Beam forming method and device for large-scale users

Abstract

The invention discloses a beam forming method and device for large-scale users, and relates to the field of wireless communication. The method is used for solving the problem that the broadband communication system cannot better optimize the system performance due to the problems of a beam offset effect, a coupling relation and the like existing in an existing beam forming design method of the broadband communication system in a large-scale user scene. According to the method, channel clustering processing is carried out based on channel state information so as to distinguish user channel characteristics of different frequencies; secondly, constructing a joint optimization model comprising a digital beam former, an analog beam former and subcarrier allocation; and finally, solving the joint optimization model through an iterative optimization algorithm to obtain an optimized beamforming matrix and subcarrier allocation scheme.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication, and more particularly to a beamforming method and apparatus for a large number of users. Background Art

[0002] With the commercial deployment of the fifth-generation mobile communication technology and the research progress of the sixth-generation mobile communication technology, broadband communication systems for a large number of users have become an important development direction of the next-generation wireless communication systems. In high-density scenarios such as urban hotspots, enterprise office buildings, and transportation hubs, the number of users shows an exponential growth, and the demand for high-speed, low-latency, and highly reliable wireless connections is becoming increasingly urgent. In addition, the rapid development of emerging application scenarios such as industrial Internet of Things, smart home, and smart city has further promoted the demand for the communication capabilities of a large number of concurrent devices. These application scenarios pose higher technical requirements on wireless communication systems, including but not limited to: higher system bandwidth, better spectrum utilization efficiency, and more flexible resource scheduling capabilities to meet the fairness requirements and quality of service guarantees in multi-user scenarios.

[0003] In the prior art, broadband communication systems for a large number of users mainly adopt beamforming technologies based on multiple radio frequency chains to achieve multi-user services through space division multiple access. However, this technical solution has obvious limitations: the number of radio frequency chains in the system directly determines the independent generation ability of spatial beams. Specifically, since each user requires an independent digital baseband data stream to achieve spatial separation, and each radio frequency chain can only support one independent data stream, the upper limit of the number of radio frequency chains strictly restricts the number of users that the system can serve simultaneously. When the radio frequency chain resources are insufficient, the system cannot allocate independent beams to all users, resulting in a significant reduction in the total number of servable users.

[0004] To overcome the technical bottleneck brought by the limitation of the number of radio frequency chains, the prior art has proposed a hybrid access scheme combining frequency division multiple access. This scheme designs a subcarrier allocation strategy through a heuristic algorithm and performs beamforming design accordingly, which alleviates the problem of limited radio frequency chain resources to a certain extent. However, this scheme still has the following technical defects: firstly, due to the influence of the beam offset effect, the performance of the analog beamformer designed by the existing method needs to be further improved in the broadband scenario; secondly, there is a coupling relationship between the digital beamforming matrix, the analog beamforming matrix, and the subcarrier allocation scheme, which requires joint optimization. However, the existing method designs the subcarrier allocation scheme first and then designs the beamforming, and this step-by-step design strategy cannot better optimize the system performance.

[0005] Currently, the beamforming design methods for broadband communication systems in large-scale user scenarios still have significant technical defects in terms of system performance, resource utilization efficiency, and optimization strategies, and there is an urgent need to propose new technical solutions to solve the above problems. Summary of the Invention

[0006] An embodiment of the present invention provides a beamforming method and apparatus for a large number of users, which are used to solve the problems of beam offset effect, coupling relationship, etc. existing in the beamforming design method of a broadband communication system in the existing large-scale user scenario, resulting in the problem that the broadband communication system cannot better optimize the system performance.

[0007] An embodiment of the present invention provides a beamforming method for a large number of users, including:

[0008] Based on the number of radio frequency chains, the total number of user equipments, and the total number of subcarriers included in the set system, clustering the user channel vectors of each subcarrier through the K-means algorithm to determine the final user set of each channel cluster;

[0009] For each channel cluster included in each subcarrier, select the final user with the largest channel gain to generate an initial subcarrier allocation matrix; determine the equivalent channel vector according to the initial analog beamformer and the user channel vector, and iteratively optimize the receive combiner, mean square error, and digital beamformer. When the difference between the sums of the mean square errors of adjacent iterations is less than the first threshold, determine the optimal digital beamformer;

[0010] Expand the analog beamformer into a vector, and use the conjugate gradient method to iteratively update the analog beamformer based on the conjugate Euclidean gradient of the objective function until the change amount of the objective function between adjacent iterations is less than the second threshold, and then determine the optimal analog beamformer;

[0011] According to each column included in the hybrid beamforming matrix of each subcarrier, determine the signal-to-interference-plus-noise ratio (SINR) of the final user, select the final user with the largest SINR to allocate the precoding vector, and generate an optimized subcarrier allocation matrix.

[0012] An embodiment of the present invention provides a beamforming apparatus for a large number of users, including:

[0013] A first determination unit, configured to cluster the user channel vectors of each subcarrier through the K-means algorithm based on the number of radio frequency chains, the total number of user equipments, and the total number of subcarriers included in the set system, and determine the final user set of each channel cluster;

[0014] A second determination unit, configured to, for each channel cluster included in each subcarrier, select the final user with the largest channel gain to generate an initial subcarrier allocation matrix; determine the equivalent channel vector according to the initial analog beamformer and the user channel vector, and iteratively optimize the receive combiner, mean square error, and digital beamformer. When the difference between the sums of the mean square errors of adjacent iterations is less than the first threshold, determine the optimal digital beamformer;

[0015] A third determination unit, configured to expand the analog beamformer into a vector, and based on the conjugate Euclidean gradient of the objective function, use the conjugate gradient method to iteratively update the analog beamformer until the change in the objective function between adjacent iterations is less than a second threshold, and then determine the optimal analog beamformer;

[0016] A generation unit, configured to determine the signal-to-interference-plus-noise ratio (SINR) of each end user according to each column included in the hybrid beamforming matrix of each subcarrier, select the end user with the largest SINR to allocate a precoding vector, and generate an optimized subcarrier allocation matrix.

[0017] An embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor is caused to execute the method for beamforming for a large number of users as described in any one of the above.

[0018] An embodiment of the present invention provides a computer-readable storage medium, storing a computer program. When the computer program is executed by a processor, the processor is caused to execute the method for beamforming for a large number of users as described in any one of the above. Description of the Drawings

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0020] Figure 1 It is a schematic flowchart of a method for beamforming for a large number of users provided by an embodiment of the present invention;

[0021] Figure 2 It is a curve graph showing the variation of the total rate of different beamforming methods with the signal-to-noise ratio provided by an embodiment of the present invention;

[0022] Figure 3 It is a schematic curve graph showing the variation of the total rate of different beamforming methods with the number of users provided by an embodiment of the present invention;

[0023] Figure 4 It is a schematic structural diagram of a device for beamforming for a large number of users provided by an embodiment of the present invention. Detailed Embodiments

[0024] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0025] Figure 1 It is a schematic flowchart of a beamforming method for a large number of users provided by an embodiment of the present invention. The following will be combined with Figure 1 , and the beamforming method provided by the embodiment of the present invention will be introduced in detail. As Figure 1 shown, the method includes the following steps:

[0026] Step 101: Based on the number of radio frequency chains, the total number of user equipment, and the total number of subcarriers included in the set system, cluster the user channel vectors of each subcarrier through the K-means algorithm to determine the final user set of each channel cluster;

[0027] Step 102: For each channel cluster included in each subcarrier, select the user with the largest channel gain to generate an initial subcarrier allocation matrix; determine the equivalent channel vector according to the initial analog beamformer and the user channel vector, and through iterative optimization of the receive combiner, mean square error, and digital beamformer, when the difference between the sum of the mean square errors of adjacent iterations is less than the first threshold, determine the optimal digital beamformer;

[0028] Step 103: Expand the analog beamformer into a vector, and based on the conjugate Euclidean gradient of the objective function, use the conjugate gradient method to iteratively update the analog beamformer until the change amount of the objective function between adjacent iterations is less than the second threshold, and then determine the optimal analog beamformer;

[0029] Step 104: Determine the final user signal-to-interference-plus-noise ratio according to each column of the hybrid beamforming matrix of each subcarrier, select the final user with the largest signal-to-interference-plus-noise ratio to allocate the precoding vector, and generate an optimized subcarrier allocation matrix.

[0030] Before introducing the beamforming method provided by the embodiment of the present invention, first based on Figure 2 , the broadband communication system model involved in the embodiment of the present invention will be introduced.

[0031] As Figure 2 shown, the system is a single-cell broadband large-scale user large-scale antenna system, which is equipped with multiple transmit antennas N t and multiple radio frequency chains N RF , and the multiple transmit antennas and multiple radio frequency chains are used to provide services for multiple user equipment N U , where N t ≥NRF , N U > N RF .

[0032] Furthermore, the system uses multiple subcarriers K, combines spatial division multiple access technology, and serves multiple users through beamforming. In the beamforming architecture of the base station, the data of the system can be represented as a preset matrix of N s ×K for representing data. Each row of the preset matrix represents the dimension N of the data stream s , and each column of the preset matrix represents the dimension of the subcarrier.

[0033] First, beamforming is performed through a preset low-dimensional baseband digital beamformer (initial digital beamformer) to achieve preliminary signal adjustment and direction optimization. Then, through the inverse fast Fourier transform (IFFT) of multiple subcarriers in parallel by multiple radio frequency chains, the frequency-domain signal is converted into the time domain. Next, a cyclic prefix is added to the transformed time-domain signal to resist inter-symbol interference caused by the multipath channel. Finally, through the processing of a preset radio frequency analog beamformer , the signal is adjusted in an appropriate beam direction and sent to multiple user devices through multiple transmit antenna arrays.

[0034] To introduce the method provided by the embodiments of the present invention, it is necessary to further formulate the system model variables.

[0035] Set the subcarrier allocation matrix Γ In practical applications, when Γ(k, u) = 1, it means that the k-th subcarrier is allocated to the u-th user; when Γ(k, u) = 0, it means that the k-th subcarrier is not allocated to the u-th user.

[0036] Furthermore, to meet the physical limitations of the system, since the dimension of each column vector s[k] is N s , this means that the k-th subcarrier can serve at most N s users simultaneously. Therefore, for any k-th subcarrier, it needs to satisfy the following constraint condition:

[0037] ‖Γ(k, :)‖2 ≤ N s (1)

[0038] where ‖Γ(k, :)‖2 represents the l2 norm of the k-th row of the subcarrier allocation matrix Γ, that is, the number of users served by the k-th subcarrier cannot exceed the data stream dimension, and N s represents the data stream dimension. In the embodiments of the present invention, N s = N RF .

[0039] At this time, the signal received by the i-th user on the k-th subcarrier is represented by the following formula:

[0040]

[0041] where y u [k] represents the signal received by the u-th user on the k-th subcarrier; Γ(k,u) represents the allocation relationship between the k-th subcarrier and the u-th user in the subcarrier allocation matrix, K represents the total number of subcarriers used by the entire system, N U represents the total number of user equipments included in the entire system; k represents the subcarrier serial number, u represents the user serial number; h u [k] represents the channel vector of the u-th user on the k-th subcarrier, N t represents the number of base station transmitting antennas, represents the conjugate transpose of h u [k]; F represents the analog beamformer; w u [k] represents the beamforming vector corresponding to the u-th user on the k-th subcarrier, which is the u-th column vector of W[k], N RF represents the number of radio frequency chains included in the entire system; w i [k] represents the beamforming vector corresponding to the i-th user on the k-th subcarrier; s u [k] represents the symbol transmitted to the u-th user on the k-th subcarrier, and E{|s u [k]|} = 1; s i [k] represents the symbol transmitted to the i-th user on the k-th subcarrier, satisfying E{|s i [k]|} = 1; Γ(k,i) represents the allocation relationship between the k-th subcarrier and the i-th user in the subcarrier allocation matrix; n u [k] represents the noise of the u-th user on the k-th subcarrier.

[0042] It should be noted that in the above formula (1), when Γ(k,u) = 1, it means that the k-th subcarrier is allocated to the u-th user equipment; when Γ(k,u) = 0, it means that the k-th subcarrier is not allocated to the u-th user equipment; F represents the analog beamformer, which is used to perform beamforming operation on the signal in the analog domain. The analog beamformer is an N t ×N RF dimensional complex matrix, N t represents the number of base station transmitting antennas, N RF represents the number of radio frequency chains. y u[k] is a semaphore that incorporates multiple factors and can be used later to calculate the achievable rate of the user, etc.; h u [k] is a complex vector that describes the channel characteristics from the base station to the u-th user on the k-th subcarrier; the meaning of Γ(k,i) is basically the same as that of Γ(k,u), but in this formula, that is, in the summation term, it is used to determine whether the other user i except u is allocated the k-th subcarrier, so as to determine the interference signal situation for the u-th user; n u [k] represents the additive white Gaussian noise (AWGN) of the u-th user on the k-th subcarrier, whose mean is zero and variance is

[0043] Furthermore, in order to measure the speed performance of data transmission of each user on its subcarrier, the achievable rate of the u-th user on the k-th subcarrier can be determined by the following formula:

[0044]

[0045] where R u [k] represents the achievable rate of the u-th user on the k-th subcarrier, K represents the total number of subcarriers used by the entire system, represents the noise variance of the u-th user on the k-th subcarrier, and B represents the bandwidth of the system. In this formula, reflects the power magnitude of the noise. The noise will interfere with signal transmission and affect the achievable rate of the user.

[0046] Furthermore, assume that the number of channel clusters between the base station and the user is N nl , and the number of rays contained in each channel cluster is N ray , then the d-beat delay channel of the u-th user on the k-th subcarrier can be determined by the following formula:

[0047]

[0048] where h u,d represents the d-beat delay channel vector of the u-th user on the k-th subcarrier, N nl represents the number of channel clusters existing in the millimeter-wave channel, representing the clustering number of signal propagation paths in the channel, N ray represents the number of rays contained in each channel cluster, that is, the specific path number of signal propagation in each clustering, N t represents the number of base station transmit antennas, dT - τ un represents the input parameter of the filter, T represents the sampling period, τ unDenote the time delay between the \(u\)-th user and the \(n\)-th channel cluster, which reflects the propagation delay time of the signal from the base station to this user through \(n\) channel clusters, \(\theta\). unr Denote the emission angle of the \(r\)-th ray in the \(n\)-th channel cluster for the \(u\)-th user, which determines the propagation direction of the signal, \(\alpha\). unr Denote the complex path gain of the \(r\)-th ray in the \(n\)-th channel cluster for the \(u\)-th user, \(a(\theta\). unr , \(f)\) represents the vector related to the emission angle \(\theta\). unr and the frequency \(f\), which is used to describe the radiation characteristics of the antenna array in a specific direction and frequency. \(a(\theta, f)\) represents the modified transmission array steering vector of the base station at the frequency \(f\), and \(p(\tau)\) represents the raised cosine pulse shaping filter.

[0049] In the implementation of the present invention, the modified steering vector can be expressed as:

[0050]

[0051] Among them, \(a(\theta\). ucr , \(f)\) represents the vector related to the emission angle \(\theta\). unr and the frequency \(f\), \(f_0\) represents the reference carrier frequency, \(\theta\). ucr Denote the emission angle of the \(r\)-th ray in the \(n\)-th channel cluster for the \(u\)-th user. Denote the complex exponential term, which reflects the phase change caused by the changes in the emission angle and frequency. Among them, \(j\) is the imaginary unit. is a part of the parameters in the complex exponential term, which together with the emission angle \(\sin\theta\). unr determines the phase change amount together.

[0052] In the frequency domain, the channel vector of the \(u\)-th user on the \(k\)-th subcarrier can be expressed as:

[0053]

[0054] Among them, \(h\). u [k] represents the channel vector of the \(u\)-th user on the \(k\)-th subcarrier, \(h\). u,d represents the channel vector with \(d\) beat delays of the \(u\)-th user on the \(k\)-th subcarrier. \(d\) represents the number of delay beats, and its value range is \(0\leq d\leq D - 1\). \(D\) represents the total number of delay beats, representing the number of different delay states considered. Denote the phase factor, which reflects the phase rotation of the signals with different delays \(d\) on the \(k\)-th subcarrier and is used to adjust the phase when superimposing the channel vectors with different delays in the frequency domain.

[0055] Furthermore, in the embodiments of the present invention, the system sum rate maximization is used as the optimization objective to illustrate the embodiments. The optimization problem of system rate maximization aims to maximize the total transmission performance of the system by jointly optimizing the subcarrier allocation matrix and the hybrid beamformer including the optimal digital beamformer and the optimal analog beamformer. The problem of maximizing the system sum rate can be described as:

[0056]

[0057] Among them, the constraint formulas (7-2) and (7-3) respectively ensure binary subcarrier allocation and the maximum number of users that can be served on each subcarrier. It shows the constraint condition Γ(k,u) ∈ {0,1}, for each k-th subcarrier (k corresponds to the K subcarriers in the system) and each u-th user (u corresponds to the N U user equipment). Then it is limited that ||Γ(k,:)||2 ≤ N s which is applicable to each k-th subcarrier; the constraint (7-4) is the constant modulus constraint of the analog beamformer. It means that |F(i1,j1)| = 1 holds for each element of the analog beamformer matrix F (the analog beamformer matrix F is represented by i1 for the row index and j1 for the column index). The constraint (7-5) limits the transmit power budget of each subcarrier. Then it is limited that || which is applicable to each k-th subcarrier.

[0058] Based on the above-provided broadband communication system model, the beamforming method provided by the embodiments of the present invention is introduced in detail as follows: Figure 2 The broadband communication system model provided above is used to introduce in detail the beamforming method provided by the embodiments of the present invention:

[0059] In step 101, according to the single-cell broadband large-scale user large-scale antenna system provided above, it is assumed that the number of radio frequency chains, the number of base station transmit antennas, the total number of user equipment included in the system, and the total number of subcarriers used by the system are known.

[0060] At the first iteration, several initial users are randomly selected from the total number of user equipments included in the system as the initial cluster centers of the first subcarrier. Here, the number of randomly selected initial users is the same as the number of radio frequency chains included in the system. Further, according to the number of user equipments included in the system, the normalized distances between each initial user and each initial cluster center are determined in sequence. The distances between each determined initial user and the initial cluster center are sorted, and each initial user is assigned to a channel cluster that is the closest to it in distance, so as to obtain the initial user set of each channel cluster. In the embodiment of the present invention, the number of channel clusters is equal to the number of initial cluster centers, that is, if there are several initial cluster centers, there will be several corresponding channel clusters. Further, the sum of the distances between each initial user included in the first channel cluster and the initial users included in other channel clusters (the second channel cluster) is determined, and the initial user with the maximum distance is determined as the updated cluster center of the first channel cluster.

[0061] It should be noted that the first channel cluster here is any one in the channel cluster set, and the channel cluster set includes a first channel cluster and multiple second channel clusters. In practical applications, the total number of the first channel cluster and multiple second channel clusters included in the channel cluster is the same as the number of initial cluster centers. In the above introduction, in order to avoid confusion caused by multiple channel clusters, the first channel cluster is taken as an example for introduction. When determining the sum of the distances between each initial user included in the first channel cluster and the initial users included in other channel clusters, all other channel clusters in the channel cluster set except the first channel cluster can be collectively referred to as the second channel cluster, and the specific number of the second channel cluster is not limited here.

[0062] Further, after determining the updated cluster center of the first channel cluster, the updated cluster centers of multiple second channel clusters included in the channel cluster set can be determined according to the same method.

[0063] Specifically, the normalized distance between each initial user and each initial cluster center is determined according to the following formula:

[0064]

[0065] Where, represents the normalized distance used for clustering of the u init th initial user and the i init th initial user on the kth subcarrier, represents the conjugate transpose of, represents the channel vector of the u init th user on the kth subcarrier, represents the channel vector of the i init th initial user on the kth subcarrier, and ‖·‖2 represents the L2 norm.

[0066] Further, each initial user is assigned to the nearest channel cluster according to the following formula:

[0067]

[0068] where n ★ represents the index of the nearest channel cluster, within the range of 1 ≤ n ≤ N s such that the value of n when obtains the minimum value, that is, the index of the nearest channel cluster to which the u init th initial user is assigned, and N s represents the data stream dimension, represents the normalized distance between the u init th initial user and the initial cluster center μ n [k] of the nth channel cluster on the kth subcarrier, and μ n [k] represents the initial cluster center of the nth channel cluster on the kth subcarrier.

[0069] Further, after determining the sum of the distances between each initial user included in the first channel cluster and all initial users included in each second channel cluster, the initial user with the maximum distance is determined as the updated cluster center of the first channel cluster through the following formula:

[0070]

[0071] where, represents the updated cluster center of the nth channel cluster on the kth subcarrier, which is determined by finding the initial user with the maximum sum of the distances to all initial users in other channel clusters (second channel clusters) in the current nth channel cluster (first channel cluster), and argmax represents the maximization operator, represents the updated cluster center of the nth channel cluster corresponding to the kth subcarrier, which is determined by finding the user with the maximum sum of the distances to all initial users in other channel clusters (second channel clusters) in the current nth channel cluster (first channel cluster), and μ n [k] represents the cluster center of the nth channel cluster on the kth subcarrier. Here, the center of the channel cluster can include any one of the initial cluster center, updated cluster center, and iterative cluster center, represents the normalized distance used for clustering between the u init th initial user and the i init th initial user on the kth subcarrier. It can also be understood as the normalized clustering metric between the initial user u init belonging to a certain channel cluster (second channel cluster) and another initial user i init on the kth subcarrier, which is used to calculate the distance relationship between initial users to determine the updated cluster center or iterative cluster center of the first channel cluster. Indicates the temporary allocation result of the initial users in the n-th channel cluster of the k-th subcarrier, that is, it contains all the initial users divided into the n-th channel cluster.

[0072] It should be noted that after the first iteration, after determining the updated cluster center of each channel cluster based on the initial cluster center of the channel cluster, if the convergence condition of the K-means algorithm is not satisfied, then based on the updated cluster center of each channel cluster obtained in the first iteration, that is, regarding the updated cluster center of each channel cluster obtained in the first iteration as the initial cluster center in the first iteration, and then according to the above method, obtain the updated user set of each channel cluster and the iterative cluster center of each channel cluster. Based on the K-means algorithm, it is judged whether the iterative cluster center obtained in this iteration satisfies the convergence condition. If the convergence condition of the K-means algorithm is satisfied, the updated user set of each channel cluster can be determined as the final user set.

[0073] In practical applications, when the number of iterations reaches the initially limited number of iterations, the updated user set of each channel cluster obtained in the last iteration can also be determined as the final user set.

[0074] For example, assume N RF = 3, K = 8, N U = 15. For the k = 3 subcarrier, the following is a complete example of the implementation of the K-means algorithm:

[0075] Initial setting, in this embodiment, since N RF = 3, so randomly select 3 initial users as the initial cluster center of the 3rd subcarrier. Assume the selected initial users are 2, 6, and 11 respectively, then there are initial cluster centers μ1[3] = 2, μ2[3] = 6, μ3[3] = 11.

[0076] First iteration: Allocate the initial users to the channel cluster with the closest distance. For the u = 4th user, its normalized distance from each initial cluster center can be determined by formula (8) According to formula (9), n ★ = 2, that is, the 4th initial user is allocated to the 2nd channel cluster. In the same way, allocate the 14 initial users to the channel cluster with the closest distance to them. Assume that after allocating all the initial users, the initial user set of the 1st channel cluster Ω1[3] = {2, 5, 9}, the initial user set of the 2nd channel cluster Ω2[3] = {4, 6, 7, 10}, and the initial user set of the 3rd channel cluster Ω3[3] = {11, 12, 13, 15}.

[0077] Further, for the first channel cluster, calculate the sum of the distances between each initial user included in the first channel cluster and all the initial users included in other channel clusters (the second channel clusters, namely the second and third channel clusters), that is with other channel clusters (the second channel clusters) the sum of the distances to all the initial users Suppose it is found that when u = 5 after calculation, is the maximum, then the updated cluster center of the first channel cluster can be determined For the second channel cluster, based on the above method, the updated cluster center of the second channel cluster can be determined Similarly, determine the updated cluster center of the third channel cluster

[0078] Second iteration: Based on the updated cluster centers determined in the first iteration as the basis, recalculate the normalized distance between each initial user and the updated cluster center. For example, for the u init = 8th user, its normalized distance from each initial cluster center can be determined by formula (8): According to formula (9), n ★ = 1 can be obtained, that is, the 8th initial user is assigned to the first channel cluster. In the same way, and assign the 14 initial users to the channel clusters with the closest distance to them respectively. Suppose after all the initial users are assigned, the updated user set Ω1[3] of the first channel cluster = {2, 5, 8, 9}, the updated user set Ω2[3] of the second channel cluster = {4, 6, 7, 10}, and the updated user set Ω3[3] of the third channel cluster = {11, 12, 13, 15}.

[0079] Further, for the first channel cluster, recalculate the sum of the distances between each updated user included in the first channel cluster and all the updated users included in other channel clusters. Suppose it is found that when u = 5 after calculation, that is is the maximum, then the iterative cluster center of the first channel cluster can be determined Similarly, determine the iterative cluster center of the second channel cluster the iterative cluster center of the third channel cluster

[0080] Since the iterative cluster centers remain unchanged after the second iteration (the same as the updated cluster centers after the first iteration), meeting the convergence condition of the K-means algorithm, the iteration can be stopped, and the updated user set of each channel cluster is determined as the final user set of the channel cluster (channel clustering result).

[0081] In step 102, the channel gain of each end user included in each channel cluster can be determined according to the set of end users of each channel cluster included in each subcarrier, and then the end user with the maximum channel gain in each channel cluster can be selected for service, so as to obtain an initial subcarrier allocation matrix.

[0082] Specifically, after determining the channel gain of each end user, the end user with the maximum channel gain in each channel cluster can be selected for service through the following formula:

[0083]

[0084] where, u f,n [k] represents the number of the end user selected for service in the nth channel cluster on the kth subcarrier, n represents the index of the channel cluster, and the value range is 1 ≤ n ≤ N s , N s is the data stream dimension and also represents the number of channel clusters, k represents the subcarrier serial number, represents the channel vector of the u f th end user on the kth subcarrier, and Ω n [k] represents the set of end users in the nth channel cluster on the kth subcarrier, that is, it includes all users divided into the nth channel cluster and corresponding to the kth subcarrier.

[0085] For example, assume there are N s = 3 channel clusters (data stream dimension), K = 4 subcarriers (k = 1, 2, 3, 4), and at the same time there are N U = 6 initial users (u = 1, 2, 3, 4, 5, 6).

[0086] First of all, it is necessary to define the set of end users Ω n [k] of each channel cluster on each subcarrier. For the k = 1 subcarrier, it includes 3 channel clusters, and the set of end users of each channel cluster is respectively: Ω1[1] = {1, 2, 3}, Ω2[1] = {4, 5}, Ω3[1] = {6}; for the k = 2 subcarrier, it includes 3 channel clusters, and the set of end users of each channel cluster is respectively: Ω1[2] = {1, 3, 6}, Ω2[2] = {2, 4}, Ω3[2] = {5}; for the k = 3 subcarrier, it includes 3 channel clusters, and the set of end users of each channel cluster is respectively: Ω1[3] = {2, 4, 5}, Ω2[3] = {1, 6}, Ω3[3] = {3}; for the k = 4 subcarrier, it includes 3 channel clusters, and the set of end users of each channel cluster is respectively: Ω1[4] = {3, 5, 6}, Ω2[4] = {1, 2, 4}, Ω3[4] = {1}.

[0087] Next, assume that the channel vectors of each end user on each subcarrier are as follows: for the \(u = 1\)st end user, \(h_1[1]=[1,2]\), \(h_1[2]=[3,4]\), \(h_1[3]=[5,6]\), \(h_1[4]=[7,8]\); for the \(u = 2\)nd end user, \(h_2[1]=[2,3]\), \(h_2[2]=[4,5]\), \(h_2[3]=[6,7]\), \(h_2[4]=[8,9]\); for the \(u = 3\)rd end user, \(h_3[1]=[3,4]\), \(h_3[2]=[5,6]\), \(h_3[3]=[7,8]\), \(h_3[4]=[9,10]\); for the \(u = 4\)th end user, \(h_4[1]=[4,5]\), \(h_4[2]=[6,7]\), \(h_4[3]=[8,9]\), \(h_4[4]=[10,11]\); for the \(u = 5\)th end user, \(h_5[1]=[5,6]\), \(h_5[2]=[7,8]\), \(h_5[3]=[9,10]\), \(h_5[4]=[11,12]\); for the \(u = 6\)th end user, \(h_6[1]=[6,7]\), \(h_6[2]=[8,9]\), \(h_6[3]=[10,11]\), \(h_6[4]=[12,13]\).

[0088] Then, according to formula (11), select the end user with the maximum channel gain in each channel cluster. For the \(k = 1\)st subcarrier, in \(\Omega_1[1]=\{1,2,3\}\), there are \(h_1[1]=[1,2]\), \(h_2[1]=[2,3]\), and \(h_3[1]=[3,4]\). Further: According to formula (11), \(u\) n [k]=u1[1]=3. That is, the number of the end user selected for service in the first channel cluster on the \(k = 1\)st subcarrier is 3. It can also be said that the 3rd end user in the first channel cluster on the 1st subcarrier is selected for service.

[0089] According to the above method, for the \(k = 1\)st subcarrier, in \(\Omega_2[1]=\{4,5\}\), \(u\) n [k]=u2[1]=5. In \(\Omega_3[1]=\{6\}\), \(u\) n [k]=u3[1]=6.

[0090] Similarly, for the \(k = 2\)nd subcarrier, \(u\) n [k]=u1[2]=6, \(u\) n [k]=u2[2]=4, \(u\) n [k]=u3[2]=5; for the \(k = 3\)rd subcarrier, \(u\) n [k]=u1[3]=5, \(u\) n [k]=u2[3]=6, \(u\) n [k]=u3[3]=3; for the \(k = 4\)th subcarrier, \(u\)n [k]=u1[4]=6, u n [k]=u2[4]=4, u n [k]=u3[4]=1.

[0091] Furthermore, based on the above content, the initial subcarrier allocation matrix can be obtained:

[0092]

[0093] Among them, the i-th row (i = 1, 2, 3) of the initial subcarrier allocation matrix represents the i-th channel cluster, the j-th column (j = 1, 2, 3, 4) represents the j-th subcarrier, and the elements in the initial subcarrier allocation matrix represent the number of the end user selected for service in this channel cluster on this subcarrier.

[0094] Furthermore, the equivalent channel vectors are obtained according to the initial analog beamformer and the channel vectors of each end user on each subcarrier.

[0095] In a wireless communication system, the initially provided digital beamformer can perform weighted processing on the signals on each subcarrier and is obtained by adjusting the amplitude and phase of the signals. However, the initially provided analog beamformer at this time is only an initial state and is not necessarily optimal.

[0096] Furthermore, by iteratively optimizing the receive combiner, the mean square error, and the digital beamformer, when the difference between the sums of the mean square errors of adjacent iterations is less than the first threshold, the optimal digital beamformer is determined.

[0097] Specifically, based on the equivalent channel vectors, the initial digital beamformer, and the noise variance, the receive combiners of each end user included on each subcarrier, the mean square error of each end user receiving signals on each subcarrier, and the digital beamformers corresponding to each end user on each subcarrier are obtained.

[0098] In practical applications, the equivalent channel vector of the first end user on the first subcarrier can be determined first. Based on the equivalent channel vector of the first end user on the first subcarrier, the beamforming vector (initial beamformer) corresponding to the first end user on the first subcarrier, and the noise variance of the first end user on the first subcarrier, the receive combiner of the first end user on the first subcarrier, the mean square error of the first end user receiving signals on the first subcarrier, and the designed digital beamformer of the first end user on the first subcarrier are obtained.

[0099] The first end user here is any one of the end users, and the end users are determined by the initial subcarrier allocation matrix obtained according to the above steps; the first subcarrier is also any one of the multiple subcarriers.

[0100] Specifically, the equivalent channel vector of the first end user on the first subcarrier is determined by the following formula:

[0101]

[0102] Where represents the conjugate transpose of represents the equivalent channel vector of the u f -th end user on the k-th subcarrier, F represents the analog beamformer, represents the channel vector of the u f -th end user on the k-th subcarrier, represents the conjugate transpose of

[0103] Furthermore, the receive combiner of the first end user on the first subcarrier, the mean square error of the received signal of the first end user on the first subcarrier, and the digital beamformer of the first end user on the first subcarrier are sequentially determined by the following formulas:

[0104]

[0105] Where represents the receive combiner of the u f -th end user on the k-th subcarrier, represents the beamforming vector corresponding to the u f -th end user on the k-th subcarrier, represents the noise variance of the u f -th end user on the k-th subcarrier, represents the set of end users on the k-th subcarrier, represents the mean square error of the received signal of the u f -th end user on the k-th subcarrier, represents the weighting coefficient of the u f -th end user; J[k] represents a matrix on the k-th subcarrier, represents the weighting coefficient of the i f -th end user; represents the i f -th end user on the k-th subcarrier for the mean square error of the received information, represents the i fFor the receiver combiner of the end user, λ[k] represents the Lagrange multiplier of the k-th subcarrier.

[0106] During the iterative process, if the difference between the total mean square error of all end users on all subcarriers in the current iteration period and the total mean square error of all end users on all subcarriers in the previous iteration period is less than the first threshold, then the digital beamforming corresponding to each end user on each subcarrier in the current iteration period is determined as the optimal digital beamformer.

[0107] Specifically, each iterative process will calculate the equivalent channel vector, receive combiner, mean square error, and design digital beamformer of the first end user on each subcarrier. On this basis, it is necessary to determine the total mean square error of all end users on all subcarriers in the first iteration. After two consecutive iterations, it is necessary to determine the difference between the total mean square error of the previous iteration and the total mean square error of the current iteration. Then, according to the size of the difference and the cyclic iteration setting value, it is judged whether to stop the iteration. If the difference between the error sums is less than the setting value and the task reaches convergence, the iteration can be stopped; if the difference between the error sums is not less than the setting value, but the number of iterations is equal to the setting value, then whether it converges or not, the iteration is also stopped.

[0108] When the iteration stops, the designed digital beamformer of each end user on each subcarrier in the last iteration is determined as the optimal digital beamformer.

[0109] For example, assume there are K = 4 subcarriers (k = 1, 2, 3, 4), the base station transmitting antenna N t = 8, the entire system includes radio frequency chains N RF = 2, N s = 2 channel clusters (data stream dimensions), and at the same time there are N U = 6 initial users (u = 1, 2, 3, 4, 5, 6).

[0110] At the same time, set the maximum number of iterations for digital beamformer optimization to 5 times, and the convergence judgment criterion is that the difference between the total mean square error of all users on all subcarriers in two adjacent iterations is less than 0.001.

[0111] Initial setting, randomly generate the subcarrier allocation matrix Γ, which is a 4*6 binary matrix: It satisfies Γ(k,u) ∈ {0, 1} and ‖Γ(k,:)‖2 ≤ N s . Randomly generate the analog beamformer F, which is an 8*2 complex matrix, as follows: It satisfies |F(i1,j1)| = 1. The initial digital beamformer Each W[k] is a 2*1 complex matrix, for example

[0112] The first iteration of the digital beamforming optimizer loop: For the k = 1st subcarrier, if the set of end users served on the k = 1st subcarrier is then the equivalent channel vectors of the u f = 1 end user on the k = 1st subcarrier and the u f = 3 end users on the k = 1st subcarrier can be determined respectively by formula (13), specifically: Assume there are: Calculation gives and

[0113] Furthermore, according to formula (14), calculate successively the receive combining matrix of the u f = 1 end user on the k = 1st subcarrier and the receive combining matrix of the u f = 3 end users on the k = 1st subcarrier, specifically: Assume ζ1[1] and ζ3[1] can be obtained. e u [k] represents the mean square error of the received signal of the u f = 1 end user on the k - 1st subcarrier.

[0114] Furthermore, according to formula (15), calculate the mean square error of the received signal of the u f = 1 end user on the k = 1st subcarrier and the mean square error of the received signal of the u f = 3 end users on the k = 1st subcarrier. Furthermore, design the digital beamformer according to formulas (16) and (17). For k = 2, 3, 4 subcarriers, the calculation process for k = 1 subcarrier can be repeated to obtain the mean square error of the received signal of each end user on each subcarrier

[0115] Furthermore, calculate the sum of the mean square errors MSE of all end users on all subcarriers in the first iteration sum1 :

[0116]

[0117] Second iteration: For the k = 1st subcarrier, use the parameters such as W1[1] and W3[1] updated in the previous iteration, and repeat the steps of calculating the equivalent channel vector, receive combining matrix, mean square error, and designing the digital beamformer.

[0118] For the subcarriers with \(k = 2, 3, 4\), the above calculation steps are repeated; calculate the sum of mean square errors \(MSE\) of the received signals of all end-users on all subcarriers in the second iteration. sum2 :

[0119]

[0120] Furthermore, according to \(diff = |MSE\) sum2 - MSE\) sum1 |, calculate the difference between the sum of mean square errors in the first iteration and the sum of mean square errors in the second iteration. If \(diff < 0.001\), it is considered that convergence is achieved, the iteration is stopped, and the designed digital beamformer obtained in the second iteration is determined as the optimal digital beamformer. If \(diff\geq0.001\) and the number of loop iterations is less than the set value, the next iteration continues; if the number of loop iterations reaches the set value, the iteration is also stopped regardless of whether convergence is achieved.

[0121] After obtaining the optimal digital beamformer, an analog beamformer can be designed. In the embodiment of the present invention, there is the following optimization problem:

[0122]

[0123] In practical applications, due to the non-convex constant modulus constraint in the design of the analog beamformer (i.e., the modulus value is always 1 in the constraint condition shown in formula (7-4)), this problem is difficult to solve directly.

[0124] Note that the vector \(x = vec(F)\) actually constitutes a manifold, and the definition of the manifold here is:

[0125] M m = x\in\mathbb{C} m : |x_1| = |x_2| = \cdots = |x m | = 1\ (19)

[0126] where \(M m represents the manifold composed of the vector \(x\), where the vector \(x\) is the vector obtained by expanding the analog beamformer by columns, that is, \(x = vec(F)\); \(m = N t N RF and \(x m represents the \(m\)-th element of the vector \(x\), and \(m\) represents the dimension of the vector \(x\).

[0127] In practical applications, the manifold optimization method can be used to obtain the local optimal solution of the analog beamformer. Similar to the gradient descent in the Euclidean space, the manifold optimization is essentially an iterative optimization based on the Riemannian Gradient in the Tangent Space. For the manifold \(M mThe vector x on it, whose tangent space is expressed as:

[0128]

[0129] where, T x M m represents the tangent space of the manifold M m at the point x, z represents a vector in the tangent space T x M m , denotes the Hadamard product, that is, the corresponding elements of two matrices or vectors of the same dimension are multiplied, x * represents the conjugate vector of the vector x, 0 m represents the zero vector of m dimensions, indicating that the real part in the constraint conditions of the tangent space is the zero vector.

[0130] Furthermore, the Riemannian gradient is the orthogonal projection of the Euclidean gradient on the tangent space, and its expression is as follows:

[0131]

[0132] where, gradf(x) represents the Riemannian gradient of the function f(x) at the point x on the manifold M m , represents the orthogonal projection on the tangent space T x M m .

[0133] Through the above expressions of the Riemannian gradient and the complex circular manifold, manifold optimization can search for the optimal solution by means of iterative gradient descent. In actual optimization, the traditional Euclidean gradient descent algorithm (such as the conjugate gradient method) can be used to optimize the analog beamformer. The conjugate gradient method is an efficient iterative optimization algorithm that can reduce the error of the objective function by constructing conjugate directions.

[0134] In step 104, the analog beamformer is expanded into a vector. Based on the conjugate Euclidean gradient of the objective function, the conjugate gradient method is used to iteratively update the analog beamformer until the change amount of the objective function between adjacent iterations is less than the second threshold, and then the optimal analog beamformer is determined. Specifically, according to the initial analog beamformer, a manifold is obtained, and the conjugate Euclidean gradient of the objective function is obtained according to the set of final users served on each subcarrier, the optimal digital beamformer, the channel vector of each final user on each subcarrier, and the noise variance:

[0135]

[0136] where, represents the conjugate Euclidean gradient of the objective function f(x) with respect to the vector x, k represents the subcarrier number, and W[k] represents the precoding matrix of the k-th subcarrier, Denote the channel vector of the \(u\)th f end user on the \(k\)th subcarrier, Denote the conjugate transpose of, \(W[k]\) represents the hybrid beamforming matrix corresponding to the \(k\)th subcarrier, \(W\) * [k] represents the conjugate matrix of \(W[k]\), \(W\) T [k] represents the transpose matrix of \(W[k]\), \(f(x)\) represents the objective function, Denote the f noise variance of the \(u\)th * end user on the \(k\)th subcarrier, \(x\) t represents the conjugate vector of \(x\), \(x\) represents the \(m\)-dimensional complex vector obtained by expanding the analog beamforming matrix \(F\), \(m\) represents the dimension of the vector \(x\), \(m = N\) RF \(N\) t where \(N\) represents the number of transmit antennas, the number of transmit antennas, \(N\) RF represents the number of RF chains, Denote the transpose matrix of, Denote the conjugate matrix of, Denote the concatenated matrix obtained by removing the column corresponding to the \(u\)th f end user from the \(W[k]\) matrix, Denote the Kronecker product, \(B\) represents the system bandwidth, Denote the set of end users on the \(k\)th subcarrier.

[0137] During the iteration process, if the change in the minimum value of the objective function obtained in two adjacent iterations is less than the second threshold and the updated analog beamforming matrix satisfies the constraint conditions, stop the iteration and determine the updated analog beamforming matrix obtained in the current iteration as the optimal analog beamforming matrix.

[0138] For example, assume \(K = 3\), \(N\) t \(= 3\), \(N\) RF \(= 2\), \(N\) U \(= 5\), \(B = 1\), the maximum number of iterations is 10, and the convergence criterion is that the relative change in the objective function value in two adjacent iterations is less than \(0.01\).

[0139] For the initial analog beamforming matrix, randomly generate a \(4\times2\) complex matrix \(F\) as follows:

[0140] which satisfies \(|F(i1,j1)| = 1\).

[0141] The first iteration of the analog beamforming matrix optimization iteration process: Straighten the analog beamforming matrix \(F\) by column to get \(x=\text{vec}(F)\), and calculate the conjugate Euclidean gradient of the objective function First, determine the set of users Ω[k] served on each subcarrier k. Assume that Ω[1] = {1, 3}, Ω[2] = {2, 4}, and Ω[3] = {1, 5}. Given W[k] (optimized by the digital beamformer in the previous step), for example: h u [k] is known. For example, h1[1] = [1 + j2 - j3 + j4 - j] 2 , known, for example etc. Substitute the above into formula (22) for calculation

[0142] Furthermore, construct the conjugate direction d according to the conjugate gradient method, search for the minimum value of the objective function in the conjugate direction d to obtain the step size α, and update x: x = x + αd; reconvert the updated x into the matrix F and ensure that |F(i, j)| = 1; if not satisfied, make it satisfy the manifold constraint through the projection method.

[0143] Calculate the value of the objective function for this iteration Assume β u = 1, Calculate the achievable rate of each final user on each subcarrier through formula R u [k] and sum them up.

[0144] Second iteration: Repeat the above steps of calculating the conjugate Euclidean gradient, constructing the conjugate direction, searching for the minimum value, updating x and F.

[0145] Calculate the objective function f2 for this iteration and calculate the relative change If the relative change Δ < 0.01 (the second threshold), it is considered that convergence is reached, stop the iteration, and determine the currently iteratively obtained updated analog beamformer as the optimal analog beamformer; if the relative change Δ > 0.01 and the number of iterations is less than 10, continue the next iteration; if the number of iterations reaches 10, stop the iteration regardless of whether it converges.

[0146] After obtaining the optimal digital beamformer and the optimal analog beamformer respectively based on the above steps, the hybrid beamformer can be obtained.

[0147] In the embodiment of the present invention, due to the constraint conditions shown in formulas (7 - 2) and (7 - 3) and are for each independent subcarrier, each subcarrier can be optimized separately to achieve global optimality. For the k-th subcarrier, its optimization problem can be rewritten as:

[0148]

[0149] In practical applications, since the objective function only depends on the end users, it is only necessary to find the optimal end user for each column of the precoding matrix W[k].

[0150] In step 105, the end user signal-to-interference-plus-noise ratio is determined according to each column included in the hybrid beamforming matrix of each subcarrier, the end user with the largest signal-to-interference-plus-noise ratio is selected to allocate the precoding vector, and an optimized subcarrier allocation matrix is generated.

[0151] Specifically, each column vector of the hybrid beamformer corresponding to each subcarrier is determined. According to the channel vector of each end user on each subcarrier and the noise variance of each end user on each subcarrier, for each subcarrier, the ratio of each end user corresponding to each column vector of the hybrid beamformer is determined. Then, for a subcarrier and a column vector of the hybrid beamformer, the maximum ratio is selected from the ratios of multiple end users, that is, there is a data group with the following relationship: "subcarrier - column vector - maximum ratio". Here, the maximum ratio obtained from a column vector of the hybrid beamformer corresponding to each subcarrier can be determined as the end user signal-to-interference-plus-noise ratio.

[0152] In the embodiment of the present invention, by repeating the above method, multiple groups of "subcarrier - column vector - maximum ratio" can be obtained. Then, according to the corresponding relationship between the data group "subcarrier - column vector - maximum ratio" and the subcarrier allocation matrix, the subcarrier allocation matrix is updated. Here, the corresponding relationship is that the "subcarrier" in the data group corresponds to the row of the subcarrier allocation matrix, the "column vector" in the data group corresponds to the column of the subcarrier allocation matrix, and the "maximum ratio" in the data group corresponds to the specific value determined by the row and column of the subcarrier allocation matrix.

[0153] In the embodiment of the present invention, for the i-th column of the hybrid beamformer W[k] corresponding to the k-th subcarrier, the end user signal-to-interference-plus-noise ratio can be determined by the following formula:

[0154]

[0155] Wherein, represents the index of the end user with the largest ratio selected on the k-th subcarrier, represents the set of end users on the k-th subcarrier, represents the u f -th end user's channel vector on the k-th subcarrier, represents the conjugate transpose of, represents the u f -th end user's noise variance on the k-th subcarrier, Represents the i-th column vector of the hybrid beamformer W[k] corresponding to the k-th subcarrier, Represents the j-th column vector of the hybrid beamformer W[k] corresponding to the k-th subcarrier, W[k] represents the hybrid beamformer corresponding to the k-th subcarrier, argmax represents selecting the end user with the largest ratio, |·| 2 Represents the square of the absolute value of a complex number.

[0156] For example, assume N s = 2 channel clusters (data stream dimensions), K = 3, N U = 4, given that the hybrid beamformer has been determined, the precoding matrix

[0157] The channel vector of the u = 1st end user at the k = 1st subcarrier is: The channel vector of the u = 2nd end user at the k = 1st subcarrier is: The channel vector of the u = 3rd end user at the k = 1st subcarrier is: The channel vector of the u = 4th end user at the k = 1st subcarrier is: (This is just an example. In practice, the channel vectors of different subcarriers and end users will be generated according to the channel model). The noise variance

[0158] For k = 1 subcarrier: For the 1st column vector of the hybrid beamformer W[1] corresponding to the k = 1st subcarrier Select the first end user, calculate the ratios of the u = 1st end user, u = 2nd end user, u = 3rd end user, and u = 4th end user. Assume that the ratio of the u = 2nd end user is the largest, that is That is, the 1st column precoding vector of the k = 1st subcarrier is assigned to the u = 2nd end user.

[0159] For the 2nd column vector of W[1], according to the above algorithm, assume that the ratio of the u = 3rd end user is the largest, that is That is, the 2nd column precoding vector of the k = 1st subcarrier is assigned to the u = 3rd end user.

[0160] Furthermore, update the first row of the subcarrier allocation matrix according to the above results, Γ(1,2) = 1, Γ(1,3) = 1, and the remaining elements Γ(1,1) = 0, Γ(1,4) = 0. At the same time, check whether ‖Γ(1,:)‖2≤N s , here The constraint condition is satisfied.

[0161] For \(k = 2\) subcarriers and \(k = 3\) subcarriers, the above steps are repeated. Finally, \(\Gamma(2,2)=1\), \(\Gamma(2,4)=1\), and the remaining elements are 0, and \(\|\Gamma(2,:)\|_2\leq N\) s ; \(\Gamma(3,2)=1\), \(\Gamma(3,3)=1\), and the remaining elements are 0, and \(\|\Gamma(3,:)\|_2\leq N\) s .

[0162] Finally, the complete subcarrier allocation matrix \(\Gamma\) is obtained: This matrix is the result after subcarrier allocation optimization. In this way, the sum rate of the system on each subcarrier is improved as much as possible under the condition of meeting the constraint conditions.

[0163] To more clearly introduce a beamforming method for a large number of users provided by an embodiment of the present invention, specific values are set for simulation in the embodiment of the present invention. For various parameters in the broadband millimeter-wave system, specific values are set, and the following parameter settings remain unchanged in the simulation results. The center frequency is 73 GHz, the bandwidth is 3 GHz, and the number of subcarriers is set to \(K = 64\); the number of transmit antennas of the base station is \(N\) t \(= 32\), the number of RF chains is \(N\) RF \(= 4\), the number of transmit data streams is \(N\) s \(= 4\), the number of user equipment is \(N\) U \(= 48\). Assume the number of clusters is \(N\) cl \(= 5\), and the number of rays included in each channel cluster is \(N\) ray \(= 10\). The path gain \(\alpha\) ucr \(\sim CN(0,1)\), the mean value of the emission angle \(\theta\) ucr obeys a uniform distribution in the interval \([0, 2\pi]\), and the angular spread within each channel cluster is a Laplace distribution of 10 degrees. Assume that the power constraints of all subcarriers are the same, that is, \(P_1 = P_2=\cdots=P\) K . In the subsequent numerical results, the signal-to-noise ratio is defined as in the sum rate optimization problem

[0164] Figure 2 is the curve of the total rate of different beamforming methods provided by the embodiment of the present invention changing with the signal-to-noise ratio. As shown in Figure 2 , the method provided by the embodiment of the present invention is significantly superior to the matrix decomposition method and the step-by-step design method in terms of total rate optimization, especially in the scenario with a large number of RF chains. As the signal-to-noise ratio increases, the proposed method shows a trend of asymptotically approaching the performance upper limit of pure digital zero-forcing precoding, while the gap between other benchmark methods and the upper limit further expands with the increase of the signal-to-noise ratio. This shows that the method effectively improves the system performance while making full use of RF chains and system resources, and shows better robustness and optimization potential under high signal-to-noise ratio conditions.

[0165] Figure 3 This is a schematic diagram of the variation curve of the total rate of different beamforming methods provided by the embodiments of the present invention with respect to the number of users. As Figure 3 shown, the performance of the method provided by the embodiments of the present invention is superior to that of the other two benchmark methods in all cases of the number of users.

[0166] In summary, the embodiments of the present invention provide a beamforming method and device for a large number of users. The method performs channel clustering processing based on channel state information to distinguish the user channel characteristics of different frequencies; secondly, constructs a joint optimization model including a digital beamformer, an analog beamformer, and subcarrier allocation; finally, solves the joint optimization model through an iterative optimization algorithm to obtain an optimized beamforming matrix and subcarrier allocation scheme. This method combines space division multiple access and frequency division multiple access, enabling the system to serve a large number of users whose number exceeds the number of radio frequency chains, effectively overcoming the technical bottleneck brought by the limitation of the number of radio frequency chains in the large-scale user scenario; further, using an iterative alternating optimization method to simultaneously optimize the digital beamformer, the analog beamformer, and the subcarrier allocation scheme, providing a more accurate beamforming design method and a more general subcarrier allocation scheme, effectively improving the transmission performance of the system.

[0167] Based on the same inventive concept, the embodiments of the present invention provide a beamforming device for a large number of users. Since the principle of the device for solving technical problems is similar to that of a beamforming method for a large number of users, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be described again.

[0168] Figure 4 This is a schematic structural diagram of a beamforming device for a large number of users provided by the embodiments of the present invention. As Figure 4 shown, the device includes: a first determination unit 401, a second determination unit 402, a third determination unit 403, and a obtaining unit 404.

[0169] The first determination unit 401 is configured to cluster the user channel vectors of each subcarrier through the K-means algorithm based on the number of radio frequency chains included in the set system, the total number of user devices, and the total number of subcarriers, and determine the final user set of each channel cluster;

[0170] The second determination unit 402 is configured to, for each channel cluster included in each subcarrier, select the final user with the largest channel gain to generate an initial subcarrier allocation matrix; determine the equivalent channel vector according to the initial analog beamformer and the user channel vector, and through iterative optimization of the receive combiner, the mean square error, and the digital beamformer, when the difference between the sums of the mean square errors of adjacent iterations is less than a first threshold, determine the optimal digital beamformer;

[0171] A third determination unit 403 is configured to expand the analog beamformer into a vector, and based on the conjugate Euclidean gradient of the objective function, iteratively update the analog beamformer by using the conjugate gradient method until the change amount of the objective function between adjacent iterations is less than a second threshold, and then determine the optimal analog beamformer;

[0172] A generation unit 404 is configured to determine the signal-to-interference-plus-noise ratio (SINR) of each end user according to each column included in the hybrid beamforming matrix of each subcarrier, select the end user with the largest SINR to allocate a precoding vector, and generate an optimized subcarrier allocation matrix.

[0173] It should be understood that the units included in the above-described beamforming apparatus for a large number of users are only logically divided according to the functions implemented by the device. In practical applications, the above units can be superimposed or split. Moreover, the functions implemented by the beamforming apparatus for a large number of users provided in this embodiment correspond one by one to the functions of the beamforming method for a large number of users provided in the above embodiment. For the more detailed processing flow implemented by this device, it has been described in detail in the first method embodiment above, and will not be described in detail here.

[0174] Another embodiment of the present invention further provides a computer device, which includes a processor and a memory; the memory is used to store computer program code, and the computer program code includes computer instructions; when the processor executes the computer instructions, the electronic device executes each step of the beamforming method for a large number of users described in the above method embodiment.

[0175] Another embodiment of the present invention further provides a computer-readable storage medium, in which computer instructions are stored. When the computer instructions run on a computer device, the computer device is caused to execute each step of the beamforming method for a large number of users described in the above method embodiment.

[0176] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed as including the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0177] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A beamforming method for a large number of users, characterized in that Including: Based on the number of radio frequency chains included in the set system, the total number of user equipments, and the total number of subcarriers, clustering the user channel vectors of each subcarrier by the K-means algorithm to determine the final user set of each channel cluster; For each channel cluster included in each subcarrier, selecting the final user with the maximum channel gain to generate an initial subcarrier allocation matrix; determining the equivalent channel vector according to the initial analog beamformer and the user channel vector, and iteratively optimizing the receive combiner, the mean square error, and the digital beamformer. When the difference between the sums of the mean square errors of adjacent iterations is less than the first threshold, determining the optimal digital beamformer; Expanding the analog beamformer into a vector, and using the conjugate gradient method to iteratively update the analog beamformer based on the conjugate Euclidean gradient of the objective function until the change amount of the objective function between adjacent iterations is less than the second threshold, then determining the optimal analog beamformer; Determining the signal-to-interference-plus-noise ratio (SINR) of the final user according to each column included in the hybrid beamforming matrix of each subcarrier, selecting the final user with the maximum SINR to allocate the precoding vector, and generating an optimized subcarrier allocation matrix.

2. The method according to claim 1, wherein The step of clustering the user channel vectors of each subcarrier by the K-means algorithm based on the number of radio frequency chains included in the set system, the total number of user equipments, and the total number of subcarriers to determine the final user set of each channel cluster specifically includes: Selecting the initial users consistent with the number of radio frequency chains as the initial cluster centers of the first subcarrier, successively determining the normalized distances between each initial user and each of the initial cluster centers, and allocating each initial user to the channel cluster with the closest distance to obtain the initial user set of each channel cluster; Determining the sum of the distances between each initial user included in the first channel cluster and all the initial users included in each second channel cluster, and determining the initial user with the maximum distance as the updated cluster center of the first channel cluster; wherein, the channel cluster set includes one first channel cluster and multiple second channel clusters, and the number included in the channel cluster set is equal to the number of the initial cluster centers. Determining the updated user set of each channel cluster with the updated cluster centers, and determining the iterative cluster center of the first channel cluster with the updated user having the maximum distance included in the first channel cluster. When the iterative cluster center meets the convergence condition, determining the updated user set of each channel cluster as the final user set of each channel cluster.

3. The method according to claim 2, wherein Determining the normalized distance between each initial user and each of the initial cluster centers through the following formula: Allocating each initial user to the channel cluster with the closest distance through the following formula: Determining the initial user with the maximum distance as the updated cluster center of the first channel cluster through the following formula: Among them, represents the normalized distance of the clustering usage of the \(u\)th init initial user and the \(i\)th init initial user on the \(k\)th subcarrier, represents the conjugate transpose of, represents the channel vector of the \(u\)th init user on the \(k\)th subcarrier, represents the channel vector of the \(i\)th init initial user on the \(k\)th subcarrier, \(\|\cdot\|_2\) represents the L2 norm; \(n\) ＊ represents the index of the nearest channel cluster, argmin represents the minimization operator, \(N\) s represents the data stream dimension, represents the normalized distance between the \(u\)th init initial user and the initial cluster center \(\mu\) n [k] of the \(n\)th channel cluster on the \(k\)th subcarrier, \(\mu\) n [k] represents the initial cluster center of the \(n\)th channel cluster on the \(k\)th subcarrier; represents the updated cluster center of the \(n\)th channel cluster on the \(k\)th subcarrier, argmax represents the maximization operator, represents the temporary allocation result of the initial users in the \(n\)th channel cluster in the \(k\)th subcarrier.

4. The method according to claim 1, characterized in that The step of selecting the user with the maximum channel gain to generate an initial subcarrier allocation matrix for each channel cluster included in each subcarrier specifically includes: According to the number of channel clusters included in each subcarrier and the final user set included in each channel cluster, determining the final user set of each channel cluster in each subcarrier; According to the channel vectors of each final user on each subcarrier, determining the final user with the maximum channel gain in each channel cluster through the following formula An initial subcarrier allocation matrix is obtained according to the number of channel clusters included in each subcarrier and the end users with the maximum channel gain in each channel cluster; the number of rows and columns of the initial subcarrier allocation matrix is consistent with the number of channel clusters and subcarriers respectively; where, u f,n [k] represents the number of the final user selected for service in the n-th channel cluster on the k-th subcarrier, n represents the index of the channel cluster, k represents the subcarrier sequence number, represents the u f -th final user's channel vector on the k-th subcarrier, and Ω n [k] represents the set of final users in the n-th channel cluster on the k-th subcarrier.

5. The method according to claim 1, wherein Determining the equivalent channel vector according to the initial analog beamformer and the user channel vectors, and iteratively optimizing the receive combiner, the mean square error, and the digital beamformer. When the difference between the sums of the mean square errors of adjacent iterations is less than the first threshold, the optimal digital beamformer is determined, which specifically includes: Obtaining the equivalent channel vector according to the initial analog beamformer and the channel vectors of each end user on each subcarrier; Based on the equivalent channel vector, the initial digital beamformer, and the noise variance, obtaining the receive combiners of each end user included on each subcarrier, the mean square error of the received signals of each end user on each subcarrier, and the digital beamformer corresponding to each end user on each subcarrier; In the iterative process, if the difference between the total mean square error of all end users on all subcarriers in the current iteration period and the total mean square error of all end users on all subcarriers in the previous iteration period is less than the first threshold, then the digital beamformer corresponding to each end user on each subcarrier in the current iteration period is determined as the optimal digital beamformer.

6. The method according to claim 1, wherein Obtaining the conjugate Euclidean gradient of the objective function through the following formula: Among them, denotes the conjugate Euclidean gradient of the objective function \(f(x)\) with respect to the vector \(x\), \(k\) denotes the subcarrier index, and \(W[k]\) denotes the precoding matrix for the \(k\)-th subcarrier. denotes the \(u\)- f -th end user's channel vector on the \(k\)-th subcarrier. denotes 's conjugate transpose, \(W[k]\) denotes the hybrid beamformer corresponding to the \(k\)-th subcarrier, \(W\) * [k] denotes the conjugate matrix of \(W[k]\), \(W\) T [k] denotes the transpose matrix of \(W[k]\), \(f(x)\) denotes the objective function. denotes the noise variance of the \(u\)- f -th end user on the \(k\)-th subcarrier, \(x\) * denotes the conjugate vector of \(x\), \(x\) denotes the \(m\)-dimensional complex vector obtained by expanding the analog beamformer \(F\), \(m\) denotes the dimension of the vector \(x\), and \(m = N\) t N RF N t denotes the number of transmit antennas, the number of transmit antennas, \(N\) RF denotes the number of RF chains. denotes 's transpose matrix. denotes 's conjugate matrix. denotes the concatenated matrix obtained by removing the columns corresponding to the \(u\)- f -th end user from the \(W[k]\) matrix. denotes the Kronecker product, \(B\) denotes the system bandwidth. denotes the set of end users on the \(k\)-th subcarrier.

7. The method according to claim 1, wherein Determining the equivalent channel vector, the receive combiners of each end user on each subcarrier, the mean square error of the end users served on each subcarrier, and the designed digital beamformer of each end user on each subcarrier through the following formula: wherein, denotes the conjugate transpose of, denotes the equivalent channel vector of the u f -th end user on the k-th subcarrier, F denotes the analog beamformer, denotes the channel vector of the u f -th end user on the k-th subcarrier, denotes the conjugate transpose of, denotes the receive combiner of the u f -th end user on the k-th subcarrier, denotes the beamforming vector corresponding to the u f -th end user on the k-th subcarrier, denotes the noise variance of the u f -th end user on the k-th subcarrier, denotes the set of end users on the k-th subcarrier, denotes the mean square error of the received signal of the u f -th end user on the k-th subcarrier, denotes the weighting coefficient of the u f -th end user; J[k] denotes a matrix on the k-th subcarrier, denotes the weighting coefficient of the i f -th end user; denotes the mean square error of the information received by the i f -th end user on the k-th subcarrier, denotes the receive combiner of the i f -th end user on the k-th subcarrier, and λ[k] denotes the Lagrange multiplier on the k-th subcarrier.

8. The method according to claim 1, characterized in that, Before determining the end user signal-to-interference-plus-noise ratio, determining the ratio of the end user through the following formula: Among them, represents the index of the end user with the maximum ratio selected on the k-th subcarrier, represents the set of end users on the k-th subcarrier, represents the u f -th end user's channel vector on the k-th subcarrier, represents the conjugate transpose of, represents the noise variance of the u f -th end user on the k-th subcarrier, represents the i-th column vector of the hybrid beamformer W[k] corresponding to the k-th subcarrier, represents the j-th column vector of the hybrid beamformer W[k] corresponding to the k-th subcarrier, W[k] represents the hybrid beamformer corresponding to the k-th subcarrier, argmax represents selecting the end user with the maximum ratio, |·| 2 represents the square of the absolute value of a complex number.

9. A beamforming device for a large number of users, characterized in that, Including: A first determination unit, configured to cluster the user channel vectors of each subcarrier by using the K-means algorithm based on the number of radio frequency chains included in the set system, the total number of user equipments, and the total number of subcarriers, and determine the set of end users of each channel cluster; A second determination unit, configured to, for each channel cluster included in each subcarrier, select the end user with the maximum channel gain to generate an initial subcarrier allocation matrix; determine the equivalent channel vector according to the initial analog beamformer and the user channel vectors, and iteratively optimize the receive combiner, the mean square error, and the digital beamformer. When the difference between the sums of the mean square errors of adjacent iterations is less than the first threshold, determine the optimal digital beamformer; A third determination unit, configured to expand the analog beamformer into a vector, and iteratively update the analog beamformer by using the conjugate gradient method based on the conjugate Euclidean gradient of the objective function until the change amount of the objective function between adjacent iterations is less than the second threshold, and determine the optimal analog beamformer; A generation unit, configured to determine the end user signal-to-interference-plus-noise ratio according to each column included in the hybrid beamforming matrix of each subcarrier, select the end user with the maximum signal-to-interference-plus-noise ratio to allocate the precoding vector, and generate an optimized subcarrier allocation matrix.

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