Communication device for beamforming in a communication system

Abstract

The invention relates to a communication device (100) for a communication system (500). The communication device (100) comprises a set of antenna elements (120) disposed in an antenna aperture (130), which may also be represented as a monolithic surface. The communication device (100) determines a transformation matrix based on a coupling matrix, the coupling matrix comprising a coupling coefficient between each antenna element in the set of antenna elements (120). A second beamforming matrix is obtained by multiplying the transformation matrix with the first beamforming matrix. Based on the second beamforming matrix, the communication device (100) transmits communication signals in a wireless channel over the set of antenna elements (120). An improved beamforming gain is thus provided. The communication device (100) may be a network access node or a client device. The invention further relates to a corresponding method and to a computer program.

Description

Technical Field

[0001] The embodiment of the present invention relates to a communication device for beamforming in a communication system. In addition, the present invention also relates to a corresponding method and a computer program. Background Art

[0002] Massive MIMO technology is one of the key components of 3GPP 5G New Radio (NR), which improves the performance of wireless communication systems compared to previous generations. Nevertheless, in order to meet the high-speed requirements, 6G and beyond technologies are still seeking further improvements. In this technology route, holographic wireless is considered to be the next step in massive MIMO.

[0003] Continuous surfaces are thought to enable holographic wireless links. For example, a simple mathematical model for a line-of-sight (LoS) holographic wireless channel with a continuous surface has been proposed. It is reported that in LoS links, the power gain of this mathematical model is several times dB relative to that of conventional massive MIMO systems. One way to achieve a near-continuous holographic surface is to further densify the conventional antenna array, i.e., by packing more antenna elements (also known as radiating units) in a given aperture of a transmitting antenna array or a receiving antenna array, which in the limit can approximate a continuous surface. Such a dense antenna array is also called a holographic surface. These holographic surfaces can be made of low-cost transformable wireless planar structures composed of sub-wavelength metal or dielectric scattering particles, which are expected to be able to shape electromagnetic waves according to the desired target and fully tap the potential information transfer capabilities of the wireless medium. Summary of the invention

[0004] The purpose of the embodiments of the present invention is to provide a solution to reduce or solve the disadvantages and problems of traditional solutions.

[0005] Another object of an embodiment of the present invention is to provide a beamforming solution to provide a higher gain than a conventional solution.

[0006] The above objects and others are achieved by the subject matter of the independent claims. Further embodiments of the invention are provided in the dependent claims.

[0007] According to a first aspect of the present invention, the above and other objects are achieved by a communication device for a communication system, wherein the communication device comprises a set of antenna elements arranged in an antenna aperture; the communication device is used for:

[0008] Determine a transformation matrix T based on a coupling matrix C, wherein the coupling matrix C includes coupling coefficients between each antenna element in the set of antenna elements;

[0009] Multiplying the transformation matrix T by the first beamforming matrix f1 to obtain a second beamforming matrix f2;

[0010] Based on the second beamforming matrix f2, a communication signal x is transmitted through the set of antenna elements.

[0011] The advantage of the communication device according to the first aspect is that the obtained second beamforming matrix f2 can take into account the spatial relationship between the transmitter and the receiver through the first beamforming matrix f1, and the mutual coupling effect between the antenna elements in the antenna aperture through the transformation matrix T, so that the achievable beamforming gain of the second beamforming matrix f2 can be maximized and is significantly higher than the achievable beamforming gain of the first beamforming matrix f1.

[0012] In an implementation manner of the communication device according to the first aspect, the coupling matrix C is determined based on any one of the following groups, wherein the group includes: the geometry of the antenna aperture, the position of the antenna element in the antenna aperture, the relative position of the antenna element in the antenna aperture, the spacing between the antenna elements in the antenna aperture, and the radiation power pattern of each antenna element.

[0013] The advantage of this implementation is that the determined coupling matrix C can fully characterize the mutual coupling effect between antenna elements in the antenna aperture.

[0014] In an implementation manner of the communication device according to the first aspect, the coupling matrix C is determined based on the following equation:

[0015]

[0016] Wherein, m and n are antenna element indexes, N is the total number of antenna elements in the antenna element set, is the set of all points on a sphere centered at the origin with unit radius, G n (u) is the radiation power pattern of the nth antenna element in direction u, t n is the position of the nth antenna element in the antenna aperture, and λ is the wavelength of the communication signal x.

[0017] The advantage of this implementation is that it provides an explicit solution for calculating the coupling matrix C, which can characterize the mutual coupling effects between antenna elements in the antenna aperture. In the case of an explicit closed-form expression, the coupling matrix C can be calculated by analytically solving the integral to obtain a concise expression. In the general case where it is not integrable, numerical integration can be applied to obtain an explicit expression of the coupling matrix C. In both cases, the coupling matrix C only needs to be calculated (offline) once and can be applied to beamforming design and channel implementation in any communication scenario.

[0018] In an implementation of the communication device according to the first aspect, the transformation matrix T is determined based on a second root of the inverse matrix of the coupling matrix C.

[0019] The advantage of this implementation is that, through the transformation matrix T determined in this way, the obtained second beamforming matrix f2 can achieve the maximum beamforming gain of the antenna array.

[0020] In an implementation of the communication device according to the first aspect, the transformation matrix T is determined based on a subset of K eigenvectors v k , where the eigenvectors v k have corresponding eigenvalues λ k of the coupling matrix C with dimension N×N, where K < N, and N is the total number of antenna elements in the antenna element set.

[0021] The advantage of this implementation is that, through the transformation matrix T determined in this way, the obtained second beamforming matrix f2 can avoid the numerical precision problem when calculating the second root of the inverse matrix of the coupling matrix C. Due to the very small spacing between the antenna elements in the antenna aperture and / or the very large aperture size of the antenna aperture, numerical precision problems will occur when the coupling matrix C is close to a singular matrix and contains eigenvalues close to zero. Therefore, the second root of the reciprocal of these eigenvalues close to zero may be very sensitive to the numerical precision of these eigenvalues close to zero, that is, in the calculation of the coupling matrix C, a very small precision error will cause a very large difference in the result value of the second root of the inverse matrix of the coupling matrix C.

[0022] In an implementation of the communication device according to the first aspect, the transformation matrix T is determined based on the following equation:

[0023]

[0024] where α is a scaling factor, and

[0025] The advantage of this implementation is that, through the transformation matrix T determined in this way, the obtained second beamforming matrix f2 can capture and utilize most of the mutual coupling effects between the antenna elements in the antenna aperture, achieve a beamforming gain significantly greater than the beamforming gain achieved by the first beamforming matrix f1, and an appropriate value of the scaling factor α can be selected to meet the power constraint at the transmitter.

[0026] In an implementation of the communication device according to the first aspect, the K feature vectors v k The subset includes all eigenvectors of the coupling matrix C, and the corresponding eigenvalues ​​λ of all eigenvectors k is equal to or greater than the threshold value Γ.

[0027] The advantage of this implementation is that, by appropriately setting the value of the threshold Γ according to the numerical accuracy of the software used to calculate the second root of the inverse matrix of the coupling matrix C, the second beamforming matrix f2 obtained by the transformation matrix T determined in this way can achieve a good trade-off between avoiding numerical accuracy problems and achievable beamforming gain.

[0028] In an implementation manner of the communication device according to the first aspect, a spacing between the antenna elements in the antenna aperture is less than half of the wavelength λ of the communication signal x.

[0029] The advantage of this implementation is that when the spacing between antennas is less than half the wavelength of the communication signal x, the mutual coupling between the antenna elements will take effect, which can be used to achieve higher beamforming gain.

[0030] In an implementation manner of the communication device according to the first aspect, the communication device is used to:

[0031] The communication signal x is transmitted through the set of antenna elements based on the second beamforming matrix f2 and a scaling factor α depending on a power constraint.

[0032] The advantage of this implementation is that by transmitting the communication signal x using the second beamforming matrix f2, the achievable beamforming gain and the received signal power at the receiver can be maximized. At the same time, the scaling factor α can be used to ensure that the power constraint at the transmitter is met.

[0033] In an implementation manner of the communication device according to the first aspect, the first beamforming matrix f1 is a beamforming matrix predetermined according to a communication standard.

[0034] The advantage of this implementation is that, using the first beamforming matrix f1 predetermined according to the communication standard, the corresponding second beamforming matrix f2 can generate a beam pattern pointing to a predetermined spatial direction determined by the first beamforming matrix f1. When the number of first beamforming matrices {f1} is predetermined according to the communication standard to form a beam codebook, the corresponding set of second beamforming matrices {f2} can be used to generate a set of beam patterns covering a range of spatial directions of interest (e.g., a new beam codebook). At the same time, by considering the mutual coupling effect between antenna elements in the antenna aperture, a beamforming gain higher than the beamforming gain of the predetermined first beamforming matrix {f1} is achieved.

[0035] In an implementation manner of the communication device according to the first aspect, the first beamforming matrix f1 is a beamforming matrix determined based on any one of the following groups, wherein the group includes: a target beamforming direction, the position of the antenna element in the antenna aperture, the relative position of the antenna element in the antenna aperture, and a radiation power pattern of each antenna element in the target beamforming direction.

[0036] The advantage of this implementation is that, using the first beamforming matrix f1 determined based on any one of the above information groups, the corresponding second beamforming matrix f2 can generate a beam pattern pointing to any target spatial direction, and the desired spatial direction can be freely changed to adapt to the spatial direction of the receiver relative to the transmitter, even if the receiver keeps moving.

[0037] In an implementation manner of the communication device according to the first aspect, the communication device is a network access node (eg, a base station) or a client device (eg, a user equipment).

[0038] The advantage of this implementation is that densely deployed antenna element arrays can be equipped on both the base station and the user equipment, thereby achieving enhanced beamforming gain on both sides to improve system performance.

[0039] According to a second aspect of the present invention, the above and other objects are achieved by a method for a communication device, wherein the communication device comprises a set of antenna elements arranged in an antenna aperture, and the method comprises:

[0040] Determine a transformation matrix T based on a coupling matrix C, wherein the coupling matrix C includes coupling coefficients between each antenna element in the set of antenna elements;

[0041] Multiplying the transformation matrix T by the first beamforming matrix f1 to obtain a second beamforming matrix f2;

[0042] Based on the second beamforming matrix f2, a communication signal x is transmitted through the set of antenna elements.

[0043] The method according to the second aspect can be extended to an implementation corresponding to the implementation of the communication device according to the first aspect. Therefore, the implementation of the method includes one or more features of the corresponding implementation of the communication device.

[0044] The advantages of the method according to the second aspect are the same as the advantages of the corresponding implementation of the communication device according to the first aspect.

[0045] An embodiment of the present invention further relates to a computer program, wherein the program code, when executed by at least one processor, causes the at least one processor to perform any method described in the embodiment of the present invention. In addition, an embodiment of the present invention further relates to a computer program product, comprising a computer-readable medium and the computer program, wherein the computer program is included in the computer-readable medium and may include one or more of the following groups: read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), flash memory, electrically erasable PROM (EEPROM), hard disk drive, etc.

[0046] Other applications and advantages of embodiments of the present invention will be apparent from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings are intended to illustrate and explain different embodiments of the present invention, in which:

[0048] Figure 1 A communication device according to an embodiment of the present invention is shown;

[0049] Figure 2 A flow chart of a method for a communication device according to an embodiment of the present invention is shown;

[0050] Figure 3 shows a set of antenna elements in an antenna aperture according to an embodiment of the present invention;

[0051] Figure 4 A communication system according to an embodiment of the present invention is shown;

[0052] Figure 5 A block diagram showing components of a communication device according to an embodiment of the present invention;

[0053] Figure 6 shows a 3D coordinate system of an exemplary holographic wireless system according to an embodiment of the present invention;

[0054] Figure 7 shows the coupling coefficient between two isotropic / directional antennas m and n with different spacings;

[0055] Figure 8 The achievable beamforming gain of a square holographic surface with a side length of L=2λ and different spacings between antenna elements in each row / column of a uniform rectangular antenna array (URA) within the antenna aperture is shown, and the disclosed beamforming taking into account the mutual coupling effect (solid curve) and the conventional beamforming without taking into account the mutual coupling effect (dashed curve) are plotted;

[0056] Fig. 9 The achievable beamforming gain of the disclosed beamforming method in a square holographic surface with different side lengths and different spacing between antenna elements in each row / column of the URA is shown;

[0057] Fig.10 Horizontal cuts of the radiated power pattern achieved by (a) conventional beamforming and (b) the disclosed beamforming method using a square holographic surface with side length L = 2λ deployed with isotropic URAs with different spacings are shown, where the horizontal angle θ∈[-π,π] is as follows: Figure 6 As shown;

[0058] Fig.11 Horizontal cuts of the radiated power pattern achieved by (a) conventional beamforming and (b) the disclosed beamforming method using a square holographic surface with side length L = 2λ deployed with directional URAs with different spacings are shown, where the horizontal angle θ∈[-π,π] is as follows: Figure 6 shown. DETAILED DESCRIPTION

[0059] When the antenna array is densely packed for the overall wireless system, more antenna elements are placed in the same aperture size of the array, making the spacing between the antenna elements smaller, which causes mutual influence between the antenna elements. Specifically, when the transmission circuit transmits the transmission signal vector x = (x1x2…x N ) T When feeding the N-element antenna array of the transmission holographic surface, the corresponding current (i.e., x n ,) generates an electromagnetic field, which, when propagating to each other transmitting antenna element (for example, antenna n′), induces current on the other transmitting antenna elements, expressed as Afterwards, feed to other antennas {x n |n≠n ′ The current induced on each transmitting antenna (e.g., antenna n′) by the current of ) will also generate a new electromagnetic field, which can then propagate to each of the other antenna elements (for example, antenna element n ″ ), and induces a new current on the latter, expressed as This interaction continues indefinitely until convergence occurs, and eventually the active feed current x and all induced currents The superposition of will form a new signal vector, which is emitted from the transmission holographic surface and propagates into the wireless RF channel. This new signal vector can be called the coupled transmission signal vector and can be expressed as It indicates that,

[0060] In most research works on conventional antenna arrays (including massive MIMO), the interaction between antenna elements is not considered. This is because when the spacing between antenna elements is large enough (e.g., half the wavelength), this effect is weak and has negligible impact on the design and analysis of communication links. However, when dense antenna arrays are involved (the spacing between antenna elements can be arbitrarily small), the mutual influence between antenna elements should be considered. Therefore, not considering the above electromagnetic interactions between antenna elements placed close to each other within the aperture of the holographic metasurface may degrade the beamforming performance.

[0061] It is therefore an object of an embodiment of the present invention to disclose a beamforming scheme for a communication system by deploying a holographic surface with an arbitrarily dense array of antennas. To this end, a characterization of the mutual coupling effects of a general holographic surface consisting of densely packed radiating antenna elements with arbitrary deployment and radiation power pattern of each antenna element is also disclosed.

[0062] Figure 1 FIG. 1 shows a communication device 100 according to an embodiment of the present invention. Figure 1 In the illustrated embodiment, the communication device 100 includes a processor 102, a transceiver 104, and a memory 106. The processor 102 is connected to the transceiver 104 and the memory 106 via a communication component 108 known in the art. The communication device 100 can be used for wireless and / or wired communication in a communication system. Wireless communication capabilities can be provided by an antenna array connected to the transceiver 104. The antenna array includes a set of antenna elements 120 arranged in an antenna aperture 130. Wired communication capabilities can be provided by a wired communication interface 112 (for example, which is connected to the transceiver 104).

[0063] The processor 102 may be referred to as one or more general-purpose CPUs, one or more digital signal processors (DSPs), one or more application-specific integrated circuits (ASICs), one or more field programmable gate arrays (FPGAs), one or more programmable logic devices, one or more discrete gates, one or more transistor logic devices, one or more discrete hardware components, or one or more chipsets. The memory 106 may be a read-only memory, a random access memory (RAM), or a non-volatile RAM (NVRAM). The transceiver 304 may be a transceiver circuit, a power controller, or an interface that provides the ability to communicate with other communication modules or communication devices (e.g., network nodes and network servers). The transceiver 104, the memory 106, and / or the processor 102 may be implemented in a separate chipset or in a common chipset. In the present disclosure, the communication device 100 used to perform certain actions may be understood to mean that the communication device 100 includes suitable components for performing the action, such as the processor 102 and the transceiver 104.

[0064] According to an embodiment of the present invention, Figure 3 As shown, the communication device 100 includes a set of antenna elements 120 arranged in an antenna aperture 130. Therefore, a communication device 100 is disclosed herein for beamforming using a holographic surface made of deployed antenna elements. The disclosed scheme is applicable to any deployment of antenna elements in the antenna aperture and any radiation power pattern of each radiating element in the array. However, in an embodiment of the present invention, the spacing between the antenna elements in the antenna aperture 130 is less than Figure 3 The antenna aperture 130 is half of the wavelength λ of the communication signal x shown, that is, the antenna aperture 130 is a densely deployed antenna aperture.

[0065] The communication device 100 is used to determine a transformation matrix T based on a coupling matrix C, wherein the coupling matrix C includes coupling coefficients between each antenna element in the antenna element set 120. The communication device 100 is also used to multiply the transformation matrix T with the first beamforming matrix f1 to obtain a second beamforming matrix f2. The communication device 100 is also used to transmit a communication signal x through the antenna element set 120 based on the second beamforming matrix f2.

[0066] Figure 2 It shows that Figure 11 , a flow chart of a corresponding method 200 performed in a communication device 100 or the like as shown, the communication device 100 comprising a set of antenna elements 120 arranged in an antenna aperture 130. The method 200 comprises: determining 202 a transformation matrix T based on a coupling matrix C, wherein the coupling matrix C comprises coupling coefficients between each antenna element in the set of antenna elements 120. The method 200 further comprises multiplying 204 the transformation matrix T with a first beamforming matrix f1 to obtain a second beamforming matrix f2. The method 200 further comprises transmitting 206 a communication signal x through the set of antenna elements 120 based on the second beamforming matrix f2. Depending on the application, the first beamforming matrix f1 may also be represented as a first beamforming vector f1, and the second beamforming matrix f2 may also be represented as a second beamforming vector f2.

[0067] Figure 4 A communication system 500 according to an embodiment of the present invention is shown. The communication system 500 in the disclosed example includes a communication device 100 and an additional second communication device 300 for communicating and operating in the communication system 500. For simplicity, the communication system 500 shown includes only one communication device 100 and one additional communication device 300. However, the communication system 500 may include any number of communication devices 100 and any number of additional communication devices 300 without departing from the scope of the present invention.

[0068] In a non-limiting example, the communication device 100 may be used or configured as a network access node, thereby communicating with an additional communication device 300 used or configured as a client device. However, it may be noted that the reverse order is also possible, i.e. the additional communication device 300 is used as a network access node, while the communication device 100 is used as a client device. The communication device 100 may also be represented as a transmitter device or a transmitter. Accordingly, the additional communication device 300 may be represented as a receiver device or a receiver. Therefore, according to an embodiment of the present invention, the communication device 100 is a network access node (e.g., a base station) or a client device (e.g., a user device).

[0069] In general, the second beamforming matrix / vector is configured by converting or transforming from a predetermined first beamforming matrix / vector, wherein the transform operation can be characterized by a transformation matrix T constructed based on the mutual coupling effects between antenna elements in the antenna aperture 130. The present disclosure also provides an analytical characterization of the transformation matrix T, which can be calculated based on the geometric deployment of the antenna elements in the antenna aperture 130 and the radiation power pattern of each antenna element.

[0070] Figure 51 shows a block diagram of a communication device 100 according to an embodiment of the present invention. In a determination block 152, a transformation matrix T is determined based on a coupling matrix C, wherein the coupling matrix C includes the coupling coefficients calculated in a calculation block 156. The calculation of the coupling matrix C can be based on the positions and radiation power patterns of the antenna elements in the antenna element set 120. By understanding the coupling coefficients, the first beamforming vector f1 obtained in the acquisition block 154 is traversed through the transformation matrix T by multiplication in a multiplication block 158 to generate an optimized second beamforming vector, i.e., f2=T·f1. In a multiplication block 160, the second beamforming vector f2 is multiplied by the signal flow Multiply to obtain the communication signal x transmitted by the antenna element set 120. The signal stream may include information of interest to the receiver, which may be a binary bit sequence obtained from the output of the source coding block, and then the information is encoded with a specific error correction coding scheme (e.g., Turbo coding, LDPC coding, and polarization coding), and modulated with a specific modulation scheme (e.g., BPSK, QPSK, and QAM). The coded and modulated sequence may also be modulated using orthogonal frequency division multiplexing (OFDM) or discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-spread-OFDM, DFT-s-OFDM). However, other types of signal processing that may conform to different communication standards are also applicable.

[0071] refer to Figure 6 , the communication device 100 may be equipped with a holographic surface, also represented herein as an antenna aperture 130, which includes an antenna array of N antenna elements in the antenna element set 120. The antenna elements may be densely placed in the antenna aperture 130. Without loss of generality, a three-dimensional (3D) coordinate system may be established such that the center of the holographic surface t0 is located at the origin of the coordinate system, i.e., t0 = (0 0 0) T , and the position of any point in this coordinate system can be represented by a real vector p=(p x p y p z ) T Indicates that, p x 、p y and p z Represent the coordinates of point p on the x-axis, y-axis, and z-axis respectively.

[0072] like Figure 6 As shown, taking the square holographic surface corresponding to the antenna aperture 130 with a side length of L as an example, the position and radiation power pattern of the nth (n=1, 2, ..., N) antenna element are respectively represented by tn and G n (u) means, where For any orientation, is the set of all points on a sphere with unit radius centered at the origin, and the radiation power pattern of each antenna element satisfies

[0073]

[0074] This ensures the physical principle of energy conservation when each antenna element is deployed individually.

[0075] The antenna aperture 130 can be used to face the target spatial direction u t Transmitting unit power signal flow (Right now ). To illustrate the beamforming scheme, consider the following t The position r0 is a position with a horizontal angle of φ, a vertical angle of θ and a sufficiently large distance D from the origin (i.e., the center of the antenna aperture 130) 0,x r 0,y r 0,z ) T A single receiving isotropic antenna at . This yields

[0076] r0=(r 0,x r 0,y r 0,z ) T =Du t , where u t =(sinθcosφsinθsinφcosθ) T (2)

[0077] Also, the free space line-of-sight (LoS) channel between the antenna aperture 130 and the receiving isotropic antenna can be written as

[0078]

[0079] Where λ is the wavelength of the communication signal x.

[0080] For signal flow Given a beamforming vector f, the transmission signal vector fed to the antenna aperture 130 is given by

[0081]

[0082] And the corresponding transmission power can be written as

[0083] If the antenna elements in the antenna aperture 130 are densely deployed, the mutual coupling effect between the antenna elements will change the communication signal x and generate different transmission signals, which are called coupled transmission signals x. (c) , the coupled transmission signal x (c) observed outside the antenna aperture 130 and propagated to the wireless channel h(u t ). Therefore, the received signal at the receiving isotropic antenna is

[0084] y=h H (u t )x (c) +z(5)

[0085] Where z is the additive noise at the receiver device. The communication signal vector x and the coupled transmission signal vector x (c) The relationship between depends on the mutual coupling effect of the antenna elements within the antenna aperture 130. For an arbitrary holographic surface, an analytical expression for this relationship is not yet known.

[0086] In the conventional scheme, the design of the beamforming vector does not consider the mutual coupling effect between the antenna elements in the antenna aperture 130, that is, by assuming

[0087] x (c) ≈x(6)

[0088] Set the beamforming vector to correspond to the wireless channel h(u t ) matches, that is

[0089]

[0090] In the disclosed solution, a linear transformation T is performed on the first beamforming vector f1 to generate a second beamforming vector f2, thereby taking into account the mutual coupling effect between the antenna elements, that is,

[0091] f2=Tf1(8)

[0092] Therefore, according to an embodiment of the present invention, the communication device 100 can be used to transmit a communication signal x through the antenna element set 120 based on the second beamforming matrix f2. The achieved beamforming gain is used as a design metric for optimizing the beamforming vector. The transformation in equation (8) is used to further improve the achievable beamforming gain at the receiver device.

[0093] In an embodiment of the present invention, the first beamforming matrix f1 is a beamforming matrix predetermined according to a communication standard. For example, the mentioned standard may be a 3GPP standard such as 5G and 6G. However, in other embodiments of the present invention, the first beamforming matrix f1 is a beamforming matrix determined based on any one of the following groups, wherein the group includes: a target beamforming direction, a position of an antenna element in the antenna aperture 130, a relative position of an antenna element in the antenna aperture 130, and a radiation power pattern of each antenna element in the target beamforming direction. For example, based on the position (relative position) of the antenna element and its radiation power pattern in the target beamforming direction, a spatial steering vector toward the target beamforming direction may be first constructed. Thereafter, the first beamforming matrix f1 may be determined as the conjugate transpose of the constructed spatial steering vector with a suitable scaling factor to meet the power constraint of the transmitter.

[0094] Two general embodiments of the present invention are hereinafter referred to as a first embodiment and a second embodiment, respectively, to configure a transformation matrix T. However, the embodiments of the present invention are not limited thereto.

[0095] In a first embodiment of the present invention, the transformation matrix T is based on the mutual coupling matrix of the antenna aperture 130 to maximize the achievable beamforming gain, wherein the coupling matrix in turn depends on the positions and radiation power patterns of the antenna elements in the antenna aperture 130. Theorem 1 provides an analytical computation of the coupling matrix of a general antenna aperture 130 containing an array of arbitrarily deployed antenna elements, each with an arbitrary radiation power pattern.

[0096] In a second embodiment of the present invention, the transformation is based only on a subset of the eigenvalues / eigenvectors of the coupling matrix, which can be determined by adopting an additional threshold. The second embodiment has the advantage that it is more numerically stable as the spacing between the radiating elements in the antenna aperture 130 decreases and / or the number of radiating elements increases. In some exemplary implementations of the disclosed beamforming scheme, several dB gains can be achieved by array densification compared to conventional antenna arrays with half-wavelength spacing, after taking into account mutual coupling effects.

[0097] In the first embodiment, based on the physical principle of energy conservation, an analytical method for calculating the coupling matrix C of the antenna aperture 130 including an N-element antenna array is disclosed, which is expressed as C={c m,n}∈C N×N This result is applicable to a general antenna aperture 130 with an arbitrary antenna array deployment and each antenna element having an arbitrary radiation power pattern. Using the disclosed coupling matrix C construction method, the communication signal vector x and the coupled communication signal vector x (c)The relationship between is expressed in closed form analytical expressions. This relationship and the elements of the coupling matrix C are detailed in the following theorem. The proof of the theorem is given in the appendix.

[0098] Theorem 1: For an antenna aperture 130 including N antenna elements, the position and radiation power pattern of the nth (n=1, 2, ..., N) antenna element are p n and G n (u), the communication signal vector x fed to the antenna aperture 130 and the corresponding coupled communication signal vector x emitted from the antenna aperture 130 (c) The relationship between can be expressed as

[0099] x (c) =C -1 / 2 x(9)

[0100] Where C = {c m,n}∈C N×N is the coupling matrix of the antenna aperture 130, the elements of which are given by the following equations

[0101]

[0102] In order to calculate the coupling matrix C using equation (10), the positions of the radiating antenna elements (or their relative positions) and the radiated power pattern of each antenna element are required. According to Theorem 1, the transformation matrix T in equation (8) can be calculated based on the following equation

[0103] T=T1=αC -1 / 2 (11) Wherein, α is a scaling factor for satisfying the transmitter power constraint. Therefore, according to the first embodiment, the transformation matrix T is determined based on the second root of the inverse matrix of the coupling matrix C.

[0104] The principle of equation (11) can be as follows. By substituting equation (4) and equation (9) into equation (5), we can rewrite the received signal at the receiving antenna as

[0105]

[0106] in, is a coupling channel vector that combines the joint effect of the wireless channel and the mutual coupling effect of the antenna aperture 130. According to the maximum ratio combining (MRC) principle, the optimal beamforming vector should be designed to be equal to the coupling channel vector Matching, rather than matching with the wireless channel h(u t ) matches, that is

[0107]

[0108] When equation (11) holds, it is consistent with equation (8), and The advantage of the first embodiment is that the transformation matrix T1 in equation (11) fully considers the mutual coupling effect of the antenna aperture 130, and the received signal power obtained in this way is maximized, which means the optimal solution.

[0109] In the second embodiment, the coupling matrix C and the relationship between the communication signal vector x and the coupled communication signal vector x are characterized in the same way as in Theorem 1, and the transformation matrix T in equation (8) is determined based on the following equation: (c) where α is a scaling factor that satisfies the transmitter power constraint,

[0110]

[0111] where λ λ k and v k are respectively the k-th largest eigenvalue of the coupling matrix C and its corresponding eigenvector, that is,

[0112]

[0113] where K < N, and N is the total number of antenna elements in the antenna element set 120 according to the second embodiment. Therefore, the transformation matrix T is determined based on a subset of K eigenvectors v k of the corresponding eigenvalues λ k of the coupling matrix C with dimension N×N.

[0114] In the implementation of the second embodiment, the communication device 100 can use a predetermined threshold Γ to select eigenvalues. In one example, according to the numerical accuracy of the algorithm for performing the eigenvalue decomposition of the coupling matrix C, the predetermined threshold Γ is set to a positive real number, and in the following cases, the calculation of the transformation matrix T2 involves eigenvalues

[0115] λ k ≥Γ(16)

[0116] Γ(Γ>0) is a predetermined positive real number. Therefore, according to the embodiments of the present invention, the subset of K eigenvectors v k includes all eigenvalues λ k of the coupling matrix C that are equal to or greater than the threshold Γ.

[0117] The second embodiment has advantages because when the antenna elements in the antenna aperture 130 are densely deployed and the spacing between the antenna elements is very small, the coupling matrix C tends to be singular and contains eigenvalues that are very close to zero. Therefore, due to the inverse operation of the nearly singular coupling matrix C, directly using equation (11) to calculate the transformation matrix T becomes numerically unstable, and thus the obtained beamforming design becomes sensitive to the numerical calculation accuracy.

[0118] Since the transformation matrix T2 in equation (14) is calculated in a manner independent of the near-zero eigenvalues / eigenvectors of the coupling matrix C, the second embodiment can avoid this numerical difficulty. This is equivalent to transforming the transmission signal vector x and the second beamforming vector f2 and the coupled transmission signal vector x (c) Restricted to the space spanned by a subset of the eigenvectors of the coupling matrix C, these eigenvectors and their eigenvalues ​​can be computed exactly.

[0119] In the next section, some numerical results are given to demonstrate the advantages of the disclosed beamforming scheme by considering the mutual coupling effect between antenna elements in the beamforming design. Specifically, we consider a square antenna aperture (i.e., area) with a side length of L. The square antenna aperture consists of a total number of N antenna elements deployed on a uniform grid within the given antenna aperture to form a uniform rectangular antenna array (URA) with N elements in each row / column. 1 / 2 vibrators, corresponding to the spacing between adjacent rows / columns d = L / (N 1 / 2 -1). Assume that the URA in the square holographic surface is deployed in the (y, z) plane centered at the origin of the 3D coordinate system, and the rows and columns of the URA are parallel to the y-axis and z-axis, respectively, as Figure 6 As shown. Two types of radiation power patterns of antenna elements in the antenna aperture are considered: isotropic and directional. For the directional radiation power pattern, it is assumed that all antenna elements have the same radiation power pattern as defined in the specification "Channel Model Study for Frequencies from 0.5 GHz to 100 GHz (Version 16)" (document 3GPP TR 38.901V16.1.0, December 2019) (see Appendix B for details) and are placed in the same direction as the positive semi-axis of the x-axis, that is, the normal direction of the surface. In addition, the maximum directional gain of these antenna elements is scaled from 8 dBi to 9.8256 dBi to meet the energy conservation principle under the lossless assumption of each antenna.

[0120] We first check the coupling coefficient c between the two antenna elements m and n in the antenna aperture calculated based on Theorem 1 m,n . Figure 7 The isotropic and directional cases are plotted. m,n The relationship between the value of and the distance between the two antenna elements. Figure 7In the figure, we can observe that the mutual coupling effect is stronger when the antenna spacing is small (for example, less than half a wavelength). When the spacing between the two antenna elements increases, the mutual coupling effect of isotropic and directional antennas weakens in an oscillatory manner. Specifically, as long as the spacing between the isotropic antennas is an integer number of half wavelengths, the isotropic antennas can be decoupled, which is consistent with the traditional array deployment with half-wavelength spacing, making the mutual coupling effect negligible. Even if the spacing of the directional antennas is half a wavelength, the directional antennas are still coupled. Based on the developed method, the minimum decoupling spacing is about 0.93λ, after which the mutual coupling effect disappears much faster than that of the isotropic antennas.

[0121] We then evaluate the achievable beamforming gain of such a holographic metasurface compared to a conventional array with half-wavelength spacing in the same aperture size of the holographic metasurface. For this purpose, the beamforming gain of the transmit array / holographic metasurface is defined as the gain in received signal power relative to that achieved by transmitting the same signal with the same transmit power using a single isotropic transmit antenna located at the center of the holographic metasurface. Specifically, when the holographic metasurface is replaced by an isotropic antenna located at its center, both the coupling matrix C and the transformation matrix T simplify to unit scalar values, so the equivalent channel vector reduces to the scalar given by

[0122]

[0123] Therefore, the beamforming gain achieved by an arbitrary beamforming vector f is defined as

[0124]

[0125] As a benchmark, we consider the traditional beamforming design in equation (7) for comparison. Both the traditional beamforming method and the disclosed beamforming method are implemented in MATLAB 2019a. We find through numerical calculation that the threshold Γ should be no less than 10 –12 , in order to ensure stable calculation. For other types of actual implementations, the value of the threshold Γ can be set accordingly according to the computing power of the processor.

[0126] Figure 8The relationship between the achievable beamforming gain in the normal direction of the holographic surface using the prior art and the disclosed beamforming design and the spacing between adjacent antenna elements in each row / column is plotted, where the side length of the square holographic surface is set to L = 2λ. It can be seen that in the isotropic and directional cases, the maximum beamforming gain can be approximately achieved by deploying antenna elements with a spacing of λ / 2 by conventional beamforming without considering the mutual coupling effect between antennas, and when the mutual coupling effect between antenna elements is not included in the beamforming design, further densification of the antenna array will not bring additional beamforming gain. However, by using the disclosed beamforming method that considers the mutual coupling effect between antennas, the achievable beamforming gain can be further increased as the antenna densification increases. When d = λ / 10, the effect of densification becomes saturated, and further array densification will only bring marginal gain.

[0127] exist Fig. 9 In , we further plot the achievable beamforming gain of the disclosed beamforming method in square holographic metasurfaces with different side lengths and array densities. It can be seen that when the array is dense enough, i.e., when the spacing is d = λ / 20, the gain of array densification (using the disclosed beamforming method) decreases with increasing antenna aperture relative to the gain achieved with a conventional half-wavelength spacing array in the same aperture. In both the isotropic and directional cases, the gain is about 7.5 dB when the metasurface aperture is 0.5λ×0.5λ, and decreases to less than 4 dB when the antenna aperture is 4λ×4λ.

[0128] Finally, we evaluate the radiation power pattern of the entire holographic surface with different array densities and using different beamforming methods. We fix the antenna aperture to L = 2λ and choose the steering direction to be the normal direction of the holographic surface, that is, the positive half of the x-axis. Fig.10 and Fig.11 In Figure 1, we plot horizontal cuts (in the (x,y) plane) of the radiated power patterns of a holographic metasurface deployed with isotropic and directional URAs with different spacings and beamforming methods. It can be seen that conventional beamforming does not benefit from array densification in terms of beamforming gain or beamwidth, while the disclosed beamforming method achieves a significant improvement in beamforming gain after array densification. Figure 8 In addition to the higher beamforming gain shown in , narrower beamwidths can also be achieved. This means that the holographic metasurface can support potentially higher degrees of freedom compared to conventional uncoupled antenna arrays within the same aperture size due to the effective use of the mutual coupling effects of the antenna elements in the antenna aperture.

[0129] Proof of Theorem 1

[0130] According to equations (3) and (5), the received signal power at the receiving isotropic antenna located in any spatial direction u at a distance D from the center of the holographic surface can be written as

[0131]

[0132] Now, assume that the center of the receiving sphere is at the origin and has a sufficiently large radius D. Recall that the effective aperture size of an isotropic antenna is A. iso =λ 2 / 4π, we can calculate that in any spatial direction u, the receiving power density on such a receiving sphere is

[0133]

[0134] Therefore, the total signal power that can be collected by the entire receiving sphere is given by

[0135]

[0136] Where C = {c m,n}∈C N×N is the coupling matrix of the holographic surface, and

[0137]

[0138] On the other hand, according to the physical principle of energy conservation, the total signal power collected by the receiving sphere should be equal to the total transmission power, that is, E(x H x). Therefore, we have

[0139] P R,sphere =E(x H x)=E((x (c) ) H Cx (c) ) (A-5)

[0140] This means

[0141] x=C 1 / 2 x (c) (A-6)

[0142] or equivalently,

[0143] x (c) =C -1 / 2 x (A-7)

[0144] This completes the proof.

[0145] Radiated power pattern

[0146] In Table 7.3-1 of "Channel Model Study for 0.5 GHz to 100 GHz Frequency (Release 16)" (Document 3GPP TR38.901V16.1.0, December 2019), the definition of the radiation power pattern is shown in Table 1 below. In this table, θ 3dB =φ 3dB =65° and C = 30dB. Please note that the maximum directional gain is set to 8dBi. Due to the heat loss caused by the circuit of the transmitting antenna, the received power on the entire receiving sphere is less than the power fed to each transmitting antenna. For simplicity, in this invention, we assume that all antennas are lossless, so the maximum directional gain is scaled to 9.8256dBi to meet the principle of energy conservation.

[0147] The radiated power pattern of a directional antenna as defined in Table 1

[13]

[0148]

[0149] The network access node in this article can also be represented as a wireless first communication device, an access first communication device, an access point (AP) or a base station (BS), for example, a radio base station (RBS), which can be called a transmitter, "gNB", "gNodeB", "eNB", "eNodeB", "NodeB" or "B node" in some networks, depending on the standards, technologies and terminology used. Based on the transmission power and cell size, the wireless first communication device can be of different categories or types, such as a macro eNodeB, a home eNodeB or a mini base station. The wireless first communication device can also be a station (STA), which is any device that includes a media access control (MAC) and physical layer (PHY) interface to a wireless medium (WM) and complies with IEEE 802.11. The wireless first communication device can be used for communication in the following: 3GPP-related long term evolution (LTE), advanced LTE, fifth generation (5G) wireless systems, such as new radio (NR) and its evolutions, and IEEE-related Wi-Fi, worldwide interoperability for microwave access (WiMAX) and its evolutions.

[0150] The client device in this article can be represented as a user device, user equipment (UE), mobile station, Internet of Things (IoT) device, sensor device, wireless terminal and / or mobile terminal, capable of wireless communication in a wireless communication system (sometimes also referred to as a cellular wireless system). UE can be referred to as a mobile phone, cellular phone, tablet or laptop with wireless capabilities. For example, the UE in this context can be a portable, pocket storage, handheld, computer-based or vehicle-mounted mobile device that can communicate voice and / or data with another communication entity (such as another receiver or server) through a radio access network (RAN). UE can also be a station (STA), which is any device that includes a media access control (MAC) and physical layer (PHY) interface to a wireless medium (WM) that complies with IEEE 802.11. The UE can be used to communicate in the following: 3GPP-related long term evolution (LTE), advanced LTE, fifth generation (5G) wireless systems, such as new radio (NR) and its evolutions, and IEEE-related Wi-Fi, worldwide interoperability for microwave access (WiMAX) and its evolutions.

[0151] In addition, any method according to an embodiment of the present invention can be implemented in a computer program having a code component, and the code module causes the processing component to perform the steps of the method when the processing component is run. The computer program is included in a computer-readable medium of a computer program product. The computer-readable medium can basically include any memory, such as the read-only memory (ROM), programmable read-only memory (PROM), erasable PROM (EPROM), flash memory, electrically erasable PROM (EEPROM) or hard disk drive mentioned above.

[0152] In addition, it should be appreciated that the communication device 100 includes necessary communication capabilities in the form of functions, components, units, elements, etc., for performing or implementing embodiments of the present invention. Examples of other such components, units, elements and functions are: processors, memories, buffers, control logic, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selection units, switches, interleavers, deinterleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiving units, transmitting units, DSPs, TCM encoders, TCM decoders, power supply units, power supply feeds, communication interfaces, communication protocols, etc., which are appropriately arranged together to perform the scheme.

[0153] Thus, the one or more processors of the communication device 100 may include, for example, a central processing unit (CPU), a processing unit, a processing circuit, a processor, an application specific integrated circuit (ASIC), a microprocessor, or one or more instances of other processing logic that can interpret and execute instructions. Thus, the expression "processor" may refer to a processing circuit that includes a plurality of processing circuits, for example, any, some, or all of the above-mentioned processing circuits. The processing circuit system may also perform data processing functions for inputting, outputting, and processing data, including data buffering and device control functions, such as call processing control, user interface control, etc.

[0154] Finally, it should be understood that the present invention is not limited to the embodiments described above, but also relates to and incorporates all embodiments within the scope of the attached independent claims.

Claims

1. A communication device (100) for a communication system (500), wherein: The communication device (100) comprises an antenna element set (120) arranged in an antenna aperture (130); the communication device (100) is used for: Determining a transformation matrix T based on a coupling matrix C, wherein the coupling matrix C includes coupling coefficients between each antenna element in the set of antenna elements (120); Multiplying the transformation matrix T by the first beamforming matrix f1 to obtain a second beamforming matrix f2; Based on the second beamforming matrix f2, a communication signal x is transmitted through the set of antenna elements (120).

2. The communication device (100) according to claim 1, wherein: The coupling matrix C is determined based on any one of the following group, wherein the group includes: the geometry of the antenna aperture (130), the position of the antenna elements in the antenna aperture (130), the relative position of the antenna elements in the antenna aperture (130), the spacing between the antenna elements in the antenna aperture (130), and the radiation power pattern of each antenna element.

3. The communication device (100) according to claim 2, wherein: The coupling matrix C is determined based on the following equation: Wherein, n and m are antenna element indices, N is the total number of antenna elements in the antenna element set (120), is the set of all points on a sphere centered at the origin with unit radius, G n (u) is the radiation power pattern of the nth antenna element in direction u, t n is the position of the nth antenna element in the antenna aperture (130), and λ is the wavelength of the communication signal x.

4. The communication device (100) according to any one of claims 1 to 3, wherein: The transformation matrix T is determined based on the second root of the inverse matrix of the coupling matrix C.

5. The communication device (100) according to any one of claims 1 to 3, wherein: The transformation matrix T is determined based on a subset of K eigenvectors v k where the eigenvectors have corresponding eigenvalues λ of the coupling matrix C of dimension N×N k , where K < N, and N is the total number of antenna elements in the antenna element set (120).

6. The communication device (100) according to claim 5, wherein: The transformation matrix T is determined based on the following equation: in, 7. The communication device (100) according to claim 6, wherein: The K feature vectors v k The subset includes all eigenvectors of the coupling matrix C, and the corresponding eigenvalues ​​λ of all eigenvectors k is equal to or greater than the threshold value Γ.

8. The communication device (100) according to any one of the preceding claims, wherein: The spacing between the antenna elements in the antenna aperture (130) is less than half the wavelength λ of the communication signal x.

9. The communication device (100) according to any one of the preceding claims, wherein: The communication device (100) is used for: The communication signal x is transmitted through the set of antenna elements (120) based on the second beamforming matrix f2 and a scaling factor a depending on a power constraint.

10. The communication device (100) according to any one of claims 1 to 9, wherein: The first beamforming matrix f1 is a beamforming matrix predetermined according to a communication standard.

11. The communication device (100) according to any one of claims 1 to 9, wherein: The first beamforming matrix f1 is a beamforming matrix determined based on any one of the following groups, wherein the group includes: a target beamforming direction, a position of the antenna element in the antenna aperture (130), a relative position of the antenna element in the antenna aperture (130), and a radiation power pattern of each antenna element in the target beamforming direction.

12. The communication device (100) according to any one of the preceding claims, wherein: The communication device (100) is a network access node (eg, a base station) or a client device (eg, a user equipment).

13. A method (200) for a communication device (100), wherein: The communication device (100) comprises a set of antenna elements (120) arranged in an antenna aperture (130), and the method (200) comprises: Determining (202) a transformation matrix T based on a coupling matrix C, wherein the coupling matrix C includes coupling coefficients between each antenna element in the set of antenna elements (120); Multiplying the transformation matrix T by the first beamforming matrix f1 (204) to obtain a second beamforming matrix f2; Based on the second beamforming matrix f2, a communication signal x is transmitted (206) through the set of antenna elements (120).

14. A computer program having a program code, wherein: When the computer program is run on a computer, the program code is used to execute the method according to claim 13.

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