A robust relay network beamforming method and system with unknown second-order statistics

Abstract

The present invention relates to the field of signal processing technology, and discloses a robust relay network beamforming method and system with unknown second-order statistics, comprising the following steps: S1. receiving a signal, and establishing a relay network beamforming optimization problem based on the signal-to-interference-noise ratio and relay-by-relay power of the received signal; S2. introducing a second-order channel error on the basis of the relay network beamforming optimization problem to obtain a robust relay network beamforming optimization problem; S3. based on the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into a linear cone programming problem through the duality theorem and the semidefinite relaxation method; S4. solving the linear cone programming problem to obtain a solution to the relay network beamforming. The present invention solves the problem that the existing technology is not applicable to imperfect second-order channel states, and provides a robust relay network beamforming method and system with unknown second-order statistics, which has the characteristics of convenient calculation and high robustness.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and more specifically, to a robust relay network beamforming method and system with unknown second-order statistics. Background Art

[0002] In wireless communication systems, due to the special properties of actual wireless channels, such as long transmission distances and the influence of obstacles, the quality of signal transmission will be reduced, and it will be impossible or difficult to transmit from the transmitter to the receiver. In this case, adding relay points to the wireless communication network to perform weighted enhancement on the transmitted signals to assist in signal transmission will improve communication quality.

[0003] In the beamforming optimization problem in communications, two metrics are generally important: signal power and the signal-to-interference-plus-noise ratio (SINR) at the receiver. Typical optimization problems involve a trade-off between these two metrics to obtain the optimal solution.

[0004] Generally speaking, theoretical optimization analysis of the effectiveness and reliability of wireless communication systems typically assumes known channel state information. However, perfect channel state information is often unavailable in engineering. Therefore, it is necessary to consider the presence of errors within a certain range in channel state information, formulating a new worst-case optimization problem. This improves system robustness and makes the model more suitable for practical engineering applications.

[0005] A sparse beam design and power control method for a network-assisted full-duplex system is currently available. This method aims to maximize system summation rate, while meeting specified system quality of service (QoS), transmitter transmit power, and backhaul link consumption constraints. A mathematical optimization model is established using the transmitter and receiver beams of the remote radio head (RRH), as well as uplink user power, as design variables. This method uses an iterative sequential parametric convex approximation method to gradually transform the original non-convex optimization problem into a convex optimization problem through continuous convex approximation. The sparse beamforming vector and transmit power are then jointly determined through continuous iterative optimization.

[0006] Existing technologies still rely on accurate information about wireless communication channels. However, accurate information about wireless communication channels in actual situations is generally difficult to obtain. There will always be a certain error between the ideal estimated channel analyzed theoretically and the actual channel. Therefore, how to invent a relay network beamforming method that takes into account imperfect second-order channel state information is an urgent problem that needs to be solved in this technical field. Summary of the Invention

[0007] In order to solve the problem that the existing technology is not applicable to imperfect second-order channel states, the present invention provides a robust relay network beamforming method and system with unknown second-order statistics, which has the characteristics of convenient calculation and high robustness.

[0008] In order to achieve the above-mentioned purpose of the present invention, the technical solutions adopted are as follows:

[0009] A robust relay network beamforming method with unknown second-order statistics includes the following steps:

[0010] S1. Receive the signal and establish a relay network beamforming optimization problem based on the signal-to-interference-and-noise ratio (SINR) and relay-by-relay power of the received signal.

[0011] S2. Based on the relay network beamforming optimization problem, we introduce the second-order channel error to obtain the robust relay network beamforming optimization problem.

[0012] S3. Based on the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is transformed into a linear cone programming problem through the duality theorem and semidefinite relaxation method;

[0013] S4. Solve the linear cone programming problem and obtain the solution for relay network beamforming.

[0014] Preferably, in step 1, the relay network beamforming optimization problem is specifically:

[0015]

[0016] Where w is the optimized variable beamforming vector, w H represents the conjugate transpose of w, w n is the nth element of w, |w n | indicates the plural w n The module, R 1,1 , R 1,2 are the second-order channel matrices from the source and interference source to the relay, Q1 is the noise matrix, diag(Q1) represents the diagonal matrix of the diagonal element Q1, σ μ ,σ υ is the standard deviation of the noise, D is the second-order matrix carrying signal power and channel information, D nn is the nth diagonal element of D, P n The maximum power limit of the nth relay.

[0017] Furthermore, in step S2, the second-order channel error is specifically:

[0018] in

[0019] in

[0020] in

[0021] Among them, {ε 1,k}, ε d are the error terms {Δ 1,k}, Δ d The upper bound of the F norm is, is the estimator that can be obtained at the endpoint, ||X|| F represents the Frobenius norm of the matrix X, and X ≥ 0 means that the matrix X is positive semidefinite.

[0022] Furthermore, in step S2, the robust relay network beamforming optimization problem of the updated relay network beamforming is specifically implemented as follows:

[0023] S201. Based on the relay network beamforming optimization problem, the second-order channel error is introduced to obtain the robust relay network beamforming optimization problem:

[0024]

[0025] The per-relay power constraint is expressed as:

[0026]

[0027] in, represents w n The conjugation of .

[0028] Furthermore, in step S3, according to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into a linear cone programming problem through the duality theorem and the semidefinite relaxation method. The specific steps are:

[0029] S301. According to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into an updated optimization problem through the duality theorem;

[0030] S302. Substitute the constants of the updated optimization problem;

[0031] S303. Convert the optimization problem after substitution into a linear cone programming problem through a semidefinite relaxation method.

[0032] Furthermore, in step S301, according to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into an updated optimization problem through the duality theorem, and the specific steps are:

[0033] S3101. Simplifying the robust relay network beamforming optimization problem by introducing matrices:

[0034]

[0035] Where I is the identity matrix;

[0036] S3102. Find the minimization problem of the simplified robust relay network beamforming optimization problem. Then, according to the strong duality theorem, replace the original minimization problem with its dual problem, and update the simplified robust relay network beamforming optimization problem:

[0037]

[0038] Where tr(X) represents the trace of matrix X.

[0039] Furthermore, in step S303, the optimization problem after substitution is transformed into a linear cone programming problem by a semidefinite relaxation method, and the specific steps are as follows:

[0040] S3301. Using the semidefinite relaxation method, the optimization problem after substitution is expressed as Equation 1:

[0041]

[0042] Where ||s|| represents the 2-norm of vector s;

[0043] S3302. Convert Equation 1 into a linear cone programming problem:

[0044]

[0045] Furthermore, in step S4, a linear cone programming problem is solved to obtain a solution for relay network beamforming, specifically:

[0046] If we solve the linear cone programming problem, we get The rank of is 1, then the optimal solution of relay network beamforming is obtained by decomposition

[0047] If we solve the linear cone programming problem, we get If it is greater than 1, the approximate solution of the relay-by-relay power constraint is obtained through the Gaussian randomization method, thereby obtaining a suboptimal solution for the relay network beamforming.

[0048] Furthermore, the approximate solution of the relay-by-relay power constraint is obtained by using the Gaussian randomization method, specifically:

[0049] Gaussian randomization method 1:

[0050] Take a mean of 0 and the covariance matrix is A Gaussian distributed random vector w, that is, get:

[0051]

[0052] satisfy:

[0053]

[0054] Take a random vector sequence Define a feasible solution sequence for this random vector sequence:

[0055]

[0056] Substitute the feasible solution sequence into the updated robust relay network beamforming optimization problem to obtain the objective function value, and take the feasible solution with the largest objective function value as the final approximate solution;

[0057] Gaussian randomization method 2:

[0058] Take one Random vector, we get:

[0059]

[0060] satisfy:

[0061]

[0062] Take a random vector sequence Define a feasible solution sequence for this random vector sequence:

[0063]

[0064] The feasible solution sequence is substituted into the robust relay network beamforming optimization problem of the updated relay network beamforming to obtain the objective function value, and a feasible solution with the largest objective function value is taken as the suboptimal solution.

[0065] A robust relay network beamforming system with unknown second-order statistics includes a signal receiving module, a relay network beamforming optimization module, an objective function module, a linear cone programming transformation module, and an optimal solution module;

[0066] The receiving module is used to receive signals;

[0067] The relay network beamforming optimization module is used to establish a relay network beamforming optimization problem based on the channel state information of the signal;

[0068] The objective function module is used to introduce the second-order channel error on the basis of the relay network beamforming optimization problem to obtain the robust relay network beamforming optimization problem;

[0069] The linear cone programming conversion module is used to convert the robust relay network beamforming optimization problem into a linear cone programming problem through the duality theorem and the semidefinite relaxation method according to the robust relay network beamforming optimization problem;

[0070] The optimal solution module is used to solve the linear cone programming problem and obtain a solution for the relay network beamforming.

[0071] The beneficial effects of the present invention are as follows:

[0072] The present invention proposes a robust relay network beamforming method and system with unknown second-order statistics. The present invention takes into account imperfect second-order channel state information. The present invention establishes a relay network beamforming optimization problem based on maximizing the received signal-to-interference-and-noise ratio with a relay-by-relay constraint, introduces second-order channel errors, and then applies the strong duality theorem and semidefinite relaxation method to transform the original relay network beamforming optimization problem into a linear cone programming problem, thereby simplifying the relay network beamforming optimization problem and making it easier to solve. Finally, the linear cone programming problem is solved to obtain a solution to the relay network beamforming, thereby achieving a fast solution. The present invention has the characteristics of high robustness and close to practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 The present invention is a flowchart of a robust relay network beamforming method with unknown second-order statistics.

[0074] Figure 2 The present invention is a flowchart of a solution to an optimization problem of a robust relay network beamforming method with unknown second-order statistics.

[0075] Figure 3 A relay network model diagram of a robust relay network beamforming method with unknown second-order statistics according to the present invention.

[0076] Figure 4 The present invention is a schematic diagram of a robust relay network beamforming system with unknown second-order statistics. DETAILED DESCRIPTION

[0077] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] Example 1

[0079] like Figure 1 As shown, a robust relay network beamforming method with unknown second-order statistics includes the following steps:

[0080] S1. Receive the signal and establish a relay network beamforming optimization problem based on the signal-to-interference-and-noise ratio (SINR) and relay-by-relay power of the received signal.

[0081] S2. Based on the relay network beamforming optimization problem, we introduce the second-order channel error to obtain the robust relay network beamforming optimization problem.

[0082] S3. Based on the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is transformed into a linear cone programming problem through the duality theorem and semidefinite relaxation method;

[0083] S4. Solve the linear cone programming problem and obtain the solution for relay network beamforming.

[0084] Example 2

[0085] like Figure 1 As shown, a robust relay network beamforming method with unknown second-order statistics includes the following steps:

[0086] S1. Receive the signal and establish a relay network beamforming optimization problem based on the signal-to-interference-and-noise ratio (SINR) and relay-by-relay power of the received signal.

[0087] S2. Based on the relay network beamforming optimization problem, we introduce the second-order channel error to obtain the robust relay network beamforming optimization problem.

[0088] S3. Based on the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is transformed into a linear cone programming problem through the duality theorem and semidefinite relaxation method;

[0089] S4. Solve the linear cone programming problem and obtain the solution for relay network beamforming.

[0090] like Figure 2 As shown, the process of solving the optimization problem in this embodiment is: establishing a relay network beamforming optimization problem, introducing the uncertainty of the second-order channel error, and converting the robust relay network beamforming optimization problem into a linear cone programming problem, i.e., an LCP problem, proving the solvability of the LCP problem, and obtaining the optimal solution or suboptimal solution of the relay network beamforming.

[0091] like Figure 3 As shown, in this embodiment, the relay network includes 1 source point, 1 interference source, N relay points, and 1 end point.

[0092] In a specific embodiment, in step 1, the relay network beamforming optimization problem is specifically:

[0093]

[0094] Where w is the optimized variable beamforming vector, w H represents the conjugate transpose of w, w n is the nth element of w, |w n | indicates the plural w n The module, R 1,1 , R 1,2 are the second-order channel matrices from the source and interference source to the relay, Q1 is the noise matrix, diag(Q1) represents the diagonal matrix of the diagonal element Q1, σ μ ,σ υ is the standard deviation of the noise, D is the second-order matrix carrying signal power and channel information, D nn is the nth diagonal element of D, P n The maximum power limit of the nth relay.

[0095] In a specific embodiment, in step S2, the second-order channel error is specifically:

[0096] in

[0097] in

[0098] in

[0099] Among them, {ε 1,k}, ε d are the error terms {Δ 1,k}, Δ d The upper bound of the F norm is, is the estimator that can be obtained at the endpoint, ||X|| F represents the Frobenius norm of the matrix X, and X ≥ 0 means that the matrix X is positive semidefinite.

[0100] In a specific embodiment, in step S2, the robust relay network beamforming optimization problem of the updated relay network beamforming includes the following steps:

[0101] S201. Based on the relay network beamforming optimization problem, the second-order channel error is introduced to obtain the robust relay network beamforming optimization problem:

[0102]

[0103] The robust relay network beamforming optimization problem is equivalent to:

[0104]

[0105] The per-relay power constraint is expressed as:

[0106]

[0107] in, represents w n The conjugate of ; the relay-by-relay power constraint is equivalent to:

[0108]

[0109] In a specific embodiment, in step S3, according to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into a linear cone programming problem through the duality theorem and the semidefinite relaxation method. The specific steps are:

[0110] S301. According to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into an updated optimization problem through the duality theorem;

[0111] S302. Substitute the constants of the updated optimization problem;

[0112] S303. Convert the optimization problem after substitution into a linear cone programming problem through a semidefinite relaxation method.

[0113] In a specific embodiment, in step S301, according to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into an updated optimization problem through the duality theorem, and the specific steps are:

[0114] S3101. Simplifying the robust relay network beamforming optimization problem by introducing matrices:

[0115]

[0116] Where I is the identity matrix;

[0117] S3102. Find the minimization problem of the simplified robust relay network beamforming optimization problem. Then, according to the strong duality theorem, replace the original minimization problem with its dual problem, and update the simplified robust relay network beamforming optimization problem:

[0118]

[0119] Where tr(X) represents the trace of matrix X.

[0120] In this embodiment, a simplified minimization problem of the robust relay network beamforming optimization problem is obtained. According to the strong duality theorem, the original minimization problem is replaced with an optimization problem, and the simplified robust relay network beamforming optimization problem is updated. The specific steps are as follows:

[0121] The terms involved in the maximization of the robust relay network beamforming optimization problem are further processed as follows:

[0122]

[0123]

[0124] Solving the Cauchy-Schwarz inequality yields:

[0125]

[0126] The robust relay network beamforming optimization problem is simplified as:

[0127]

[0128] The robust relay network beamforming optimization problem is further expressed as Equation 2:

[0129]

[0130] The minimization problem of the molecular part of Formula 2 is processed and the symbols of Formula 2 are simplified:

[0131]

[0132]

[0133] The simplified robust relay network beamforming optimization problem is expressed as Equation 3:

[0134]

[0135] Process the numerator of Equation 3 and find the minimization problem in the numerator:

[0136]

[0137] Find the dual problem of the minimization problem in the numerator of Equation 3:

[0138]

[0139] because It is a strictly feasible point of the minimization problem in the numerator, and any semi-positive definite matrix X1 ≥ 0 is strictly feasible for the dual problem of the minimization problem, that is, it satisfies the strong duality theorem conditions of the linear cone programming problem. Therefore, the minimization problem in the numerator and the dual problem of the minimization problem are both solvable, and the optimal values ​​of the two problems are equal. Therefore, the simplified robust relay network beamforming optimization problem is updated:

[0140]

[0141] In a specific embodiment, in step S303, the optimization problem after substitution is converted into a linear cone programming problem by a semidefinite relaxation method, and the specific steps are as follows:

[0142] S3301. Using the semidefinite relaxation method, the optimization problem after substitution is expressed as Equation 1:

[0143]

[0144] Where ||s|| represents the 2-norm of vector s;

[0145] S3302. Convert Equation 1 into a linear cone programming problem:

[0146]

[0147] In this embodiment, the optimization problem after substitution is expressed as Formula 1 using a semidefinite relaxation method. The specific steps are:

[0148] The robust relay network beamforming optimization problem of the updated relay network beamforming is transformed into a linear cone programming relaxation problem: Introduce the variable s in the robust relay network beamforming optimization problem of the updated relay network beamforming, {s n}, we get Equation 4:

[0149]

[0150] Again

[0151]

[0152] s=[s1,...,s N ] T ,

[0153]

[0154] in ||s|| represents the 2-norm of vector s.

[0155] Performing semi-positive relaxation on Equation 4, we get Equation 1:

[0156]

[0157] In this embodiment, Equation 1 is equivalently converted into a linear cone programming problem, and the specific steps are as follows:

[0158] It can be observed that the numerator of Equation 4 is homogeneous with respect to the optimization variable, while the denominator is affine. Therefore, the affine part can be homogenized, thereby transforming the original relay network beamforming optimization problem into a traditional linear cone programming problem:

[0159]

[0160] In this embodiment, the solvability of the linear cone programming problem is also proved, that is, it is feasible, has an upper bound, and its optimal value can be reached at some feasible point. First, define the matrix:

[0161]

[0162] Then the constraints of the third and fourth lines of the linear cone programming problem are expressed as:

[0163] tr(E n W)≤s n ,n=1,...,Ν

[0164]

[0165] in

[0166] Due to the strong duality theorem of linear cone programming, if we want to prove that the linear cone programming problem is solvable, the sufficient condition is that the original problem itself is feasible and its dual problem is strictly feasible. is a feasible solution to the linear cone programming problem, and the dual problem of the linear cone programming problem can be obtained:

[0167]

[0168] Assuming v≥0 is large enough, when When (Y, {u n},{r n}, v) is a strictly feasible point of the dual problem of the linear cone programming problem. In summary, it is proved that the linear cone programming is solvable.

[0169]

[0170] In a specific embodiment, in step S4, a linear cone programming problem is solved to obtain a solution for relay network beamforming, specifically:

[0171] If we solve the linear cone programming problem, we get The rank of is 1, then the optimal solution of relay network beamforming is obtained by decomposition

[0172] If we solve the linear cone programming problem, we get If it is greater than 1, the approximate solution of the relay-by-relay power constraint is obtained through the Gaussian randomization method, thereby obtaining a suboptimal solution for the relay network beamforming.

[0173] In a specific embodiment, an approximate solution to the relay-by-relay power constraint is obtained by using a Gaussian randomization method, specifically:

[0174] Gaussian randomization method 1:

[0175] Take a mean of 0 and the covariance matrix is A Gaussian distributed random vector w, that is, get:

[0176]

[0177] satisfy:

[0178]

[0179] Take a random vector sequence Define a feasible solution sequence for this random vector sequence:

[0180]

[0181] Substitute the feasible solution sequence into the updated robust relay network beamforming optimization problem to obtain the objective function value, and take the feasible solution with the largest objective function value as the final approximate solution;

[0182] In this embodiment, the objective function value obtained is:

[0183]

[0184] So that v l The largest feasible solution is is the final approximate solution, where

[0185] l0=argmax{v l |1≤l≤L}.

[0186] Gaussian randomization method 2:

[0187] Take one Random vector, we get:

[0188]

[0189] satisfy:

[0190]

[0191] Take a random vector sequence Define a feasible solution sequence for this random vector sequence:

[0192]

[0193] The feasible solution sequence is substituted into the robust relay network beamforming optimization problem of the updated relay network beamforming to obtain the objective function value, and a feasible solution with the largest objective function value is taken as the suboptimal solution.

[0194] Traditional methods only consider perfect channel state information, while this patent considers imperfect channel state information. In this embodiment, the channel in the present invention consists of two parts: an ideal estimated channel and a channel error. The present invention establishes a relay network beamforming optimization problem based on maximizing the received signal-to-interference-and-noise ratio with relay-by-relay constraints, and introduces second-order channel errors. Then, the strong duality theorem and semidefinite relaxation are used to transform the original relay network beamforming optimization problem into a linear cone programming problem, which simplifies and makes the relay network beamforming optimization problem easier to solve. In this embodiment, it is also proved that the problem is solvable. Finally, matrix decomposition or Gaussian randomization method is used to solve the convex problem, achieving a fast solution. The present invention has the characteristics of high robustness and close to practical applications.

[0195] Example 3

[0196] like Figure 4 As shown, a robust relay network beamforming system with unknown second-order statistics is characterized by comprising a signal receiving module, a relay network beamforming optimization module, an objective function module, a linear cone programming transformation module, and an optimal solution module;

[0197] The receiving module is used to receive signals;

[0198] The relay network beamforming optimization module is used to establish a relay network beamforming optimization problem based on the channel state information of the signal;

[0199] The objective function module is used to introduce the second-order channel error on the basis of the relay network beamforming optimization problem to obtain the robust relay network beamforming optimization problem;

[0200] The linear cone programming conversion module is used to convert the robust relay network beamforming optimization problem into a linear cone programming problem through the duality theorem and the semidefinite relaxation method according to the robust relay network beamforming optimization problem;

[0201] The optimal solution module is used to solve the linear cone programming problem and obtain a solution for the relay network beamforming.

[0202] Obviously, the above embodiments of the present invention are merely examples for the purpose of illustrating the present invention, and are not intended to limit the embodiments of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A robust relay network beamforming method with unknown second-order statistics, characterized by: The following steps are involved: S1. Receive the signal and establish a relay network beamforming optimization problem based on the signal-to-interference-and-noise ratio (SINR) and relay-by-relay power of the received signal. S2. Based on the relay network beamforming optimization problem, we introduce the second-order channel error to obtain the robust relay network beamforming optimization problem. S3. Based on the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is transformed into a linear cone programming problem through the duality theorem and semidefinite relaxation method; S4. Solve the linear cone programming problem and obtain the solution for relay network beamforming; In step 1, the relay network beamforming optimization problem is specifically: Where w is the optimized variable beamforming vector, w H represents the conjugate transpose of w, w n is the nth element of w, |w n | indicates the plural w n The module, R 1,1 , R 1,2 are the second-order channel matrices from the source and interference source to the relay, Q1 is the noise matrix, diag(Q1) represents the diagonal matrix of the diagonal element Q1, σ μ ,σ υ is the standard deviation of the noise, D is the second-order matrix carrying signal power and channel information, D nn is the nth diagonal element of D, P n is the maximum power limit of the nth relay; In step S2, the second-order channel error is specifically: in in in Among them, {ε 1,k }, ε d are the error terms {Δ 1,k }, Δ d The upper bound of the F norm is, is the estimator that can be obtained at the endpoint, ||X|| F represents the Frobenius norm of the matrix X, X ≥ 0 means that the matrix X is semi-positive definite; In step S2, the robust relay network beamforming optimization problem of the updated relay network beamforming is specifically performed as follows: S201. Based on the relay network beamforming optimization problem, the second-order channel error is introduced to obtain the robust relay network beamforming optimization problem: The per-relay power constraint is expressed as: in, represents w n conjugation of; In step S3, according to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into a linear cone programming problem through the duality theorem and the semidefinite relaxation method. The specific steps are: S301. According to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into an updated optimization problem through the duality theorem; S302. Substitute the constants of the updated optimization problem; S303. Convert the optimization problem after substitution into a linear cone programming problem by using a semidefinite relaxation method; In step S301, according to the robust relay network beamforming optimization problem, the robust relay network beamforming optimization problem is converted into an updated optimization problem through the duality theorem. The specific steps are: S3101. Simplifying the robust relay network beamforming optimization problem by introducing matrices: Where I is the identity matrix; S3102. Find the minimization problem of the simplified robust relay network beamforming optimization problem. Then, according to the strong duality theorem, replace the original minimization problem with its dual problem, and update the simplified robust relay network beamforming optimization problem: X1≥0. Where tr(X) represents the trace of matrix X; In step S303, the optimization problem after substitution is transformed into a linear cone programming problem by a semidefinite relaxation method, and the specific steps are as follows: S3301. Using the semidefinite relaxation method, the optimization problem after substitution is expressed as Equation 1: st||s||≤s W nn ≤s n ,n=1,...,N W≥0,X1≥0. Where ||s|| represents the 2-norm of vector s; S3302. Convert Equation 1 into a linear cone programming problem: ||s||≤s W nn ≤s n ,n=1,...,N W≥0,X1≥0.

2. The robust relay network beamforming method with unknown second-order statistics according to claim 1, characterized in that: In step S4, a linear cone programming problem is solved to obtain a solution for relay network beamforming, specifically: If W obtained by solving the linear cone programming problem ＊ The rank of is 1, then the optimal solution W for relay network beamforming is obtained by decomposition ＊ =w ★ w ★H ; If W obtained by solving the linear cone programming problem ★ If it is greater than 1, the approximate solution of the relay-by-relay power constraint is obtained through the Gaussian randomization method, thereby obtaining a suboptimal solution for the relay network beamforming.

3. The robust relay network beamforming method with unknown second-order statistics according to claim 2, wherein: The approximate solution to the relay-by-relay power constraint is obtained by using the Gaussian randomization method, specifically: Gaussian randomization method 1: Take a mean of 0 and a covariance matrix of W ★ / t ＊ A Gaussian distributed random vector w, that is, get: satisfy: Take a random vector sequence Define a feasible solution sequence for this random vector sequence: Substitute the feasible solution sequence into the updated robust relay network beamforming optimization problem to obtain the objective function value, and take the feasible solution with the largest objective function value as the final approximate solution; Gaussian randomization method 2: Take one Random vector, we get: satisfy: Take a random vector sequence Define a feasible solution sequence for this random vector sequence: The feasible solution sequence is substituted into the robust relay network beamforming optimization problem of the updated relay network beamforming to obtain the objective function value, and a feasible solution with the largest objective function value is taken as the suboptimal solution.

4. A robust relay network beamforming system with unknown second-order statistics, characterized by: Used to execute the robust relay network beamforming method with unknown second-order statistics as described in any one of claims 1 to 3, comprising a signal receiving module, a relay network beamforming optimization module, an objective function module, a linear cone programming conversion module, and an optimal solution module; The receiving module is used to receive signals; The relay network beamforming optimization module is used to establish a relay network beamforming optimization problem based on the channel state information of the signal; The objective function module is used to introduce the second-order channel error on the basis of the relay network beamforming optimization problem to obtain the robust relay network beamforming optimization problem; The linear cone programming conversion module is used to convert the robust relay network beamforming optimization problem into a linear cone programming problem through the duality theorem and the semidefinite relaxation method according to the robust relay network beamforming optimization problem; The optimal solution module is used to solve the linear cone programming problem and obtain a solution for the relay network beamforming.

Images