Multi-beam codebook design and training method for near-field wireless communication

Abstract

This present disclosure involves a multi-arm beam codebook design and training method for near-field wireless communications, comprising: modeling near-field channels and signals based on a spherical wave assumption for both linear antenna arrays and planar antenna arrays; sampling angles for steering vectors at equal intervals; forming a polar domain transformation matrix from the near-field steering vectors; constructing a near-field single-arm beam codebook; obtaining a near-field hashing multi-arm beam training codebook through a hash function; and determining a matching single-arm beam codeword by a soft decision and voting mechanism. This method, under near-field electromagnetic radiation conditions, demonstrates better applicability with the designed near-field hashing multi-arm beam training codebook compared to far-field codebooks, with a significant improvement in identification accuracy and training overhead compared to the hierarchical training.

Description

MULTI-BEAM CODEBOOK DESIGN AND TRAINING METHOD FOR NEARFIELD WIRELESS COMMUNICATIONCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to Chinese Patent Application No. CN202311158740.3, filed September 8, 2023, the disclosure of which is incorporated by reference herein in its entirety.FIELD OF INVENTION

[0002] The application relates to the field of electromagnetic radiation near-field region and beam training technology, and in particular, to a codebook design and multi-arm beam training method for near-field wireless communications.BACKGROUND

[0003] Millimeter wave (mmWave) communications at high-frequency bands has become a highly sought-after next-generation mobile communications technology due to its extremely wide bandwidth, its ability to effectively suppress multipath effects and clutter echoes, and its ability to allow the integration of more antennas. However, the high-frequency nature of mmWave leads to severe obstacle occlusion and path loss in the direct link between the base station (BS) and the users it serves, thus mmWave systems integrate a large number of antennas to improve antenna gain. At the same time, the pencil-shaped beams generated by mmWave massive antennas have high requirements for beam alignment between the transmitter and receiver during communications, requiring a large number of beam directions to cover the space of interest, which makes mmWave beam alignment a challenge.

[0004] Among the existing beam training techniques, the exhaustive approach selects the best-aligned beam by exhausting all possible beam directions, which requires scanning the entire beam space, leading to huge delays and training overheads. Hierarchical beam training, on the other hand, uses multiple layers, dividing the beam space into halves at a time until the resolution meets the requirements. Its main drawback is that using wide beams at the early layers leads to a reduction in beamforming gain, so it may not be ableto identify the correct wide beam at low signal-to-noise ratio (SNR) and eventually fail to detect the best-aligned beam direction. In addition, since the hierarchical beam training requires a comparative judgment of the scan results at each layer before determining the scanned sub-codebook for the next layer, this leads to additional delays.

[0005] The above-mentioned exhaustive and hierarchical beam training approaches are performed with a single-arm beam, while the equal-interval beam training approach uses a multi-arm beam training sequence determined in advance, and does the ensemble operation to obtain the best-aligned beam direction after multiple rounds of scanning. The scanning method of multi-arm beam has obvious advantages over the single-arm beam in terms of complexity, but the problem with the equal-interval beam training method is that it is highly dependent on the result of the first round, and at the same time its fixed beam composition method leads to fixed leakage interference, and interference cancellation is not possible, which limits the identification accuracy of beam training to some extent. Other methods such as compressed sensing, which rarely combine high accuracy and low complexity, and require the acquisition of prior knowledge, make beam training difficult.

[0006] In addition, existing techniques target the far-field region of the electromagnetic radiation field for research. However, unlike the current 5G massive MIMO where the Rayleigh distance is negligible, the Rayleigh distance of future 6G XL MIMO can reach several hundred meters because the number of antennas increases dramatically, so the study of the electromagnetic radiation near field is extremely important. The problem is that the existing far-field codebook does not match the near-field channel model, the near- field steering vector cannot show sparsity in the angular domain, and using the original far-field beam training will lead to serious performance loss in near-field communications. Therefore, how to design a codebook for near-field beam training and a training method with high accuracy and low complexity is an urgent problem that needs to be solved.SUMMARY

[0007] This present disclosure addresses the issues of existing beam training technologies that are only applicable to the far field, with high beam identification errors and significant time delays. Targeting both cases of the linear antenna arrays and planarantenna arrays, the invention proposes a novel hashing multi-arm beam training technique for the near field through a codebook design method.

[0008] The object of the present disclosure is achieved by the following technical scheme: a multi-arm beam codebook design and training method for near-field wireless communications, the method comprising: modeling the near-field channels and signals utilizing antenna steering vectors; sampling angles and distances to construct the steering vectors, where the angles are sampled at equal intervals, and the distance is sampled to minimize the column coherence among any two near-field steering vectors; forming a polar domain transformation matrix IV from the near-field steering vectors, and constructing a near-field single-arm beam codebook C = W through the polar domain transformation matrix, where each column of the codebook matrix serves as a codeword; obtaining a multi-arm beam direction combination through hash functions, and truncate and concatenate the near-field single-arm beam codebook to create a near-field hashing multi-arm beam training codebook; iterating through all pre-defined codewords, and performing soft decision and voting on the received signal power vector, ultimately obtaining the keyword with the highest number of votes and the matching beam.

[0009] Further, the near-field channel model obtained in step 1 includes an antenna array composed of multiple antennas at the transmitter and receiver, which comprises either linear antenna arrays or planar antenna arrays.

[0010] Further, the sampling process specifically includes: first, sampling different 2 direction angles 6 at equal intervals - and then for any sampled angle dj, performing Sj distance samples, where5) = S, and S represents the total number of distance sampling points.

[0011] Further, the polar domain transformation matrix is a combination of J submatrices; in the channel model of the linear antenna array, the j -th sub-matrix Wj is composed of Sj steering vectors, such that:where 6j = — j — , j = 1,2, ... , / , and cr(-) is the near-field steering vector. In the channel model of the planar antenna array, which comprises NxX Nyantennas, the j -th sub-matrix W® is composed of Sj steering vectors, such that:where b(rs, 6S) represents the steering vector at the base station (BS) planar array antenna of the channel between the BS and user k.

[0012] Further, the sampling of spatial angle and distance information is designed to minimize the column coherence between near-field steering vectors as follows: for any two columns of near-field steering vectors, the column coherence is represented by the inner product. Then, by approximating with a second-order Taylor expansion and performing variable substitution, this inner product is transformed into an analytically solvable Fresnel function, with spatial angle and distance as variables. By setting a threshold for the column correlation, the sampling constraint conditions for spatial angles and distances can be determined when the column correlation is below the threshold.

[0013] Further, step 4 is specifically implemented as follows: apply L = O(loglV) rounds of hashing to the near-field single-arm beam codebook. In each round, a randomly selected hash function is used to uniformly distribute the keywords of the near-field single-arm beam codebook into B buckets. All codewords in each bucket represent a multi-arm beam. Each multi-arm beam from each round is a codeword of the near-field hashing multi-arm beam codebook, thereby obtaining the hashing multi-arm beam codebook.

[0014] Further, the specific method of uniformly distributing the keywords (codeword indices) of the near-field single-arm beam codebook into B buckets is: the hash function is used to calculate the hash values corresponding to the keywords contained in the near- field single-arm beam codebook. Keywords with the same hash value are hashed into the same bucket and treated as a sub -beam.

[0015] Further, the design of the hashing multi-arm beam training codebook is that, the linear antenna array or the planar antenna array is segmented according to the number of sub-beams for each segment. Each antenna segment is used to generate each sub-beam within the multi-arm beam. The amplitude and phase information corresponding to the antenna positions of the sub-beams is obtained by extracting codewords with the same angle and distance information from the near-field single-arm beam codebook.

[0016] Further, the specific method of traversing codewords involves the transmitter continuously sending training symbols into space with uniform power. During each training symbol’s duration, the receiver’s receive beamforming vector selects a codewordfrom the near-field hashing multi-arm beam training codebook, and the received signal power value for each time slot is recorded.

[0017] Further, the L highest received signal power values correspond to the multi-arm beams that contain the index of the matching codeword. Voting on the keywords included in the multi-arm beams determined by the soft decision, the codeword index with the highest number of votes is identified. This index corresponds to the codeword index in the near-field single-arm beam codebook, which is the best matching codeword.

[0018] The beneficial effects of this invention are described hereafter. Under the condition of the near-field electromagnetic radiation, the designed near-field wireless communication codebook demonstrates better applicability compared to the far-field codebook, significantly improving the beam training identification accuracy.

[0019] The hashing multi-arm beam training can achieve 98.3% of the performance of the exhaustive training. Although the increase in the number of sub-beams leads to greater leakage interference between sub-beams, which affects the decision-making, the hashing multi-arm beam training still exhibits superior performance compared to the hierarchical training. Even at very low SNR, there is a significant improvement in the identification accuracy.

[0020] The scanning time for hashing multi-arm beam training is at a logarithmic level, which can significantly reduce training overhead compared to the exhaustive training. Additionally, hashing multi-arm beam training has lower delay in practical applications compared to the hierarchical training. This is because the former only makes a voting decision after multiple rounds of scanning are completed, while the latter is multi-level training, which requires a decision at each level to determine the refined training beams for the next level.BRIEF DESCRIPTION OF THE DRAWINGS

[0021] For a more complete understanding of the present application and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings.

[0022] FIG. l is a diagram of a communication scenario for a linear antenna array for the research problem of the present application.

[0023] FIG. 2 is an example diagram of a uniform hashing in one-dimensional space of the present application.

[0024] FIG. 3 shows the hashing multi-arm beam and codebook construction method of the present application.

[0025] FIG. 4 is a voting process for the linear array of the present application.

[0026] FIG. 5 is a diagram of the communication scenario of the planar antenna array for the research problem of the present application.

[0027] FIG. 6 is an example diagram of uniform hashing in two-dimensional space of the present application.

[0028] FIG. 7 is a simulation of the SNR versus the identification accuracy of the present application.

[0029] FIG. 8 is a simulation of the designed codebook size versus training overhead of the present application.DETAILED DESCRIPTION

[0030] The advantages, features, and methods of the present application may be embodied by the embodiments described below for use in conjunction with the accompanying drawings. However, the various embodiments used to describe the principles of the present application in this patent document are by way of illustration only, and various changes may be made thereto, and should not be construed in any way to limit the scope of the present application. It will be understood by those skilled in the art that the principles of the present application may be implemented in any suitably arranged system.

[0031] Hereinafter, embodiments of the present disclosure are described in detail with reference to the accompanying drawings.

[0032] As shown in FIGS. 1 to 4, embodiments of the linear antenna array situation of the present application are provided.

[0033] 1.1 Channel and signal modeling: A two-dimensional mmWave communication scenario is shown in FIG. 1, with an operating frequency of Freq, and a signal wavelength of Ac, where a BS with a uniform linear array is located on the y-axis, and contains N antennas with a spacing of d = ACi / 2, and the coordinates of the n-th antennaMultiple single-antenna users are distributed in theplane space.

[0034] Since the electromagnetic radiation field in wireless communication can be divided into far-field and near-field regions, different field regions will lead to different channel models. The boundary between these two fields is determined by the Rayleigh distance c , where D represents the array aperture. The near-field channel model isbased on the spherical wave assumption, and the near-field channel from the BS to the user can be expressed as:where hkis the channel gain of the BS-user k link, a(rs, 0S) is the steering vector at the BS end of the BS-user k channel, and rs, 6Srepresents the distance between the main path scatterer of the BS-user channel and the origin, the sine of the angle with the positive direction of the x-axis.s the distance from the scatterer to the n-th antenna.

[0035] In the uplink, the user sends the signal xk, then the signal received by the BS can be expressed as:where v is the received beamforming vector of the BS and nk~CN (0, <J2) is the additive noise.

[0036] In the far-field region, the channel matrix can be transformed to the angular domain by the discrete Fourier transform because the number of scatterers is limited and the far-field steering vector is only angle dependent, so the channel matrix exhibits sparsity in the angular domain, and beam training can be performed based on this sparsity. However, the spherical wave model of Eq. (1.2) shows that the phase of the steering vector is nonlinear with respect to the antenna subscripts and thus < / (•) is not a discrete Fourier vector. In this case, the near-field steering vectors < / (•) can be described jointly using several far-field Fourier vectors. As a result, the energy of a near-field path component is no longer concentrated in one angle, but spreads to several angles. This energy spreading effect means that the angle-domain near-field channel may no longer be sparse in the near field, and therefore existing far-field channel estimation schemes basedon angle-domain sparsity will suffer severe performance degradation in XL-MIMO systems.

[0037] Although the sparsity of the angular domain is not valid, the number of paths is still finite and therefore the near-field channel hkis compressible. The reason for the sparsity of the far-field channel in the angular domain is that the angular domain transform matrix F consists of exactly many far-field steering vectors. Since the near- field steering vector cr(-) is determined by the distance r and angle 0, similarly, a new transform matrix W that consists of many near-field steering vectors a(r, 0) is proposed, where the distance r and angle 0 are sampled from the entire angle-distance domain. In this way, the angular and distance information of the near-field path components are fully utilized by the transform matrix W, which is called the polar domain transform matrix. Specifically, the polar domain representation hkcan be expressed as: (1.4)With the correct design of W, the polar representation hkis sparse.

[0038] 1.2 Near-field single-arm beam codebook design: To design the transform2 matrix W, the angles 0 are first sampled at equal intervals - Then, for any sampled angle 0j, the distance is sampled Sj times, where £7=^7Then W can be considered as a combination of J submatrices, i.e. W = [W±, W2, Wj], The j-th submatrix consists of Sj steering vectors, i.e. where The sampling of the distance r is the fundamentaldifference between the angular and polar representations. Aiming to design a distance sampling method that enables hkcan be most accurately recovered. According to the knowledge of compression sensing, the distance sampling method should make the column coherencedenotes the column coherence between the two columns of thenear-field steering vector of the j-th submatrix. For simplicity of expression, we ignore the subscript j. The following Theorem 1 roughly derives the approximate form of

[0039] Theorem 1: For two near-field steering vectors sampled at the same angle 6 but at different distances rpand rq, then the column coherence / (0, rp, rq~) can be approximated as: dz. areFresnel functions.

[0040] Proof: f |, Approximated by second-orderexpansion equation (a) isdue to Vl + x « l + -x — -x2. Thus thus:2 8o 1 oApproximate equation (b) is obtained by letting n x = - t ; equation (c) is due to / ? = yixN 2 ’If rp> rq, then x < 0. Because F(x) = F*(— x), we obtain / (0, rp, rq) = |G*( / ?)|.

[0041] According to Theorem 1, in order to make the coherencelower than the threshold A, we can first calculate thethat satisfies | G ( / ?A) | = A. Since the function | G ( / ?) | tends to decrease with (3, it can be approximated that:N2d2where ZA= —m- At an arbitrary angle 6, if a steering vector is sampled at a distance 2^-CPA1 7 1 7-ZA(1—0 J, then in order to maintain that the coherence is below A, ^-ZA(1 — 0 ) is exactly the maximum feasible distance below ) is1 7 exactly the minimum feasible distance above -ZA(1 — 0 ). If the distance of the sampled point is: rs= izA(l - 02), s = 1,2,3 ... (1.10)Then the column coherence of the two near-field steering vectors sampled at two adjacent distances is exactly A.

[0042] Based on the designed polar transform matrix W, a single-arm beam codebook C = W for the near-field can be designed, and each column of the codebook C is used as a codeword, so the received beamforming vector v can be taken as one of the codewords, and this codebook can meet the requirements of single-arm beam training such as exhaustive and hierarchical beam training in the near field.

[0043] 1.3 Near-field hashing multi-arm beam codebook design: Based on the near- field single-arm beam codebook, a near-field hashing multi-arm beam is generated: for the codebook C containing Nccodewords, the set is denoted as Nc= [1,2, ... , Nc] . We perform a total of L rounds of hashing, and each round uses a randomly selected hash function to uniformly hash the keywords 1,2, ... , NCinto B buckets, each bucket containing R = Nc / B keywords. Specifically, the hash value of the keyword is calculated, and the hash value is used as an index to store the keywords in buckets. Therefore, the multi-arm beam direction is expressed as:where df = [df (1), ... , df ( / ?)] denotes the b-th multi-arm beam of the 1-th round. As in FIG. 2, the schematic hash function hashes the codewords 1—16 uniformly into 4 buckets, so the hashing result of the hash function is Di=[l,4,l 1 , 15;2,6, 12, 14;3,8, 10, 16;5,7,9, 13] .

[0044] The corresponding near-field hashing multi-arm beam codebook C can be ~ ~ ~ ~ ~ T constructed from the codebook C, denoted as C = [c-J , ... , cf , ... , c£, ... , cf ] , where each column of the codebook C corresponds to a multi-arm beam. Since each multi-arm beam is composed of R sub-beams, we generate each sub-beam with M = N / R adjacentantennas. Therefore, the codeword corresponding to the b-th multi-arm beam of the 1-th round is expressed as:where C(m1: m2, ri) denotes the elements of the matrix C from row m1to row m2and column n. As shown in FIG. 3, the left part shows three codewords of the near-field single-arm beam and the corresponding beam pattern, and the right part shows the hashing multi-arm beam codeword obtained by interception and stitching and the beam pattern of this codeword, where the number of sub-beams is R = 4.

[0045] 1.4 Decision mechanism: In the uplink, the user continuously sends training symbols with the same power, and at each training symbol duration (time slot), the BS’s receive beamforming vector v selects a column from the codebook C until all the predefined codewords are traversed, so a total of Q = BL time slots are needed, and the time slot number is denoted as Q = [1, ... , Q], yielding Q received signal power values, denoted as P = [P(l), ... , P(Q)].

[0046] To find the best-aligned codeword c* for the user in the near-field single-arm beam codebook C, a soft decision approach is utilized. Since for each hash function, the sample point (rs* , 0$) corresponding to the codeword c* is assigned to only one of the multi-arm beams, the number of samples is taken is equal to the number of rounds of the hashing L. First, the received signal power vectors P are arranged in descending order to obtain a rearrangement of the time slot numbers Q, and the time slot number corresponding to the largest L power value is Q(l: L). Next, the keywords contained in the multi-arm beam of the Q(l: L)-th time slot are voted, i.e. D(Q(1: L), : ). , where : denotes all the elements of the row / column. Eventually, the keyword n* with the most votes and the best-aligned codeword c* = C(n* , : ) are obtained. As in FIG. 4, assuming that direction 6 is the best-aligned direction, in the first three rounds of hashing multi-arm beam training, the received signal power of the 2nd, 5th, and 12th time slots is the largest, so we vote on the multi-arm beam sets [6, 12, 14, 2], [6, 4, 13, 8], [6, 11, 3, 15] and get the direction with the highest number of votes as 6, thus the beam training result is correct.

[0047] As shown in FIGS. 5 and 6, embodiments of the planar antenna array case of the present application are provided

[0048] 2.1 Channel and signal modeling: FIG. 5 shows a two-dimensional mmWave communication scenario with an operating frequency of Freq, and a signal wavelength of Ac, where a BS with a uniform planar array is located on the y-axis, containing NxX Nyantennas with an antenna spacing of d = Ac / 2, and the coordinates of the antenna in column u row1, ... , Ny. Multiple single-antenna users are distributed in the planar space.

[0049] The near-field channel model is based on the spherical wave assumption, and the near-field channel from the BS to the user k can be expressed as:where hkis the channel gain of the BS-user k link, b(rs, 0S) is the steering vector of the planar array antenna at the BS-end of the BS-user k channel, and rs, 0Srepresents the distance between the main path scatterer of the BS-user channel with the origin and the sine of the angle with the positive direction of the x-axis. hfc,where D(v, it) = Jr2+ yj— 2rxyv0sis the distance from the scatterer to the antenna element at row v and column it.

[0050] In the uplink, the user sends the signal xk, then the signal received by the BS can be expressed as:where v is the received beamforming vector of the BS and nfc~ClV(0, <J2) is the additive noise.

[0051] As with linear arrays, the phase of the steering vector is nonlinear with respect to the antenna subscript it, v, so b(-) is not a discrete Fourier vector, and exists also energy spreading effects, as a consequence, near-field channels exhibit sparsity in the polar domain rather than the angular domain. Similarly, we propose a new transform matrix W' consisting of many near-field steering vectors b(r, 0), where the distances r and angles 0 are sampled from the entire angle-distance domain. In this way, the angular and distance information of the near-field path components are fully utilized by the transformation matrix W , which is called the polar domain transformation matrix. Specifically, the polar domain representation hkcan be expressed as:hk= W'hpk(2.4)

[0052] Near-field single-arm beam codebook design: To design the transform matrixW', the angles 0 are firstly sampled at equal intervals Then, for any sampled angle 0y, the distance is sampled Sj times, where £7=^7 =Then W' can be considered as a combination of J submatrices, i.e. W' =The j-th submatrix consists ofSj steering vectors, i.e.where Oj =2j J 1, j = 1,2, ... , / . In order to most accurately recover / / ' = should be made as small as possible, where f'(0, Tjp, rjq) = (.rj,q> Oj) I denotes the column coherence between the p-th and q-thcolumns of the near-field steering vector of the j -th submatrix W- .

[0053] Because:make the coherence f = (0, rp, rq) below the threshold A,At an arbitrary angle 0, the distance of the sampled point is:which makes the column coherence of the two near-field steering vectors sampled at two adjacent distances be exactly A.

[0054] According to the designed polar domain transform matrix W', since= hk(W')~1b(rs, 0s), near-field single-arm beam codebook C = IV' can be designed, this codebook can meet the requirements of single-arm beam training for near-field antenna planar arrays. Since each column of the codebook is treated as a codeword, the received beam assignment vector v can take one of the codewords.

[0055] 2.3 Near-field hashing multi-arm beam codebook design: Near-field hashing multi-arm beam can be generated based on the near-field single-arm beam codebook: for the Nc codewords contained in the codebook C', the set is denoted as JATj = [1,2, ... , N^] . There are L' rounds of hashing, and each round uses a randomly selected hash function to hash the keywords JATj uniformly into B' buckets, with each bucket containing R’ = Nc / B' keywords. Therefore, the multi-arm beam direction is expressed as:where d’b= [d[fc(l), ..., d’b( / ?')] denotes the b-th multi-arm beam of the 1-th round. As shown in FIG. 6, the illustrated hash function hashes the 16 codewords evenly into 4 buckets, so the hashing result is D[ = [[3,1],[2,3],[3,3],[4,4];[2,1],[1,2],[3,4],[4,3];[2,4],[2,2],[3,2],[4,2];[1,1],[1,3],[1,4],[4,1]].

[0056] The corresponding near-field hashing multi-arm beam codebook C' can be constructed from the codebook C', denoted aswhere each column of the multi-arm beam codebook C corresponds to a multi-arm beam. Since each multi-arm beam consists of R sub-beams, which can be generated by M' = NxNy / R' adjacent antennas. Therefore, the codeword corresponding to the b-th multi-arm beam of the 1-th round is expressed asC'((R' — 1)M' + l: NxNy, d'b( / ?')] (2.10)

[0057] 2.4 Decision mechanism: In the uplink, the user continuously sends training symbols with the same power, and at each training symbol duration (time slot), the BS’s receive beamforming vector v selects a column from the codebook C' until all thepredefined codewords are traversed, so a total of Q' = B'L' time slots are needed, and the time slot number is denoted as Q' = [1, ... , Q'], yielding Q' received signal power value, denoted as P' = [P'(l), ... , P'(Q')].

[0058] To find the best-aligned codeword c'* for the user in the near-field single-arm beam codebook C', a soft decision approach is utilized. Since for each hash function, the sample point (rs'*, 6s'*~) corresponding to the codeword c'* is assigned to only one of the multi-arm beams, the number of samples is taken is equal to the number of rounds of the hashing L' .

[0059] Firstly, the received signal power vector P' is sorted in descending order to obtain the rearrangement Q' of the time slot number, and the time slot number corresponding to the largest L' power value is Q'(l: IS). Next, the keywords contained in the multi-arm beam of the Q'(l: L')-th time slot are voted, i.e. £)'(Q'(1: L'), : ). At last, the keyword ri* with the most votes, and the best-aligned codeword c'* =: ) is obtained.

[0060] The functions and effects of this application are further illustrated and demonstrated by the following simulation experiments.

[0061] Simulation conditions: The operating frequency is set to Freq = 28 GHz, and the signal wavelength is set to A = 0.01m, where the linear antenna array of BS contains N = 128 antenna, and the spacing between the antennas is d = A / 2. Neglecting the small-scale fading, the channel gain of the BS-user link hkis equal to the large-scale channel gain 2.2.

[0062] Simulation results: FIG. 7 plots the effect of SNR on the identification accuracy. With the same simulation setup, we use exhaustive, hierarchical beam training with the near-field codebook and the exhaustive training with the far-field codebook as the baseline. It can be firstly found that as the SNR increases, the influence of noise becomes smaller and the identification accuracy of all beam training methods gradually increases; using the same exhaustive beam training, the accuracy with the near-field codebook converges to 1, while that with the far-field codebooks is quite lower, which confirms the effectiveness of the designed codebook in near-field conditions.

[0063] In addition, to compare the performance of different beam training methods, the performance of hierarchical beam training is significantly lower compared to the exhaustive approach under the same conditions of utilizing near-field codebooks. Inhashing multi-arm beam training, when the number of multi-arm beams B > 36 and the SNR is not less than 5 dB, 98.3% of the performance under the exhaustive training can be achieved, and the accuracy is significantly improved even when the SNR is quite small. However, as the number of multi-arm beams B decreases, the accuracy gradually decreases because the number of sub-beams R increases as B decreasing, which makes the leakage interference between sub-beams have a greater impact on the decision.

[0064] FIG. 8 plots the effect of different codebook sizes on the beam training overhead. The exhaustive approach traverses the entire beam space and the scan time is proportional to the codebook size, resulting in a very high training overhead. Hashing multi-arm beam training is at the logarithmic level with a scan time of Q = BL = O(B log IV), which can significantly reduce the training overhead compared to exhaustive beam training. Although the number of scans in hierarchical beam training is the lowest in the figure, it leads to higher latency in practice because it requires decisions at each layer to determine the subdivision beams of the next layer, while hashing multi-arm beam training only makes voting and soft decision at the BS end after multiple rounds of scanning are completed.

[0065] The above exemplary embodiments are intended only to explain the application and should not be construed as a limitation. Although a number of example embodiments have been described, it will be readily appreciated by those skilled in the art that many modifications and changes can be made in the example embodiments without materially departing from the novel teachings and advantages of the example embodiments. Accordingly, all such modifications and changes should fall within the scope of protection of the example embodiments as defined in the claims.

Claims

WHAT IS CLAIMED IS:

1. A multi-arm beam codebook design and training method for near-field wireless communications, comprising: modeling near-field channels and signals utilizing near-field antenna steering vectors; sampling angles and distances to construct the steering vectors, wherein the angles are sampled at equal intervals, and the distances are sampled to minimize a column coherence among any two near-field steering vectors; forming a polar domain transformation matrix IV from the near-field steering vectors, and construct a near-field single-arm beam codebook C = W through the polar domain transformation matrix, wherein each column of the codebook matrix serves as a codeword; obtaining a multi-arm beam direction combination through hash functions, and truncating and concatenating the near-field single-arm beam codebook to create a near-field hashing multiarm beam training codebook; and iterating through all pre-defined codewords, performing a soft decision and voting on a received signal power vector, ultimately obtaining a codeword with a highest number of votes and a matching beam.

2. The multi-arm beam codebook design and training method for near-field wireless communications of claim 1, wherein the modeled near-field channel comprises an antenna array composed of multiple antennas at a transmitter and a receiver, the antenna array comprising linear antenna arrays or planar antenna arrays.

3. The multi-arm beam codebook design and training method for near-field wireless communications of claim 1, wherein the sampling comprises sampling different direction angles26 at equal intervals and, for each sampled angle 6j, performing Sj distance samples, wherein= S, and S represents the total number of distance sampling points.

4. The multi-arm beam codebook design and training method for near-field wireless communications of claim 1, wherein: the polar domain transformation matrix is a combination of J sub-matrices; in the channel model of a linear antenna array, a j-th sub-matrix Wj is composed of Sj steering vectors, such that Wj =1, j =1,2, ... , / , cr(-) is a near-field steering vector; and in the channel model of a planar antenna array which comprises NxX Nyantennas, a j-th sub-matrix 14)° is composed of Sj steering vectors, such that W- == where b(rs, 0g) represents a steering vectorat a base station (BS) planar array antenna of a channel between the BS and a user k.

5. The multi-arm beam codebook design and training method for near-field wireless communications of claim 1, wherein the sampling the angles and the distances comprises: representing the column coherence for any two columns of near-field steering vectors by an inner product; approximating with a second-order Taylor expansion and performing variable substitution, the inner product is transformed into an analytically solvable Fresnel function, with a spatial angle and a distance as variables; and determining, by setting a threshold for the column coherence, sampling constraint conditions for spatial angles and distances when the column coherence is below a threshold.

6. The multi-arm beam codebook design and training method for near-field wireless communications of claim 1, wherein the obtaining comprises: applying L = 0 (log IV) rounds of hashing to the near-field single-arm beam codebook, wherein in each round, a randomly selected hash function is used to uniformly distribute codewords of the near-field single-arm beam codebook into B buckets; wherein all codewords in each bucket represent a multi-arm beam; and wherein each multi-arm beam from each round is a codeword of the near-field hashing multi-arm beam codebook, thereby obtaining the hashing multi-arm beam codebook.

7. The multi-arm beam codebook design and training method for near-field wireless communications of claim 6, wherein to uniformly distribute the codewords of the near-field single-arm beam codebook into B buckets comprises: using the hash function to calculate hash values corresponding to codewords contained in the near-field single-arm beam codebook, wherein codewords with a same hash value are hashed into a same bucket and treated as a sub-beam.

8. The multi-arm beam codebook design and training method for near-field wireless communications of claim 1, wherein a design of the hashing multi-arm beam training codebook comprises: segmenting a linear antenna array or a planar antenna array according to a number of subbeams for each segment; wherein each antenna segment is used to generate each sub-beam within a multi-arm beam; and wherein amplitude and phase information corresponding to antenna positions of each subbeam is obtained by extracting codewords with a same angle and distance information from the near-field single-arm beam codebook.

9. The multi-arm beam codebook design and training method for near-field wireless communications according to claim 1, wherein the iterating through all the pre-defined codewords comprises: a transmitter continuously sending training symbols into space with uniform power; wherein during time slots of each of the training symbols, a received beamforming vector selects a codeword from the near-field hashing multi-arm beam training codebook, and a received signal power value for each of the time slots is recorded.

10. The multi-arm beam codebook design and training method for near-field wireless communications of claim 6, wherein an L highest received signal power values correspond to multi-arm beams comprising an index of a matching codeword, and the method further comprises: voting on the codewords included in the multi-arm beams determined by the soft decision and identifying a codeword index with a highest number of votes,wherein the codeword index corresponds to a codeword index in the near-field single-arm beam codebook that is a best matching codeword.

11. A method comprising: modeling near-field communication channels between a plurality of reconfigurable intelligent surfaces (RISs) and a base station using near-field steering vectors as a near-field channel model; sampling from the near-field channel model to construct the near-field steering vectors; constructing a near-field single-arm beam codebook by applying a polar domain transformation to the near-field steering vectors; obtaining a near-field multi-arm beam codebook from the near-field single-arm beam codebook over a plurality of scanning rounds; and obtaining an optimized matching codeword through iterating over the near-field multiarm beam codebook and performing a soft decision and voting on a received signal power vector.

12. The method of claim 11, wherein the polar domain transformation comprises a polar domain transformation matrix IV and wherein a j-th sub-matrix Wj is characterized by Wj = [-= a(rj <z (rj,Sj> fy)] when the near-field channel model is a linear antenna arraymodel.

13. The method of claim 11, wherein the polar domain transformation comprises a polar domain transformation matrix W and wherein a j-th sub-matrix Wj is characterized by Wj = (ri 0, )] when the near-field channel model is a planar antennaarray model.

14. The method of claim 11, wherein the sampling comprises: sampling a plurality of angles from the near-field channel model at equally spaced intervals; and sampling a corresponding plurality of distances for each of the plurality of angles to form the near-field steering vectors, wherein a column coherence of the near-field steering vectors is minimized during the sampling the corresponding plurality of distances.

15. The method of claim 14, wherein the column coherence is minimized by: determining an inner product of a first near-field steering vector and a second near-field steering vector; transforming the inner product into a Fresnel function via a second-order Taylor expansion approximation; and updating a sampling constraint condition for the sampling from the near-field channel model so the transformed inner product remains within a column coherence threshold.

16. The method of claim 11, wherein each of the plurality of scanning rounds comprises: hashing the near-field single-arm beam codebook using a randomly selected hash function; configuring the plurality of RISs using the hashed near-field single-arm beam codebook; receiving a plurality of user signals reflected by the plurality of configured RISs; measuring the signal strengths of the plurality of user signals; and storing the signal strengths inside a plurality of received signal power vectors corresponding to each of the plurality of RISs.

17. The method of claim 16, wherein the performing the soft decision comprises: sorting the stored signal strengths inside the received signal power vector; and obtaining a plurality of high power signals from the received signal power vector based on the plurality of scanning rounds.

18. The method of claim 16, wherein the plurality of user signals comprise training symbols that are transmitted using a uniform power by a user equipment.

19. The method of claim 16, wherein: the plurality of scanning rounds is characterized by L = 0 (log IV); and the hashing comprises applying the randomly selected hashing function to uniformly distribute codewords of the near-field single-arm beam codebook into a plurality of buckets, wherein each of the plurality of buckets represent a multi-arm beam of the near-field multi-arm beam codebook.

20. The method of claim 19, wherein the applying comprises: calculating hash values corresponding to the codewords of the near-field single-arm beam codebook; and hashing codewords with a shared hash value into a corresponding bucket, wherein each of the codewords with the shared hash represent a sub-beam.

21. The method of claim 11, wherein the near-field communication channels comprise: a plurality of corresponding near-field communication channels between the plurality of RISs and the base station; and a plurality of corresponding near-field communication channels between a plurality of user equipment and the plurality of RISs.

22. The method of claim 11, wherein: each of the plurality of RISs and the base station comprise multiple antennas; and the multiple antennas are modeled as linear antenna arrays or planar antenna arrays.

23. The method of claim 22, further comprising: segmenting the linear antenna arrays and the planar antenna arrays into segments based on a number of sub-beams; generating a sub-beam of a multi-arm beam for each of the segments; and determining an amplitude and a phase corresponding to each of the segments using the near-field single-arm beam codebook.

24. The method of claim 11, wherein the near-field channel model is modeled based on a spherical wave assumption.

25. The method of claim 11, wherein a column of the polar domain transformation serves as a codeword.

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