Optimization Method for IRS-Assisted Cloud Radio Access Network Uplink Transmission under Non-Ideal Channel State Information

Abstract

The present invention discloses an IRS-assisted cloud access network uplink transmission optimization method under non-ideal channel information. Since the BBU pool obtains ideal channel information, it will increase the system load, resulting in higher energy consumption, and will also reduce the system gain brought by the IRS. Therefore, the present invention considers the problem of maximizing the statistical average uplink transmission and rate of multi-antenna users in IRS-assisted C-RAN under non-ideal channel information, under the constraints of fronthaul link capacity, IRS phase shift and transmit power. It is characterized by the design of the covariance matrix of active beamforming at the user end, passive beamforming of the IRS and compression noise of the fronthaul link. The present invention is aimed at the multi-antenna user uplink transmission system of IRS-assisted C-RAN under non-ideal channel information, and maximizes the uplink transmission and rate of the system by jointly optimizing the active beamforming at the user end, the passive beamforming of the IRS and the compression noise of the fronthaul link.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a method for optimizing the reachable uplink and rate maximization of an uplink transmission system for multi-antenna users in an intelligent reflecting surface (IRS)-assisted cloud access network (C-RAN) under non-ideal channel information. Background Art

[0002] With the commercialization of 5G and the continuous development of the Internet of Things, Industrial Internet of Things and mobile Internet, the demand for wireless communication services has shown exponential growth, and the requirements for the effectiveness of communication transmission systems have become increasingly higher. Traditional wireless communication systems face many challenges in terms of system efficiency and construction economy.

[0003] Cloud-based access network (C-RAN) is a wireless communication system that holds promise for alleviating current communication demands. Unlike traditional communication systems, it offloads baseband processing from traditional base stations to a cloud-based baseband unit (BBU) pool. User signals are compressed by remote radio heads (RRHs) and then transmitted to the BBU pool via limited fronthaul links. However, because some users within a cell are far from the RRHs or obstructed by obstacles, communication quality between them and the RRHs degrades, affecting RRH data compression and increasing the burden on the fronthaul links. Therefore, intelligent reflective surfaces (IRSs) are used to facilitate user access to the RRHs. Unlike traditional relays, IRSs are low-cost, passive reflective surfaces, each integrated with numerous reflective elements that independently control the phase and amplitude of incident electromagnetic waves. Because each reflective element is independently controllable, passive beams tailored to channel transmission are generated by controlling the reflective elements. Therefore, IRSs are easy to deploy, cost-effective, and power-efficient, effectively improving wireless network performance.

[0004] In practical communication systems, obtaining complete channel information consumes significant resources and increases system energy consumption. To balance system effectiveness and economy, the non-ideal channel information known to the BBU pool is considered. Under non-ideal channel information, IRS-assisted C-RAN multi-antenna user access RRHs can effectively improve system performance. In this system, RRHs receive signals sent by multi-antenna users via direct and reflected links, compress the received signals using a point-to-point (P2P) compression method, and transmit the compressed signals to the BBU pool via a limited-capacity wired fronthaul link. The BBU pool then decompresses the signals to restore the original signals. For this system, under fronthaul link capacity constraints, IRS phase shift constraints, and transmit power constraints, an uplink transmission and rate maximization optimization problem can be established. This optimization problem is characterized by active beamforming at the user end, passive beamforming at the IRS, and fronthaul link compression noise. By jointly optimizing these three factors, the uplink transmission and rate from users to the BBU pool can be further improved. Summary of the Invention

[0005] The present invention aims to provide a method for optimizing the maximum summation rate in an IRS-assisted C-RAN multi-antenna user uplink transmission system under non-ideal channel conditions. Specifically, under the constraints of fronthaul link capacity, IRS phase shift matrix, and transmit power, the method iteratively optimizes active beamforming at the user end, passive beamforming at the IRS, and fronthaul link compression noise to maximize the uplink system transmission summation rate.

[0006] The technical solutions of the present invention are as follows:

[0007] This IRS-assisted cloud access network uplink transmission optimization method under non-ideal channel information uses IRS to assist C-RAN multi-antenna users under non-ideal channel information. Under the constraints of fronthaul link capacity, IRS phase shift matrix, and transmit power, the optimization problem is to maximize the uplink system sum rate. The user-side precoding matrix, IRS phase shift matrix, and covariance matrix of the fronthaul link compression noise are jointly optimized. The specific steps are as follows:

[0008] 1.1) In the IRS-assisted C-RAN multi-antenna user communication system under non-ideal channel information, the multi-antenna user communicates with the BBU pool through the RRH. Multiple IRSs are deployed between the user and the RRH to assist the user in accessing the RRH. There are K multi-antenna users in the system, and each user has N U There are L transmit antennas, each RRH has N R There are M receiving antennas deployed between the user and RRH, and each IRS has N IThe RRH compresses the received signal through point-to-point (P2P) compression and transmits the compressed signal to the BBU pool via a wired fronthaul link with limited capacity. The BBU pool then recovers the original signal through decompression.

[0009] 1.2) The user sends a pilot signal, and the BBU pool estimates the channel based on the signal received by the RRH. Therefore, the direct link channel matrix from user k to RRH l and the channel matrix from user k to RRH l through the IRS are:

[0010]

[0011]

[0012] in represents the estimated channel matrix from user k to RRH1, represents the channel estimation error matrix from user k to RRH1, which obeys the complex normal distribution represents the nth (n=1,2,...,N) I ) reflective elements, represents the estimated channel gain from the n-th reflective element of IRSm to RRH1. is the cascade channel estimation error of user-IRS-RRH, which obeys the complex normal distribution

[0013] 1.3) The precoding information flow sent by user k, k = 1, ..., K, to RRH l, l = 1, ..., L is expressed as:

[0014] x k =F k s k

[0015] in is the data stream vector sent by the user, which obeys Gaussian distribution and its covariance matrix is The precoding matrix of the transmitter, i.e. the beamforming of the user end, must meet the power constraint

[0016] The RRH receives user signals transmitted via the direct link and the reflected link of the IRS. The received signal for RRH1 can be expressed as:

[0017]

[0018] in represents the estimated channel matrix of the direct channel from the user set to RRH1, represents the set of all users, represents the channel estimation error of the direct channel from the user set to RRH1. represents the estimated channel matrix from IRSm to RRH1, represents the estimated channel matrix from all IRSs to RRH l, Represents the set of all IRSs. represents the cascade channel estimation error of all users passing through each reflective element to reach the RRH, represents the channel estimation error of the concatenated channel from user k to RRH1. represents the channel matrix from user k to all IRSm, represents the channel matrix from user k to all IRSs, Represents the channel matrix from the user set to all IRSs. The phase shift matrix of IRS is a diagonal matrix whose diagonal elements are taken from the vector (IRS only performs phase adjustment, so |θ m,n |=1), represents all the transmitting elements of IRSm, Θ m,n represents the nth reflective element of IRSm. Indicates the precoding information flow sent by all users to RRH, is the precoding matrix for all users, Indicates the information flow sent by all users. l Represents additive Gaussian noise, with mean 0 and variance σ 2 The complex Gaussian distribution of .

[0019] 1.4) The RRH compresses the received signal point-to-point and then transmits it to the BBU pool via the limited capacity fronthaul link. The BBU pool decompresses and recovers the original signal, which can be expressed as:

[0020]

[0021] in represents the quantization noise of RRH1, which obeys the complex Gaussian distribution, Ω l is its covariance matrix.

[0022] 1.5) The uplink rate from the user to the BBU pool can be expressed as:

[0023]

[0024] in Estimate the channel matrix for direct connections from all users to all RRHs, Represents the set of all RRHs, Represents the direct link channel estimation error from the user set to all RRHs. is the estimated channel matrix from all IRSs to all RRHs, It represents the channel estimation error of the concatenated channel from the user set to all RRHs. By Ω l The block diagonal matrix composed of represents the compressed noise covariance matrix of all RRHs. In addition:

[0025]

[0026] For the convenience of expression, here is the definition Therefore, the achievable uplink sum rate can be expressed as:

[0027]

[0028] in

[0029] 1.6) Each RRH uses point-to-point compression, and the compression rate of each RRH fronthaul link must be less than the fronthaul link capacity C l , using Jensen’s inequality, the fronthaul link capacity is converted into the following form:

[0030]

[0031] in The forward transmission capacity constraint is then expressed as:

[0032]

[0033] Furthermore, an optimization method for maximizing the reachable uplink and rate under fronthaul link capacity, IRS phase shift, and transmit power constraints for IRS-assisted uplink communication of C-RAN multi-antenna users under non-ideal channel information is characterized by designing the user-side precoding matrix, IRS phase shift matrix, and covariance matrix of the fronthaul link compression noise. The specific steps are as follows:

[0034] 2.1) The optimization problem for uplink transmission and rate maximization can be expressed as:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] 2.2) Determine the maximum number of iterations T for joint optimization max , and select the initial Θ (0) and

[0041] 2.3) The optimization problem (P1) in step 2.1) can be transformed into the following form:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in

[0048] 2.4) Perform iterative optimization, first fix F k , Θ and Ω l and through For W, Σ and E l to update.

[0049] 2.5) Fix W, Σ and E again l F k , Θ and Ω l Optimize.

[0050] 2.5.1) Here we first fix Θ and Ω l , for F k For optimization, the optimization problem (P2) can be written as follows: The sub-optimization problem (P2-1) can be expressed as:

[0051]

[0052]

[0053]

[0054] The sub-optimization problem (P2-1) is solved using convex optimization tools (such as CVX), and the optimal solution is: (represents the solution to the sub-optimization problem (P2-1) in this step).

[0055] 2.5.2) Then fix F k For Θ and Ω lPerforming joint optimization, the optimization problem (P2) can be transformed into the following sub-optimization problem (P2-2)

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] in A⊙B T Represents A and B T The Hadamard For column vectors, the matrix The diagonal elements of

[0062] is a constant term. For column vectors, the matrix The diagonal elements of is a constant term. The constraints are ignored by semidefinite relaxation (SDR) Then, the optimization problem after SDR relaxation is solved by convex optimization tools, and the optimized solution is obtained as follows: (represents the optimized solution of the sub-optimization problem (P2-2) in this step).

[0063] 2.6) Further judgment Check whether the constraint C1 of the neutron optimization problem (P2-2) in step 2.5.2) is satisfied. If so, perform eigenvalue decomposition directly: make represents the optimized column vector, which is a column vector consisting of the diagonal elements of the phase shift matrix and a column vector consisting of 1; if the constraint C1 of the neutron optimization problem (P2-2) in step 2.5.2) is not satisfied, multiple suboptimal solutions are generated by the following method: First, let in are independent random variables, uniformly distributed on the unit circle in the complex plane (i.e. θ i Independently and uniformly distributed in [0,2π]), and then by lScaling is performed so that the resulting optimized solution satisfies the constraint C1 of the neutron optimization problem (P2-2) in step 2.5.2). Finally, the one that minimizes the objective function of the neutron optimization problem (P2-2) in step 2.5.2) is selected as the optimal solution. The final optimized solution is: precoding matrix Phase shift matrix Θ (t) and the covariance matrix of the compression noise t=1,...,T max Indicates the number of iterations. Then bring the optimized solution into the objective function of the sub-optimization problem (P2-2) in step 2.5.2) to obtain f (t) , which means that the optimization solution is brought into the value of the objective function, and then the solution of the previous iteration is Θ (t-1) and Also bring in the objective function of the sub-optimization problem (P2-2) in step 2.5.2) of this round to obtain f (t-1) , for comparison, if f (t) ≤f (t-1) The optimization solution of the previous round is used as the optimization solution of this round.

[0064] 2.7) Substitute the optimized solution of step 2.6) into the uplink and rate expressions Get the sum rate of this round of iteration And with the previous iteration For comparison, if Then stop the iteration and determine the optimal result Output optimized solution Θ * and Where ▽ represents the allowable error range; if Then determine whether the number of iterations exceeds T max If it does not exceed T max , return to step 2.4) and continue iterative optimization; if it exceeds T max , then output the final optimized solution and

[0065] 2.8) For the case where the IRS reflector phase is discrete, first obtain Θ * and Among them, Θ * The diagonal elements θ m,n Mapped to discrete phase points, namely: Where φ represents the discrete phase, τ = 2 b ,b=1,2.Indicates discrete levels. Scaling to obtain So that it satisfies the constraint C1 in step 2.1).

[0066] The beneficial effects of the present invention are as follows: the present invention significantly improves the system uplink transmission and rate for a communication system with multi-antenna user access in an IRS-assisted C-RAN under non-ideal channel information by optimizing the user-side precoding matrix, the IRS phase shift matrix, and the covariance matrix of the fronthaul link compression noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Schematic diagram of a multi-antenna user system in a smart reflector-assisted cloud access network under non-ideal channel information;

[0068] Figure 2 The figure shows the average uplink sum rate of the uplink transmission system for multi-antenna users in the smart reflector-assisted cloud access network under non-ideal channel information after adopting the joint optimization method of the present invention; the figure shows the relationship between the system average uplink sum rate and the number of reflective units of a single smart reflector; Figure 2 They represent the average uplink sum rate under continuous phase, 2-bit discrete phase, 1-bit discrete phase, random phase and no smart reflector in the case of point-to-point compression. DETAILED DESCRIPTION

[0069] The transmission process of the communication system with multi-antenna user access in IRS-assisted C-RAN under non-ideal channel information is as follows: Figure 1 The transmission process is as follows: users communicate with the BBU pool through the RRH. The RRH receives the user's signal through direct and reflected links, compresses the received signal using a point-to-point compression method, and then transmits it to the BBU pool via a wired fronthaul link with limited capacity. The system sum rate is improved by jointly optimizing the user's precoding matrix, the IRS phase shift matrix, and the covariance matrix of the fronthaul link compression noise.

[0070] The IRS-assisted cloud access network uplink transmission optimization method under non-ideal channel information is as follows:

[0071] 1.1) In the IRS-assisted C-RAN multi-antenna user communication system under non-ideal channel information, the multi-antenna user communicates with the BBU pool through the RRH. Multiple IRSs are deployed between the user and the RRH to assist the user in accessing the RRH. There are K multi-antenna users in the system, and each user has N U There are L transmit antennas, each RRH has N R There are M receiving antennas deployed between the user and RRH, and each IRS has N IThe RRH compresses the received signal through point-to-point (P2P) compression and transmits the compressed signal to the BBU pool via a wired fronthaul link with limited capacity. The BBU pool then recovers the original signal through decompression.

[0072] 1.2) The user sends a pilot signal, and the BBU pool estimates the channel based on the signal received by the RRH. Therefore, the direct link channel matrix from user k to RRH l and the channel matrix from user k to RRH l through the IRS are:

[0073]

[0074]

[0075] in represents the estimated channel matrix from user k to RRH1, represents the channel estimation error matrix from user k to RRH1, which obeys the complex normal distribution represents the nth (n=1,2,...,N) I ) reflective elements, represents the estimated channel gain from the n-th reflective element of IRSm to RRH1. is the cascade channel estimation error of user-IRS-RRH, which obeys the complex normal distribution

[0076] 1.3) The precoding information flow sent by user k, k = 1, ..., K, to RRH l, l = 1, ..., L is expressed as:

[0077] x k =F k s k

[0078] in is the data stream vector sent by the user, which obeys Gaussian distribution and its covariance matrix is The precoding matrix of the transmitter, i.e. the beamforming of the user end, must meet the power constraint

[0079] The RRH receives user signals transmitted via the direct link and the reflected link of the IRS. The received signal for RRH1 can be expressed as:

[0080]

[0081] in represents the estimated channel matrix of the direct channel from the user set to RRH1, represents the set of all users, represents the channel estimation error of the direct channel from the user set to RRH1. represents the estimated channel matrix from IRSm to RRH1, represents the estimated channel matrix from all IRSs to RRH l, Represents the set of all IRSs. represents the cascade channel estimation error of all users passing through each reflective element to reach the RRH, represents the channel estimation error of the concatenated channel from user k to RRH1. represents the channel matrix from user k to all IRSm, represents the channel matrix from user k to all IRSs, Represents the channel matrix from the user set to all IRSs. The phase shift matrix of IRS is a diagonal matrix whose diagonal elements are taken from the vector (IRS only performs phase adjustment, so |θ m,n |=1), represents all the transmitting elements of IRSm, Θ m,n represents the nth reflective element of IRSm. Indicates the precoding information flow sent by all users to RRH, is the precoding matrix for all users, Indicates the information flow sent by all users. l Represents additive Gaussian noise, with mean 0 and variance σ 2 The complex Gaussian distribution of .

[0082] 1.4) The RRH compresses the received signal point-to-point and then transmits it to the BBU pool via the limited capacity fronthaul link. The BBU pool decompresses and recovers the original signal, which can be expressed as:

[0083]

[0084] in represents the quantization noise of RRH1, which obeys the complex Gaussian distribution, Ω l is its covariance matrix.

[0085] 1.5) The uplink rate from the user to the BBU pool can be expressed as:

[0086]

[0087] in Estimate the channel matrix for direct connections from all users to all RRHs, Represents the set of all RRHs, Represents the direct link channel estimation error from the user set to all RRHs. is the estimated channel matrix from all IRSs to all RRHs, It represents the channel estimation error of the concatenated channel from the user set to all RRHs. By Ω l The block diagonal matrix composed of represents the compressed noise covariance matrix of all RRHs. In addition:

[0088]

[0089] For the convenience of expression, here is the definition Therefore, the achievable uplink sum rate can be expressed as:

[0090]

[0091] in

[0092] 1.6) Each RRH uses point-to-point compression, and the compression rate of each RRH fronthaul link must be less than the fronthaul link capacity C l , using Jensen’s inequality, the fronthaul link capacity is converted into the following form:

[0093]

[0094] in The forward transmission capacity constraint is then expressed as:

[0095]

[0096] 2. According to claim 1, an IRS-assisted C-RAN multi-antenna user uplink communication system transmission method under non-ideal channel information, an optimization method for maximizing the reachable uplink and rate under fronthaul link capacity constraints, IRS phase shift constraints, and transmit power constraints, characterized by designing the user-side precoding matrix, the IRS phase shift matrix, and the covariance matrix of the fronthaul link compression noise, specifically comprising the following steps:

[0097] 2.1) The optimization problem for uplink transmission and rate maximization can be expressed as:

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] 2.2) Determine the maximum number of iterations T for joint optimization max , and select the initial Θ (0) and

[0104] 2.3) The optimization problem (P1) in step 2.1) can be transformed into the following form:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] in

[0111] 2.4) Perform iterative optimization, first fix F k , Θ and Ω l and through For W, Σ and E l to update.

[0112] 2.5) Fix W, Σ and E again l F k , Θ and Ω l Optimize.

[0113] 2.5.1) Here we first fix Θ and Ω l , for F k For optimization, the optimization problem (P2) can be written as follows: The sub-optimization problem (P2-1) can be expressed as:

[0114]

[0115]

[0116]

[0117] The sub-optimization problem (P2-1) is solved using convex optimization tools (such as CVX), and the optimal solution is: (represents the solution to the sub-optimization problem (P2-1) in this step).

[0118] 2.5.2) Then fix F k For Θ and Ω lPerforming joint optimization, the optimization problem (P2) can be transformed into the following sub-optimization problem (P2-2)

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] in A⊙B T Represents A and B T The Hadamard For column vectors, the matrix The diagonal elements of

[0125] is a constant term. For column vectors, the matrix The diagonal elements of is a constant term. The constraints are ignored by semidefinite relaxation (SDR) Then, the optimization problem after SDR relaxation is solved by convex optimization tools, and the optimized solution is obtained as follows: (represents the optimized solution of the sub-optimization problem (P2-2) in this step).

[0126] 2.6) Further judgment Check whether the constraint C1 of the neutron optimization problem (P2-2) in step 2.5.2) is satisfied. If so, perform eigenvalue decomposition directly: make represents the optimized column vector, which is a column vector consisting of the diagonal elements of the phase shift matrix and a column vector consisting of 1; if the constraint C1 of the neutron optimization problem (P2-2) in step 2.5.2) is not satisfied, multiple suboptimal solutions are generated by the following method: First, let in are independent random variables, uniformly distributed on the unit circle in the complex plane (i.e. θ i Independently and uniformly distributed in [0,2π]), and then by lScaling is performed so that the resulting optimized solution satisfies the constraint C1 of the neutron optimization problem (P2-2) in step 2.5.2). Finally, the one that minimizes the objective function of the neutron optimization problem (P2-2) in step 2.5.2) is selected as the optimal solution. The final optimized solution is: precoding matrix Phase shift matrix Θ (t) and the covariance matrix of the compression noise t=1,...,T max Indicates the number of iterations. Then bring the optimized solution into the objective function of the sub-optimization problem (P2-2) in step 2.5.2) to obtain f (t) , which means that the optimization solution is brought into the value of the objective function, and then the solution of the previous iteration is Θ (t-1) and Also bring in the objective function of the sub-optimization problem (P2-2) in step 2.5.2) of this round to obtain f (t-1) , for comparison, if f (t) ≤f (t-1) The optimization solution of the previous round is used as the optimization solution of this round.

[0127] 2.7) Substitute the optimized solution of step 2.6) into the uplink and rate expressions Get the sum rate of this round of iteration And with the previous iteration For comparison, if Then stop the iteration and determine the optimal result Output optimized solution Θ * and Where ▽ represents the allowable error range; if Then determine whether the number of iterations exceeds T max If it does not exceed T max , return to step 2.4) and continue iterative optimization; if it exceeds T max , then output the final optimized solution and

[0128] 2.8) For the case where the IRS reflector phase is discrete, first obtain Θ * and Among them, Θ * The diagonal elements θ m,n Mapped to discrete phase points, namely: Where φ represents the discrete phase, τ = 2 b ,b=1,2.Indicates discrete levels. Scaling to obtain So that it satisfies the constraint C1 in step 2.1).

[0129] Computer simulations show that, under non-ideal channel conditions, the IRS-assisted C-RAN multi-antenna user uplink transmission communication system, after adopting the joint optimization method of this patent, has a system uplink transmission and rate significantly higher than the traditional C-RAN system uplink transmission and rate.

Claims

1. An IRS-assisted cloud access network uplink transmission optimization method under non-ideal channel information, characterized in that: Under non-ideal channel information, the IRS assists C-RAN multi-antenna user uplink communication. To maximize system uplink transmission and rate, the method jointly optimizes user active beamforming, IRS passive beamforming, and fronthaul link compression noise, including the following steps: 1.1) In an IRS-assisted C-RAN multi-antenna user communication system under non-ideal channel information, the multi-antenna user communicates with the baseband processing unit (BBU) pool through the remote radio head (RRH). Multiple smart reflectors (IRSs) are deployed between the user and the RRH to assist the user in accessing the RRH. There are K multi-antenna users in the system, and each user has N U There are L transmit antennas, each RRH has N R There are M receiving antennas deployed between the user and RRH, and each IRS has N I The RRH compresses the received signal through point-to-point compression and transmits the compressed signal to the BBU pool via a wired fronthaul link with limited capacity. The BBU pool then restores the original signal through decompression. 1.2) The user sends a pilot signal, and the BBU pool estimates the channel based on the signal received by the RRH. Therefore, the direct link channel matrix from user k to RRH l and the channel matrix from user k to RRH l through the IRS are: in Indicates user k to RRH l The estimated channel matrix, represents the channel estimation error matrix from user k to RRH1, which obeys the complex normal distribution represents the channel estimation error covariance of Represents user k and IRS m ( m＝1,2,...,M )'s nth (n=1,2,...,N I ) reflective elements, Indicates the nth reflective element of IRSm to RRH l The estimated channel gain of is the cascade channel estimation error of user-IRS-RRH, which obeys the complex normal distribution 1.3) The precoding information flow sent by user k, k = 1, ..., K, to RRHl, l = 1, ..., L is expressed as: k =F k s k in is the data stream vector sent by the user, which obeys Gaussian distribution and its covariance matrix is The precoding matrix of the transmitter, i.e. the beamforming of the user end, must meet the power constraint Tr represents the trace of the matrix, P k represents the transmit power of user k; RRH receives user signals transmitted through direct links and IRS reflection links; l The received signal can be expressed as: in represents the estimated channel matrix of the direct channel from the user set to RRH l, represents the set of all users, represents the channel estimation error of the direct channel from the user set to RRH1; represents the estimated channel matrix from IRSm to RRH1, Indicates all IRSs to RRH l The estimated channel matrix, represents the set of all IRSs; represents the cascade channel estimation error of all users passing through each reflective element to reach the RRH, represents the channel estimation error of the concatenated channel from user k to RRH1; represents the channel matrix from user k to all IRSm, represents the channel matrix from user k to all IRSs, represents the channel matrix from the user set to all IRSs; the phase shift matrix of IRS is a diagonal matrix whose diagonal elements are taken from the vector IRS only performs phase adjustment, so |θ m,n |=1, Indicates IRS m All emitting elements, Θ m,n Indicates IRS m The nth reflective element, m refers to the set The mth one, n also refers to N I The nth of the reflective elements; Indicates the precoding information flow sent by all users to RRH, is the precoding matrix for all users, Indicates the information flow sent by all users; the last n l Represents additive Gaussian noise, with mean 0 and variance σ 2 The complex Gaussian distribution of 1.4) The RRH compresses the received signal point-to-point and then transmits it to the BBU pool via a fronthaul link with limited capacity; The original signal decompressed and restored by the BBU pool is expressed as: in represents the quantization noise of RRH1, which obeys the complex Gaussian distribution, Ω l is its covariance matrix; 1.5) The uplink rate from the user to the BBU pool is expressed as: in Represents the set of all RRHs, Estimate the channel matrix for direct connections from all users to all RRHs, represents the direct link channel estimation error from the user set to all RRHs; is the estimated channel matrix from all IRSs to all RRHs, represents the channel estimation error of the concatenated channel from the user set to all RRHs; By Ω l The block diagonal matrix composed of represents the covariance matrix of the compressed noise of all RRHs, It is the representation of mathematical expectation, which represents the expectation of the matrix; also: For the convenience of expression, here is the definition Therefore, the achievable uplink sum rate is expressed as: in 1.6) Each RRH uses point-to-point compression, and the compression rate of each RRH fronthaul link must be less than the fronthaul link capacity C l , using Jensen’s inequality, the fronthaul link capacity is converted into the following form: in The forward transmission capacity constraint is then expressed as: The specific steps for designing the user terminal precoding matrix, IRS phase shift matrix, and compression noise covariance matrix are as follows: 2.1) The optimization problem for uplink transmission and rate maximization is expressed as: 2.2) Determine the maximum number of iterations T for joint optimization max , and select the initial Θ (0) and 2.3) The optimization problem P1 in step 2.1) is converted into the following form: in W is the receiving matrix, Σ is the covariance matrix of the posterior criterion estimated data symbols, E l is an auxiliary variable; 2.4) Perform iterative optimization, first fix F k , Θ and Ω l and through For W, Σ and E l Make updates; 2.5) Fix W, Σ and E again l F k , Θ and Ω l Optimize; 2.5.1) Here we first fix Θ and Ω l , for F k For optimization, the optimization problem P2 can be written as the following sub-optimization problem P2-1: The sub-optimization problem P2-1 is solved by convex optimization tools, and the optimal solution is obtained as follows: represents the solution of the sub-optimization problem P2-1 in this step, and Re represents the real part; 2.5.2) Then fix F k For Θ and Ω l Perform joint optimization, and the optimization problem P2 can be transformed into the following sub-optimization problem P2-2 in A⊙B T Represents A and B T The Hadamard For column vectors, the matrix The diagonal elements of is a constant term; For column vectors, the matrix The diagonal elements of is a constant term, and the SDR constraint is ignored by relaxing the semi-positive definite Then, the optimization problem after SDR relaxation is solved by convex optimization tools, and the optimized solution is obtained as follows: represents the optimal solution of the sub-optimization problem P2-2 in this step; 2.6) Further judgment Check whether the constraint C1 of the neutron optimization problem P2-2 in step 2.5.2 is satisfied. If so, perform eigenvalue decomposition directly: make represents the optimized column vector, which is a column vector consisting of the diagonal elements of the phase shift matrix and a column vector consisting of 1; if the constraint C1 of the neutron optimization problem P2-2 in step 2.5.2) is not satisfied, multiple suboptimal solutions are generated by the following method: First, let in are independent random variables, uniformly distributed on the unit circle in the complex plane, that is, θ i Independently and uniformly distributed in [0,2π], and then by l Scaling is performed to make the generated optimized solution satisfy the constraint C1 of the neutron optimization problem P2-2 in step 2.5.2). Finally, the one that minimizes the objective function of the neutron optimization problem P2-2 in step 2.5.2) is selected as the optimal solution; the optimized solution is: precoding matrix Phase shift matrix Θ (t) and the covariance matrix of the compression noise t=1,...,T max represents the number of iterations; then the optimized solution is brought into the objective function of the sub-optimization problem P2-2 in step 2.5.2) to obtain f (t) , which means that the optimization solution is brought into the value of the objective function, and then the solution of the previous iteration is Θ (t-1) and Also bring in the objective function of the sub-optimization problem P2-2 in step 2.5.2) of this round to obtain f (t-1) , for comparison, if f (t) ≤f (t-1) The optimization solution of the previous round is used as the optimization solution of this round; 2.7) Substitute the optimized solution of step 2.6) into the uplink and rate expressions Get the sum rate of this round of iteration And with the previous iteration For comparison, if Then stop the iteration and determine the optimal result Output optimized solution Θ * and in Indicates the allowable error range; if Then determine whether the number of iterations exceeds T max If it does not exceed T max , return to step 2.4) and continue iterative optimization; if it exceeds T max , then output the final optimized solution and 2.8) For the case where the IRS reflector phase is discrete, first obtain Θ * and Among them, Θ * The diagonal elements θ m,n Mapped to discrete phase points, namely: Where φ represents the discrete phase, τ = 2 b ,b=1,2 represents discrete level; Scaling to obtain So that it satisfies the constraint C1 in step 2.1).

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