Method for solving problem of maximum minimum rate optimization in active RIS-assisted uplink multi-user MISO system

Abstract

The invention discloses a method for solving the problem of optimization of maximum and minimum rates in an active RIS-assisted uplink multi-user MISO system. According to the method, joint optimization is carried out on a receiving beam forming matrix, an active RIS reflection coefficient matrix and user transmitting power by taking maximum and minimum rates as targets. The method has the advantages of being low in calculation complexity and high in system calculation efficiency, and similar performance can be obtained under the complexity far lower than that of a genetic algorithm. And compared with a passive RIS assisted system, the minimum user rate performance is obviously improved. In addition, scenes considered in the method are suitable for most RIS auxiliary systems, and effective guidance is provided for performance optimization of systems of the same type.

Description

Technical field:

[0001] The invention relates to an optimization method for a mobile communication system, and in particular to a solution method for maximizing the minimum rate optimization problem in an active RIS-assisted uplink multi-user MISO system, and belongs to the field of wireless mobile communications. Background technology:

[0002] With the development of technology and the improvement of software and hardware capabilities, the capacity of communication networks is expected to increase a thousandfold in the next decade. However, highly complex networks, high-cost hardware and increasing energy consumption have become key issues facing future wireless communications. As an innovative, efficient, spectrum- and resource-friendly future wireless network technology, Reconfigurable Intelligent Surface (RIS) can actively and intelligently control electromagnetic waves in space in a programmable manner, forming electromagnetic fields with controllable parameters such as amplitude, phase, polarization and frequency, and improving the wireless propagation environment. With its advantages of low cost, low power consumption and easy deployment, it has received widespread attention from academia and industry in recent years.

[0003] Most existing research focuses on passive RIS, which has an inherent disadvantage: the reflected signal suffers from multiplicative fading, resulting in a very weak received signal. To overcome the multiplicative fading effect, an active RIS and its corresponding signal model and system design method are proposed. Active RIS integrates a reflective active power amplifier in each reflective element to simultaneously perform phase control and high-gain amplification on the reflected signal, thereby compensating for the path loss caused by multiplicative fading.

[0004] There are many studies on passive RIS-assisted communication systems, but few studies consider the introduction of active RIS. In addition, most existing works only consider the downlink, and the optimization objective function is often the user and rate, without considering the service quality of users with poor channels.

[0005] Therefore, it is necessary to improve the existing technology to solve the shortcomings of the existing technology. Summary of the invention:

[0006] The present invention aims to solve the problems existing in the above-mentioned prior art and provides a method for maximizing the minimum rate optimization problem in an active RIS assisted uplink multi-user MISO system. The method aims to maximize the minimum rate and jointly optimizes the receiving beamforming matrix, the active RIS reflection coefficient matrix and the user transmission power, so as to obtain a better minimum rate optimization solution under lower polynomial complexity.

[0007] The technical solution adopted by the present invention is: a method for solving the optimization problem of maximizing the minimum rate in an active RIS-assisted uplink multi-user MISO system, the steps of which are as follows:

[0008] Step S1: Establish an active RIS-assisted uplink multi-user MISO system, in which the base station is equipped with N antennas and the active RIS is equipped with M active reflective elements; the base station serves K single-antenna users with the assistance of active RIS, and the set of RIS reflective elements is defined as Define the set of all users as The channels between the base station and RIS, RIS and the kth user, and the base station and the kth user adopt the Rice channel model, which is defined as For any channel matrix G, Given, where PL represents the path loss, d represents the distance between devices, κ represents the Rice factor, and G LoS and G NLoS They represent the line-of-sight path and Rayleigh fading components respectively. The reflection coefficient matrix of active RIS is expressed as where α m Satisfy the amplification factor amplitude of each component of active RIS and satisfy α m ≤α max , phase shift coefficient φ m Satisfy φ m ∈[0,2π);

[0009] Step S2: Using the time division duplex mode, all users send their own data signals to the base station at the same time, and the k-th user signal received by the base station is expressed as:

[0010]

[0011] in, represents the transmission signal of the kth user, p k represents the corresponding transmission power, represents the receiving beamforming vector of the base station for the kth user, and denote the additive white Gaussian noise vectors at the RIS and the base station, respectively, represents the reflection coefficient matrix of active RIS, then the signal to interference noise ratio of the kth user is expressed as:

[0012]

[0013] The uplink achievable rate of the kth user is expressed as:

[0014] R k =log2(1+SINR k ) (3)

[0015] Establish the optimization problem of maximizing the minimum rate in the active RIS-assisted uplink multi-user MISO system:

[0016]

[0017] Among them, R k represents the rate of the kth user, represents the receiving beamforming vector of the base station for the kth user, represents the reflection coefficient matrix of active RIS, p k represents the transmission power of the kth user, P max,k represents the maximum transmission power of the kth user, represents the channel between RIS and the i-th user, σ z represents the noise variance at RIS, P RIS represents the maximum reflected power of the active RIS, [θ] m,m represents the mth row and mth column element in the RIS reflection coefficient matrix, α max Indicates the maximum amplitude amplification factor of each element of the active RIS;

[0018] Step S3: The optimization problem in step S2 is a multi-variable coupled non-convex optimization problem. The problem is divided into a receive beamforming sub-problem, an active RIS reflection coefficient design sub-problem, and a user power allocation sub-problem by using an alternating optimization method and mathematical transformation.

[0019] Step S4: For the receive beamforming subproblem in step S3, that is, fix {Θ,p k Solve for w k , through mathematical transformation, the objective function can be transformed into the generalized Rayleigh entropy form, and then the optimal solution can be obtained;

[0020] Step S5: Design a sub-problem for the active RIS reflection coefficient in step S3, that is, fix {p k ,w k Solve Θ, the objective function is a non-smooth and non-convex fractional form. First, introduce auxiliary variables to relax the optimization problem, and then use multi-fractional programming and Cauchy-Schwartz inequality to transform the original problem into a standard convex optimization problem and solve it with cvx;

[0021] Step S6: For the user power allocation subproblem in step S3, that is, fix {w k ,Θ} solve for p k First, we introduce the auxiliary variable γ to relax the optimization problem, and then introduce the fractional programming variable y k , use alternating optimization to first find the optimal y k value, transforming the problem into about {p k ,γ} is a standard convex optimization problem solved using cvx.

[0022] Further, step S4 is specifically as follows:

[0023] 1) Fixed {Θ,p k Solve for w k

[0024] When {Θ,p k After being fixed, the original problem can be divided into K sub-problems, which can be expressed as follows through mathematical transformation:

[0025]

[0026] in

[0027]

[0028] The above formula is the generalized Rayleigh entropy, so its optimal solution is:

[0029]

[0030] but The update formula is

[0031] Further, step S5 is specifically as follows:

[0032] Fixed {p k ,w k Solve for Θ

[0033] When {p k ,w k When} is fixed, an auxiliary variable κ is introduced, and the subproblem of solving Θ is expressed as:

[0034]

[0035] in Then, using the idea of ​​fractional programming, we introduce the auxiliary variable m k , the left term in constraint C4 is transformed into:

[0036]

[0037] make Get m k The optimal closed-form solution of is as follows:

[0038]

[0039] When m k After fixing, constraint C4 is rewritten as:

[0040]

[0041] To solve the above equation Regarding the non-convexity of θ, using the Cauchy-Schwartz inequality x H y≤||x||2||y||2, we get Then constraint C4 is approximately:

[0042]

[0043] The above inequality is a convex constraint on θ, so the transformed approximation problem is a convex optimization problem on {θ,κ}. In each cycle, cvx is used to solve and update {θ,κ}, and the closed-form solution is used to solve and update m. k , until convergence, the final result is Θ (r) The update style.

[0044] Further, step S6 is specifically as follows:

[0045] Fixed {w k ,Θ} solve for p k

[0046] When {w k ,Θ} is fixed, an auxiliary variable γ is introduced to solve p k The sub-problem is expressed as:

[0047]

[0048] in

[0049] Using fractional programming ideas, introduce auxiliary variables y k , transform the left formula of C3 into:

[0050]

[0051] The original optimization problem is transformed into:

[0052]

[0053] Use alternating optimization to solve {p k ,γ} and y k , in each iteration loop, let Get y k The optimal solution Fixed y k After that, about {p k ,γ} is a standard convex optimization problem, which is solved by cvx and the converged result is used to update

[0054] The present invention has the following beneficial effects: the solution to the optimization problem of maximizing the minimum rate in the active RIS-assisted uplink multi-user MISO system proposed in the present invention has the advantages of low computational complexity but high system computational efficiency, and can achieve similar performance to the genetic algorithm at a complexity far lower than that of the genetic algorithm. And compared with the passive RIS-assisted system, the minimum user rate performance is significantly improved. In addition, the scenarios considered in the present invention are applicable to most RIS-assisted systems, providing effective guidance for the performance optimization of the same type of systems. Description of the drawings:

[0055] Figure 1 Flow chart of the system in the embodiment of the present invention.

[0056] Figure 2 It is a model diagram of the system in the embodiment of the present invention.

[0057] Figure 3 It is a rate simulation curve diagram of the optimization scheme and the comparison scheme proposed in the embodiment of the present invention.

[0058] Figure 4 It is a simulation curve diagram of the optimization scheme and the comparison scheme proposed in the embodiment of the present invention under different numbers of RIS components. Specific implementation method:

[0059] The present invention will be further described below in conjunction with the accompanying drawings.

[0060] 1. System Model

[0061] An active RIS-assisted uplink multi-user MISO system is provided, in which the base station is equipped with N antennas and the RIS is equipped with M active reflective elements. The base station serves K single-antenna users with the assistance of active RIS. The set of RIS reflective elements is defined as Define the set of all users as The channels between the base station and RIS, RIS and the kth user, and the base station and the kth user adopt the Rice channel model, which is defined as and For any channel matrix G, Given. Where PL represents the path loss, d represents the distance between devices, κ represents the Rice factor, G LoS and G NLoS Represent the line-of-sight path and Rayleigh fading components respectively.

[0062] The reflection coefficient matrix of active RIS is expressed as The amplitude amplification factor α m Satisfy α m ≤α max , phase shift coefficient φ m Satisfy φm ∈[0,2π).

[0063] 2. Optimization Problem Establishment

[0064] In time division duplex mode, all users send their data signals to the base station at the same time. The k-th user signal received by the base station can be expressed as:

[0065]

[0066] in, represents the transmission signal of the kth user, p k represents the corresponding transmission power, represents the receiving beamforming vector of the base station for the kth user, and denote the additive white Gaussian noise vectors at the RIS and the base station, respectively, represents the reflection coefficient matrix of active RIS, then the signal to interference noise ratio of the kth user can be expressed as:

[0067]

[0068] The uplink achievable rate of the kth user can be expressed as:

[0069] R k =log2(1+SINR k ) (3)

[0070] Establish the optimization problem of maximizing the minimum rate in the active RIS-assisted uplink multi-user MISO system:

[0071]

[0072] Among them, constraint C1 is the maximum transmit power constraint of the user, P max,k represents the maximum transmission power of the kth user, C2 is the maximum RIS reflection power constraint, P RIS represents the maximum reflected power of the active RIS, C3 is the maximum RIS reflection amplitude constraint, α max represents the maximum amplitude amplification factor of each element of the active RIS, and C4 is the normalized constraint of the receive beamforming.

[0073] 3. Optimization Problem Solving Methods

[0074] Problem (4) can be decomposed into the receive beamforming subproblem, the active RIS reflection coefficient design subproblem and the user power allocation subproblem by using the alternating optimization method and mathematical transformation. represents {w k ,Θ,p k} in the r-1th iteration of the alternating optimization algorithm, then the following subproblems are solved in the rth iteration:

[0075] 1) Fix {Θ,pk} and solve for w k

[0076] When {Θ,p k After being fixed, the original problem can be divided into K sub-problems, which can be expressed as follows through mathematical transformation:

[0077]

[0078] in

[0079]

[0080] The above formula is the generalized Rayleigh entropy, so its optimal solution is:

[0081]

[0082] but The update formula is

[0083] 2) Fixed {p k ,w k Solve for Θ

[0084] When {p k ,w k When} is fixed, the auxiliary variable κ is introduced, and the subproblem of solving Θ can be expressed as:

[0085]

[0086] in

[0087] Then, using the idea of ​​fractional programming, we introduce the auxiliary variable m k , the left term in constraint C4 can be transformed into:

[0088]

[0089] make m k The optimal closed-form solution of is as follows:

[0090]

[0091] When m k After fixing, constraint C4 can be rewritten as:

[0092]

[0093] To solve the above equation Regarding the non-convexity of θ, using the Cauchy-Schwartz inequality x H y≤||x||2||y||2, we can get Then constraint C4 can be approximated as:

[0094]

[0095] The above inequality is a convex constraint on θ, so the transformed approximation problem is a convex optimization problem on {θ,κ}. In each cycle, cvx can be used to solve and update {θ,κ}, and a closed-form solution can be used to solve and update m. k , until convergence, the final result is Θ (r) The update style.

[0096] 3) Fixed {w k ,Θ} solve for p k

[0097] When {w k ,Θ} is fixed, an auxiliary variable γ is introduced to solve p k The sub-problem can be expressed as:

[0098]

[0099] in

[0100] Using fractional programming ideas, introduce auxiliary variables y k , transform the left formula of C3 into:

[0101]

[0102] The original optimization problem is transformed into:

[0103]

[0104] Use alternating optimization to solve {p k ,γ} and y k , in each iteration loop, let You can get y k The optimal solution Fixed y k After that, about {p k ,γ} is a standard convex optimization problem, which can be solved by cvx. The converged result is used to update

[0105] The following is a computer simulation analysis of the active RIS-assisted uplink multi-user MISO system and the proposed optimization algorithm. The base station is at (0, -40m), the active RIS is at (200m, 10m), and the users are evenly distributed in an area with (300m, 0m) as the center and a radius of 5m. It is assumed that the Gaussian thermal noise at the RIS follows the same distribution as the Gaussian thermal noise at the base station, that is, Specific simulation parameters are shown in the following table:

[0106]

[0107] Figure 3 The system performance under different RIS reflection coefficient design schemes is compared. Passive RIS means that the amplitude of each reflection element is 1, and the received signal is passively reflected to increase the user rate by only changing the phase. Compared with the passive RIS scheme, by optimizing the amplitude and phase of the active RIS, the minimum user rate performance is significantly improved, which proves the effectiveness of the proposed algorithm.

[0108] Figure 4 The minimum user rate performance under different numbers of RIS reflector elements is compared. As can be seen from the above figure, as the number of RIS reflector elements increases, the system performance continues to improve. This is because as the number of RIS elements increases, the signal path from the user to the base station also increases, further improving the diversity gain of the system. In particular, compared with the scenario without RIS-assisted communication, active RIS can significantly improve the minimum user rate by providing an additional reliable communication path between the user and the base station, proving the effectiveness of active RIS in communication scenarios.

[0109] In summary, the optimization method proposed in the present invention can effectively improve the minimum rate performance of the active RIS-assisted uplink multi-user MISO system. At the same time, the implementation steps of the method are relatively simple, and the simulation results fully demonstrate the effectiveness of the optimization method.

[0110] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A method for maximizing the minimum rate optimization problem in an active RIS-assisted uplink multi-user MISO system, characterized by: Here are the steps: Step S1: Establish an active RIS-assisted uplink multi-user MISO system, in which the base station is equipped with N antennas and the active RIS is equipped with M active reflective elements; the base station serves K single-antenna users with the assistance of active RIS, and the set of RIS reflective elements is defined as Define the set of all users as The channels between the base station and RIS, RIS and the kth user, and the base station and the kth user adopt the Rice channel model, which is defined as For any channel matrix G, Given, where PL represents the path loss, d represents the distance between devices, κ represents the Rice factor, and G LoS and G NLoS They represent the line-of-sight path and Rayleigh fading components respectively. The reflection coefficient matrix of active RIS is expressed as where α m Satisfy the amplification factor amplitude of each component of active RIS and satisfy α m ≤α max , phase shift coefficient φ m Satisfy φ m ∈[0,2π); Step S2: Using the time division duplex mode, all users send their own data signals to the base station at the same time, and the k-th user signal received by the base station is expressed as: in, represents the transmission signal of the kth user, p k represents the corresponding transmission power, represents the receiving beamforming vector of the base station for the kth user, and denote the additive white Gaussian noise vectors at the RIS and the base station, respectively, represents the reflection coefficient matrix of active RIS, then the signal to interference noise ratio of the kth user is expressed as: The uplink achievable rate of the kth user is expressed as: R k =log2(1+SINR k ) (3) Establish the optimization problem of maximizing the minimum rate in the active RIS-assisted uplink multi-user MISO system: Among them, R k represents the rate of the kth user, represents the receiving beamforming vector of the base station for the kth user, represents the reflection coefficient matrix of active RIS, p k represents the transmission power of the kth user, P max,k represents the maximum transmission power of the kth user, represents the channel between RIS and the i-th user, σ z represents the noise variance at RIS, P RIS represents the maximum reflected power of the active RIS, [θ] m,m represents the mth row and mth column element in the RIS reflection coefficient matrix, α max Indicates the maximum amplitude amplification factor of each element of the active RIS; Step S3: The optimization problem in step S2 is a multi-variable coupled non-convex optimization problem. The problem is divided into a receive beamforming sub-problem, an active RIS reflection coefficient design sub-problem, and a user power allocation sub-problem by using an alternating optimization method and mathematical transformation. Step S4: For the receive beamforming subproblem in step S3, that is, fix {Θ,p k Solve for w k , through mathematical transformation, the objective function can be transformed into the form of generalized Rayleigh entropy, and then the optimal solution can be obtained; Step S5: Design a sub-problem for the active RIS reflection coefficient in step S3, that is, fix {p k ,w k Solve Θ, the objective function is a non-smooth and non-convex fractional form. First, introduce auxiliary variables to relax the optimization problem, and then use multi-fractional programming and Cauchy-Schwartz inequality to transform the original problem into a standard convex optimization problem and solve it with cvx; Step S6: For the user power allocation subproblem in step S3, i.e., fix {wk, Θ} and solve p k First, we introduce the auxiliary variable γ to relax the optimization problem, and then introduce the fractional programming variable y k , use alternating optimization to first find the optimal y k value, transforming the problem into about {p k ,γ} is a standard convex optimization problem solved using cvx.

2. The method for maximizing the minimum rate optimization problem in an active RIS-assisted uplink multi-user MISO system as claimed in claim 1, characterized in that: Step S4 is specifically as follows: 1) Fix {Θ,pk} and solve for w k When {Θ,p k After being fixed, the original problem can be divided into K sub-problems, which can be expressed as follows through mathematical transformation: in The above formula is the generalized Rayleigh entropy, so its optimal solution is: but The update formula is 3. The method for maximizing the minimum rate optimization problem in an active RIS-assisted uplink multi-user MISO system as claimed in claim 2, characterized in that: Step S5 is specifically as follows: Fixed {p k ,w k Solve for Θ When {p k ,w k When} is fixed, an auxiliary variable κ is introduced, and the subproblem of solving Θ is expressed as: in Then, using the idea of ​​fractional programming, we introduce the auxiliary variable m k , the left term in constraint C4 is transformed into: make Get m k The optimal closed-form solution of is as follows: When m k After fixing, constraint C4 is rewritten as: To solve the above equation Regarding the non-convexity of θ, using the Cauchy-Schwartz inequality x H y≤||x||2||y||2, we get Then constraint C4 is approximately: The above inequality is a convex constraint on θ, so the transformed approximation problem is a convex optimization problem on {θ,κ}. In each cycle, cvx is used to solve and update {θ,κ}, and the closed-form solution is used to solve and update m. k , until convergence, the final result is Θ( r ) is an update form of .

4. The method for maximizing the minimum rate optimization problem in an active RIS-assisted uplink multi-user MISO system as claimed in claim 3, characterized in that: Step S6 is specifically as follows: Fix {wk,Θ} and solve for p k When {wk,Θ} is fixed, an auxiliary variable γ is introduced to solve p k The sub-problem is expressed as: in Using fractional programming ideas, introduce auxiliary variables y k , transform the left formula of C3 into: The original optimization problem is transformed into: Use alternating optimization to solve {p k ,γ} and y k , in each iteration loop, let Get y k The optimal solution Fixed y k After that, about {p k ,γ} is a standard convex optimization problem, which is solved by cvx and the converged result is used to update

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