Multi-user sum rate maximization method based on Bayesian optimization

Abstract

The invention relates to a multi-user and rate maximization method based on Bayesian optimization. The method comprises the following steps: firstly, constructing a new user utility function, and constructing an inner-layer precoding optimization problem and an outer-layer scaling coefficient optimization problem by taking error vector amplitude minimization of a multi-user system as a target; and secondly, in an inner layer optimization problem, fixing a scaling coefficient, updating a precoding matrix by using a gradient descent method, and solving the inner layer problem through a weighted minimum mean square error frame. And finally, by using Bayesian optimization, minimizing the error vector amplitude sum of all users as a target optimization scaling coefficient, and determining a final optimal precoding matrix. According to the method, the system performance under the condition of a limited symbol set is improved, so that the algorithm shows better transmission quality in various channel environments and has higher practicability and popularization value, and a low-complexity and high-performance solution is provided for multi-user multiple-input multiple-output precoding in a wireless communication network.

Description

Technical Field

[0001] The invention relates to the technical field of wireless communications, and in particular to a multi-user and rate maximization method based on Bayesian optimization. Background Art

[0002] The weighted minimum mean square error method is one of the most popular multi-user multiple-input multiple-output precoding schemes. The weighted minimum mean square error method was originally developed under the assumption that the transmitted symbols satisfy a Gaussian distribution. In this case, the objective function, i.e., the sum of the achievable rates of all users, can be calculated in a closed form by the Shannon formula. In contrast, the symbols in actual wireless communication systems are actually drawn from some discrete constellation set, such as phase shift keying or orthogonal amplitude modulation. When the scheme designed for Gaussian symbols is applied to the case of limited alphabet input, it may lead to severe rate performance degradation.

[0003] After searching the prior art, it was found that Wistron Corporation [Patent Publication No.: CN118300649A; TW202429840A] proposed a method based on dynamic causal Bayesian optimization of minimum mean square error to provide separate transmission precoding to maximize the comprehensive rate of beamforming. This method has low complexity and is easy to implement. However, due to the lack of consideration of the actual non-Gaussian distribution, there is a difference between the solution results given and the actual results. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-user and rate maximization method based on Bayesian optimization in view of the deficiencies of the prior art.

[0005] The present invention focuses on maximizing the total rate of all users in a discrete constellation set, and obtains the optimal precoding matrix through Bayesian optimization and the minimum mean square error method improved by gradient descent, thereby providing a low-complexity, high-performance solution for multi-user multi-input multi-output precoding in wireless communication networks.

[0006] Technical solution of the present invention:

[0007] A multi-user and rate maximization method based on Bayesian optimization comprises the following steps:

[0008] S1: Based on a multi-user multiple-input multiple-output system, we first construct an optimization problem with the goal of maximizing the total rate of all users. In this model, we analyze the inconsistency between theory and practice caused by assuming that symbols are Gaussian distributed. To address this problem, we introduce a scaling factor and propose a new user utility function, which limits the achievable rate of each user to between the spectral efficiency and the maximum achievable rate corresponding to its modulation and coding scheme, thus forming an inner optimization problem with the scaling factor as a hyperparameter and the precoding matrix as an optimization variable.

[0009] S2: Based on the inner optimization problem, an outer optimization problem is further constructed to minimize the error amplitude vector of all users, and the scaling factor is optimized to improve the transmission quality under discrete symbol input conditions;

[0010] S3: In the inner optimization problem, the scaling factor is fixed, the precoding matrix is ​​updated using the gradient descent method, and the inner problem is solved through the weighted minimum mean square error framework to ensure that the utility function of each user is optimal;

[0011] S4: In the outer optimization problem, the Bayesian optimization framework is used to optimize the scaling factor. The transmission quality is judged by evaluating the error vector amplitude of each user, and the scaling factor is optimized with the goal of minimizing the error vector amplitude of all users. The final optimal precoding matrix is ​​determined to minimize the error vector amplitude of all users and improve the overall transmission quality of the system.

[0012] The multi-user and rate maximization method based on Bayesian optimization described in the present invention first constructs an optimization problem with the goal of maximizing the total rate of all users, and proposes a new utility function to address the inconsistency between theory and practice caused by assuming Gaussian distribution symbols. Secondly, an outer optimization problem with the goal of minimizing the error amplitude vector of all users is constructed, and the scaling factor is optimized to improve the transmission quality under discrete symbol input conditions. Finally, in the inner optimization problem, the scaling factor is fixed, the precoding matrix is ​​updated using the gradient descent method, the inner problem is solved using the weighted minimum mean square error framework, and in the outer optimization problem, the scaling factor is optimized using the Bayesian optimization framework, the transmission quality is judged by evaluating the error vector amplitude of each user, and the scaling factor is optimized with the goal of minimizing the error vector amplitude and of all users, and the final optimal precoding matrix is ​​determined to minimize the error vector amplitude of all users and improve the overall transmission quality of the system.

[0013] Beneficial Effects

[0014] The present invention significantly enhances the traditional WMMSE algorithm in two aspects. First, the introduced scaling factors make the description of actual communication more accurate, and optimizing these factors can effectively bridge the gap between theoretical performance and actual achievable rates. Second, by optimizing the update of the precoder through gradient descent, the computational efficiency is improved, making the method more suitable for real-time or large-scale application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the process of the present invention;

[0016] Figure 2This is a comparison diagram of multi-user throughput and transmission SNR under different MSC settings of the present invention. ; DETAILED DESCRIPTION

[0017] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0018] like Figure 1 , a multi-user and rate maximization method based on Bayesian optimization, comprising the following steps:

[0019] S1: Based on a multi-user multiple-input multiple-output system, we first construct an optimization problem with the goal of maximizing the total rate of all users. In this model, we analyze the inconsistency between theory and practice caused by assuming that symbols are Gaussian distributed. To address this problem, we introduce a scaling factor and propose a new user utility function, which limits the achievable rate of each user to between the spectral efficiency and the maximum achievable rate corresponding to its modulation and coding scheme, thus forming an inner optimization problem with the scaling factor as a hyperparameter and the precoding matrix as an optimization variable.

[0020] S2: Based on the inner optimization problem, an outer optimization problem is further constructed to minimize the error amplitude vector of all users, and the scaling factor is optimized to improve the transmission quality under discrete symbol input conditions;

[0021] S3: In the inner optimization problem, the scaling factor is fixed, the precoding matrix is ​​updated using the gradient descent method, and the inner problem is solved through the weighted minimum mean square error framework to ensure that the utility function of each user is optimal;

[0022] S4: In the outer optimization problem, the Bayesian optimization framework is used to optimize the scaling factor. The transmission quality is judged by evaluating the error vector amplitude of each user, and the scaling factor is optimized with the goal of minimizing the error vector amplitude of all users. The final optimal precoding matrix is ​​determined to minimize the error vector amplitude of all users and improve the overall transmission quality of the system.

[0023] Furthermore, S1 is specifically:

[0024] Consider a downlink data link of a multi-user MIMO system, which consists of a base station and I users, where the base station is equipped with N t Each user is equipped with N transmitting antennas. r Root receiving antenna.

[0025] The channel matrix between the base station and user i is expressed as The precoder for user i is Where L represents the number of concurrently transmitted data streams. A commonly used multi-user precoding strategy is to optimize the precoder to maximize the total rate of all users. The specific form is:

[0026]

[0027] Among them, μ i is the weight coefficient for adjusting the priority of user i, P max represents the maximum transmission power of the base station, R i is the achievable rate of user i, which is in the form of:

[0028]

[0029]

[0030] in, represents the noise power received by user i.

[0031] The objective function of maximizing the total rate of all users is derived based on the assumption that the symbol bits are Gaussian distributed and have infinite code length. However, the actual transmission symbols can only be selected from some discrete constellation sets with a finite number of letters, such as PSK or QAM. Therefore, there is a significant difference between the achievable rate and the actual spectral efficiency of the actual modulation and coding scheme, which is mainly reflected in the infinite upper limit and performance overestimation.

[0032] In order to solve these two problems, the present invention proposes a new utility function as a modified version of the original achievable rate, which is in the form of:

[0033]

[0034] in is the scaling factor that adjusts the additional increment for user i, and Represent the upper and lower limits respectively, R i，0 =L·θ i log2Q i represents the spectral efficiency of the modulation and coding scheme of user i, where Q i and θ i represent the modulation order and coding rate respectively.

[0035] With the new utility function Instead of the original achievable rate R i , we get the final inner optimization problem, which is in the form of:

[0036]

[0037] The optimal solution to this optimization problem is where η=[η1,…,η I ] T .

[0038] Furthermore, S2 is specifically:

[0039] According to the 3GPP NR standard, downlink is a complex task, and it is extremely difficult, if not impossible, to express the entire transmission process in a clear mathematical formula. In fact, given the precoder After that, the quality of the transmitted signal can only be evaluated after the entire transmission is completed by checking the error vector magnitude of all users. i represents the error vector magnitude between the transmitted symbol and the estimated symbol of user i. Essentially, e i The optimized precoder These precoders themselves are functions of η, which means that we have e i =e i (η). Smaller e i (η) can be given a precoder Under the modulation order Q i and the coding rate θ i Ensure successful transmission of user i under the modulation and coding scheme.

[0040] In order to choose a suitable η, an outer optimization problem is constructed to minimize the error magnitude vector of all users, which is in the form of:

[0041]

[0042] Furthermore, S3 is specifically:

[0043] S31: In the inner optimization problem, the scaling factor η is a constant. Considering the maximum-minimum characteristics of the optimization problem, a set of auxiliary variables is introduced to obtain the equivalent form of the inner optimization problem:

[0044]

[0045]

[0046]

[0047]

[0048] Among them, {W i},{U i} and {s i} is a newly introduced auxiliary variable. E i is the minimum mean square error matrix, which is in the form:

[0049]

[0050] The block coordinate descent method is used to solve the above optimization problem. For the variable set block {W i},{U i} and {P i ,s i}, when other blocks are fixed, the optimization problem is a convex optimization problem. i ,s i}, the standard convex optimization toolkit based on the interior point method will be very time-consuming and inefficient to solve. In order to solve the problem more efficiently, the inner optimization problem is equivalently transformed into:

[0051]

[0052]

[0053]

[0054]

[0055] in, {y i The optimal solution of} satisfies:

[0056]

[0057] About {P i The optimization problem of} has the following equivalent form:

[0058]

[0059]

[0060] The problem has the following unconstrained equivalent:

[0061]

[0062] in,

[0063] The objective function is about the variable P i The gradient of is:

[0064]

[0065] S32: Initialize the precoding matrix using zero forcing method

[0066] S33: Update {U i}:

[0067]

[0068] S34: Update {W i}:

[0069]

[0070] S35: Initialize the number of iterations k=1, take the maximum number of iterations K=10, when k≤K:

[0071] calculate

[0072] Use Armijo's rule to determine the step size α, update

[0073] calculate

[0074] Update P i =β·P i ,

[0075] k increases automatically, k←k+1;

[0076] S36: Repeat S33-S35 until the algorithm converges (or reaches the maximum number of iterations) to obtain the optimal precoding matrix

[0077] Furthermore, S4 is specifically:

[0078] S41: Initialize η1 = [1, ..., 1],

[0079] S42: Calculated using the inner optimization algorithm

[0080] S43: In the given In this case, calculate

[0081] S44: Update

[0082] S45: Calculate the posterior probability of f(η):

[0083]

[0084] in,

[0085]

[0086] S46: Calculation of EI t (η)

[0087]

[0088] in Φ(·) and φ(·) are the cumulative distribution function and probability density function of the standard normal distribution, respectively.

[0089] S47: Solution in Get the next sampling point η t+1 ;

[0090] S48:

[0091] S49: t←t+1;

[0092] S410: Repeat S42-S49 until the algorithm converges and the optimal scaling factor vector η is obtained. (t) And its corresponding optimal precoding matrix

[0093] The method of the present invention aims to maximize the total rate of all users under actual transmission conditions, proposes a utility function, uses the gradient descent method to update the precoding matrix, solves the inner layer problem through a weighted minimum mean square error framework, optimizes the scaling coefficient using a Bayesian optimization framework, and determines the optimal precoding matrix.

[0094] Figure 2 This is a comparison chart of multi-user throughput and transmission signal-to-noise ratio between the Bayesian optimized gradient descent improved minimum mean square error method (BO-WMMSE-GD) of the present invention and the minimum mean square error (WMMSE) and zero forcing (ZF) methods under different MSC settings, verifying the BO-WMMSE-GD algorithm proposed in the present invention under a more realistic system setting. This study was conducted by using MATLAB5G toolbox to perform 5G link-level simulation, and the MCS of each user was adjusted according to the transmission SNR through the outer loop link adaptation scheme. The results show that the proposed BO-WMMSE-GD scheme outperforms the pure WMMSE and zero forcing (ZF) precoding methods in terms of multi-user throughput, and performs well in wireless communication systems that follow the 3GPP standard.

[0095] In addition, it should be noted that the specific embodiments described in this specification may be named differently, and the above contents described in this specification are merely examples of the structure of the present invention. Any small or simple changes made based on the structure, features and principles of the present invention are included in the protection scope of the present invention. Those skilled in the art of the present invention may make various modifications or supplements to the specific examples described or adopt similar methods, as long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.

Claims

1. A multi-user and rate maximization method based on Bayesian optimization, characterized in that: The following steps are involved: S1: Based on a multi-user multiple-input multiple-output system, we first construct an optimization problem with the goal of maximizing the total rate of all users. In this model, we analyze the inconsistency between theory and practice caused by assuming that symbols are Gaussian distributed. To address this problem, we introduce a scaling factor and propose a new user utility function, which limits the achievable rate of each user to between the spectral efficiency and the maximum achievable rate corresponding to its modulation and coding scheme, thus forming an inner optimization problem with the scaling factor as a hyperparameter and the precoding matrix as an optimization variable. S2: Based on the inner optimization problem, an outer optimization problem is further constructed to minimize the error amplitude vector of all users, and the scaling factor is optimized to improve the transmission quality under discrete symbol input conditions; S3: In the inner optimization problem, the scaling factor is fixed, the precoding matrix is ​​updated using the gradient descent method, and the inner problem is solved through the weighted minimum mean square error framework to ensure that the utility function of each user is optimal; S4: In the outer optimization problem, the Bayesian optimization framework is used to optimize the scaling factor. The transmission quality is judged by evaluating the error vector amplitude of each user, and the scaling factor is optimized with the goal of minimizing the error vector amplitude of all users. The final optimal precoding matrix is ​​determined to minimize the error vector amplitude of all users and improve the overall transmission quality of the system.

2. The multi-user and rate maximization method based on Bayesian optimization according to claim 1, characterized in that: S1 is specifically: Consider a downlink data link of a multi-user MIMO system, which consists of a base station and I users, where the base station is equipped with N t Each user is equipped with N transmitting antennas. r Root receiving antenna; The channel matrix between the base station and user i is expressed as The precoder for user i is Where L represents the number of concurrently transmitted data streams; a commonly used multi-user precoding strategy is to optimize the precoder to maximize the total rate of all users, specifically in the form of: Among them, μ i is the weight coefficient for adjusting the priority of user i, P max represents the maximum transmission power of the base station, R i is the achievable rate of user i, which is in the form of: in, represents the noise power received by user i; The new utility function, as a modified version of the original achievable rate, is of the form: in is the scaling factor that adjusts the additional increment for user i, and Represent the upper and lower limits respectively, R i，0 =L·θ i log2Q i represents the spectral efficiency of the modulation and coding scheme of user i, where Q i and θ i Represent the modulation order and coding rate respectively; With the new utility function Instead of the original achievable rate R i , we get the final inner optimization problem, which is in the form of: The optimal solution to this optimization problem is where η=[η1,…,η I ] T .

3. The multi-user and rate maximization method based on Bayesian optimization according to claim 1, characterized in that: S2 is specifically: Remember i represents the error vector magnitude between the transmitted symbol and the estimated symbol of user i, e i The optimized precoder These precoders themselves are functions of η, equivalently, we have e i =e i (η); In order to choose a suitable η, an outer optimization problem is constructed to minimize the error magnitude vector of all users, which is in the form of:

4. The multi-user and rate maximization method based on Bayesian optimization according to claim 1, characterized in that: S3 is specifically: S31: In the inner optimization problem, the scaling factor η is a constant; considering the maximum-minimum characteristics of the optimization problem, a set of auxiliary variables is introduced to obtain the equivalent form of the inner optimization problem: Among them, {W i },{U i } and {s i } is a newly introduced auxiliary variable; E i is the minimum mean square error matrix, which is in the form: The block coordinate descent method is used to solve the above optimization problem. For the variable set block {W i },{U i } and {P i ,s i }, when other blocks are fixed, the optimization problem is a convex optimization problem; the inner optimization problem is equivalently transformed into: in, {y i The optimal solution of} satisfies: About {P i The optimization problem of} has the following equivalent form: The problem has the following unconstrained equivalent: in, The objective function is about the variable P i The gradient of is: S32: Initialize the precoding matrix using zero forcing method S33: Update {U i }: S34: Update {W i }: S35: Initialize the number of iterations k=1, take the maximum number of iterations K=10, when k≤K: calculate Use Armijo's rule to determine the step size α, update calculate renew k increases automatically, k←k+1; S36: Repeat S33-S35 until the algorithm converges or reaches the maximum number of iterations to obtain the optimal precoding matrix 5. The multi-user and rate maximization method based on Bayesian optimization according to claim 1, characterized in that: S4 is specifically: S41: Initialize η1 = [1, ..., 1], S42: Calculated using the inner optimization algorithm S43: In the given In this case, calculate S44: Update S45: Calculate the posterior probability of f(η): in, S46: Calculation of EI t (η) in Φ(·) and φ(·) are the cumulative distribution function and probability density function of the standard normal distribution, respectively; S47: Solution in Get the next sampling point η t+1 ; S48： S49: t←t+1; S410: Repeat S42-S49 until the algorithm converges and the optimal scaling factor vector η is obtained. (t) And its corresponding optimal precoding matrix

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