficient RF front ends and low-power control interfaces. Additionally, advanced algorithms for beamforming and signal processing may be implemented to maximize antenna array performance while reducing the computational overhead associated with large-scale element control. These improvements may enable the practical deployment, for example, of high -density millimeterwave arrays for next-generation communication systems, including 6G wireless networks, satellite communication, and high-speed data links.

[0037] In accordance with various implementations disclosed herein, efficient and scalable control of a large-scale antenna array may be achieved by employing innovative techniques that reduce the complexity and power consumption associated with conventional approaches. For example. 2-bit. low-resolution control of each antenna element facilitates power-efficient scaling to arrays with large numbers of elements while maintaining performance comparable to traditional high-resolution systems. This approach overcomes limitations of existing methods, particularly in systems operating at millimeter-wave frequencies, where power and efficiency are design considerations.

[0038] In various implementations, the control sy stem employs 2-bit resolution per antenna element, dramatically reducing the digital processing overhead, interconnect complexity, and power requirements compared to conventional systems that A pically require 8-10 bits of control per antenna element. This low-resolution control is achieved without sacrificing overall array performance by leveraging the unique properties of nonlinear signal processing at the antenna element level.

[0039] For example, rather than having each antenna element radiate a linear copy of the input signal, each antenna element is configured to radiate a nonlinear copy of the signal, such as a constant-envelope signal modulated by 2-bit phase shifts. When combined across elements of the array, these nonlinear signals collectively reconstruct a high-fidelity linearDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTsignal. The number of antenna elements utilized to reconstruct the linear signal is generally based on application. By carefully controlling the phase of each element's constant-envelope output, the combined radiation pattern exhibits the desired linear beamforming characteristics, such as precise directional gain and side-lobe suppression.

[0040] FIG. 1 illustrates an example host system 100 including RF front-end circuitry for controlling individual antenna elements 146 of an antenna array 134, in accordance with embodiments of the present disclosure. The host system 100 includes host control circuitry 110, digital control circuitry 120, and the antenna array 134. The host control circuitry 110 interfaces with the digital control circuitry 120, which manages the operation of the antenna array 134. The antenna array 134, implemented as an integrated circuit, includes multiple antenna elements 146 and an RF system-on-chip (SoC 130) with an RF front-end module 132. The antenna array 134 is communicatively coupled to the host system 100 through the digital control circuitry 120 and host control circuitry 110.

[0041] Each antenna element 146a-n is driven by corresponding circuitry (e.g.. referred to as channel circuitry) that includes a multiplier 140a-n, a phase shifter 142a-n, and a power amplifier (PA 144a-n). The RF signal 148 is distributed to each channel, where it is fed through a corresponding multiplier 140 and phase shifter 142, which is controlled by the 2-bit control signal generated by adaptive control circuitry 138. The RF signal 148 may be a local oscillator. This 2-bit signal allows the phase shifter 142 to switch between four discrete phase states — 0, 90, 180, or 270 degrees in the disclosed embodiments. In some cases, the phase shifters 142a-n may be, or may include, quadrature phase shifters. In some cases, processing / placement of the phase shifters 142a-n after the multipliers 140a-n in the pipeline may avoid non-linearities associated with processing / placement of the multipliers 140a-n after the phase shifters 142a-n. The phase-shifted signal is amplified by power amplifier 144, which is powered by a voltage supply 150, and transmitted via the corresponding antenna element 146. In some cases, the PAs 144a-n may also have less stringent linear characteristics and / or operated at efficiencies (e.g., peak efficiencies) close to saturation.

[0042] The architecture of the illustrated embodiment enables a high-speed, low-resolution, phase shifter (e.g., phase shifters 142a-n) that is capable of operating at high data rates (e.g., >10Gbps) to switch between the four discrete phase states on each channel. This enables precise, per-element control, with a 2-bit digital code directly modulating phase shifters (e.g., D-band phase shifters), which support high-speed, low-latency modulation suitable for advanced communication systems.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0043] In some aspects, the architecture may provide built-in spatial filtering. In some cases, spatial filtering of the beam may be performed to eliminate quantization noise that appear as sidelobes. For example, by utilizing a very fast phase shifter in accordance with one or more embodiments, digital sequences associated with smaller sidelobes may be determined / identified rapidly. On average other codes may be used to transmit a given constellation point to control where the sidelobe levels are high or low or on average to spread them out. In some cases, 2-bit phase control functions may be slower than a symbol rate to synthesize spatial filtering.

[0044] The system employs a coarse quantization of both the phase and amplitude in each channel. In some embodiments, control signals include 2 -bits per phase and 1 -bit for each PA (on or off). While such low' resolution might be inadequate for conventional linear systems, the disclosed architecture compensates through rapid, independent phase switching in each channel. In addition to slow phase control (e.g., tens of Megahertz in some implementations) relative to the disclosed architecture, conventional linear systems may also require circuitry / processing as to not distort a modulated intermediate frequency (IF) signal and / or otherwise introduce nonlinearities into transmissions. As non-limiting examples, conventional linear systems may utilize linear PAs, PA backoff operation, and / or other circuitry / processing to maintain linearity. The system generates fast, precise digital control signals to modulate the phase shifters directly, reducing the power consumption associated with distributing high-resolution signals across thousands of elements while maintaining system performance. For example, such phase control may be implemented with digital circuitry that operates at in the Gigahertz range, although other frequency ranges may be utilized dependent on application. Additionally, the architecture can coordinate rapid phase transitions across channels, allowing flexible beamforming and waveform generation.

[0045] The antenna array 134 and digital control circuitry enable the host system 100 to support w ireless communications for a wide range of applications. The host system 100 may¬ be any device and / or system capable of transmitting RF signals via the antenna array, such as a radar system, mobile phone system, a manned or unmanned vehicle, of other wireless device and / or system.

[0046] In various embodiments, the host control circuitry 110 may include one or more logic devices and memory devices configured to perform operations of the host system 100. Similarly, the digital control circuitry- 120 may include one or more logic devices and memory devices (e.g., memory- 122) configured to control the antenna array 134 as describedDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTherein. A logic device may be implemented, for example, as a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a microcontroller, a programmable logic device (PLD), a field-programmable gate array (FPGA), or other programmable logic device(s). The logic device and other components may be configured through hardwiring, software execution, or a combination of both. In various embodiments, the logic device may include one or more memory devices designed to retain data, such as software instructions for execution by the logic device.

[0047] The memory may include volatile and non-volatile memories, such as registers, random-access memory (RAM), dynamic RAM (DRAM), static RAM (SRAM), non-volatile random-access memory (NVRAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically-erasable programmable read-only memory (EEPROM), flash memory, hard disk drives, or other memory types. The logic device may be configured to execute software instructions residing in the memory, thereby accomplishing processing steps and operations.

[0048] The system of FIG. 1 provides an energy-efficient solution (e.g., at 140 GHz) for controlling an antenna array. The illustrated control system may remove various linear elements found in conventional control systems and / or reduce linearity requirements various elements, and directly generate the signal at each antenna element through a 2 -bit phase control process disclosed herein. In various embodiments, instead of linear RF distribution, the system may distribute a non-linear signal with two digital lines to control the phase shifter through digital states.

[0049] The various components of FIG. 1 are illustrative and may be adapted and / or rearranged depending on the implementation. For example, certain components may be combined into a single module, while others may be separated or distributed in the system as other components. Alternative configurations may also involve variations in the number of communication paths, antennas, phase shifters, or other associated components to suit specific performance requirements. Alternative embodiments, for example, may incorporate additional components, such as mixed-signal integrated circuits for on-chip digital-to-analog conversion, feedback loops for dynamic performance optimization, or machine learning algorithms for adaptive beam steering and interference cancellation.

[0050] FIG. 2 illustrates an example plot 200 illustrating the performance of a 4-channel array with 2 -bits of phase control per channel, in accordance with embodiments of the presentDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTdisclosure. In some embodiments, the system generating this plot 200 may be the system of FIG. 1, in which the antenna array 136 includes a plurality of 4-channel arrays with 2-bits of phase control per channel. This example illustrates how the 4-channel array can effectively steer a beam across an angular range of -30-degrees to 30-degrees. While FIG. 2 demonstrates a 4-channel array with 2-bit phase control, alternative configurations could incorporate a higher number of channels or increased phase resolution to enhance performance.

[0051] Beyond beam steering, the phase shifts applied by the phase shifter 142 may also contribute to digital modulation and signal linearization. By introducing controlled phase variations as part of the transmitted signal, the system encodes information directly into the phase states. For example, a 2-bit phase control allows quadrature phase modulation (QPSK) for data encoding, where each phase state represents two bits of information. This integration of modulation functionality into the beamforming architecture simplifies the design and improves efficiency. The disclosed system also uses phase shifts to compensate for nonlinearities. By carefully adjusting the phase relationships between channels, the system mitigates distortions that could otherwise degrade the signal's fidelity.

[0052] FIG. 3 illustrates an example of digital control for four antenna elements, in accordance with embodiments of the present disclosure. In this embodiment, an FPGA 300 (e.g., digital control circuitry 120 of FIG. 1) is configured to generate digital control signals, labeled Do, Di, D2, and D3. Each of these control signals, Dk, is serialized 310 into a stream of data for transmission to the phase shifters. Table 320 illustrates an example decoding scheme where each 2-bits corresponds to a specific phase shift. In this regard, as illustrated in table 320, 2-bits of each serialized control signal form a symbol. Each symbol is associated a state which in turn corresponds to a phase (e.g., 0°, 90°, 180°, 270°). The 2-bit control signals may be decoded by the phase shifter (or related circuitry) as illustrated in the table 320. For example, the 2-bit code / sy mbol 00 could correspond to a 0-degree phase shift, 01 could correspond to a 90-degree phase shift, 10 could correspond to a 180-degree phase shift, and 11 could correspond to a 270-degree phase shift. This mapping enables each antenna element to rapidly and independently adjust its phase state based on the control signal received, facilitating beam steering and signal modulation.

[0053] Table 330 provides an example of how digital bits that form part of serial data may be converted (e.g., using modulation circuitry) into phase states for each of four antenna elements. Each time instance tk is associated with a bit for each of the serial data Do, Di, D2,Docket No. 61658.154WO01 Client Ref. No. PER-577-PCTand D3. The 2-bit digital signal would generate different digital control states for each of the four phase shifters. For example, with reference to Do, the 2-bit signal 1,1 (e.g., at tk = 0 and tk = 1) is a 270-degree phase shift, 0,1 is a 90-degree phase shift, 1,0 is a 180-degree phase shift, and 0,0 is a 0-degree phase shift. These digital sequences allow precise phase modulation across the antenna array. For each antenna element, the digital control circuitry transmits a continuous stream of serialized 2-bit codes, with every two bits dictating the next phase state for a particular antenna. The phase shifters decode these bit pairs in real time, dynamically adjusting the phase at the front end of the antenna array. Moreover, in the illustrated embodiment, the serial data rate is designed to operate at twice the modulated symbol rate of the antenna array, ensuring seamless phase transitions and efficient system operation.

[0054] In some embodiments, the FPGA 300 may have an embedded DSP with memory. The antenna array and control circuitry can be used to switch among different modulation schemes using the FPGA / DSP. In some embodiments, the control circuitry includes one or more of a DSP, FPGA, and a microcontroller. In conventional systems, an RF-SOC is provided, which includes a large array of DACs (e.g., 8-bit DAC per channel), which can be sampled at high rates. A drawback of this approach is that it is hard to scale to hundreds of antenna elements.

[0055] In some embodiments, the digital control circuitry is configured to allow the antenna array to switch between different modulation schemes, such as M-ary phase-shift keying (MPSK) (e.g., QPSK), M-ary quadrature amplitude modulation (M-QAM) (e.g., 16-QAM), OFDM, and the like, depending on the application or communication environment. The digital control circuitry may include a DSP, FPGA, microcontroller, or other circuitry configured to adaptively control phase and modulation parameters based on external inputs or feedback from the host system. In some embodiments, the digital control circuitry includes and FPGA and an embedded DSP with memory, enabling advanced signal processing and dynamic reconfiguration.

[0056] In conventional systems, RF system-on-chip (RF-SoC) solutions often rely on a large array of high-resolution DACs (e.g., 8-bit DACs per channel) to generate analog signals sampled at high rates. While effective for small-scale arrays, this approach becomes challenging to scale for arrays with hundreds or thousands of antenna elements due to significant power, complexity, and cost overheads. By contrast, the disclosed system replaces the DACs with a scalable digital architecture that uses low-resolution, energy-efficient digitalDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTcontrol signals for each antenna element. This innovation enables the practical implementation of large-scale antenna arrays for high-frequency communication systems while maintaining low power consumption and reduced design complexity.

[0057] In some embodiments, the system may implement adaptive resolution, increasing phase control precision when higher beamforming accuracy is required. In some embodiments, multiple FPGAs or DSPs could be used to control larger arrays, dividing the workload among subsets of elements. The system may include on-chip feedback mechanisms used to monitor array performance in real time, dynamically adjusting phase states for optimal beamforming and signal fidelity.

[0058] FIG. 4 illustrates an alternate encoding example for four antenna elements, in accordance with embodiments of the present disclosure. In this approach, a 4-level encoding of the signal is used to directly decode each of the four levels directly to a phase state. This approach may reduce the symbol rate (e.g., digital signaling rate) by a factor of two, without changing the modulation symbol rate. For example, digital I / O systems often use PAM-4 (pulse amplitude modulation), in which serial data may be captured at the symbol rate.

[0059] In the illustrated embodiment, an FPGA 400 (e.g., digital control circuitry 120 of FIG. 1) is configured to generate four control signals Do-3. Each control signal, Dk, is serialized 410 and transmitted to a phase shifter for a corresponding antenna element. As shown in table 420, each 4-level symbol may be mapped directly to a phase state (e.g., using modulation circuitry). For example, the symbol 0 could correspond to a 0-degree phase shift, 1 could correspond to a 90-degree phase shift, 2 could correspond to a 180-degree phase shift, and 3 could correspond to a 270-degree phase shift.

[0060] Table 430 further illustrates how sequences of 4-level symbols are converted into phase states for four antenna elements. For instance, a symbol 3 translates to a 270-degree phase shift, 1 to a 90 degree phase shift, 2 to a 180 degree phase shift, and 0 to a 0 degree phase shift. Each phase shifter decodes the incoming symbol to adjust the phase of the RF signal to the corresponding state. This process enables efficient phase control while reducing the data transfer rate requirements from the digital control circuitry to the antenna elements, conserving power and improving scalability for large antenna arrays.

[0061] FIG. 5 illustrates an example implementation of digital beamforming for an N-channel antenna array (e.g., as described with reference to FIG. 1), according to embodiments of the present disclosure. Each channel may include channel circuitry. In this embodiment, anDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTindependent set of 2-bit digital sequences 532a-n is provided to the phase shifter 542a-n in each channel. In this embodiment, a digital signal processor or similar processing circuitry is configured to generate 2N digital bits corresponding to the control signals for the N channels.

[0062] The 2N digital bits are demultiplexed 520 into independent, 2-bit control signals, each corresponding to a specific channel in the antenna array. Each of the 2-bit control signals is provided to a corresponding phase shifter 542a-n of the channel circuitry, which modulate the RF carrier signals independently for each channel, enabling precise beamforming and phase control. In this regard, independent digital sequences may modulate the phase shifters of the antenna array. In some cases, the channel circuitry may include modulation circuitry that converts digital sequences to RF phase states (e.g., (0°, 90°, 180°, 270°). In the illustrated embodiment, the phase shifters 542 for a channel are positioned after the corresponding multipliers 540 in the signal chain of the channel circuitry to prevent the introduction of nonlinearities that could otherwise degrade signal integrity and beamforming accuracy.

[0063] This architecture allows each phase shifter 542 to receive a unique phase modulation signal derived from its respective 2-bit control sequence, ensuring independent and highly configurable beamforming across the N-channel array. As illustrated, the X-axis represents the indices of the digital bitstream, while the Y-axis indicates the binary on (1) or off (0) states of the control bits. The resulting bitstreams are modulated onto the RF carrier and transmitted as a digital input stream. By multiplexing and demultiplexing the digital signals, the system may efficiently scale to a large number of antenna elements without significantly increasing the computational or power burden, making it well-suited for advanced millimeter-wave applications and other high-frequency communication systems.

[0064] FIG. 6 is a plot 600 of an example beam pattern for an 8-element antenna array utilizing 2-bit phase control, in accordance with embodiments of the present disclosure. In this configuration, each signal channel is modulated with one of four discrete phase states (0°, 90°, 180°, 270°), enabling beam steering within an angular range. As the size of the antenna array increases, the main beam becomes narrower, enhancing directivity. However, one drawback of the coarse 2-bit phase control is that sidelobes may remain relatively high compared to systems with higher-resolution phase control, where finer adjustments can potentially suppress sidelobes more effectively. This can degrade overall system performance by reducing the signal-to-interference ratio in applications requiring high beam precision. To mitigate this limitation, the fast digital phase control described in the present disclosure mayDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTbe used to dynamically adjust the beam pattern, leveraging rapid reconfiguration of phase states across the array. This approach enhances array scalability and makes the system suitable for high-frequency applications, such as millimeter-wave communication and radar, where large arrays are commonly used.

[0065] Referring to FIG. 7, digital phase shift keying (PSK) can be implemented in arbitrary beam directions using low-resolution phase control. Digital modulation for wireless communication typically involves a single carrier modulated with discrete phase states, e.g., as in PSK. The present disclosure extends 2-bit control to operate with other modulation protocols, such as quadrature amplitude modulation (QAM), where both phase and amplitude are simultaneously varied. By leveraging 2-bit phase shifters, the disclosed system achieves fast, energy -efficient modulation while maintaining compatibility with advanced wireless communication standards.

[0066] For example, in a 16-PSK constellation, the system may be configured to generate phase states that align closely with the ideal constellation 720. The corresponding array pattern 710 is shown for an 8-element array, demonstrating beam pointing at a 45 -degree angle (e.g., the angle associated with the highest peak in plot 710). The algorithms disclosed herein may identify and select optimal quantized symbols (circles in plot 730) for the system requirements, for example, selecting quantized symbols that minimize error compared to the ideal constellation. The plot 730 illustrates 16 phase shifts that approximate the ideal phase states, enabling precise beam steering without requiring high-resolution phase control. This approach effectively balances system complexity, power efficiency, and performance.

[0067] The system is capable of dynamically adjusting its phase states to steer the beam in other arbitrary directions. For instance, when steering the beam to 15 degrees (see plot 750), the system computes a new set of digital sequences to generate 16 phase states that correspond to the desired beam direction. The algorithm adapts to the chosen beam angle, ensuring minimal error between the quantized constellation points (circles in plot 770) and ideal constellation points (asterisks in plots 760 and 770). This flexibility enables the array to achieve high-performance beamforming and modulation in various directions with minimal computational overhead.

[0068] In conventional systems, achieving similar performance may require high-resolution phase shifters, such as using 8-bit control, which increases power consumption and slows processing. In contrast, the present disclosure uses only 2-bit phase shifters, allowing phaseDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTshifts to occur faster than the modulation symbol rate, significantly improving speed and energy efficiency. The low-resolution phase shifters may be associated with low-power and exhibit reduced loss, making them useful for wideband applications. Additionally, the system can interpolate between coarse phase states, such as 0° and 90°, by modulating faster than the symbol rate to effectively achieve intermediate phase states like 45°. This technique avoids the need for additional resolution, simplifying the circuitry while maintaining precise beam control.

[0069] Referring to FIG. 8, the circles in plot 830 illustrates all possible (I, Q) amplitudes in a given direction. An arbitrary 16-QAM can be generated based on a desired angle (such as ~30-degress in plot 810). The quantized values may be selected to minimize error, for example, finding the points where the mean squared array pattern amplitude is lower than M-PSK due to lower power constellation points. Other error functions may be used in other implementations. The low resolution approach can be used to approximate any linear waveform. The bottom figures 840 and 850 illustrate quadrature amplitude modulation.

[0070] Small deviations are shown, but good low error representation of the ideal signal is provided in a given direction. As illustrated in plot 810, the beam is steered at approximately 30-degrees and the 16 QAM are generated (plot 820). As previously discussed, digital signals are repetitive, and to modulate in an arbitrary direction, the digital sequences may rotate across different channels. This repetition and rotation may be leveraged to reduce the number of digital sequences that need to be transmitted, for example, as illustrated in FIG. 5.

[0071] Referring to FIG. 9, an example 2-bit phase state algorithm 900 will now be described, in accordance with embodiments of the present disclosure. As illustrated in the plot 910, the I-Q space may be determined, which includes all the possible array patterns in a particular direction. The algorithm may select quantized points (circles in plot 920) that approximate the ideal constellation for a particular beam direction (e.g., 45-degrees as illustrated in plot 930) by minimizing error between the generated constellation points and the ideal constellation points. The selected points are used to calculate the array pattern and corresponding serial input streams. The system then generates serial input streams 950 for the N channels of the array.

[0072] FIG. 9 illustrates an example of an 8-channel array using 16-PSK modulation with a beam steered to 45-degrees. After selecting a constellation and a direction, the digital sequences may be precomputed (e.g., using one or more logic devices, such as in the hostDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTcontrol circuitry 110 of FIG. 1) and stored in a memory (e.g., the memory 122 of FIG. 1). The phase settings may be represented, for example, as illustrated in table 940, where each row corresponds to one of the 16 constellation points, and each column represents one of the 8 antennas. As one example, a first row (e.g., topmost row) of the table 940 provides a digital sequence (e.g., also referred to as a digital code or a configuration) associated with one of the quantized constellation points of 16-PSK shown in the plot 920. This digital sequence provides antenna element 1, 2, 3, 4, 5, 6, 7, and 8 with a phase shift of 0°, 90°, 270°, 0°, 180°, 270°, 0°, and 180°, respectively. Each of these phase shifts may be represented using 2-bits. These 2-bits may be referred to as 2-bit control signals. In this regard, a given digital sequence is formed of 2-bit control signals for the antennas of the antenna array, where each 2-bit control signal indicates the phase state associated with a respective one of the antennas or, equivalent, the phase shift for applying to a signal associated with the respective one of the antennas. As another example, a next row (e.g., second topmost row) of the table 940 provides a digital sequence associated with another of the quantized constellation points of 16-PSK shown in the plot 920. This digital sequence provides antenna element 1, 2, 3, 4. 5, 6, 7, and 8 with a phase shift of 0°, 180°, 270°, 0°, 180°, 270°, 90°, and 180°, respectively. After the constellation and direction are selected, the digital sequences tend to repeat. The phase settings may be stored in a local memory to minimize the processing and data transmission and facilitate high-speed modulation of the antenna array, as the system can quickly retrieve and apply the appropriate phase settings for a desired symbol.

[0073] Even though the approach uses a multiplier followed by a coarse phase shifter, in some embodiments it may be compatible with orthogonal frequency-division multiplexing (OFDM) signals. A mathematical representation of OFDM signals is provided below to further assist with an understanding of the present disclosure.

[0074] OFDM baseband:1 \1\1I 2np(n — IT~)\s(n) = J^ 2_, / .di. PexP ( / - T - )

[0075] Digital representation of OFDM:S(t) = |s(t)|exp ( / 0s(t))

[0076] Analog representation of OFDM:Docket No. 61658.154WO01 Client Ref. No. PER-577-PCTy(0 = rk|s(t)|2kCOS (2nNfIFt + A0s(t) + A0PW(t))fc=l

[0077] By integrating a high-speed phase shifter at the antenna level, a large number of subcarriers in the OFDM signal can be efficiently modulated and steered in the desired beam direction. The high-speed phase shifter enables unwrapping of N-fold phase advances caused by N-fold multiplications in the signal path. In typical OFDM systems, the multiplication of the carrier signal introduces N-fold phase advances, which can complicate signal processing. The present disclosure addresses this issue by de-embedding the phase shifts using the phase shifter, enabling precise modulation of OFDM waveforms even with coarse-resolution phase control.

[0078] Referring to FIG. 10, an example operation of a phase shifter circuit 1000 capable of rapid phase transitions is illustrated, in accordance with embodiments of the present disclosure. The circuit 1000 is configured to receive 4-bit serial inputs representing phase states in an I-Q space and process these inputs synchronized by a clock signal 1010 (CLK) for precise and efficient modulation. This implementation may be used for digital modulation schemes such as quadrature phase shift keying (QPSK) or other protocols where phase states may be determined based on constellation points of the digital modulation scheme, such as described herein. In some embodiments, an offline algorithm generates the 4-bit serial input binary codes corresponding to the phase states (e.g., corresponding to 0, 90, 180, and 270-degrees) for the output channels.

[0079] As illustrated, the 4-bit serial input that encodes the desired phase state is provided to a shift register 1002, which is synchronized by the clock signal, CLK 1010. The shift register 1002 temporarily stores the incoming serial data and then transfers its contents, under control of the clock signal to a hold register 1004, which acts as an intermediary buffer ensuring that subsequent decoding occurs without timing disruptions.

[0080] From the hold register 1004, the data is passed to a one-shot decoder 1006 associated with each channel. The one-shot decoder 1006 translates the 4-bit binary input into states, based on a predefined mapping that aligns with the digital modulation scheme (e.g., QPSK). The one-shot decoder generates control signals for the high-speed phase shifter, which adjusts the output signal in accordance with the decoded phase state. This rapid transition between phase states enables dynamic modulation and beamforming, suitable for example for high-speed communication systems.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0081] In some embodiments, the 4-bit input signals are pre-generated by an offline algorithm that optimizes the encoding for a given modulation scheme. The algorithm mitigates error between the desired and actual constellation points by carefully selecting the 4-bit binary codes for each state. These pre-computed codes may be loaded into a local memory, reducing the computational overhead during real-time operation.

[0082] FIG. 11 illustrates an example phase shifter 1100 designed to facilitate high-speed, low-power operation, in accordance with embodiments of the present disclosure. The phase shifter 1100 may be included, for example, as a component for precise phase control in modem communication systems. As illustrated, the phase shifter 1100 includes transformer circuits 1110, inductors L1-L4, MOSFET switches M1-M6, resistors R1-R4, and capacitors C1-C8 to achieve efficient and accurate phase modulation across four distinct phase states (e.g., 0°, 90°. 180°, and 270°). These components form part of the RF front-end, where signals are modulated for beamforming or digital communication applications.

[0083] The MOSFET switches (M3-M6) are digitally controlled, for example, by the input from the previously disclosed digital control circuitry (e.g., as described with reference to FIG. 10 or otherwise as described herein). These switches are arranged and activated to select the appropriate phase path to select among the four phase states. The digital control for each pair of channels resides centrally, reducing routing complexity and signal latency.

[0084] FIGs. 12A and 12B illustrate example die implementations of a 2-bit control system and antenna array, in accordance with one or more embodiments of the present disclosure. FIG. 12A provides further detail on the digital control circuitry, including an example die layout for components such as previously discussed with reference to FIG. 10. This integrated design allows the phase shifter to operate efficiently within a small area, making it ideal for densely packed antenna arrays.

[0085] FIG. 12B illustrates an example die layout for a 4-channel digital to mm-Wave TX circuitry, such as described with reference to FIG. 11. In this embodiment, an example 22-nm FD-SOI CMOS is illustrated. The die area is 1.905 mm x 2.15 mm (4.1 mm2) and fits 4 channels, though other dimensions may be use in various implementations. This compact implementation meets half-wavelength array spacing requirements of many antenna array implementations. The digital and RF inputs for each channel are shared with its neighboring channel but still allow for unique modulation per channel. In some aspects, solder bumps may be used as the I / O connection to a LTCC carrier. The silicon die may be flip-chip bonded to aDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTLTCC carrier that handles DC / RF / Digital routing and include D-band antennas. Vivaldi antennas may be used to offer high directivity and allow for 2-dimensional scaling in the z-direction.

[0086] Referring to FIGs. 13 and 14, an algorithm 1300 for determining desired phase states of antennas in a phased array system will now be described, in accordance with embodiments of the present disclosure. This algorithm is described in the context of a 1-D phased array with QPSK digital modulation. In operation 1302, possible digital codes / sequences are generated for the array, resulting in 4Nvalues for an array of N elements. For a given digital code / sequence, each antenna element may be associated with one of the possible phase states (e.g., 0°, 90°, 180°, and 270°). In various embodiments, the code generation may be exhaustive, generating all potential digital codes / sequences. In some cases, the 4Npossible digital codes / sequences may collectively be referred to as a sequence book or a code book for the N antenna elements, with each digital code / sequence associated with a code index. In operation 1304, the generated codes / sequences are used to synthesize all beam patterns. Each code / sequence may be associated with a respective one of the synthesized beam patterns. These beam patterns may be patterns that are possible / accessible to (e.g., achievable by) the antenna array and may be referred to as accessible beam patterns or simply accessible patterns.

[0087] In operation 1306, based on a desired beam direction and the synthesized beam patterns, the codes / sequences that are associated with the desired beam direction are identified / determined. The desired beam direction may also be referred to as a predetermined beam direction or a pre-selected beam direction. The codes / sequences may be determined based on signal amplitudes and / or sidelobes associated with the synthesized beam patterns. For example, the codes / sequences that are identified / determined may include at least those that generate a peak amplitude in the desired beam direction. In some cases, only the codes / sequences that generate a peak amplitude in the desired direction may be determined / identified in operation 1306.

[0088] In operation 1308, based on a desired constellation (e.g., QPSK), the codes / sequences determined / identified in operation 1306 are refined. In some cases, the codes / sequences determined in operation 1306 may be refined by finding a subset of these codes / sequences determined in operation 1306 that minimize the error between each desired constellation point and accessible pattern. In some cases, in operation 1308, a respective one code / sequence may be identified / determined for each constellation point of the desiredDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTconstellation. In some cases, in operation 1308, codes / sequences may be determined for a set of desired constellation points. A desired constellation point may also be referred to as a predetermined constellation point or a pre-selected constellation point. In various embodiments, the code selection and / or error determination may be made based on one or more implementation criteria (e.g., peak amplitude, closest to ideal constellation, mitigation of side lobes, etc.). For example, the codes may be refined in operation 1308. where the desired constellation (e.g., QPSK) is compared against the generated beam patterns. The algorithm may calculate the error between the desired constellation points and the actual array patterns and select the codes that minimize this error. This step ensures that the resulting beam patterns align closely with the ideal constellation points for accurate digital modulation.

[0089] In some embodiments, the codes / sequences associated with various directions and constellation points of various digital modulation schemes may be determined using the process 1300 and stored for later use. With the digital codes / sequences stored in memory (e.g., the memory 122 of FIG. 1), after selecting a constellation point(s) and a direction, the predetermined / precomputed channel phases digital sequences may be retrieved from the memory and utilized for phase control. The antenna array may be configured to transmit in a desired direction according to a desired digital modulation scheme (e.g., one or more constellation points thereof) based on the using the appropriate digital codes / sequences stored in memory.

[0090] As the number of array elements N grows larger, the number of codes / sequences can become extremely large leading the algorithm becoming computationally infeasible for some implementations. In various implementations, the codes / sequences may be reviewed to identify the codes that meet two criteria: generating peak amplitude in the desired direction and achieving the desired phase shifts with minimal error. This method provides precise beamforming, even for large arrays, by iteratively refining the codes / sequences to achieve the best possible alignment with the ideal beam pattern.

[0091] Referring to FIG. 14, operations 1304, 1306, and 1308 are further illustrated. In operations 1304, all possible array patterns of phase states may be synthesized. The vertical axis provides signal amplitude values and the horizontal axis provides beam steering angle. A beam steering angle may also be referred to simply as a beam direction or a direction. In this regard, the vertical axis illustrates signal amplitude values at a desired beam direction (e.g., -50-degrees in the illustrated embodiment) for all possible array patterns of phase states. InDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTthis embodiment, the array is N=8 antenna elements. In operation 1306, at the desired direction, the array of codes / sequences is determined based on amplitudes (e.g., peak amplitudes) of the beam patterns associated with the desired direction. In some embodiments, the constellation of values for those array of codes is mapped onto a 2-D plane with the horizontal axis being imaginary values. From this constellation, the algorithm determines the sample points of the modulation scheme, e.g., QPSK. In some embodiments, the codes may be selected using additional criteria, such as codes that also reduce sidelobes, reduce error, or other criteria.

[0092] For example, when the direction is set to a 30-degree angle, the algorithm can generate QPSK constellation points. The QPSK constellation has four constellation points. For example, Point 1 = 0.9994-0.0299i, Point 2 = 0.0299+.9994i, Point 3 = -0.9994 + 0.299i, and Point 4 = -0.0299 - 0.9994i. Points 1-4 are constellation points corresponding to symbols 00, 01, 10, and 11 (QPSK), however, it will be appreciated that other modulation schemes may be used (e.g., QAM). The phase value of each antenna associated with an index N, for example, may be selected to provide a well-structured phase rotation across antenna elements and points (P1-P4). For example, for Point 1, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 0, 90, 180, 270, 0, 90, 180, and 270 degrees, respectively; for Point 2, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 90, 180, 270, 0, 90, 180, 270, and 0 degrees; for Point 3, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 180, 270, 0, 90, 180, 270, 0, and 90 degrees; and for Point 4, N = 1, 2, 3. 4, 5, 6. 7, and 8 may have a code / sequence of phase shifts of 270, 0, 90, 180. 270, 0, 90, and 180 degrees. In some cases, each of these phase states / shifts may be associated with the 2-bits as shown in the Table 320 of FIG. 3. These structured rotations enable the array to approximate the desired constellation points while mitigating error by selecting codes that closely match the desired patterns.

[0093] With reference to FIG. 13 and the above example of 30-degree angle, in operation 1302, given N = 8 antenna elements and four phase shifts per antenna element (0°, 90°, 180°, and 270°), all 48possible digital codes / sequences may be determined. In some cases, the 48possible digital codes / sequences may collectively be referred to as a sequence book or a code book for the 8 antenna elements, with each digital code / sequence associated with a code index. In operation 1304, beam patterns for all the possible digital codes / sequences across the 8 antenna elements may be synthesized. In operation 1306, based on a desired beam direction, a desired constellation, and all the synthesized beam patterns, the digitalDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTcodes / sequences associated with constellation points (Points 1-4) of the desired constellation may be determined / identified. In this example, four codes / sequences (e.g., one for each of the Points 1-4) may be identified in operation 1306. In operation 1308, based on the desired constellation point(s) (e.g., one or more of Points 1-4), the code / sequence(s) associated with the desired constellation point(s) may be determined / identified. For example, if Point 2 is the desired constellation point, the code / sequence is 90, 180, 270, 0, 90, 180, 270, and 0 degrees to effectuate / apply these phase shifts for signals transmitted by N = 1, 2, 3, 4, 5, 6, 7, and 8, respectively. In other cases, more than four codes / sequences may be determined in operation 1306 and further refining is performed in operation 1308.

[0094] Similarly, for a beam direction of 45-degrees, the algorithm can generate QPSK points such as Point 1 = 0.9043-0.1218i, Point 2 = 0.1218 + 0.9043i, Point 3 = -0.9043 + 0.1218i, and Point 4 = -0.1218 - 0.9043i. The value of each antenna associated with an index N, for example, may be selected to provide a well-structured phase rotation across antenna elements and points (P1-P4). For example, for Point 1, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 0, 90, 270, 0, 180, 270, 0, and 180 degrees, respectively; for Point 2, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 90, 180, 0, 90, 270, 0, 90, and 270 degrees; for Point 3, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 180, 270, 90, 180, 0, 90, 180, and 0 degrees; and for Point 4, N = 1, 2, 3, 4, 5, 6, 7, and 8 may have a code / sequence of phase shifts of 270, 0, 180, 270, 90, 180, 270, and 90 degrees. In some cases, these phase shifts may be associated with the 2-bits as shown in the Table 320 of FIG. 3. The phase rotation across the elements (N = 1 through N = 8) may follow a structured pattern, ensuring consistency in the beamforming process. In this example, each element has a unique value, but rotation jumps 1 or 2 steps.

[0095] In summary, the algorithm generally proceeds through four steps: (1) generating a codebook of all possible configurations, (2) synthesizing beam patterns for each configuration, (3) identifying codes in the desired direction based on signal levels (e.g., peak signal amplitudes and / or side lobe levels), and (4) refining the codes to minimize error relative to the desired constellation points. This approach ensures accurate and efficient beamforming for digital modulation schemes such as QPSK or QAM using only 2-bits of control. The structured phase rotations across the antenna elements enable seamless integration of the algorithm into practical phased array systems.

[0096] While N=8 antenna elements have been described, it will be appreciated that other numbers of antenna elements may be used in other implementations. The proposedDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTtransmitter architecture further allows for wide bandwidth that is beneficial in radar applications. The range resolution of a radar front-end is dependent on the bandwidth available. In the implementation of this architecture, a simulated RF bandwidth of 29.5 GHz and larger has been achieved, corresponding to a range resolution of 5.09 mm. The proposed transmitter architecture can also be utilized for high data-rate backhaul communication due to the large RF bandwidth and high DC-RF efficiency.

[0097] Additional linearization benefits are also achieved. Each channel is not necessarily linear by itself. Each 4-channel die has all the DC biases connected across the chip.Therefore, in many implementations the power output per channel on a particular die cannot be adjusted for each channel. However, when scaling to a 2D array, each 4-channel LTCC module can be adjusted independently with respect to a neighboring 4-channel LTCC module. Therefore, when scaling to a large element array, the overall linearization can be improved by adjusting the output power of each LTCC module based on where the beam is pointed.

[0098] Spatial filtering of the beam may be performed to eliminate quantization noise that appear as sidelobes. For example, because we have a very fast phase shifter, we can find other codes that reduce the sidelobes instantaneously. On average other codes may be used to transmit the same constellation point to control where the sidelobe levels are high or low or on average to spread them out. In some cases, 2-bit control functions may be slower than a symbol rate to synthesize spatial filtering.

[0099] Temporal filtering of the signal using only phase control for frequency shaping. In some cases, 2-bit control functions may be faster than the symbol rate to synthesize the temporal filtering. In this regard, the 2-bit control functions include changing the phase states faster than the symbol rate. Because linear amplitude control may be performed over the signal, conventional techniques such as raised-cosine filtering may be implemented by changing the phase states faster than the symbol rate, which allows implementation of an approximation of raised-cosine response which gives frequency shaping and ability to control frequency emissions out of band. Non-linearity of coarse / low resolution technologies have poor emissions out of band because the non-linearity generally spreads the signal out of band, the fast phase shifter (time domain filtering) allows shaping of the frequency response at the antenna.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0100] In one or more embodiments, pattern searching may be performed to determine phase states / values (e.g.. also referred to as channel phases) for each antenna element based on a subset, rather than a full set, of all possible codes / sequences associated with an antenna array with N antenna elements. In some aspects, such pattern searching utilize 2-bit phase control, such that the channel phase of each antenna element may be represented using two bits. In some cases, the 2-bit channel phase applied to each antenna element (e.g., by a phase shifter 542a-n of FIG. 5 coupled to an antenna element) may be one of 0°, 90°, 180°, or 270°. Through 2-bit phase control in accordance with one or more embodiments, a 2-bit channel phase system, which exhibits nonlinear behavior, may be utilized to approximate / represent constellation point phases of digital modulation schemes. Dependent on applications and / or associated computational resource availability, computation time requirements, threshold phase error between realizable channel phase and ideal constellation point phase, and so forth, pattern searching may be utilized to allow scaling of the size of an antenna array (e.g., increasing the number of antennas N of the antenna array), reduction of computation load, and so forth while determining phase states of the antennas of the antenna array appropriate for a predetermined beam direction and a constellation point(s) of a predetermined digital modulation scheme. In an aspect, a direction may be referred to as an angle of departure (AODs) or simply an angle. In some aspects, dithering (e.g., phase dithering) may be applied to the antennas. In some cases, the dithering may be applied to facilitate pattern searching in relation to certain beam directions, as further described herein.

[0101] FIG. 15 illustrates a flow diagram of an example process 1300 for performing pattern searching to determine phase states (e.g., channel phases) of antennas of an antenna array based on constellation points of a predetermined digital modulation scheme in accordance with one or more embodiments of the present disclosure. The digital modulation scheme may be M-ary PSK (e.g., PSK, 16-PSK) or M-ary QAM. In operation 1505, first sets of phase values (e.g., also referred to as phase states) are determined based on a predetermined beam direction. The predetermined beam direction may be denoted as θincident. In an aspect, a predetermined beam direction may also be referred to as a desired beam direction or a pre-selected beam direction. Each set of phase values may be a digital sequence of phase values. Each phase value may be applied to an antenna element (e.g.. phase shift applied to a signal associated with an antenna element) of an antenna array. For example, for an antenna array with Nchan antenna elements, each set of phase values may include M / wn phase values (e.g., one phase value per antenna element).Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0102] The number of sets of phase values may be based on a search resolution parameter L (e.g., also referred to as a resolution parameter). The resolution parameter L is generally application dependent (e.g., computational time / resources, performance desires / requirements, etc.). A higher resolution parameter £ generally facilitates identification of phase states that better approximate the ideal phase states associated with the constellation points of the digital modulation scheme. In some cases, the resolution parameter £ is a positive integer and each set of phase values may be associated with a respective resolution index (e.g., also referred to as a resolution identifier). In such cases, the first sets of phase values may include a zeroth set of phase values, a first set of phase values, a second set of phase values, and so forth up to an (L-1)thset of phase values. It is noted that the index / identifier associated with each set of phase states may be arbitrary and utilized for convenience for referring to any particular set of phase states and / or in association with processing of any particular set of phase states. In some cases, a phase value of an lthset of phase value and an nthantenna element may be represented as θideal(l, n) as further described herein, where / may be any non-negative integer value between 0 and L - 1, inclusive, and n may be any non-negative integer value between 0 and Nchan - 1, inclusive. In some cases, a value may be determined / selected empirically for the resolution parameter £. In some cases, different values of resolution parameters may be utilized for different predetermined directions and / or antenna systems of different number Nchan of antenna elements.

[0103] In operation 1510, second sets of phase values are determined based on the first sets of phase values and a phase control parameter. Each first set of phase values may be processed to obtain a corresponding one of the second sets of phase values. In some cases, operation 1510 may include rounding the first sets of phase values according to the phase control parameter defining a phase space to obtain the second sets of phase values within the phase space defined by the phase control parameter. In an aspect, the phase control parameter may indicate a number of bits for implementing phase control associated with the antenna array and / or may indicate a phase space (e g., possible phase states) of each antenna element of the antenna array. In this regard, each phase value of each of the second sets of phase values may provide a closest (e.g., best fit) phase value to the corresponding phase value of the corresponding first set of phase value that may be represented according to the phase control parameter.

[0104] In some embodiments, each phase value of each set is formed of 2-bit control signals for 2-bit phase control. In such embodiments, the phase control parameter may haveDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTa value indicating that the phase control is based on 2-bit control signals. As an example, the 2-bit control signals may be indicative of a phase shift of 0°, 90°, 180°. or 270°. Each phase value of the second set of phase values is one of 0°, 90°, 180°, or 270°. For each index I and n, the closest (e.g., best fit) 2-bit phase to the corresponding phase value θideal(l, n) of the first set of phase values may be determined to obtain a corresponding phasevaluen) of the second set of phase values. As an example, each 2-bit phase may be mapped / decoded to 0°, 90°, 180°, or 270° according to table 320. In some cases, each second set of phase values may be, may be indicative of, and / or may be referred to as a digital sequence. In some cases, θideal(l, n) and θ2bit(l, n) for between 0 and / . - 1, inclusive, and n between 0 and Nchan - I, inclusive, may each be represented as an array ofZ rows and Nchan columns. For example, θ2bit(3, n) may be considered a digital sequence (formed of 2-bits per antenna element) associated with the resolution index l = 3 and corresponding to θideal(3, n), where each of the n = 0,..., Nchan - 1 antenna elements (e.g., associated with and / or referred to as channels) is associated with 2-bits of the digital sequence θ2bit(3, n).

[0105] In operation 1515, gain values (e.g., complex gain values) are determined based on the second sets of phase values and the predetermined direction. Each gain value is associated with a respective resolution index / and may be denoted as Gi. In some cases, a given gain value Gi may be based on a sum of exponential functions, as further described herein. The exponential function may be based on the predetermined direction and the phase values of the second sets of phase values associated with the lthindex. In the example of 2-bit phase control, the phase values of the second sets of phase values associated with the lthindex may be denoted as θ2bit(l, n)

[0106] In operation 1520, a respective resolution index 7 is determined for each constellation point (e.g., also referred to as phase constellation point) of the digital modulation scheme based on the gain values. The digital modulation scheme may include M phase constellation points, with each constellation point having a phase. In some cases, the phase of an mthconstellation point of a digital modulation scheme having AT constellation 360°points may be provided by [im=As such, operation 1520 provides M indices (e g., one index for each of the M constellation points). As an example, the digital modulation scheme 8-PSK has M= 8 phase states with phases 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315° for m = 0. 1, 2, 3. 4, 5, 6, and 7, respectively.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0107] In operation 1520, for a given constellation point m, the resolution index I associated with a phase of the gain value Gi that is closest to the phase of the constellation point may be determined / identified. This resolution index / for which the phase of the gain value Gi is determined to be closest to the phase of the constellation point may be denoted as Imin(m). In an aspect, a difference between the phase of the gain value Gi and the phase of the constellation point may be referred to as a phase constellation error. The phase of the gain value Gi may be denoted as 6’(. In some cases, the resolution index I may be determined by finding the resolution index / that minimizes a function that relates the phasewith the phase pmof the constellation point. In some cases, the phases of the gain values Gi determined in operation 1515 may be referred to as the available phases (e.g., possible phases, accessible phases) based ultimately on the first sets of phase values defined in operation 1505 for the pattern searching.

[0108] In operation 1525, channel phase (e.g., phase values / shifts) for each antenna element are determined for each constellation point of the digital modulation scheme based on the respective resolution index associated with the constellation point. In this regard, for an mthconstellation point, the channel phase for the antenna elements may be provided by θ2bit(Imin(m), n) hi this regard, for an m- constellation point, operations 1520 and 1525 collectively identify, from among the second set of phase values obtained in operation 1510, a set of phase values (e.g., a digital sequence) θ2bit(Imin(m), n) that best approximate the constellation point m. In some aspects, the digital sequences θ2bit(Imin(m), n) may be stored in a memory. In some aspects, phase dithering (e.g., also referred to simply as dithering) may be applied to at least a subset of the antennas. As further described herein, phase dithering may be applied for certain AODs that have a non-ideal (e.g., sparse, limited) phase state population. Furthermore, although the process 1300 of FIG. 15 determines an index (and associated channel phases) for each of the Al constellation points of the desired digital modulation scheme, in some aspects an index (and associated channel phases) may be determined for fewer than all of the Al constellation points.

[0109] In some aspects, the channel phases (e.g., which form digital sequences) associated with various directions and constellation points of various digital modulation schemes may be determined (e.g., by using one or more logic devices, such as in the host control circuitry 110 of FIG. 1, to perform the process 1300) and stored for later use. With the channel phases stored in a memory (e.g., the memory 122 of FIG. 1), when a beam is desired to be transmitted in the predetermined direction and using the predetermined digital modulationDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTscheme, the predetermined / precomputed channel phases digital sequences may be retrieved from the memory’ and provided (e.g., to phase shifters 542a-n of FIG. 5) for phase control of the antenna array (e.g., the antenna elements 546a-n). The antenna array may be configured to transmit in the predetermined direction according to the predetermined digital modulation scheme (e.g., one or more constellation points thereof) based on using the appropriate digital codes / sequences stored in memory.

[0110] Using various embodiments, these channel phases determined from the pattern searching integrates modulation with beamforming and allow phase modulation across the antenna array and beamforming accuracy. In an aspect, a resolution parameter associated with higher search resolution is generally associated with higher performance characteristics (e.g., associated with modulation functionality and / or beamforming functionality). The resolution parameter is generally selected based on application (e.g., associated computational costs, performance thresholds and / or requirements, etc.). In some aspects, dithering (e.g., phase dithering) may be applied to at least a subset of the antennas, as further described herein. The dithering may include a respective phase offset applied to each antenna element of the subset of antenna elements. In some cases, the channel phases that are stored may already incorporate any applied dithering. In other cases, the channel phases and the dithering (e.g., the phase offsets) may be separately stored and combined together when needed.[OHl] FIG. 16 illustrates a flow diagram of an example process 1600 for performing pattern searching to determine phase states (e.g., channel phases) of antennas of an antenna array based on constellation points of a predetermined digital modulation scheme in accordance with embodiments of the present disclosure. The description of the process 1300 of FIG. 15 generally applies to the process 1600 of FIG. 16, with various notation provided with reference to the process 1300 also applying to the process 1600, and vice versa. In some embodiments, the process 1600 may provide example equations that may facilitate implementation of the process 1300 of FIG. 15 for a case when a phase control parameter indicates 2-bit phase control.

[0112] For the pattern searching, the resolution parameter L may be selected (e.g., dependent on application). The antenna array may have Nchan antenna elements. The patterning searching may start in operations 1605 and 1610 by defining an array θideal(l, n) of L rows and Nchan columns for a given AOD (e.g., also referred to as a direction) 6 incident-In some cases, operations 1605 and 1610 may collectively be, may collectively include, orDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTmay collectively be a part of operation 1505. In operation 1605, 0° to 360° is divided according to the resolution parameter L for every channel Nchan. The resolution parameter L defines the search resolution. A higher resolution parameter is generally associated with a higher phase state population, which may facilitate minimizing phase constellation error. In operation 1610, the predetermined direction is defined. Accordingly, in operations 1605 and 1610, the array θideal(l, n) may be constructed as follows:360°θideal(l, n) = (360° / L · l + 2π sin(θincident) · n)where l = 0, 1, ..., L-1 and n = 0, 1, ..., Nchan - 1.

[0113] In operation 1615, for each index I and n, a closest (e.g.. best fit) 2-bit phase to the phase θideal(l, n) may be determined, which results in an array of 2-bit phase values θ2bit(l, n). In this regard, each phase value that forms the array θideal(l, n) may be converted to a corresponding phase value within the 2-bit phase domain [0°, 90°, 180°, 270°] available in 2-bit phase control to obtain each phase value θ2bit(l, n). The array θ2bit(l, n) may be stored (e.g., as a lookup table) for use in subsequent look up of these 2-bit phase values based, for example, on the index I. In some cases, operation 1615 may involve a rounding function applied to each phase value θideal(l, n). For example, as shown in FIG.16, the rounding function may round a phase value θideal(l, n) to one of 0°, 90°, 180°. or 270°. In this example, the phase values θ2bit(l, n) may be one of 0°, 90°, 180°, or 270°. As an example, each 2-bit phase may be mapped to 0°, 90°, 180°, or 270° according to table 320. In some cases, operation 1615 may be, may include, or may be a part of operation 1510.

[0114] From θ2bit(l, n) and a known gain alignment correction for the direction ^incidentacomplex gain array G may be constructed in operations 1620, 1625, and 1630:Nchan 1_ 1 X \ — ’ ‘Ti'sin(— 0 incident?)CmNchanIn some cases, operation 1620 may represent a receiver that removes phase applied in operation 1610. In operation 1625, the arrayn) is provided in a complex exponential function to result in an array having array elements yt n. In operation 1630, the complex exponential functions are then summed.

[0115] In operation 1635, phases associated with constellation points of the predetermined 360°digital modulation scheme may be determined by βm= m -, where M is the number ofDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTphase constellation points and m = 0, 1,..., M - 1. For example, a 16-PSK modulation scheme has M= 16 phase constellation points. The constellation points have phases of 0°.22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, 180°, 202.5°, 225°, 247.5°, 270°, 292.5°, 315°, and 337.5° for index m = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15, respectively.

[0116] In operation 1640, for each constellation point of the predetermined digital modulation scheme, a resolution index I that is associated w ith a gain value Gi closest in phase to the phase of the constellation point is determined. In this regard, the phases of the gain values Gl, denoted asprovide the phases that are available in the pattern searching based on the array θideal(l, n) and the associated array θ2bit(l, n) defined in operations 1610 and 1615 to provide the basis for the pattern searching. For a given constellation point m, the index I associated with the gain value Gi closest in phase to the phase of the constellation point m may be denoted as / inin(m). This index Imin(m) may be provided by:Imin(m) = minI e^Gl I

[0117] This equation finds the index l that minimizes the function 1 - |ejβ_m / Gl|. Forexample, whenis substantially equal to βm,is substantially equal to 1 and thus I eJzGq1 — is substantially equal to 0.

[0118] In operation 1645, for each constellation point m of the predetermined digital modulation scheme and for each antenna element n of the antenna array, a channel phase (e.g., also referred to simply as a phase value) is determined based on the indexIn some aspects, the channel phases associated with the constellation point m may be provided by:channel_phase(m, n) = θ2bit(Imin(m), n)In this regard, the channel phases associated with the constellation point m is associated with one row of the array θ2bit(l, n) output from operation 1615. Each channel phase is 2 -bits and indicates to (e.g., can be decoded by) a phase shifter (e.g., one of phase shifters 542a-n of FIG. 5) the phase shift (e.g., one of 0°, 90°, 180°, or 270°) to be applied to a signal output by a corresponding antenna element (e.g., one of the antenna elements 546a-n of FIG. 5). In some cases, the θ2bit(l, n) may be stored as a lookup table whose contents may be accessed / retrieved based on a resolution index I and an antenna index n. Although theDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTprocess 1600 of FIG. 16 does not include dithering, dithering may be applied to at least a subset of the antennas, as further described herein.

[0119] FIGS. 17A and 17B illustrate example plots showing realizable / available channel phase state and realizable / available channel gain state, respectively, for a phase sweep search space implemented by pattern searching in accordance with one or more embodiments of the present disclosure. In some aspects, the pattern searching may be implemented using a process such as and / or similar to the process 1300 of FIG. 15 and / or the process 1600 of FIG.16. In FIGS. 17A and 17B, the pattern searching is for the direction of 40° and the digital modulation scheme 16-PSK, and involves 2-bit phase control of Vcto = 32 channels (e.g., associated with 32 antenna elements). With the 2-bit phase control, each antenna element is associated with a phase shift selected from a 2-bit phase space (0°, 90°, 180°, 270°). For 16-PSK, the constellation points have phases of 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, 180°. 202.5°. 225°, 247.5°, 270°, 292.5°, 315°, and 337.5°. The horizontal axis of FIGS. 17A and 17B provides the phase sweep search space in degrees. The vertical axis of FIGS. 17A and 17B provides the realizable 2-bit array phase and the realizable 2-bit array gain, respectively. In FIG. 17A. a curve 1705 illustrates all realizable / available (e.g., also referred to as accessible and / or possible) phase states in the search space and circles in the plot show a 2-bit array phase among the realizable / available phase states that is a best fit for a constellation point of 16-PSK. The curve 1705 shows a stair case pattern. In FIG. 17B, a curve 1710 illustrate all realizable / available (e.g., also referred to as accessible and / or possible) gain states in the search space and circles in the plot show a best fit for a constellation point of 16-PSK.

[0120] As shown in FIG. 17A, a resolution parameter L associated with the pattern searching is sufficiently large such that the 2-bit phase control of the 32 channels allows for best fit channel phase states close to the constellation phases of 16-PSK. For example, with reference to FIGS. 15 and 16, each row of the array 0tdeai(J->n) (which has L rows and Nchan columns) is offset by a fractional phase amount to provide a sufficiently fine population sampling that results in sufficient phase constellation representation, thus resulting in the stair case pattern. Through 2-bit phase control in accordance with one or more embodiments, a 2-bit channel phase system which exhibits nonlinear behavior is utilized to represent constellation point phases of digital modulation schemes. The resolution parameter L is set dependent on application and is based on available computational costs / resources, desiredDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTand / or required performance characteristics (e.g., for modulation and / or beamforming functionality), and so forth.

[0121] In some aspects, the array size of 9ideail,n) may be based on needing to ensure an adequate solution space for the AOD-specific gam alignment phase raster. Gaps may result in coverage (e.g., possible phase states along the vertical axis of FIG. 17A) if the resolution parameter L is set to too small a value, as population is under sampled and may cause poor alignment to a desired phase constellation(s). The resolution parameter L and / or the number of channels Nchan may be empirically determined. As a non-limiting empirically determined example range, the resolution parameter / . (e.g., number of rows of the array 9(1, n)) may be between around 1,500 and around 8,000 to provide an adequate solution space for most AODs.

[0122] FIGS. 18A and 18B illustrate example plots showing realizable / available channel phase state and realizable / available channel gain state, respectively, for a phase sweep search space implemented by pattern searching when a resolution parameter is too small. The description of FIGS. 17A and 17B generally apply to FIGS. 18A and 18B, with examples of differences and other description provided herein. As in FIGS. 17A and 17B, the pattern searching associated with FIGS. 18A and 18B is for the direction of 40° and the digital modulation scheme 16-PSK. and involves 2-bit phase control of 32 channels (e.g., associated with 32 antenna elements). However, the resolution parameter associated with FIGS. 18A and 18B is lower than the resolution parameter associated with FIGS. 17A and 17B. In FIG.18A, circles show a 2-bit array phase among the realizable / available phase states that is a best fit for a constellation point of 16-PSK. As shown in FIG. 18 A, some of the constellation points of 16-PSK are not close to the realizable 2-bit array phases. As such, the resolution parameter and / or the number of channels may need to be increased in order to allow modulation and beamforming in the desired direction. In some cases, the channel phases (e.g., digital sequences) determined by the pattern searching associated with FIGS. 18A and 18B might not be stored, as better pattern searching results may be obtained by adjusting the resolution parameter and / or the antenna array (e.g., to increase the number of antenna elements). In this regard, pattern searching for any given AOD and / or digital modulation scheme may be an iterative process involving adjusting a resolution parameter and / or adjusting / redesigning an antenna array (e.g., to change the number of antenna elements and / or other antenna element and / or antenna array properties).Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0123] FIG. 19A illustrates an example result of pattern searching in accordance with one or more embodiments of the present disclosure. The pattern search result illustrates a cumulative phase at electrical boresight for a direction of 42°, 16-PSK scheme, and 12 channel antenna system. A gain is shown by a distance toward an outer circumference of the unit circle. FIG. 19B illustrates an example plot showing a phase error relative to 16-PSK symbols (e.g., 16-PSK constellation points) for the pattern searching associated with the result shown in FIG. 19A in accordance with one or more embodiments of the present disclosure. FIG. 19C illustrates an example plot showing a gain for each of the 16-PSK symbols for the pattern searching associated with the result shown in FIG. 19A in accordance with one or more embodiments of the present disclosure. In some aspects, the constellation phase error shown in FIG. 19B may be sufficiently small such that the channel phases determined from the pattern searching may be stored for future use in transmitting a beam in the 42° direction. In FIGS. 19B and 19C, PSK symbols 1, 2, 3,..., 15, and 16 may represent the constellation points with phases of 0°, 22.5°, 45°,..., 315°, and 337.5°, respectively.

[0124] FIG. 20 illustrates an example plot showing results of pattern searching in accordance with one or more embodiments of the present disclosure. In some aspects, the pattern searching may be implemented using a process such as and / or similar to the process 1300 of FIG. 15 and / or the process 1600 of FIG. 16. In FIG. 20, the pattern searching is for the direction of 42° and the digital modulation scheme 16-PSK, and involves 2-bit phase control of 128 channels (e.g., associated with 128 antenna elements). The plot shows a curve 2005 and a curve 2010 that illustrates a constellation phase error and a constellation gain error, respectively, relative to each 16-PSK symbol. In FIG. 20, PSK symbols 1, 2, 3,..., 15, and 16 may represent the constellation points with phases of 0°, 22.5°, 45°,..., 315°, and 337.5°, respectively. As shown in FIG. 20, the higher number of channels may allow7for lower phase error and gain error.

[0125] In some embodiments, phase dithering (e.g., also referred to simply as dithering) may be applied to at least a subset of the antennas. Phase dithering may be applied for certain AODs that have a non-ideal (e.g., sparse, limited) phase state population. The dithering may include a respective phase offset applied to each antenna element of the subset of antenna elements. In some cases, the dithering may be applied to facilitate pattern searching in relation to certain beam directions.

[0126] As a non-limiting example, for an antenna array with eight antenna elements, each antenna element may have a different, static phase offset applied. In this example, a zeroth,Docket No. 61658.154WO01 Client Ref. No. PER-577-PCTfirst, second, third, fourth, fifth, sixth, and seventh antenna may have a phase offset of 0°, 7°, 13°, 23°, 37°, 43°, 67°, and 83° applied. For this example, the zeroth antenna element has a 0° phase offset applied and thus has a 2-bit phase space of [0°, 90°, 180°, 270°], the first antenna element has a 7° phase offset applied and thus has a 2-bit phase space of [7°, 97°, 187°, 277°], the seventh antenna element has a 83° phase offset applied and thus has a 2-bit phase space of [83°, 173°, 263°, 353°], and so forth. Although in this example each antenna element has a different phase offset applied, in other implementations one or more antenna elements may have the same phase offset (e.g., including 0° offset) applied. In some cases, the phase offsets utilized in the dithering may generally be determined empirically and / or iteratively adjusted as appropriate to handle a given AOD.

[0127] In some aspects, a determination may be made as to whether to include dithering based on a phase state population associated with a desired AOD. In some cases, the phase state population may be determined as part of performing the process 1300 and / or the process 1600. If the phase state population is determined to be non-ideal (e.g., sparse) for a given AOD, the determination may be made that dithering should be performed to mitigate (e.g., allow better phase state population of) the non-ideal phase state population associated with the AOD.

[0128] FIG. 21A illustrates a phase population of all possible combinations (e.g., 4N) associated with 2-bit phase control of an antenna array with N antenna elements in a direction of 0° and a 16-PSK digital modulation scheme with no phase dithering implemented in accordance with one or more embodiments of the present disclosure. As show n in FIG. 21 A, the phase population of 4Ncollapses into a sparse checkerboard square in the population complex space. In this regard, while the population of all possible combinations generally allow s a reasonable intersection of a desired beam direction and desired constellation states, at certain AODs this population of the constellation space has limited state choices and thus generally results in larger phase and amplitude errors. In some cases, such AODs may be associated with channel phase periodicity. To break this cyclic nature across channel, dithering may be performed to add in certain static phase offset to each channel.

[0129] FIG. 21B illustrates a phase population of all possible combinations (e.g.. 4N) associated with 2-bit phase control of an antenna array with N antenna elements in a direction of 0° and a 16-PSK digital modulation scheme with phase dithering implemented in accordance with one or more embodiments of the present disclosure. In this regard, FIG. 21 B may differ from FIG. 21 A only in that phase dithering is applied to obtain the results of FIG.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT21B. By contrast to FIG. 21A, FIG. 21B shows that the phase dithering implemented through adding in certain static phase offsets to each channel may provide a more desirable phase state population for the direction of 0°. Although FIGS. 21 A and 21B are described in relation to finding all possible 4Ncombinations, dithering may be applied to phase values utilized during the pattern searching of the process 1300 of FIG. 15 and / or the process 1600 of FIG. 16.

[0130] Further aspects of the present disclosure include the following:

[0131] Aspect 1 includes a method includes determining a first plurality of sets of phase values based on a predetermined direction. Each set of phase values is associated with a respective resolution index of a plurality of resolution indices. Each set of phase values includes a respective phase value for each antenna element of a plurality of antenna elements of an antenna array. The method further includes determining a second plurality of sets of phase values based on the first plurality of sets of phase values and a phase control parameter. The method further includes determining a plurality of gain values based on the second plurality of sets of phase values and the predetermined direction. The method further includes, for each constellation point of a digital modulation scheme, determining a respective resolution index of the plurality of resolution indices based on the plurality of gain values. The method further includes, for each constellation point of the digital modulation scheme, determining a channel phase for each antenna element of the plurality of antenna elements based on the respective resolution index for the constellation point.

[0132] Aspect 2 includes the method of aspect 1, wherein the phase control parameter is indicative of 2 -bit phase control.

[0133] Aspect 3 includes the method of any of aspects 1 and 2, wherein each phase value of the second plurality of sets of phase values is one of 0, 90°, 180°, and 270°.

[0134] Aspect 4 includes the method of any of aspects 1-3, wherein the determining the second plurality of sets of phase values comprises rounding the first plurality of sets of phase values based on the phase control parameter.

[0135] Aspect 5 includes the method of any of aspects 1-4, further comprising transmitting, by the antenna array, a signal in the predetermined direction based on the channel phases associated with one of the constellation points of the digital modulation scheme.Docket No. 61658.154WO01 Client Ref. No. PER-577-PCT

[0136] Aspect 6 includes the method of any of aspects 1-5, wherein the digital modulation scheme is an M-ary phase-shift-keying or an M-ary quadrature amplitude modulation.

[0137] Aspect 7 includes the method of any of aspects 1-6, wherein each of the plurality of gain values is associated with a respective one of the plurality of resolution indices.

[0138] Aspect 8 includes the method of any of aspects 1-7, wherein, for each constellation point, the determining the respective resolution index is based on a phase of each of the plurality of gain values and a phase associated with the constellation point.

[0139] Aspect 9 includes the method of any of aspects 1-8, further comprising applying dithering to at least a subset of the plurality of antenna elements, wherein the second plurality of sets of phase values is further based on the applying.

[0140] Aspect 10 includes the method of aspect 9, wherein the applying the dithering comprises applying a respective phase offset to each antenna element of the subset of antenna channels.

[0141] Aspect 11 includes the method of any of aspects 9 or 10, further comprising determining whether to apply the dithering based on the predetermined direction, wherein the applying is performed in response to determining to apply the dithering.

[0142] Aspect 12 includes a system includes a radio frequency (RF) front end circuit coupled to an antenna array including a plurality of antenna elements. The RF front end circuit includes a plurality of channels, where each channel includes channel circuitry configured to adjust a phase of an RF signal for output to a corresponding antenna element of the plurality of antenna elements. The system further includes control circuitry configured to control the channel circuitry corresponding to each channel. The control circuitry is configured to control the channel circuitry by determining a first plurality' of sets of phase values based on a predetermined direction, where each set of phase values is associated with a respective resolution index of a plurality of resolution indices and each set of phase values includes a respective phase value for each antenna element of the plurality of antenna elements. The control circuitry is configured to control the channel circuitry further by determining a second plurality of set of phase values based on the first plurality of sets of phase values and a phase control parameter. The control circuitry’ is configured to control the channel circuitry further by determining a plurality of gain values based on the second plurality of sets of phase values and the predetermined direction. The control circuitry' is configured to control the channel circuitry further by, for each constellation point of a digitalDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTmodulation scheme, determining a respective resolution index of the plurality- of resolution indices based on the plurality’ of gain values and determining a channel phase for each antenna element of the plurality of antenna elements based on the respective resolution index for the constellation point..

[0143] Aspect 13 includes the system of aspect 12, wherein the phase control parameter is indicative of 2 -bit phase control.

[0144] Aspect 14 includes the system of any of aspects 12 or 13, wherein each phase value of the second plurality of sets of phase values is one of 0, 90°, 180°, and 270.

[0145] Aspect 15 includes the system of any of aspects 12-14, wherein the determining the second plurality of sets of phase values comprises rounding the first plurality of sets of phase values based on the phase control parameter.

[0146] Aspect 16 includes the system of any of aspects 12-15, further comprising the antenna array, wherein the antenna array is configured to transmit a signal in the predetermined direction based on the channel phases associated with one of the constellation points of the digital modulation scheme.

[0147] Aspect 17 includes the system of any of aspects 12-16, wherein the digital modulation scheme is M-ary phase-shift-keying or an M-ary quadrature amplitude modulation.

[0148] Aspect 18 includes the system of any of aspects 12-17, wherein each of the plurality of gain values is associated with a respective one of the plurality of resolution indices.

[0149] Aspect 19 includes the system of any of aspects 12-18, wherein the determining the respective resolution index is based on a phase of each of the plurality of gain values.

[0150] Aspect 20 includes the system of any of aspects 12-19, wherein the control circuitry is configured to control the channel circuitry corresponding to each channel further by applying dithering to at least a subset of the plurality of antenna elements, wherein the second plurality of sets of phase values is further based on the applying.

[0151] Aspect 21 includes the system of aspect 20, wherein the applying the dithering comprises applying a respective phase offset to each antenna element of the subset of antenna elements.

[0152] Aspect 22 includes the system of any of aspects 20 or 21, wherein the control circuitry is configured to control the channel circuitry corresponding to each channel furtherDocket No. 61658.154WO01 Client Ref. No. PER-577-PCTby determining whether to apply the dithering based on the predetermined direction, wherein the applying is performed in response to determining to apply the dithering.

[0153] Aspect 23 includes the system of any of aspects 1-22, wherein the channel circuitry comprises a phase shifter configured adjust the phase of the RF signal in response to a 2-bit control signal received from the control circuitry to obtain a phase-shifted RF signal.

[0154] Aspect 24 includes the system of any of aspects 1-23, wherein the 2-bit control signal is associated with one of the channel phases for the plurality of antenna elements.

[0155] Aspect 25 includes the system of aspect 23, wherein the channel circuitry further comprises: a multiplier circuit configured to receive the RF signal and generate an output RF signal at a predetermined frequency; and wherein the phase shifter is configured to receive the output RF signal from the multiplier circuit and adjust the phase of the output RF signal to obtain the phase-shifted RF signal.

[0156] Aspect 26 includes the system of any of aspects 23 or 25, wherein the channel circuitry further comprises a power amplifier configured to amplify the phase-shifted RF signal for transmission through the corresponding antenna element.

[0157] Aspect 27 includes the system of any of aspects 23, 25, or 26, wherein the channel circuitry further includes modulation circuitry' configured to convert digital sequences to RF phase states associated with the channel phases.

[0158] Aspect 28 includes the system of any of aspects 1-27, wherein the control circuitry comprises a memory configured to store data indicative of the channel phases for controlling phase adjustment of the RF signal in each channel.

[0159] The detailed description set forth above is intended as a description of various configurations of the subject technology and is not intended to represent the only configurations in which the subject technology can be practiced. The appended drawings are incorporated herein and constitute a part of the detailed description. The detailed description includes specific details for the purpose of providing a thorough understanding of the subject technology. However, it will be clear and apparent to those skilled in the art that the subject technology7is not limited to the specific details set forth herein and may be practiced using various embodiments.

[0160] Where applicable, various embodiments provided by the present disclosure can be implemented using hardware, software, or combinations of hardware and software. Also,Docket No. 61658.154WO01 Client Ref. No. PER-577-PCTwhere applicable, the various hardware components and / or software components set forth herein can be combined into composite components comprising software, hardware, and / or both without departing from the spirit of the present disclosure. Where applicable, the various hardware components and / or software components set forth herein can be separated into sub-components comprising softw are, hardware, or both without departing from the spirit of the present disclosure. In addition, where applicable, it is contemplated that software components can be implemented as hardware components, and vice-versa.

[0161] Software in accordance with the present disclosure, such as non-transitory- instructions, program code, and / or data, can be stored on one or more non-transitory machine-readable mediums. It is also contemplated that software identified herein can be implemented using one or more general purpose or specific purpose computers and / or computer systems, networked and / or otherwise. Where applicable, the ordering of various steps described herein can be changed, combined into composite steps, and / or separated into sub-steps to provide features described herein.

[0162] Embodiments described above illustrate but do not limit the present disclosure. It should also be understood that numerous modifications and variations are possible in accordance with the principles of the present disclosure. Accordingly, the scope of the invention is defined only by the following claims.

Claims

Docket No 61658154WO01 Client Ref No PER-577-PCTCLA1MSWhat is claimed is:

1. A method comprising:determining a first plurality of sets of phase values based on a predetermined direction, wherein each set of phase values is associated with a respective resolution index of a plurality of resolution indices, and wherein each set of phase values comprises a respective phase value for each antenna element of a plurality of antenna elements of an antenna array;determining a second plurality of sets of phase values based on the first plurality of sets of phase values and a phase control parameter;determining a plurality of gain values based on the second plurality of sets of phase values and the predetermined direction;for each constellation point of a digital modulation scheme, determining a respective resolution index of the plurality of resolution indices based on the plurality of gain values; and for each constellation point of the digital modulation scheme, determining a channel phase for each antenna element of the plurality of antenna elements based on the respective resolution index for the constellation point.

2. The method of claim 1, wherein the phase control parameter is indicative of 2-bit phase control.

3. The method of claim 2, wherein each phase value of the second plurality of sets of phase values is one of 0, 90°, 180°, and 270°.

4. The method of claim 1, wherein the determining the second plurality of sets of phase values comprises rounding the first plurality of sets of phase values based on the phase control parameter.

5. The method of claim 1, further comprising transmitting, by the antenna array, a signal in the predetermined direction based on the channel phases associated with one of the constellation points of the digital modulation scheme.Docket No 61658154WO01 Client Ref No PER-577-PCT6. The method of claim 1, wherein the digital modulation scheme is an M-ary phaseshift-keying or an M-ary quadrature amplitude modulation.

7. The method of claim 1, wherein each of the plurality of gain values is associated with a respective one of the plurality of resolution indices.

8. The method of claim 7, wherein, for each constellation point, the determining the respective resolution index is based on a phase of each of the plurality of gain values and a phase associated with the constellation point.

9. The method of claim 1, further comprising applying dithering to at least a subset of the plurality of antenna elements, wherein the second plurality of sets of phase values is further based on the applying.

10. The method of claim 9, wherein the applying the dithering comprises applying a respective phase offset to each antenna element of the subset of antenna channels.

11. The method of claim 9, further comprising determining whether to apply the dithering based on the predetermined direction, wherein the applying is performed in response to determining to apply the dithering.

12. A system comprising:a radio frequency (RF) front end circuit coupled to an antenna array comprising a plurality of antenna elements, wherein the RF front end circuit comprising a plurality of channels, wherein each channel comprises channel circuitry configured to adjust a phase of an RF signal for output to a corresponding antenna element of the plurality of antenna elements; and control circuitry configured to control the channel circuitry corresponding to each channel by:determining a first plurality of sets of phase values based on a predetermined direction, wherein each set of phase values is associated with a respective resolution index of a plurality of resolution indices, and wherein each set of phase values comprises a respective phase value for each antenna element of the plurality of antenna elements;Docket No 61658154WO01 Client Ref No PER-577-PCTdetermining a second plurality of set of phase values based on the first plurality of sets of phase values and a phase control parameter;determining a plurality of gain values based on the second plurality of sets of phase values and the predetermined direction;for each constellation point of a digital modulation scheme, determining a respective resolution index of the plurality of resolution indices based on the plurality’ of gain values; andfor each constellation point of the digital modulation scheme, determining a channel phase for each antenna element of the plurality of antenna elements based on the respective resolution index for the constellation point.

13. The system of claim 12, wherein the phase control parameter is indicative of 2-bit phase control.

14. The system of claim 13, wherein each phase value of the second plurality of sets of phase values is one of 0, 90°, 180°, and 270°.

15. The system of claim 12, wherein the determining the second plurality of sets of phase values comprises rounding the first plurality of sets of phase values based on the phase control parameter.

16. The system of claim 12, further comprising the antenna array, wherein the antenna array is configured to transmit a signal in the predetermined direction based on the channel phases associated with one of the constellation points of the digital modulation scheme.

17. The system of claim 12, wherein the digital modulation scheme is M-ary phase-shift-keying or an M-ary quadrature amplitude modulation.

18. The system of claim 12, wherein each of the plurality of gain values is associated with a respective one of the plurality of resolution indices.

19. The system of claim 12, wherein the determining the respective resolution index is based on a phase of each of the plurality of gain values.Docket No 61658154WO01 Client Ref No PER-577-PCT20. The system of claim 12, wherein the control circuitry is configured to control the channel circuitry corresponding to each channel further by applying dithering to at least a subset of the plurality of antenna elements, wherein the second plurality of sets of phase values is further based on the applying.

21. The system of claim 20, wherein the applying the dithering comprises applying a respective phase offset to each antenna element of the subset of antenna elements.

22. The system of claim 21, wherein the control circuitry is configured to control the channel circuitry corresponding to each channel further by determining whether to apply the dithering based on the predetermined direction, wherein the applying is performed in response to determining to apply the dithering.

23. The system of claim 12, wherein the channel circuitry comprises:a phase shifter configured adjust the phase of the RF signal in response to a 2-bit control signal received from the control circuitry to obtain a phase-shifted RF signal.

24. The system of claim 23, wherein the 2-bit control signal is associated with one of the channel phases for the plurality of antenna elements.

25. The system of claim 23, wherein the channel circuitry further comprises:a multiplier circuit configured to receive the RF signal and generate an output RF signal at a predetermined frequency; andwherein the phase shifter is configured to receive the output RF signal from the multiplier circuit and adjust the phase of the output RF signal to obtain the phase-shifted RF signal.

26. The system of claim 23, wherein the channel circuitry further comprises a power amplifier configured to amplify the phase-shifted RF signal for transmission through the corresponding antenna element.Docket No 61658154WO01 Client Ref No PER-577-PCT27. The system of claim 23, wherein the channel circuitry further includes modulation circuitry configured to convert digital sequences to RF phase states associated with the channel phases.

28. The system of claim 12, wherein the control circuitry comprises a memory configured to store data indicative of the channel phases for controlling phase adjustment of the RF signal in each channel.

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