Deep learning based network massive mimo precoding method

Abstract

This invention discloses a deep learning-based precoding method for massive MIMO networks, applicable to downlink precoding design in massive MIMO transmissions where multiple base stations cooperate to transmit data for a group of users. For precoding designs maximizing system sum and rate, the method is equivalently transformed into a weighted minimum mean square error (WMMSE) problem. A WMMSE precoder is obtained through two iterative layers and represented by low-dimensional parameters. The precoding design problem is then transformed into an optimization problem with low-dimensional variables. Deep learning is used to solve the optimization problem for the low-dimensional parameters, and the precoding vector is calculated using a closed-form expression. This invention solves high-dimensional precoding design problems by solving low-dimensional parameter problems, achieving near-optimal sum and rate performance with lower computational complexity and higher computational efficiency.

Description

Technical Field

[0001] This invention relates to downlink precoding in wireless communication, and more particularly to a network massive MIMO precoding method and its deep learning design. Background Technology

[0002] Massive multiple-input multiple-output (MIMO) is a technology that deploys a large number of antenna arrays on the base station (BS) side to provide efficient communication services to a large number of users. It can provide high data transmission rates, high efficiency and signal robustness, and meet the high data demand, low latency and high reliability requirements of immersive communication.

[0003] In massive MIMO transmission in networks, utilizing the collaborative data transmission of all base station antennas within a service cluster provides more available degrees of freedom, more efficient use of spectrum, and improved transmission reliability and robustness, especially for users at the cell edge. However, the use of massive antenna arrays significantly increases the number of iterations required for the precoding iterative algorithm of the massive MIMO system to converge, and the computational complexity of each iteration also increases dramatically. Therefore, it is necessary to further reduce the computational complexity. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a deep learning-based method for large-scale MIMO precoding in networks, in order to overcome the shortcomings of existing technologies, achieve optimal sum rate performance, and reduce computational complexity.

[0005] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] A deep learning-based method for network massive MIMO precoding is proposed. In this method, multiple base stations are involved in the massive MIMO transmission, with multiple single-antenna users randomly distributed across the coverage area. Each base station is equipped with multiple antennas, and the multiple base stations cooperate to transmit data for a group of users. The optimization objective during iterative solution of the WMMSE precoder is to maximize the system sum and rate. in and Let be the downlink channels and precoding vectors from all base stations to the k-th user, respectively. This is the channel vector from the l-th base station to the k-th user; It is the precoding vector sent from the l-th base station to the k-th user. Let σ be the covariance matrix of the sum of virtual interference and noise for the k-th user, σ be the noise power, H be the superscript indicating matrix conjugate transpose, T be the superscript indicating matrix transpose, L be the number of base stations, K be the number of users, and M be the number of antennas for each base station.

[0007] In the precoding method, a WMMSE precoder that maximizes the system and rate is obtained through two-layer iteration. The WMMSE precoder is represented by low-dimensional parameters. Then, the precoding design problem is transformed into an optimization problem of low-dimensional variables. Deep learning is used to solve the optimization problem for low-dimensional parameters, and the precoding vector is calculated through a closed expression.

[0008] Furthermore, the problem of maximizing the sum and rate of a large-scale MIMO system under per-base-station power constraints is expressed as:

[0009]

[0010] In the formula, P l D represents the maximum transmission power of the l-th base station. l It is a block diagonal matrix, where the l-th diagonal block is an M-order identity matrix I. M The remaining diagonal blocks are M-order all-zero matrices. M×M .

[0011] Furthermore, in the two-layer iteration, the precoding design problem of maximizing system and rate is first equivalently transformed into a convex optimization problem of minimizing weighted minimum mean-square-error (WMMSE). In the outer iteration, the equivalent problem is solved iteratively by alternately optimizing the receiver, weights, and precoding vectors according to the first-order optimality condition using the block coordinate descent (BCD) method. In each outer iteration, the inner iteration process is obtained by using the BCD method on the quantities related to each base station, decoupling the precoding problem jointly designed by each base station into a problem solved independently by each base station, and solving the dual variables corresponding to the power constraints of the base station in the subproblem.

[0012] Furthermore, in the outer iteration, the iteration expression is:

[0013]

[0014] In the formula:

[0015]

[0016] The superscripts (t) and (t+1) of the parameters represent the t-th and t+1-th iterations, respectively. and B (t) v is an intermediate variable in the iterative calculation process. k For the receiver of the k-th user, w k As weight, These are dual variables.

[0017] Furthermore, in the inner iteration, the iteration expression is:

[0018]

[0019] In the formula, the superscript (t,q) represents the q-th inner iteration in the t-th outer iteration, and (t,q+1) represents the (q+1)-th inner iteration in the t-th outer iteration. for The vector extracted from it. For B (t) submatrix

[0020]

[0021] The optimal dual variable is obtained by binary search.

[0022] Furthermore, the precoding vector expression corresponding to the stable point at which the two-layer iterative algorithm converges depends only on the low-dimensional feature parameters and the channel vector, transforming the precoding problem into an optimization problem with respect to low-dimensional variables. The precoding method based on low-dimensional variables includes: calculating the direction of the precoding vector using the low-dimensional variables, calculating the allocated power, and constructing the precoding vector using the direction and power of the precoding vector.

[0023] Furthermore, the optimization problem for low-dimensional variables can be expressed as:

[0024]

[0025] In the formula, λ = [λ1, ..., λ2] K ] T μ = [μ1, ..., μ] L ] T , λ k , and μ l , Let Ξ be the decision variable and Ξ be the intermediate variable. ρ represents the direction of the precoding vector for user k. κ This represents the total power allocated to user k.

[0026] Furthermore, a neural network is used to solve the optimization problem with respect to low-dimensional variables. The neural network consists of convolutional layers, fully connected layers, and normalization layers. Specifically, the real and imaginary parts of the channel matrix are used as inputs to the two channels of the convolutional layer, respectively. The features extracted by the convolutional layer are vectorized and used together with the signal-to-noise ratio as inputs to the fully connected layer. Finally, the output of the fully connected layer is normalized and used as the output of the network.

[0027] Furthermore, neural network training includes offline and online phases;

[0028] In the offline phase, the dataset is generated. For each sample in the dataset, a pair of channel matrices and signal-to-noise ratios are first generated, and normalized low-dimensional parameters are calculated using the WMMSE precoder. in, Normalized l =[ l 1, ..., l K ] T and m =[ m 1, ..., m L ] T The neural network is trained using the dataset in combination with the channel matrix H and the signal-to-noise ratio γ.

[0029] In the online phase, low-dimensional parameters are calculated using the trained neural network, and then substituted into the structure of the WMMSE precoder to calculate the pre-encoding vector. The steps include:

[0030] 1) Calculate the direction of the precoding vector using low-dimensional variables

[0031]

[0032] 2) Calculate the allocated power

[0033]

[0034] 3) Constructing precoding vectors using the direction and power of the precoding vectors.

[0035] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the deep learning-based network massive MIMO precoding method.

[0036] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0037] (1) A two-layer iterative WMMSE precoding method is proposed for large-scale MIMO systems and rate maximization problems. The precoding vector expression corresponding to its stable point shows that it can be reconstructed by low-dimensional parameters. Therefore, the precoding design problem is re-expressed as an optimization problem with low-dimensional parameters.

[0038] (2) For the low-dimensional parameter optimization problem, a neural network design method is proposed, which utilizes deep learning to solve the problem. By performing equivalent transformations on the learning target and the network input, the complexity of network training is effectively reduced. The pre-encoded vector can be directly calculated based on the output of the neural network, which significantly reduces the complexity of online computation while maintaining performance close to that of an iterative algorithm. Attached Figure Description

[0039] Figure 1 Diagram of a large-scale MIMO precoding transmission scenario in a network;

[0040] Figure 2 A schematic diagram of the neural network structure in deep learning design for large-scale MIMO precoding of the network. Detailed Implementation

[0041] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0042] like Figure 1 As shown in the embodiments of the present invention, the deep learning-based network massive MIMO precoding method involves multiple base stations in the network massive MIMO transmission. Multiple single-antenna users are randomly distributed in the coverage area, each base station is equipped with multiple antennas, and multiple base stations cooperate to transmit data for a group of users. When iteratively solving the WMMSE precoder, the optimization objective is to maximize the system sum and rate. In the precoding method, a WMMSE precoder that maximizes the system sum and rate is obtained using two iterative layers. The WMMSE precoder is represented by low-dimensional parameters, and then the precoding design problem is transformed into an optimization problem with low-dimensional variables. Deep learning is used to solve the optimization problem for the low-dimensional parameters, and the precoding vector is calculated using a closed-form expression.

[0043] In the two-layer iteration, the precoding design problem of maximizing system and rate is first equivalently transformed into a convex optimization problem of minimizing weighted mean square error (WMMSE). In the outer iteration, the equivalent problem is solved iteratively by alternately optimizing the receiver, weights, and precoding vectors according to the first-order optimality condition using the block coordinate descent method. In each outer iteration step, the block coordinate descent method is used to obtain the inner iteration process for the quantities related to each base station, decoupling the precoding problem of joint design of each base station into a problem that each base station solves independently, and solving the dual variables corresponding to the power constraints of the base station in the subproblem.

[0044] The precoding vector expression corresponding to the stable point at which the two-layer iterative algorithm converges depends only on the low-dimensional feature parameters and the channel vector, transforming the precoding problem into an optimization problem with respect to low-dimensional variables. The precoding method based on low-dimensional variables includes: calculating the direction of the precoding vector using the low-dimensional variables, calculating the allocated power, and constructing the precoding vector using the direction and power of the precoding vector.

[0045] The method utilizes neural networks to solve optimization problems involving low-dimensional variables. The neural network consists of convolutional layers, fully connected layers, and normalization layers. Specifically, the real and imaginary parts of the channel matrix are used as inputs to the two channels of the convolutional layer, respectively. The features extracted by the convolutional layer are vectorized and used together with the signal-to-noise ratio as inputs to the fully connected layer. Finally, the output of the fully connected layer is normalized and used as the output of the network.

[0046] The embodiments of the present invention will be described in detail below, combining a specific system model, problem statement and transformation, and deep learning design. In this embodiment, L base stations cooperate to transmit signals to K users within the coverage area. Each base station is equipped with M antennas, and each user is equipped with a single antenna.

[0047] 1) System Model and Problem Statement

[0048] The downlink received signal y of the kth user k for:

[0049]

[0050] In the formula, This is the channel vector from the l-th base station to the k-th user; It is the precoded vector sent from the l-th base station to the u-th user, satisfying the power constraint. P l d represents the maximum transmit power of the l-th base station, where the superscript H denotes the matrix conjugate transpose; k For the data stream of the k-th user, d u For the data stream of the u-th user; n k For noise, the downlink channels from all base stations to the k-th user are concatenated with the precoding vector as follows: and The downlink precoding vectors from all base stations to the u-th user are concatenated as follows:

[0051] Assuming the user side has accurate CSI, the sum of received interference and noise will be... Consider covariance as Given Gaussian noise, the sum rate of the system is:

[0052]

[0053] The problem of maximizing the sum and rate of a large-scale MIMO system in a network under per-base-station power constraints is expressed as:

[0054]

[0055] in, It is a block diagonal matrix, where the l-th diagonal block is an M-order identity matrix I. MThe remaining diagonal blocks are M-order all-zero matrices. M×M .

[0056] 2) Iterative WMMSE precoder

[0057] The receiver on the user side is denoted as v. k Then the mean-squared error (MSE) of the received signal can be expressed as:

[0058]

[0059] in, For a given precoder, the optimal receiver for the MSE minimization problem is:

[0060]

[0061] in This yields the minimum mean-squared error (MMSE).

[0062]

[0063] Problem P1 can be equivalently transformed into the following weighted MSE minimization problem.

[0064]

[0065] in v = [v1, ..., v] K ] and w = [w1, ..., w k ] represents the precoder, receiver, and weights for all users, respectively.

[0066] The objective function and constraints of problem P2 are convex with respect to P, v, and w, and can be solved by iteratively updating these variables using the BCD method.

[0067] For the t-th iteration, according to the first-order optimality condition, the weight w k The calculation formula is:

[0068]

[0069] The optimal receiver is the MMSE problem. Solution:

[0070]

[0071] Substituting equations (8) and (9) into problem P2, the convex optimization problem concerning the preencoder in the t-th iteration becomes...

[0072]

[0073] The Lagrangian function for question P3 is:

[0074]

[0075] Where, {μ l ≥0} are the dual variables corresponding to the power constraint. B (t) , They are respectively

[0076]

[0077]

[0078] about The first-order optimal condition is

[0079]

[0080] Combining equation (16) with equations (8) and (9), we obtain the iterative expression for the precoding vector.

[0081]

[0082] To determine the dual variables The problem needs to be further broken down into units of each business unit (BS), and each BS should be searched individually. For a given v... (t) and w (t) Problem P3 can be decomposed into L independent problems:

[0083]

[0084] Problem P4 can be decoupled from the optimization for each base station by using the BCD method.

[0085] According to variable p k，l First-order condition

[0086]

[0087] in for The vector extracted from it. For B (t) submatrix

[0088]

[0089] The iterative formula for the precoding vector is:

[0090]

[0091] Here, the superscript (t, q) represents the q-th inner iteration within the t-th outer iteration. Optimal dual variable It can be obtained through binary search.

[0092] In summary, the WMMSE precoding method can be summarized into the following steps:

[0093] Step 1: Initialize the precoding vector and dual variables

[0094] Step 2: Calculate the receiver according to equation (9)

[0095] Step 3: Calculate the weights according to equation (8).

[0096] Step 4: Calculate according to equation (21) and

[0097] Step 5: Repeat steps 2-4 until the inner iterations converge;

[0098] Step 6: Calculate according to equation (17)

[0099] Step 5: Repeat steps 2-6 until the outer iteration converges.

[0100] The solution obtained from the above steps is called the WMMSE precoder.

[0101] 3) Equivalent optimization problems involving low-dimensional optimization variables

[0102] When the above algorithm converges, we can obtain At this point, equation (17) can be written as

[0103]

[0104] in, All are scalars. According to equation (22), it is known that... In this case, Completely composed of α k , λ k , and μ l , Decision, where α k Its energy is determined by λ. k , and μ l , Decide on the direction.

[0105] Therefore, the precoder design problem can be transformed into the following optimization problem with low-dimensional variables.

[0106]

[0107] Where α = [α1, ..., α2] k ] T , λ=[λ1,...,λ K ] T μ = [μ1, ..., μ] L ] T .

[0108] According to equation (22), we can obtain

[0109]

[0110] in, remember according to Computable

[0111]

[0112] Therefore, the total power allocated to the k-th user is

[0113]

[0114] Therefore, the precoding vector can be obtained using only λ and μ. The optimization problem for low-dimensional variables can be further equivalent to...

[0115]

[0116] The precoding method based on low-dimensional variables λ and μ can be summarized as follows:

[0117] Step 1: Calculate the normalized precoding vector according to equations (27a)-(27b).

[0118] Step 2: Calculate the allocated power ρ based on (27d). k ,

[0119] Step 3: Construct the precoding vector based on (27e)

[0120] The precoding vector is constructed using λ and μ. The steps are denoted as functions

[0121] P = f(λ, μ; H) (28)

[0122] in,

[0123] 4) Deep Learning Design

[0124] According to equation (28), the precoding vector can be determined by the low-dimensional parameters λ and μ. Therefore, we can use a neural network to learn the λ and μ obtained by the WMMSE precoder and solve problem P6.

[0125] To eliminate the order-of-magnitude fluctuations in λ and μ, consider scaling λ and μ proportionally, which will result in the function value P being scaled inversely, i.e.

[0126]

[0127] Therefore, λ can be... k , and μ l , Normalization l k =τλ k , m l =τμ l ,in The precoding vector and the normalized parameters satisfy the following relationship:

[0128]

[0129] According to equation (33), the power allocated to all users is proportionally scaled by the parameter τ. Therefore, the value of τ can be obtained by summing equation (33) over all users. And no additional learning is required. Normalized l =[ l 1, ..., l K ] T and m =[ m 1, ..., m L ] T Depends only on the power constraint value P l With noise variance σ 2 The proportion γ = [P1 / σ] 2 , ..., P L / σ 2 ] T Without needing to know their specific values, γ can be used as the input to the neural network.

[0130] like Figure 2As shown, a neural network is constructed using convolutional neural networks and fully connected layers. The real and imaginary parts of the channel matrix H are used as two input channels. First, channel features are extracted through convolutional layers, then vectorized and concatenated with vector γ before being input into the fully connected layers. Each convolutional layer employs max pooling with a rectified linear unit (ReLU) activation function.

[0131] The structure of a neural network can be represented as:

[0132]

[0133] z (i) =Conv(z (i-1) ), i = 1, ..., L C (35)

[0134] o (0) =[z (i) ,γ] (36)

[0135] o (i) =FC(o (i-1 ), i = 1, ..., L F (37) Among them, L C With L F These represent the depths of the convolutional layer and the fully connected layer, respectively. Conv(·) represents a single convolutional layer computation, and FC(·) represents a single fully connected layer computation. (i) with o (i) These represent the outputs of the i-th layer of the convolutional layer and the fully connected layer, respectively.

[0136] A normalization layer is used after the fully connected layer to eliminate amplitude fluctuations in the output value of the neural network.

[0137]

[0138] Among them, o k Output for the last fully connected layer The k-th element in O K+l for The (K+1)th element in.

[0139] The neural network structure of equations (34)-(39) can be represented as a function

[0140]

[0141] in,

[0142] The deep learning design of large-scale MIMO precoding in networks is divided into two stages: offline and online.

[0143] The offline phase is used to generate the dataset and train the neural network. When generating the dataset, for each pair of channel matrices and signal-to-noise ratios (SNR), a low-dimensional parameter is calculated using the WMMSE preencoder as the corresponding label, and this label is combined with the channel matrix and SNR to form a sample in the dataset. The specific steps for generating the offline dataset are as follows:

[0144] Step 1: Generate channel vectors Noise variance and power constraint values The superscript (n) indicates the nth sample;

[0145] Step 2: Obtain the WMMSE precoder through iterative calculation. and the corresponding dual variable

[0146] Step 3: Calculation

[0147] Step 4: Calculate the normalized parameters and in

[0148] Step 5: and Combined into the nth sample;

[0149] Step 6: Repeat steps 1-5 until a sufficient number of samples are generated.

[0150] Let the dataset generated in the above steps be denoted as . The goal of deep learning training is to minimize the following MSE cost function.

[0151]

[0152] in, Represents the size of the dataset, a vector β (n) =[( l (n) ) T , ( m (n) ) T ] T , This is the output of the neural network.

[0153] In the online phase, the channel matrix and signal-to-noise ratio are used as input to the trained neural network to obtain predicted values ​​for low-dimensional parameters, and the precoding vector is calculated. The specific steps are as follows:

[0154] Step 1: Calculate using a neural network

[0155] Step 2: Calculate the direction of the precoding vector according to equations (30)-(31).

[0156] Step 3: Calculate the distributed power ρ according to equations (32)-(33). k ,

[0157] Step 4: Calculate the precoding vector

[0158] Please pass steps 2-4 above. and Constructing precoding vectors The steps are denoted as functions

[0159]

[0160] An embodiment of the present invention discloses a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the deep learning-based network massive MIMO precoding method.

[0161] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A deep learning-based method for large-scale MIMO precoding, characterized in that, The massive MIMO transmission in the network involves multiple base stations, with multiple single-antenna users randomly distributed in the coverage area. Each base station is equipped with multiple antennas, and the multiple base stations cooperate to transmit data for a group of users. When iteratively solving the WMMSE precoder, the optimization problem is expressed as: The optimization objective is to maximize system performance and speed. ;in and Let be the downlink channels and precoding vectors from all base stations to the k-th user, respectively. For from the first The channel vector from each base station to the k-th user; It is the first The precoded vector sent by the base station to the k-th user Let the sum of virtual interference and noise for the k-th user be the covariance matrix. The noise power is represented by the superscript H, which indicates the matrix conjugate transpose, and the superscript T, which indicates the matrix transpose. L represents the number of base stations, K represents the number of users, and M represents the number of antennas equipped for each base station. For the first The maximum transmission power of each base station It is a block diagonal matrix, whose first... Each diagonal block is an M-order identity matrix. The remaining diagonal blocks are M-order all-zero matrices. ; In the precoding method, a WMMSE precoder that maximizes the system and rate is obtained by using two-layer iteration. The WMMSE precoder is characterized by low-dimensional parameters, and then the precoding design problem is transformed into an optimization problem of low-dimensional variables. Deep learning is used to solve the optimization problem for low-dimensional parameters, and the precoding vector is calculated using a closed-form expression. In the two-layer iteration, the precoding design problem of maximizing the system and rate is first equivalently transformed into a convex optimization problem of minimizing the weighted mean square error (WMMSE). In the outer iteration, the equivalent problem is solved iteratively by alternately optimizing the receiver, weights, and precoding vector using the block coordinate descent method based on the first-order optimality condition. In each outer iteration step, the block coordinate descent method is used on the quantities related to each base station to obtain the inner iteration process, decoupling the precoding problem of joint design of each base station into a problem that each base station solves independently, and solving the dual variables corresponding to the power constraints of the base station in the subproblems. In the outer iteration, the iterative expression is: ； In the formula: ； ； ； ； The superscripts (t) and (t+1) of the parameters represent the t-th and t+1-th iterations, respectively, and the superscript * indicates conjugate. and As intermediate variables in the iterative calculation process, For the receiver of the k-th user, As weight, As dual variables; In the inner iteration, the iteration expression is: ； In the formula, the superscript (t,q) represents the q-th inner iteration in the t-th outer iteration, and (t,q+1) represents the (q+1)-th inner iteration in the t-th outer iteration. for The vector extracted from it. for submatrix ； The optimal dual variable is obtained by binary search. .

2. The deep learning-based large-scale MIMO precoding method according to claim 1, characterized in that, The precoding vector expression corresponding to the stable point when the two-layer iterative algorithm converges depends only on the low-dimensional feature parameters and the channel vector, thus transforming the precoding problem into an optimization problem with respect to low-dimensional variables; Precoding methods based on low-dimensional variables include: calculating the direction of the precoding vector using low-dimensional variables, and calculating the assigned power; Precoding vectors are constructed using the direction and power of the precoding vectors.

3. The deep learning-based large-scale MIMO precoding method according to claim 1, characterized in that, The optimization problem concerning low-dimensional variables is represented as: ； In the formula, , , and As decision variables, As an intermediate variable, The direction of the precoding vector for user k. The total power allocated to user k, Describes the 2-norm of a vector. This indicates taking the absolute value.

4. The deep learning-based large-scale MIMO precoding method for networks according to claim 1, characterized in that, Using neural networks to solve optimization problems with low-dimensional variables; The neural network consists of convolutional layers, fully connected layers, and normalization layers. Specifically, the real and imaginary parts of the channel matrix are used as the inputs to the two channels of the convolutional layer, respectively. The features extracted by the convolutional layer are vectorized and used together with the signal-to-noise ratio as the inputs to the fully connected layer. Finally, the output of the fully connected layer is normalized and used as the output of the network.

5. The deep learning-based large-scale MIMO precoding method according to claim 3, characterized in that, Neural network training includes offline and online phases; In the offline phase, the dataset is generated. For each sample in the dataset, a pair of channel matrices and signal-to-noise ratios are first generated, and normalized low-dimensional parameters are calculated using the WMMSE precoder. , ,in, , , , ; after normalization and With channel matrix and signal-to-noise ratio Combine the datasets and train the neural network. In the online phase, low-dimensional parameters are calculated using the trained neural network, and then substituted into the structure of the WMMSE precoder to calculate the pre-encoding vector. The steps include: 1) Calculate the direction of the precoding vector using low-dimensional variables ； 2) Calculate the allocated power ； 3) Constructing precoding vectors using the direction and power of the precoding vectors. .

6. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the deep learning-based large-scale MIMO precoding method for networks according to any one of claims 1-5.

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