A joint transceiver design method based on channel statistics

Abstract

The present invention provides a joint transceiver design method based on channel statistics, belonging to the fields of wireless communications and digital signal processing. The method comprises: establishing a signal transmission model based on a multi-RIS-assisted airborne non-cellular network architecture; each aerial AP sends a detection signal to a central processing unit for weighted combined detection; performing an equivalent transformation on the optimization problem of maximizing the user weighted sum rate to obtain a matrix weighted sum variance minimization problem; alternately optimizing the weighted combined detection matrix of the central processing unit, the uplink precoding matrix of the ground user, and the phase shift matrix of the RIS, and obtaining an asymptotic expression of the optimization result using operator-valued free probability theory; and transmitting the converged uplink precoding matrix and phase shift matrix to each aerial AP, RIS, and ground user for the next round of uplink signal transmission and detection. The method can effectively improve user uplink rates while reducing the information exchange overhead between the aerial AP and the central processing unit.

Description

Technical Field

[0001] The present invention belongs to the fields of wireless communication and digital signal processing, and in particular relates to a joint transceiver design method based on channel statistical information. Background Art

[0002] Cell-free networks adopt a user-centric approach, eliminating the traditional concept of cell boundaries during data transmission. By deploying multiple geographically separated access points (APs) to simultaneously serve all users, they effectively shorten the distance between users and APs, achieving macrodiversity gain and effectively increasing communication system capacity. Airborne cell-free networks combine cell-free networks with airborne systems, using drones as aerial APs to provide collaborative services to users on the ground. Specifically, airborne cell-free networks leverage the flexible deployment of drones while providing users with uniform network coverage using a cell-free service architecture, minimizing interference between users and ensuring a high-quality communication experience.

[0003] In airborne, cellular-free networks, due to the high flight altitudes of drones, ground-to-air and air-to-ground wireless communication channels primarily consist of line-of-sight (LoS) channels. This can cause the channel matrix to be under-ranked, leading to a decrease in channel capacity. Furthermore, the communication link between aerial APs and users can be blocked by obstacles, severely degrading communication quality. To address this issue, reconfigurable intelligent reflective surfaces (RIS) can be deployed in airborne, cellular-free networks to provide additional reflection paths, thereby increasing the rank of the channel matrix and improving channel capacity.

[0004] Furthermore, in airborne, non-cellular networks, aerial APs need to transmit channel state information and received user signals to the central processing unit via a fronthaul link to enable collaborative signal processing. In terrestrial, non-cellular networks, fronthaul links typically consist of low-latency, high-capacity fiber optic links. However, in airborne, non-cellular networks, fronthaul links are typically wireless links, which have high communication latency and limited transmission capacity, making them difficult to support the large amounts of information exchange between aerial APs and the central processing unit. Summary of the Invention

[0005] The purpose of the present invention is to propose a joint transceiver design method based on channel statistical information, which can effectively improve the user uplink rate while reducing the information interaction overhead between the aerial AP and the central processing unit.

[0006] The present invention is achieved through the following technical solutions:

[0007] A joint transceiver design method based on channel statistical information includes the following steps:

[0008] Step S1: Establish a signal transmission model based on a multi-RIS-assisted airborne non-cellular network architecture. The airborne non-cellular network architecture includes N ground users, L aerial APs, K RISs, and a central processing unit. The signal transmission model includes a receiving signal model of each aerial AP and a channel matrix between the ground user and each aerial AP.

[0009] Step S2: Each aerial AP performs local received signal detection and sends the detection signal to the central processing unit for weighted combined detection;

[0010] Step S3: Based on the signal transmission model, an optimization problem of maximizing user weighted sum rates is established, and an equivalent transformation is performed on the optimization problem to obtain a matrix weighted sum variance minimization problem. This problem involves the uplink precoding matrix of each ground user, the phase shift matrix of each RIS, and the weighted combined detection matrix of the central processing unit.

[0011] Step S4: Set the maximum number of iterations, the initial uplink precoding matrix of each ground user, the initial phase shift matrix of each RIS, and obtain the initial receiver of each aerial AP;

[0012] Step S5: The central processing unit alternately optimizes the weighted combined detection matrix of the central processing unit, the uplink precoding matrix of the terrestrial user, and the phase shift matrix of the RIS based on the matrix weighting and variance minimization problem in step S3, and obtains an asymptotic expression of the optimization result using the operator-valued free probability theory until the maximum number of iterations is reached.

[0013] Step S6: The central processing unit transmits the converged uplink precoding matrix of the ground user and the phase shift matrix of the RIS to each aerial AP, RIS and ground user for the next round of uplink signal transmission and detection.

[0014] Furthermore, in step S1, the received signal model of the lth aerial AP is expressed as Among them, W n represents the uplink precoding matrix of the nth terrestrial user, satisfying the power constraint p n is the maximum transmission power of the nth ground user, x n is the transmitted signal of the nth ground user, vector n l is the additive white Gaussian noise at the lth aerial AP, H nl is the channel matrix from the nth ground user to the lth aerial AP.

[0015] Furthermore, in step S1, the channel matrix H from the nth ground user to the lth aerial AP nl Expressed as Among them, G l =[I R ,G 1l ,...,G Kl ], F 0.nl represents the direct channel matrix from the nth ground user to the lth aerial AP, F nk represents the direct channel matrix from the nth user to the kth RIS, G kl represents the direct channel matrix from the kth RIS to the lth aerial AP, is the phase shift matrix of the kth RIS, where L k represents the number of passive radiating elements of the kth RIS, k=1,2,...,K,I R represents the R×R unit matrix, and R represents the number of receiving antennas equipped for each aerial AR.

[0016] Furthermore, in step S1, the direct channel matrix from the nth ground user to the lth aerial AP is expressed as The direct channel matrix from the nth user to the kth RIS is expressed as The direct channel matrix from the kth RIS to the lth aerial AP is expressed as in, and Represents F 0,nl 、F nk and G kl The LoS component, and Represents F 0,nl 、F nk and G kl The random scattering component, M 0,nl 、M nk and N kl Respectively and The variance of each item is a certain non-negative value, T 0,nl 、P 0,nl 、T nk 、P nk 、R kl and C kl is a deterministic spatial correlation matrix, and the random matrix X 0,nl ,X nk ,Y kl Each element of satisfies the independent complex Gaussian distribution with zero mean,

[0017] Furthermore, step S2 includes the following steps:

[0018] Step S21: The first airborne AP uses local instantaneous channel state information to minimize the local detection signal. With the original signal x nl The mean square error between them, the MMSE receiver of the lth aerial AP is obtained as in F 0l =[F 0,1l ,...,F 0,Nl ], F k =[F 1k ,...,F Nk ],σ 2 is the noise power,

[0019] Step S22: The first aerial AP detects the signal The signal is sent to the central processing unit, which performs weighted combined detection on the received detection signals. The signal detection result of the nth ground user after weighted combination in the central processing unit is in A nl is the weighted combined detection matrix assigned by the central processing unit to the local signal detection result of the nth ground user by the lth aerial AP, The achievable rate of the nth terrestrial user is expressed as in

[0020] Furthermore, step S3 includes the following steps:

[0021] Step S31: Based on the signal transmission model, establish an optimization problem of maximizing user weighted sum rate: Among them, μ n Indicates the priority of the nth ground user, represents the uplink precoding matrix of the terrestrial user, represents the weighted combined detection matrix of the central processing unit, Θ={Θ1,...,Θ K} represents the phase shift matrix of RIS, represents the transmit power constraint, represents the phase shift range constraint;

[0022] Step S32: Convert the optimization problem of step S31 into a matrix weighted sum variance minimization problem. in, V n ≥0 T represents the auxiliary weight matrix of the nth user, 0 T represents a T×T dimensional matrix where all elements are 0, En represents the mean square error matrix,

[0023] Furthermore, in step S4, the maximum number of iterations is set to 1. MAX The initial value of iteration number i is 0, and the initial value of the uplink precoding matrix of the nth terrestrial user is The initial value of the phase shift matrix of the kth RIS is The initial receiver of the lth aerial AP is in

[0024] Furthermore, the step S5 specifically includes:

[0025] Step S51: In the i+1th iteration, the uplink precoding matrix optimized in the i-th iteration is fixed. and the phase shift matrix Θ (i) , by minimizing the sum of MSE, we get the optimized weighted merged detection matrix is a block matrix, and its (l,q)th submatrix block is Symbol {A} nn represents the nth diagonal block matrix of matrix A, z = -σ 2 , is a block matrix, Υ(z), Γ(z), represents a matrix-valued function, Indicates F l The LoS component, Represents G l The LoS component, T t =N×T, where N represents the total number of terrestrial users, T represents the number of transmit antennas allocated to each terrestrial user, and the superscript (i) of a variable indicates that the variable is the result of the i-th iteration optimization;

[0026] Step S52: Fix the uplink precoding matrix after the i-th iteration optimization and the phase shift matrix Θ (i) , substitute the optimized weighted merge detection matrix According to V n (i+1) The first-order optimality condition of , the optimized auxiliary weight matrix is ​​obtained

[0027] Step S53: Substitute the optimized weighted combined detection matrix Auxiliary weight matrix And fix the phase shift matrix Θ (i) According to the standard convex optimization algorithm and operator-valued free probability theory, the optimal asymptotic uplink precoding matrix for terrestrial users can be obtained as The optimal asymptotic uplink precoding matrix for the nth terrestrial user is Among them, λ k ≥0 indicates Lagrange multiplier;

[0028] Step S54: Substitute the optimized weighted combined detection matrix Auxiliary weight matrix Uplink precoding matrix definition in represents a vector whose elements are all 1. In the i+1th iteration, θ (i+1) Updated to in is the step size of the i-th iteration, is the gradient The i-th element of is the Euclidean gradient, Where, By separately Taking the derivative with respect to z, we get represents the conjugate of θ, Indicates the first k The kth phase shift of a RIS, for conjugation;

[0029] Step S56: Go to step S51 and perform i+2 iterations until the maximum number of iterations is reached, and obtain the converged uplink precoding matrix of the terrestrial user and the phase shift matrix of the RIS.

[0030] Furthermore, in step S51, the matrix value functions Υ(z), Γ(z), Satisfy the following fixed point equations respectively in,

[0031] and express The parameterized one-sided correlation function of and D is an arbitrary Hermitian matrix, and is a diagonal matrix with the diagonal elements being Indicates the number of passive reflective elements equipped with the RIS; and express The parameterized one-sided correlation function, Z and is any Hermitian matrix, diagonal matrix Σ nk (Z), The diagonal elements of ζk (Z) = diag(ζ 1k (Z),ζ 2k (Z),…,ζ Nk (Z)) and express The parameterized one-sided correlation function of

[0032] The present invention has the following beneficial effects:

[0033] The present invention first establishes a signal transmission model for a multi-RIS-assisted airborne, non-cellular network architecture. Each aerial AP performs local received signal detection and sends the detection signal to a central processing unit (CPU) for weighted combined detection. An optimization problem is then formulated with the goal of maximizing user sum and rate. This optimization problem is equivalently transformed into a matrix weighted sum variance minimization problem. Based on this matrix weighted sum variance minimization problem, the CPU alternately optimizes the CPU's weighted combined detection matrix, the terrestrial user's uplink precoding matrix, and the RIS's phase shift matrix. The asymptotic expression of the optimization results is derived using operator-valued free probability theory until the maximum number of iterations is reached. Finally, the CPU transmits the converged terrestrial user's uplink precoding matrix and RIS's phase shift matrix to each aerial AP, RIS, and terrestrial user for the next round of uplink signal transmission and detection. By deploying multiple intelligent reconfigurable metasurfaces and employing an asymptotic alternating optimization algorithm that relies solely on statistical channel state information, the proposed method significantly reduces the information exchange overhead between the aerial AP and the CPU while improving the user uplink sum and rate, achieving performance similar to that of the original alternating optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present invention will be described in further detail below with reference to the accompanying drawings.

[0035] Figure 1 Flowchart of the present invention.

[0036] Figure 2 This is an architecture diagram of the air-based cellular-free network assisted by intelligent reflective surface (RIS) of the present invention.

[0037] Figure 3 The simulation results show that the sum rate of users changes with the number of iterations when the number of users is different.

[0038] Figure 4 The simulation results show that the sum rate of users changes with the number of smart reflective surfaces when the number of transmitting antennas is different. DETAILED DESCRIPTION

[0039] like Figure 1 As shown, the joint transceiver design method based on channel statistical information includes the following steps:

[0040] Step S1: Establish a signal transmission model based on a multi-RIS-assisted airborne non-cellular network architecture. The airborne non-cellular network architecture includes N ground users, L aerial APs, K RISs, and a central processing unit. The signal transmission model includes a receiving signal model of each aerial AP and a channel matrix between the ground user and each aerial AP.

[0041] like Figure 2 As shown in the figure, the air-based non-cellular network architecture includes N ground users, L aerial APs, K RISs and a central processing unit. Each aerial AP is equipped with R receiving antennas, each ground user is equipped with T transmitting antennas, and each RIS is equipped with L k passive reflective elements. The total number of transmitting antennas is T t =N×T, the total number of passive reflective elements is The sum of the two can be expressed as L AR =R+L R .

[0042] Received signal model of the lth aerial AP Expressed as in, represents the uplink precoding matrix of the nth terrestrial user, satisfying the power constraint p n is the maximum transmission power of the nth ground user, is the transmitted signal of the nth ground user, vector is the additive white Gaussian noise at the lth aerial AP, σ 2 is the noise power.

[0043] The channel matrix H from the nth ground user to the lth aerial AP nl Expressed as Among them, G l =[I R ,G 1l ,…,G Kl ], represents the direct channel matrix from the nth ground user to the lth aerial AP, Indicates F 0,nl The conjugate transpose of represents the direct channel matrix from the nth user to the kth RIS, represents the direct channel matrix from the kth RIS to the lth aerial AP, is the phase shift matrix of the kth RIS, where L k represents the number of passive emitting elements of the kth RIS, k=1,2,…,K,I Rrepresents the R×R identity matrix.

[0044] For each of the above channels, the non-central Weichselberger MIMO channel model is used, and there is in, and Represents F 0,nl 、F nk and G kl The LoS component, and Represents F 0,nl 、F nk and G kl The random scattering component, M 0,nl 、M nk and N kl Respectively and The variance of each item is a certain non-negative value, T 0,nl 、P 0,nl 、T nk 、P nk 、R kl and C kl is a deterministic spatial correlation matrix, and the random matrix X 0,nl ,X nk ,Y kl Each element of satisfies the independent complex Gaussian distribution with zero mean,

[0045] In this embodiment, p n =23dBm,σ 2 =-94dBm. Figure 3 Simulation, with L = 4, K = 4, R = 8, T = 4, L k =8, N=4,8,12. Figure 4 For the simulation, N=4, L=4, K=2,4,6,8,10, R=10, T=2,4,6,8,10, L k =8.

[0046] Step S2: Each aerial AP performs local received signal detection and sends the detection signal to the central processing unit for weighted combined detection;

[0047] The specific steps include:

[0048] Step S21: The first aerial AP uses an MMSE detector based on local instantaneous channel state information to independently recover the signal of the ground user, that is, by minimizing the local detection signal With the original signal x nlThe mean square error between them, the MMSE receiver of the lth aerial AP is obtained as in σ 2 is the noise power,

[0049] Step S22: The first aerial AP detects the signal The signal is sent to the central processing unit, which performs weighted combined detection on the received detection signals. The signal detection result of the nth ground user after weighted combination in the central processing unit is in is the weighted combined detection matrix assigned by the central processing unit to the local signal detection result of the nth ground user by the lth aerial AP, The achievable rate of the nth terrestrial user is expressed as in

[0050] Step S3: Based on the signal transmission model, the optimization parameters are determined to establish an optimization problem for maximizing user weighted sum rates. This optimization problem is then equivalently transformed into a matrix weighted sum variance minimization problem. This problem involves the uplink precoding matrix of each ground user, the phase shift matrix of each RIS, and the weighted combined detection matrix of the central processing unit.

[0051] The specific steps include:

[0052] Step S31: Based on the signal transmission model, an optimization problem of maximizing the weighted sum rate of users is established. The goal of this optimization problem is to maximize the weighted sum rate of all users while satisfying the constraints. The optimization problem is expressed as Among them, μ n Indicates the priority of the nth ground user, represents the uplink precoding matrix of the terrestrial user, represents the weighted combined detection matrix of the central processing unit, Θ={Θ1,…,Θ K} represents the phase shift matrix of RIS, and the optimization variables include and Θ, represents the transmit power constraint, represents the phase shift range constraint;

[0053] Step S32: Convert the optimization problem of step S31 into a matrix weighted sum variance minimization problem. in, V n ≥0 T represents the auxiliary weight matrix of the nth user, 0 Trepresents a T×T dimensional matrix where all elements are 0, E n represents the mean square error matrix,

[0054] Step S4: Set the maximum number of iterations, the initial uplink precoding matrix of each ground user, the initial phase shift matrix of each RIS, and obtain the initial receiver of each aerial AP;

[0055] Specifically, it includes setting the maximum number of iterations to I MAX The initial value of iteration number i is 0, and the initial value of the uplink precoding matrix of the nth terrestrial user is The initial value of the phase shift matrix of the kth RIS is The initial receiver of the lth aerial AP is in

[0056] Step S5: The central processing unit alternately optimizes the weighted combined detection matrix of the central processing unit, the uplink precoding matrix of the terrestrial user, and the phase shift matrix of the RIS based on the matrix weighting and variance minimization problem in step S3, and obtains an asymptotic expression of the optimization result using the operator-valued free probability theory until the maximum number of iterations is reached.

[0057] That is, the central processing unit decomposes the matrix weighted sum variance minimization problem in step S3 into three sub-problems: weighted combined detection matrix optimization problem, user uplink precoding matrix optimization problem and RIS phase shift matrix optimization problem, and uses the asymptotic alternating optimization algorithm derived from operator value free probability theory to solve the three sub-problems in turn. Θ performs alternating optimization until the maximum number of iterations is reached, i.e. i ≥ I max When the i-th optimization is completed, the i+1-th optimization is performed, which specifically includes the following steps:

[0058] Step S51: In the i+1th iteration, the uplink precoding matrix optimized in the i-th iteration is fixed. and the phase shift matrix Θ (i) , by minimizing the sum of MSE, we get the optimized weighted merged detection matrix is a block matrix, and its (l,q)th submatrix block is Symbol {A} nn represents the nth diagonal block matrix of matrix A, z = -σ 2 , is a block matrix, Υ(z), Γ(z), represents a matrix-valued function, Indicates F l The LoS component, Represents Gl The LoS component, T t =N×T, where N represents the total number of terrestrial users, T represents the number of transmit antennas allocated to each terrestrial user, and the superscript (i) of a variable indicates that the variable is the result of the i-th iteration optimization;

[0059] Matrix-valued functions Υ(z), Γ(z), Satisfy the following fixed point equations respectively in,

[0060] and express The parameterized one-sided correlation function of and D is an arbitrary Hermitian matrix, and is a diagonal matrix with the diagonal elements being L k Indicates the number of passive reflective elements equipped with the RIS; and express The parameterized one-sided correlation function, Z and is any Hermitian matrix, diagonal matrix Σ nk (Z), The diagonal elements of ζ k (Z) = diag(ζ 1k (Z),ζ 2k (Z),…,ζ Nk (Z)) and express The parameterized one-sided correlation function of Indicates F k The random scattering component of

[0061] Step S52: Fix the uplink precoding matrix after the i-th iteration optimization and the phase shift matrix Θ (i) , substitute the optimized weighted merge detection matrix According to V n (i+1) The first-order optimality condition of , the optimized auxiliary weight matrix is ​​obtained

[0062] Step S53: Substitute the optimized weighted combined detection matrix Auxiliary weight matrix And fix the phase shift matrix Θ (i)According to the standard convex optimization algorithm and operator-valued free probability theory, the optimal asymptotic uplink precoding matrix for terrestrial users can be obtained as The optimal asymptotic uplink precoding matrix for the nth terrestrial user is Among them, λ k ≥0 represents the Lagrange multiplier, which can be obtained according to the Karush-Kuhn-Tucker condition and the bisection method;

[0063] Step S54: Substitute the optimized weighted combined detection matrix Auxiliary weight matrix Uplink precoding matrix Using the gradient descent algorithm based on Riemannian manipulativeness, the optimal solution of the phase shift matrix can be obtained: Definition in Indicates dimension L R A vector whose elements are all 1. In the i+1th iteration, θ (i+1) Updated to in is the step size of the i-th iteration, is the gradient The i-th element of is the Euclidean gradient, By separately Taking the derivative with respect to z, we get represents the conjugate of θ, Indicates the first k The kth phase shift of a RIS, for conjugation of;

[0064] Step S56: Go to step S51 and perform i+2 iterations until the maximum number of iterations is reached, and obtain the converged uplink precoding matrix of the terrestrial user and the phase shift matrix of the RIS.

[0065] Step S6: The central processing unit converts the converged uplink precoding matrix of the terrestrial user into RIS Phase Shift Matrix Transmitted to each aerial AP, RIS and ground user for the next round of uplink signal transmission and detection.

[0066] Figure 3The convergence of the present invention is demonstrated. It can be seen that in each case, the sum rate increases with the increase in the number of iterations and converges to the maximum value within 5 iterations, indicating that the proposed joint transceiver design algorithm has excellent convergence. In addition, compared with setting the weighted combination matrix, uplink precoding matrix, and phase shift matrix to the unit matrix in the initial state (when the number of iterations is 0), when N=4, N=8, and N=12, the sum rate is increased by 76.8%, 62.4%, and 49%, respectively, using the weighted combination matrix, uplink precoding matrix, and phase shift matrix after convergence. This shows that the joint transceiver design method based on channel statistical information proposed in the present invention can effectively improve the user sum rate. On the other hand, the theoretical results of each iteration are basically consistent with the simulation results, further proving the accuracy of the present invention.

[0067] Figure 4 The effect of the number of RISs on the sum rate is demonstrated. Compared to traditional airborne, non-cellular networks without RIS support (K = 0), deploying RIS in airborne, non-cellular networks significantly improves the sum rate. The sum rate increases monotonically with increasing RISs and the number of transmit antennas, demonstrating that this invention can effectively improve user sum rates.

[0068] The above description is merely a preferred embodiment of the present invention and therefore cannot be used to limit the scope of the present invention. In other words, equivalent changes and modifications made according to the scope of the patent application and the contents of the specification should still fall within the scope of the patent of the present invention.

Claims

1. A joint transceiver design method based on channel statistical information, characterized by: The steps include: Step S1: Establish a signal transmission model based on a multi-RIS-assisted airborne non-cellular network architecture. The airborne non-cellular network architecture includes N ground users, L aerial APs, K RISs, and a central processing unit. The signal transmission model includes a receiving signal model of each aerial AP and a channel matrix between the ground user and each aerial AP. Step S2: Each aerial AP performs local received signal detection and sends the detection signal to the central processing unit for weighted combined detection; Step S3: Based on the signal transmission model, an optimization problem of maximizing user weighted sum rates is established, and an equivalent transformation is performed on the optimization problem to obtain a matrix weighted sum variance minimization problem. This problem involves the uplink precoding matrix of each ground user, the phase shift matrix of each RIS, and the weighted combined detection matrix of the central processing unit. Step S4: Set the maximum number of iterations, the initial uplink precoding matrix of each ground user, the initial phase shift matrix of each RIS, and obtain the initial receiver of each aerial AP; Step S5: The central processing unit alternately optimizes the weighted combined detection matrix of the central processing unit, the uplink precoding matrix of the terrestrial user, and the phase shift matrix of the RIS based on the matrix weighting and variance minimization problem in step S3, and obtains an asymptotic expression of the optimization result using the operator-valued free probability theory until the maximum number of iterations is reached. Step S6: The central processing unit transmits the converged uplink precoding matrix of the ground user and the phase shift matrix of the RIS to each aerial AP, RIS and ground user for the next round of uplink signal transmission and detection.

2. The joint transceiver design method based on channel statistical information according to claim 1, characterized in that: In step S1, the received signal model of the lth aerial AP is expressed as Among them, W n represents the uplink precoding matrix of the nth terrestrial user, satisfying the power constraint p n is the maximum transmission power of the nth ground user, x n is the transmitted signal of the nth ground user, vector n l is the additive white Gaussian noise at the lth aerial AP, H nl is the channel matrix from the nth ground user to the lth aerial AP.

3. The joint transceiver design method based on channel statistical information according to claim 2, characterized in that: In step S1, the channel matrix H from the nth ground user to the lth aerial AP nl Expressed as Among them, G l =[I R ,G 1l ,...,G Kl ], F 0.nl represents the direct channel matrix from the nth ground user to the lth aerial AP, F nk represents the direct channel matrix from the nth user to the kth RIS, G kl represents the direct channel matrix from the kth RIS to the lth aerial AP, is the phase shift matrix of the kth RIS, where l k =1,...,L k , L k represents the number of passive emitting elements of the kth RIS, k=1,2,…,K,I R represents the R×R unit matrix, and R represents the number of receiving antennas equipped for each aerial AR.

4. The joint transceiver design method based on channel statistical information according to claim 3, characterized in that: In step S1, the direct channel matrix from the nth ground user to the lth aerial AP is expressed as The direct channel matrix from the nth user to the kth RIS is expressed as The direct channel matrix from the kth RIS to the lth aerial AP is expressed as in, and Respectively represent F 0,nl 、F nk and G kl The LoS component, and Respectively represent F 0,nl 、F nk and G kl The random scattering component, M 0,nl 、M nk and N kl Respectively and The variance of each item is a certain non-negative value, T 0,nl 、P 0,nl 、T nk 、P nk 、R kl and C kl is a deterministic spatial correlation matrix, and the random matrix X 0,nl ,X nk ,Y kl Each element of satisfies the independent complex Gaussian distribution with zero mean, 5. The joint transceiver design method based on channel statistical information according to claim 4, characterized in that: The step S2 comprises the following steps: Step S21: The first airborne AP uses local instantaneous channel state information to minimize the local detection signal. With the original signal x nl The mean square error between them, the MMSE receiver of the lth aerial AP is obtained as in F 0l =[F 0,1l ,...,F 0,Nl ], F k =[F 1k ,...,F Nk ],σ 2 is the noise power, Step S22: The first aerial AP detects the signal The signal is sent to the central processing unit, which performs weighted combined detection on the received detection signals. The signal detection result of the nth ground user after weighted combination in the central processing unit is in A nl is the weighted combined detection matrix assigned by the central processing unit to the local signal detection result of the nth ground user by the lth aerial AP, The achievable rate of the nth terrestrial user is expressed as in 6. The joint transceiver design method based on channel statistical information according to claim 5, characterized in that: The step S3 comprises the following steps: Step S31: Based on the signal transmission model, establish an optimization problem of maximizing user weighted sum rate: Among them, μ n Indicates the priority of the nth ground user, represents the uplink precoding matrix of the terrestrial user, represents the weighted combined detection matrix of the central processing unit, Θ={Θ1,...,Θ K } represents the phase shift matrix of RIS, represents the transmit power constraint, represents the phase shift range constraint; Step S32: Convert the optimization problem of step S31 into a matrix weighted sum variance minimization problem. in, V n ≥0 T represents the auxiliary weight matrix of the nth user, 0 T represents a T×T dimensional matrix where all elements are 0, E n represents the mean square error matrix, 7. The joint transceiver design method based on channel statistical information according to claim 6, characterized in that: In step S4, the maximum number of iterations is set to 1. MAX The initial value of iteration number i is 0, and the initial value of the uplink precoding matrix of the nth terrestrial user is The initial value of the phase shift matrix of the kth RIS is The initial receiver of the lth aerial AP is in 8. The joint transceiver design method based on channel statistical information according to claim 7, characterized in that: The step S5 specifically includes: Step S51: In the i+1th iteration, the uplink precoding matrix optimized in the i-th iteration is fixed. and the phase shift matrix Θ (i) , by minimizing the sum of MSE, we get the optimized weighted merged detection matrix is a block matrix, and its (l,q)th submatrix block is Symbol {A} nn represents the nth diagonal block matrix of matrix A, z = -σ 2 , is a block matrix, Υ(z), Γ(z), represents a matrix-valued function, Indicates F l The LoS component, Represents G l The LoS component, T t =N×T, where N represents the total number of terrestrial users, T represents the number of transmitting antennas allocated to each terrestrial user, and the superscript (i) of a variable indicates that the variable is the result of the i-th iteration optimization; Step S52: Fix the uplink precoding matrix after the i-th iteration optimization and the phase shift matrix Θ (i) , substitute the optimized weighted merge detection matrix According to V n (i+1) The first-order optimality condition of , the optimized auxiliary weight matrix is ​​obtained Step S53: Substitute the optimized weighted combined detection matrix Auxiliary weight matrix And fix the phase shift matrix Θ (i) According to the standard convex optimization algorithm and operator-valued free probability theory, the optimal asymptotic uplink precoding matrix for terrestrial users can be obtained as The optimal asymptotic uplink precoding matrix for the nth terrestrial user is Among them, λ k ≥0 indicates Lagrange multiplier; Step S54: Substitute the optimized weighted combined detection matrix Auxiliary weight matrix Uplink precoding matrix definition in represents a vector whose elements are all 1. In the i+1th iteration, θ (i+1) Updated to in is the step size of the i-th iteration, is the gradient The i-th element of is the Euclidean gradient, Where, By separately Taking the derivative with respect to z, we get represents the conjugate of θ, Indicates the first k The kth phase shift of a RIS, for conjugation; Step S56: Go to step S51 and perform i+2 iterations until the maximum number of iterations is reached, and obtain the converged uplink precoding matrix of the terrestrial user and the phase shift matrix of the RIS.

9. The joint transceiver design method based on channel statistical information according to claim 8, characterized in that: In step S51, the matrix value functions Υ(z), Γ(z), Satisfy the following fixed point equations respectively in, and express The parameterized one-sided correlation function of and D is an arbitrary Hermitian matrix, and is a diagonal matrix with the diagonal elements being Indicates the number of passive reflective elements equipped with the RIS; and express The parameterized one-sided correlation function, Z and is any Hermitian matrix, diagonal matrix Σ nk (Z), The diagonal elements of ζ k (Z) = diag(ζ 1k (Z),ζ 2k (Z),…,ζ Nk (Z)) and express The parameterized one-sided correlation function of

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