Robust beam design method for intelligent reflector-assisted rate division multiple access system

Abstract

The invention discloses a robust beam design method of an intelligent reflector-assisted rate division multiple access system. According to the method, the problems of system performance loss under the actual conditions of hardware damage, discrete phase deviation, imperfect channel state information and the like in a rate division multiple access system are solved through the joint design of the base station transmitting beam and the intelligent reflecting surface element phase. According to the method, the communication performance under the conditions of hardware damage, discrete phase deviation and imperfect channel state information is firstly described, then from the perspective of maximizing the communication performance, a transmitting beam matrix and an intelligent reflecting surface element phase of a base station are optimized, and finally robust beam forming of the rate division multiple access system is achieved. According to the robust beam forming method designed by the invention, the problem that the system performance loss is serious under the actual limiting condition in the rate division multiple access system in the existing method is solved, and an efficient solution is provided for the robust beam design of the rate division multiple access system assisted by the intelligent reflecting surface.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communications, and in particular relates to a robust beam design method for a rate division multiple access system assisted by an intelligent reflector under practical constraints such as hardware damage, discrete phase and imperfect channel state information. Background Art

[0002] With the development of wireless communication systems, smart reflector technology has become a key technology for next-generation wireless communication systems due to its low cost, wide coverage, and ability to adaptively control the wireless propagation environment. By jointly designing the base station beam and the smart reflector beam, smart reflectors can provide significant passive beam gain to communication systems. However, this joint design requires perfect system information. In practice, inevitable imperfections such as hardware impairments, discrete phases of smart reflectors, and imperfect channel state information can significantly degrade system performance.

[0003] In existing technologies, rate division multiple access (RDMA) technology demonstrates strong robustness to unavoidable imperfections. However, existing research often fails to fully consider the impact of all practical constraints on system performance. Furthermore, existing algorithms exhibit high complexity when optimizing discrete phase offsets, making them difficult to implement in practical systems. In summary, robust beamforming design methods that comprehensively account for unavoidable system imperfections such as hardware loss, discrete phases of smart reflector elements, and imperfect channel state information are necessary and are of great significance for the deployment of practical smart reflector-assisted rate division multiple access systems. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems existing in the prior art and provide a robust beam design method for a rate division multiple access system assisted by an intelligent reflector.

[0005] In order to achieve the above-mentioned object of the invention, the present invention specifically adopts the following technical solutions:

[0006] The present invention provides a robust beam design method for a rate division multiple access system assisted by an intelligent reflector, comprising the following steps:

[0007] S1. Construct a multi-user rate division multiple access system assisted by an intelligent reflecting surface, the system comprising a base station, an intelligent reflecting surface, and multiple users, wherein the base station communicates with the users by transmitting communication signals, and the intelligent reflecting surface assists the base station in communicating with the users by adjusting the phase of the reflected signals;

[0008] S2. After the user sends a communication request and transmits an uplink communication pilot signal to the base station, the base station receives the communication request and estimates the current channel state information consisting of the direct channel and the cascade channel, and splits the transmission information into a public part and a dedicated part before transmitting the communication signal to the communication user;

[0009] S3. Based on the estimated current channel state information, a sample average approximation and weighted minimum mean square error joint optimization method is used to determine the base station's transmit beam and the phase matrix of the smart reflector in the current time slot;

[0010] S4, performing beamforming on the communication signal based on the base station transmit beam obtained in S3 and the phase matrix of the smart reflective surface, and then transmitting the signal on the downlink;

[0011] S5. After receiving the communication signal, the communication user decodes the public part and the private part of the communication signal to obtain the information sent by the base station and completes the communication service in the current time slot;

[0012] S6. After the next time slot begins, the channel state information is acquired again, and steps S3 to S5 are repeated until the communication services in all time slots are completed, thereby realizing information transmission of the system within the entire service time.

[0013] Furthermore, in step S2, the base station transmission signal x is formed by the public part and the private part of the communication signal transmitted to the communication user, and its function form is:

[0014]

[0015] Where s c Indicates the public part of the transmitted communication signal; p,k represents the exclusive part of the kth user transmitting the communication signal; w c is the transmit beamforming vector of the common part of the communication signal, w p,k is the transmit beamforming vector of the kth user-specific part of the communication signal, κ T is the transmitter hardware loss distortion noise, whose elements follow a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance proportional to the transmit power of each antenna, that is, where β T represents the normalized transmitter distortion level, W = [w c ,w p,1 ,…,w p,K ], represents a diagonal matrix whose diagonal elements are the same as the matrix WW H The same, the off-diagonal elements are 0, and the three satisfy the power constraint P is the transmit power, and Tr(·) represents the trace of the matrix.

[0016] Furthermore, in step S3, the specific calculation process of determining the phase matrix of the base station's transmit beam and the smart reflector in the current time slot using the joint optimization method is as follows:

[0017] S31, using the downlink channel estimation method to obtain the direct channel and cascade channel of each link of the system in the current time slot, the direct channel and the cascade channel are respectively compared with their actual channel state information h BU,k ,H eff,k The relationship is expressed as:

[0018]

[0019] In the formula, the channel state information from the base station to user k is Represents the direct channel, the channel state information from the base station to the smart reflector to user k represents the cascade channel; Δh BU,k Denotes the channel estimation error of the direct channel, ΔH eff,k Represents the channel estimation error of the cascade channel, which satisfies the distribution relationship:

[0020]

[0021] Where, Used to quantify the channel estimation error of user k, N B Indicates the number of base station antennas, N I Indicates the number of smart reflective surface elements, Represents dimension N B ×N B The identity matrix, Represents dimension N I N B ×N I N B The identity matrix of

[0022] Calculate the received signal y at the user k :

[0023]

[0024]

[0025] Where, represents the kth user space propagation signal, represents the component phase of the smart reflective surface, where Indicates the 1st,...,Nth I The phase of the smart reflective surface element; n k Indicates that the mean is 0 and the variance is σ 2 Complex Gaussian communication noise; κ R,kThe mean is 0 and the variance is Receiver hardware loss distortion noise; β R,k represents the normalized receiver distortion level of the kth user; denotes expectation; the superscript H denotes conjugate transpose;

[0026] S32. Set the initial vector value w of the transmission beam of the communication signal (0) , and the initial value of the phase matrix of the smart reflector ξ (0) , as follows:

[0027]

[0028]

[0029] Where, Indicates dimension N B ×(K+1) all-one matrix, Indicates length N I A row vector of all 1s;

[0030] S33, apply equalizer g at the receiving end c,k To decode the public part of the communication signal received by the kth user , and calculate the communication performance of the received public part at any k-th user based on the signal-to-interference-noise ratio:

[0031] R c,k =log2(1+γ c,k )

[0032] In the formula

[0033] Where: * represents the conjugate of the phase ξ of the smart reflector element, ξ T represents the transposition of the element phase ξ of the smart reflective surface;

[0034] To ensure that all users can successfully decode the public data stream, the worst-case user determines the communication performance R of the public part. c =min(R c,k ), and then the common rate is distributed among users as follows: Where r c,k represents the public rate allocated to the kth user, min(R c,k ) represents the worst-case communication performance of the receiving public part at the user;

[0035] S34. For any k-th user, after subtracting the k-th common part through the continuous interference cancellation method, another equalizer g is applied at the receiving end. p,k To restore the private part of the kth user The communication performance of the receiving-specific part at the user is calculated based on the signal-to-interference-and-noise ratio:

[0036] R p,k =log2(1+γ p,k )

[0037] In the formula

[0038] S35. Construct a stochastic optimization problem with the goal of maximizing the expected weighted sum rate Used to optimize the base station's transmit beam and the phase of the smart reflector element under power constraints, common rate constraints, and discrete phase offset constraints:

[0039]

[0040] Where, represents the minimum communication performance threshold of user k; represents a discrete phase set; b represents the number of quantized bits of the smart reflector phase; η k represents the weighting coefficient;

[0041] S36, using the sample mean approximation method to solve the above random optimization problem Transformed into the following optimization problem :

[0042]

[0043] Where A represents the number of channel realizations, and the channel state information of the a-th channel realization is expressed as:

[0044]

[0045]

[0046] Where: represents the channel estimation error of the direct channel when the a-th channel is realized, represents the channel estimation error of the cascade channel when the a-th channel is realized;

[0047] S37. In each channel realization, use the weighted minimum mean square error equalizer At the receiving end, the public part of the kth user is decoded and another weighted minimum mean square error equalizer is used. At the receiving end, the dedicated part of the kth user is decoded and two weighted minimum mean square error equalizers are used as follows:

[0048]

[0049] Where,

[0050] The optimization problem will be determined Converted to the following optimization problem :

[0051]

[0052] in:

[0053]

[0054]

[0055] Where: Re{} represents the real part operation;

[0056] S38, based on the phase of the given smart reflective surface element, the optimization problem Convert to an optimization problem , used for W and r c,k To optimize:

[0057]

[0058] Where:

[0059] in:

[0060]

[0061]

[0062] The optimization problem is solved by interior point method Solve and obtain the optimal solution W ＊ and r c,k The optimal solution

[0063] S39, given W ＊ , In this case, the optimization problem Convert to an optimization problem To optimize the phase ξ of the smart reflective surface element, thereby obtaining the phase optimization result ξ of the smart reflective surface element ＊ , the optimization problem as follows:

[0064]

[0065] Where:

[0066]

[0067]

[0068] in:

[0069]

[0070] Use the alternating direction multiplier method and introduce 2K+1 auxiliary variables For equivalent optimization problems The constraints of ξ in the optimization problem are Transformed into an equivalent optimization problem :

[0071]

[0072] In the formula, ∠[z 2K+1 ] m Represents the auxiliary variable z 2K+1 The angle corresponding to the mth complex element in , ρ represents the penalty coefficient; represents the Lagrange dual variable;

[0073] The optimization problem Split into multiple sub-problems, and obtain the phase optimization results of the smart reflector element by solving each sub-problem ξ ＊ ;

[0074] S310, repeatedly executing steps S37 to S39 until a preset maximum time slot threshold is reached, and obtaining the transmit beam optimization result of the base station and the phase matrix optimization result of the smart reflective surface.

[0075] Furthermore, in step S39, the phase optimization result ξ of the smart reflective surface element is obtained by solving each sub-problem ＊ The steps include:

[0076] S391, based on optimization problem Constructing optimization subproblems :

[0077]

[0078] Based on the optimization subproblem The phase ξ of the smart reflective surface element is solved and the optimal solution is obtained as:

[0079]

[0080] Where, Indicates dimension N I The identity matrix of

[0081] S392, based on optimization problem Constructing optimization subproblems :

[0082]

[0083] Based on the optimization subproblem For variables Solve and obtain the optimal solution:

[0084]

[0085] Where η 1,k Denotes the Lagrange multiplier, and η is obtained by bisection method. 1,k :

[0086]

[0087] S393, based on optimization problem Constructing optimization subproblems :

[0088]

[0089] Based on the optimization subproblem For variables Solve and obtain the optimal solution:

[0090]

[0091] Where η 2,k Denotes the Lagrange multiplier, and η is obtained by bisection method. 2,k :

[0092]

[0093] S394, based on the optimization problem Constructing optimization subproblems :

[0094]

[0095] Where,

[0096] Based on the optimization subproblem right Traverse all phases ω in the variable z 2K+1Perform optimization and solve to obtain the optimal closed-form solution:

[0097]

[0098] S395, Update Lagrangian dual variable μ i :

[0099] μ i =z i -ξ+μ i ,i=[1,...,2K+1]

[0100] S396, repeat steps S391-S395 until the preset maximum time slot threshold is reached, and the variable ξ obtained by the latest iteration is used as the phase optimization result ξ of the smart reflector element ＊ .

[0101] As a preference, in said S391, the optimization sub-problem Solved by the first-order derivative optimality theorem.

[0102] As a preference, in said S392, the optimization sub-problem The solution is obtained by Lagrangian method.

[0103] As a preference, in said S393, the optimization sub-problem The solution is obtained by Lagrangian method.

[0104] Compared with the prior art, the present invention has the following beneficial effects:

[0105] Based on rate-division multiple access technology, the method proposed in this paper leverages the collaborative work of base stations and smart reflectors to effectively improve communication system performance despite hardware losses, discrete phase shifts of smart reflector components, and imperfect channel state information. The proposed method effectively transforms a non-convex optimization problem that cannot be directly solved into a directly solvable one, improving system robustness and achieving high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 Schematic diagram of the convergence of the robust beam design method proposed in the present invention;

[0107] Figure 2 Schematic diagram of the impact of imperfect channel state information on communication performance under different optimization schemes according to an embodiment of the present invention;

[0108] Figure 3 This is a schematic diagram of the impact of hardware loss on communication performance under different optimization schemes in an embodiment of the present invention.

[0109] Figure 4 This is a schematic diagram of the impact of the number of discrete phase shift quantization bits of the smart reflector on communication performance under different optimization schemes according to an embodiment of the present invention. DETAILED DESCRIPTION

[0110] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in the various embodiments of the present invention can be combined accordingly without conflicting with each other.

[0111] The rate-division multiple access system assisted by a smart reflector uses a base station as the transmitter and a smart reflector as the auxiliary, working together to provide communication services. The base station and the smart reflector provide communication services to users.

[0112] In a preferred implementation of the present invention, the above-mentioned smart reflector-assisted robust beam design method for rate division multiple access system includes the following steps S1 to S6, the specific implementation process of which is described in detail below.

[0113] S1. Construct a multi-user rate division multiple access system assisted by an intelligent reflecting surface. The system consists of a base station, an intelligent reflecting surface, and multiple users. The base station communicates with the users by transmitting communication signals, and the intelligent reflecting surface assists the base station in communicating with the users by adjusting the phase of the reflected signals.

[0114] S2. After the user sends a communication request to the base station and transmits an uplink communication pilot signal, the base station receives the communication request and estimates the current channel state information consisting of the direct channel and the cascade channel, and splits the transmitted information into a public part and a private part before transmitting a communication signal to the communication user.

[0115] It should be noted that in step S2, the base station transmission signal x is composed of the public part and the private part of the communication signal transmitted to the communication user, and its function form is:

[0116]

[0117] Where s c Indicates the public part of the transmitted communication signal; p,k represents the exclusive part of the kth user transmitting the communication signal; w c is the transmit beamforming vector of the common part of the communication signal, w p,kis the transmit beamforming vector of the kth user-specific part of the communication signal; k T is the transmitter hardware loss distortion noise, whose elements follow a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance proportional to the transmit power of each antenna, that is, where β T represents the normalized transmitter distortion level, W = [w c ,w p,1 ,…,w p,K ], represents a diagonal matrix whose diagonal elements are the same as the matrix WW H The same, the off-diagonal elements are 0; the three satisfy the power constraint P is the transmit power, ‖·‖ represents the 2-norm, and Tr(·) represents the trace of the matrix.

[0118] S3. Based on the estimated current channel state information, a sample average approximation and weighted minimum mean square error joint optimization method is used to determine the base station's transmit beam and the phase matrix of the smart reflector in the current time slot.

[0119] It should be noted that in step S3, the specific calculation process of determining the phase matrix of the base station's transmit beam and the smart reflector in the current time slot using the joint optimization method is:

[0120] S31, using the downlink channel estimation method to obtain the direct channel and cascade channel of each link of the system in the current time slot, wherein the direct channel, that is, the channel state information from the base station to user k Cascade channel, i.e., channel state information from the base station to the smart reflector to user k Each of them and their actual channel state information h BU,k ,H eff,k The relationship is expressed as:

[0121]

[0122] Where Δh BU,k Denotes the channel estimation error of the direct channel, ΔH eff,k Represents the channel estimation error of the cascade channel, which satisfies the distribution relationship:

[0123]

[0124] Where, Used to quantify the channel estimation error of user k, N B Indicates the number of base station antennas, N I Indicates the number of smart reflective surface elements, Represents dimension N B ×N B The identity matrix, Represents dimension NI N B ×N I N B The identity matrix of

[0125] Calculate the received signal y at the user k :

[0126]

[0127] Where, represents the kth user space propagation signal, Indicates the component phase of the smart reflective surface; Indicates the 1st,...,Nth I The phase of the smart reflective surface element; n k Indicates that the mean is 0 and the variance is σ 2 Complex Gaussian communication noise; κ R,k The mean is 0 and the variance is Receiver hardware loss distortion noise; β R,k represents the normalized receiver distortion level of the kth user; denotes expectation; the superscript H denotes conjugate transpose.

[0128] S32. Set the initial vector value W of the transmission beam of the communication signal (0) , and the initial value of the phase matrix of the smart reflector ξ (0) , as follows:

[0129]

[0130] Where, Indicates dimension N B ×(K+1) all-one matrix, Indicates length N I A row vector of all 1s.

[0131] S33, apply equalizer g at the receiving end c,k To decode the public part of the communication signal received by the kth user, that is The communication performance of the received public part at any k-th user is calculated based on the signal-to-interference-noise ratio:

[0132] R c,k =log2(1+γ c,k )

[0133] In the formula

[0134] Where: * represents the conjugate of the phase ξ of the smart reflector element, ξT Represents the transposition of the element phase ξ of the smart reflector.

[0135] To ensure that all users can successfully decode the public data stream, the communication performance of the public part is determined by the worst-case user, i.e., R c =min(R c,k ). Therefore, the common rate is distributed among users as follows, where r c,k represents the public rate allocated to the kth user, min(R c,k ) represents the worst-case communication performance of the receiving public part at the user.

[0136] S34. For any k-th user, after subtracting the k-th common part through the continuous interference cancellation method, another equalizer g is applied at the receiving end. p,k To recover the exclusive part of the kth user, The communication performance of the receiving-specific part at the user is calculated based on the signal-to-interference-and-noise ratio:

[0137] R p,k =log2(1+γ p,k )

[0138] In the formula

[0139] S35. Construct a random optimization problem with the goal of maximizing the expected weighted sum rate. It is used to optimize the base station's transmit beam and the phase of the smart reflector element under power constraints, public rate constraints, and discrete phase offset constraints. as follows:

[0140]

[0141] Where, represents the minimum communication performance threshold of user k; represents a discrete phase set; b represents the number of quantized bits of the smart reflector phase; η k Represents the weighting coefficient.

[0142] S36, using the sample mean approximation method to solve the above random optimization problem Transformed into the following optimization problem :

[0143]

[0144] Where A represents the number of channel realizations, and the channel state information of the a-th channel realization is expressed as:

[0145]

[0146]

[0147]

[0148] Where: represents the channel estimation error of the direct channel when the a-th channel is realized, It represents the channel estimation error of the cascade channel when the a-th channel is realized.

[0149] S37. In each channel realization, use the weighted minimum mean square error equalizer At the receiving end, the public part of the kth user is decoded and another weighted minimum mean square error equalizer is used. At the receiving end, the dedicated part of the kth user is decoded and two weighted minimum mean square error equalizers are used as follows:

[0150]

[0151] Where,

[0152] Optimization Problem It can be simplified to the following optimization problem :

[0153]

[0154]

[0155] in:

[0156]

[0157] S38, based on the phase of the given smart reflective surface element, the optimization problem Convert to an optimization problem For W and r c,k To optimize:

[0158]

[0159] Where:

[0160]

[0161] The above problem is a convex problem, and the optimization problem can be solved by the interior point method. Solve and obtain the optimal solution W ＊ and r c,k The optimal solution

[0162] S39, given W ＊ , In this case, the optimization problem Converted to the following optimization problem To optimize the phase ξ of the smart reflective surface element, thereby obtaining the phase optimization result ξ of the smart reflective surface element ＊ , optimization problem as follows:

[0163]

[0164] Where:

[0165]

[0166]

[0167] in:

[0168]

[0169] Use the alternating direction multiplier method and introduce 2K+1 auxiliary variables For equivalent optimization problems The constraints of ξ in the optimization problem are Transformed into the equivalent optimization problem :

[0170]

[0171] In the formula, ∠[z 2K+1 ] m Represents the auxiliary variable z 2k+1 The angle corresponding to the mth complex element in , ρ represents the penalty coefficient; represents the Lagrange dual variable;

[0172] The optimization problem Split into multiple sub-problems, and obtain the phase optimization results of the smart reflector element by solving each sub-problem ξ ＊ .

[0173] In step S39, the phase optimization result ξ of the smart reflective surface element is obtained. ＊ The steps include:

[0174] S391, based on optimization problem Constructing optimization subproblems :

[0175]

[0176] Based on the optimization subproblem The phase ξ of the smart reflector element can be solved by the first-order derivative optimal theorem, and the optimal solution is:

[0177]

[0178] Where, Indicates dimension N I The identity matrix of

[0179] S392, based on optimization problem Constructing optimization subproblems :

[0180]

[0181] Based on the optimization subproblem The variables can be calculated by Lagrange method. Solve and obtain the optimal solution:

[0182]

[0183] Where η 1,k represents the Lagrange multiplier, which can be solved using the bisection method to obtain η 1,k :

[0184]

[0185] S393, based on optimization problem Constructing optimization subproblems :

[0186]

[0187] Based on the optimization subproblem The variables can be calculated by Lagrange method. Solve and obtain the optimal solution:

[0188]

[0189] Where η 2,k represents the Lagrange multiplier, which can be solved using the bisection method to obtain η 2,k :

[0190]

[0191] S394, based on the optimization problem Constructing optimization subproblems :

[0192]

[0193] Where,

[0194] Based on the optimization subproblem right Traverse all phases ω in the variable z 2K+1 By performing optimization, we can obtain the optimal closed-form solution:

[0195]

[0196] S395, Update Lagrangian dual variable μ i :

[0197] μ i =z i -ξ+μ i ,i=[1,...,2K+1];

[0198] S396, repeat steps S391-S395 until the preset maximum time slot threshold is reached, and the variable ξ obtained by the latest iteration is used as the phase optimization result ξ of the smart reflector element ＊ .

[0199] S310, repeatedly executing steps S37 to S39 until a preset maximum time slot threshold is reached, and obtaining the transmit beam optimization result of the base station and the phase matrix optimization result of the smart reflective surface.

[0200] S4. Based on the base station transmit beam obtained in S3 and the phase matrix of the smart reflective surface, the communication signal is beamformed and transmitted on the downlink.

[0201] S5. After receiving the communication signal, the communication user decodes the public part and the private part of the communication signal respectively to obtain the information sent by the base station, and completes the communication service in the current time slot.

[0202] S6. After the next time slot begins, the channel state information is acquired again, and steps S3 to S5 are repeated until the communication services in all time slots are completed, thereby realizing information transmission of the system within the entire service time.

[0203] The feasibility and effect of the method of the present invention are verified by computer simulation. Figure 1 As shown in FIG, the figure shows the convergence of the method of the present invention. Figure 1 It can be seen that the method proposed in the present invention has different effects on the number of users K, the transmission power P and the number of smart reflective surface elements N. IIn all cases, convergence occurs after a few iterations. This rapid convergence is due to the closed-form solution of the optimization variables, which greatly speeds up the optimization process.

[0204] Figure 2 The comparison results of different schemes in terms of perceptual performance are shown. Figure 2 It can be seen that the method proposed in the present invention (the proposed scheme) performs better than the design based on continuous convex approximation (non-robust benchmark scheme 3), especially when the smart reflective surface elements are movable, and can achieve optimal perception performance (robust benchmark scheme 2). This is a pure perception system that successfully eliminates interference signals by utilizing perfect continuous interference cancellation technology, while the traditional smart reflective surface with fixed element positions cannot reach this performance upper limit (robust benchmark scheme 1).

[0205] Figure 2 The comparative results of different schemes under imperfect channel state information are shown. Figure 2 As can be seen in the figure, there is a performance gap between the method proposed in the present invention (the proposed scheme) and the benchmark. Specifically, unlike the scheme proposed in the non-robust benchmark scheme 3 that relies on fixed beamforming of the base station, the robust algorithm of the proposed scheme is more suitable for solving the problem of imperfect channel state information in the multi-user rate splitting multiple access scenario assisted by the smart reflector. In addition, although the non-robust benchmark scheme 3 takes hardware losses into account, these losses will be affected by imperfect channel state information. Therefore, as the transmit power increases in the non-robust benchmark scheme 3, the degradation of system performance will also be aggravated. This highlights the importance of developing robust algorithms that jointly consider imperfect channel state information and hardware losses to improve system performance.

[0206] Figure 3 Comparative results of different schemes under hardware loss conditions are presented. The results show that the baseline scheme's performance degrades significantly due to ignoring actual hardware loss. This highlights the urgent need to consider hardware loss in real systems to improve user service quality. Furthermore, the proposed scheme consistently outperforms the baseline scheme, demonstrating its superior ability to mitigate hardware loss and improve overall system performance.

[0207] Figure 4 The results of comparing different schemes with different quantization bit counts for smart reflector discrete phase shifts are presented. The results show that the proposed scheme (based on 3-bit quantization) outperforms the baseline scheme and achieves satisfactory performance even with low quantization bit counts, hardware loss, and imperfect channel state information. Therefore, the present invention provides an effective and computationally efficient solution to the shortcomings of smart reflector-assisted rate division multiple access systems, while ensuring robust system performance.

[0208] The embodiment described above is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Persons skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent substitution or equivalent transformation falls within the scope of protection of the present invention.

Claims

1. A robust beam design method for a rate division multiple access system assisted by an intelligent reflector, characterized in that: The following steps are involved: S1. Construct a multi-user rate division multiple access system assisted by an intelligent reflecting surface, the system comprising a base station, an intelligent reflecting surface, and multiple users, wherein the base station communicates with the users by transmitting communication signals, and the intelligent reflecting surface assists the base station in communicating with the users by adjusting the phase of the reflected signals; S2. After the user sends a communication request and transmits an uplink communication pilot signal to the base station, the base station receives the communication request and estimates the current channel state information consisting of the direct channel and the cascade channel, and splits the transmission information into a public part and a dedicated part before transmitting the communication signal to the communication user; S3. Based on the estimated current channel state information, a sample average approximation and weighted minimum mean square error joint optimization method is used to determine the base station's transmit beam and the phase matrix of the smart reflector in the current time slot; S4, performing beamforming on the communication signal based on the base station transmit beam obtained in S3 and the phase matrix of the smart reflective surface, and then transmitting the signal on the downlink; S5. After receiving the communication signal, the communication user decodes the public part and the private part of the communication signal to obtain the information sent by the base station and completes the communication service in the current time slot; S6. After the next time slot begins, the channel state information is acquired again, and steps S3 to S5 are repeated until the communication services in all time slots are completed, thereby realizing information transmission of the system within the entire service time.

2. The robust beam design method for a rate division multiple access system assisted by an intelligent reflector according to claim 1, wherein: In step S2, the base station transmission signal x is formed by the public part and the private part of the communication signal transmitted to the communication user, and its function form is: Where s c Represents the public portion of the transmitted communication signal; s p,k represents the exclusive part of the kth user transmitting the communication signal; w c is the transmit beamforming vector of the common part of the communication signal, w p,k is the transmit beamforming vector of the kth user-specific part of the communication signal, κ T is the transmitter hardware loss distortion noise, whose elements follow a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance proportional to the transmit power of each antenna, that is, where β T represents the normalized transmitter distortion level, W = [w c ,w p,1 ,…,w p,K ], represents a diagonal matrix whose diagonal elements are the same as the matrix WW H The same, the off-diagonal elements are 0, and the three satisfy the power constraint P is the transmit power and Tr(·) represents the trace of the matrix.

3. The robust beam design method for a rate division multiple access system assisted by an intelligent reflector according to claim 2, wherein: In step S3, the specific calculation process of determining the phase matrix of the base station's transmit beam and the smart reflector in the current time slot using the joint optimization method is as follows: S31, using the downlink channel estimation method to obtain the direct channel and cascade channel of each link of the system in the current time slot, the direct channel and the cascade channel are respectively compared with their actual channel state information h BU,k ,H eff,k The relationship is expressed as: In the formula, the channel state information from the base station to user k is Represents the direct channel, the channel state information from the base station to the smart reflector to user k represents the cascade channel; Δh BU,k Denotes the channel estimation error of the direct channel, ΔH eff,k Represents the channel estimation error of the cascade channel, which satisfies the distribution relationship: Where, Used to quantify the channel estimation error of user k, N B Indicates the number of base station antennas, N I Indicates the number of smart reflective surface elements, Represents dimension N B ×N B The identity matrix, Represents dimension N I N B ×N I N B The identity matrix of Calculate the received signal y at the user k : Where, represents the kth user space propagation signal, represents the component phase of the smart reflective surface, where Indicates the 1st,...,Nth I The phase of the smart reflective surface element; n k Indicates that the mean is 0 and the variance is σ 2 Complex Gaussian communication noise; κ R,k The mean is 0 and the variance is Receiver hardware loss distortion noise; β R,k represents the normalized receiver distortion level of the kth user; denotes expectation; the superscript H denotes conjugate transpose; S32. Set the initial vector value W of the transmission beam of the communication signal (0) , and the initial value of the phase matrix of the smart reflector ξ (0) , as follows: Where, Indicates dimension N B ×(K+1) all-one matrix, Indicates length N I A row vector of all 1s; S33, apply equalizer g at the receiving end c,k To decode the public part of the communication signal received by the kth user The communication performance of the received public part at any k-th user is calculated based on the signal-to-interference-noise ratio: R c,k =log2(1+γ c,k ) In the formula Where: * represents the conjugate of the phase ξ of the smart reflector element, ξ T represents the transposition of the element phase ξ of the smart reflective surface; To ensure that all users can successfully decode the public data stream, the worst-case user determines the communication performance R of the public part. c =min(R c,k ), and then the common rate is distributed among users as follows: Where r c,k represents the public rate allocated to the kth user, min(R c,k ) represents the worst-case communication performance of the receiving public part at the user; S34. For any k-th user, after subtracting the k-th common part through the continuous interference cancellation method, another equalizer g is applied at the receiving end. p,k To restore the private part of the kth user The communication performance of the receiving-specific part at the user is calculated based on the signal-to-interference-and-noise ratio: R p,k =log2(1+γ p,k ) In the formula S35. Construct a stochastic optimization problem with the goal of maximizing the expected weighted sum rate Used to optimize the base station's transmit beam and the phase of the smart reflector element under power constraints, common rate constraints, and discrete phase offset constraints: Where, represents the minimum communication performance threshold of user k; represents a discrete phase set; b represents the number of quantized bits of the smart reflector phase; η k represents the weighting coefficient; S36, using the sample mean approximation method to solve the above random optimization problem Transformed into the following optimization problem Where A represents the number of channel realizations, and the channel state information of the a-th channel realization is expressed as: Where: represents the channel estimation error of the direct channel when the a-th channel is realized, represents the channel estimation error of the cascade channel when the a-th channel is realized; S37. In each channel realization, use the weighted minimum mean square error equalizer At the receiving end, the public part of the kth user is decoded and another weighted minimum mean square error equalizer is used. At the receiving end, the dedicated part of the kth user is decoded and two weighted minimum mean square error equalizers are used as follows: Where, The optimization problem will be determined Converted to the following optimization problem in: Where: Re{} represents the real part operation; S38, based on the phase of the given smart reflective surface element, the optimization problem Convert to optimization problem For W and r c,k To optimize: Where: in: The optimization problem is solved by interior point method Solve and obtain the optimal solution W ＊ and r c,k The optimal solution S39, given W ＊ , In this case, the optimization problem Convert to optimization problem To optimize the phase ξ of the smart reflective surface element, thereby obtaining the phase optimization result ξ of the smart reflective surface element ＊ , the optimization problem as follows: Where: in: Use the alternating direction multiplier method and introduce 2K+1 auxiliary variables For equivalent optimization problems The constraints of ξ in the optimization problem are Transformed into an equivalent optimization problem In the formula, ∠[z 2K+1 ] m Represents the auxiliary variable z 2K+1 The angle corresponding to the mth complex element in , ρ represents the penalty coefficient; represents the Lagrange dual variable; The optimization problem Split into multiple sub-problems, and obtain the phase optimization results of the smart reflector element by solving each sub-problem ξ ＊ ; S310, repeatedly executing steps S37 to S39 until a preset maximum time slot threshold is reached, and obtaining the transmit beam optimization result of the base station and the phase matrix optimization result of the smart reflective surface.

4. The robust beam design method for a rate division multiple access system assisted by an intelligent reflector according to claim 3, characterized in that: In step S39, the phase optimization result ξ of the smart reflective surface element is obtained by solving each sub-problem ＊ The steps include: S391, based on optimization problem Constructing optimization subproblems Based on the optimization subproblem The phase ξ of the smart reflective surface element is solved and the optimal solution is obtained as: Where, Indicates dimension N I The identity matrix of S392, based on optimization problem Constructing optimization subproblems Based on the optimization subproblem For variables Solve and obtain the optimal solution: Where η 1,k Denotes the Lagrange multiplier, and η is obtained by bisection method. 1,k : S393, based on optimization problem Constructing optimization subproblems Based on the optimization subproblem For variables Solve and obtain the optimal solution: Where η 2,k Denotes the Lagrange multiplier, and η is obtained by bisection method. 2,k : S394, based on the optimization problem Constructing optimization subproblems Where, Based on the optimization subproblem right Traverse all phases ω in the variable z 2K+1 Perform optimization and solve to obtain the optimal closed-form solution: S395, Update Lagrangian dual variable μ i : μ i =z i -ξ+μ i ,i=[1,...,2K+1] S396, repeat steps S391-S395 until the preset maximum time slot threshold is reached, and the variable ξ obtained by the latest iteration is used as the phase optimization result ξ of the smart reflector element ＊ .

5. The robust beam design method for a rate division multiple access system assisted by an intelligent reflector according to claim 4, characterized in that: In S391, the optimization subproblem Solved by the first-order derivative optimality theorem.

6. The robust beam design method for a rate division multiple access system assisted by an intelligent reflector according to claim 4, characterized in that: In S392, the optimization subproblem The solution is obtained by Lagrangian method.

7. The robust beam design method for a rate division multiple access system assisted by an intelligent reflector according to claim 4, characterized in that: In S393, the optimization subproblem The solution is obtained by Lagrangian method.

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