Millimeter wave large-scale MIMO deep learning channel estimation method based on matrix recovery algorithm

Abstract

The invention discloses a millimeter wave large-scale MIMO deep learning channel estimation method based on a matrix recovery algorithm. The method comprises the following steps: firstly, converting a channel estimation problem into a low-rank matrix recovery problem by utilizing the sparse characteristic of a millimeter wave channel antenna angle domain; secondly, a non-convex gamma-norm is used for replacing a nuclear norm approximation channel matrix rank function, and the accuracy of channel matrix approximation is improved; according to the method, the Lagrange planning neural network model is constructed by utilizing the self-adaptability and parallelism of the neural network, so that the optimization problem can be quickly solved, and an effective solution is obtained. Simulation results show that compared with other channel estimation algorithms, namely SVT algorithms, the Lagrange planning neural network algorithm constructed by the method has faster convergence.

Description

Technical Field

[0001] The present invention relates to a millimeter wave large-scale MIMO deep learning channel estimation method based on a matrix recovery algorithm, and belongs to the technical field of mobile communications. Technical Background

[0002] Millimeter-wave massive MIMO is a multiple-input multiple-output technology used in the millimeter-wave frequency band (usually 30GHz to 300GHz). It combines the high bandwidth characteristics of millimeter-wave communication and the high energy utilization capability of massive MIMO systems, aiming to achieve higher data transmission rates and system capacity. In the millimeter-wave frequency band, communication requirements of higher speed, lower latency and greater connection density can be achieved. In millimeter-wave massive MIMO systems, channel estimation is a crucial link. The goal of channel estimation is to determine the channel state information, that is, the characteristics of the communication channel between the transmitter and the receiver. This information can help the receiver to better perform signal decoding and the transmitter to perform beamforming and other key operations. The use of traditional channel estimation algorithms will result in huge pilot overhead and high computational complexity. Using the sparsity of the millimeter-wave channel in the antenna angle domain, the compressed sensing method uses the observation matrix to reconstruct the coefficient channel. Due to the low rank shown by its sparsity, the channel matrix is ​​obtained by solving the rank function of the channel matrix using the matrix recovery algorithm. However, since it is relatively difficult to directly obtain the rank function, it is currently necessary to approximate it through the deformation of the nuclear norm, such as the γ-norm, truncated nuclear norm, or through the method of approximating the rank function by function, convert the problem into an optimization problem that is easier to achieve, and then use the optimization algorithm to solve it. Summary of the invention

[0003] The purpose of the present invention is to address the defects and shortcomings of the above-mentioned prior art, and propose a millimeter wave large-scale MIMO deep learning channel estimation method based on a matrix recovery algorithm. The method uses a Lagrangian programming neural network to add Lagrangian multipliers and quadratic penalty terms to convexify the objective function for the non-convex problem generated after the γ-norm approximates the rank function, and then uses the neural network to solve the non-convex problem. The Lagrangian programming neural network based on the Lagrangian multiplier method of the present invention is applied to solve general nonlinear constrained optimization problems. Instead of considering them in a digital way, an analog neural network is constructed, and neural dynamics are defined to control the state transition of neurons. When the network stabilizes at one of the equilibrium points, the solution is obtained by measuring the output of the neurons at the stable equilibrium point, and the channel matrix is ​​output. The neural network includes a recursive neural network and a feedforward neural network, wherein the feedforward neural network is used to solve the sub-gradient of the γ-norm of the channel matrix, and the recursive neural network is responsible for the iterative processing of variables and Lagrangian multipliers, and outputs the channel matrix.

[0004] The technical solution adopted by the present invention to solve the technical problem is: a millimeter wave large-scale MIMO deep learning channel estimation method based on a matrix recovery algorithm, the method comprising the following steps:

[0005] Step S1, constructing a millimeter wave massive MIMO system and building a system communication model;

[0006] Step S2, combining the matrix recovery algorithm of the γ-norm approximate rank function and using the Lagrangian programming neural network to solve the γ-norm minimization problem;

[0007] Step S3, after receiving the signal, the receiving end transmits it to the neural network module, and performs channel estimation in combination with the pilot signal. The neural network module is mainly composed of a recursive neural network, which cooperates with a feedforward neural network to output a channel matrix;

[0008] Step S4, performing signal difference measurement on the subsequently received signals, adjusting the network weights, and obtaining an updated channel matrix.

[0009] Furthermore, the present invention introduces Lagrangian neurons and variable neurons, and constructs a recursive neural network based on the Lagrangian multiplier method.

[0010] Furthermore, the present invention comprises:

[0011]

[0012] in is the channel matrix variable, μ is the Lagrange multiplier, c is a scalar, W is the feasible domain, S is the pilot signal, and Y is the received signal.

[0013] Furthermore, the present invention is for Part, is replaced by a feedforward neural network, the input matrix, the sub-gradient of the output matrix γ-norm, and the other parts are solved by active summation circuits.

[0014] Furthermore, the present invention uses a Lagrangian planning neural network in a matrix recovery algorithm to solve the problem after approximation. The algorithm is applied to millimeter wave large-scale MIMO to construct a deep learning module. In the millimeter wave large-scale MIMO system, a deep learning module is used in the channel estimation part. The receiver performs analog combining and digital combining on the received signals, and the output signal is passed into the module as the input of the module system. At the same time, the pilot signal is also used as the input signal, and the system outputs a channel matrix.

[0015] Furthermore, in the millimeter wave large-scale MIMO system, the present invention combines the Lagrangian planning neural network with the matrix recovery algorithm. The transmitting end sends the pilot signal multiple times, and the receiving end knows that after receiving several signals, they are transmitted to the neural network module simultaneously with the pilot signal, and the neural network is iterated. After receiving the signal again, the weights between neurons are adjusted according to the signal. At this time, the channel matrix obtained last time is used as the initial value to reduce the number of iterations, so that the system can be stabilized faster and the output can be obtained.

[0016] The present invention adopts a narrowband millimeter wave channel model, and the transceiver uses a uniform linear antenna array (ULA):

[0017]

[0018] Among them, ρ represents the transmission path loss, L represents the number of paths between the system transceiver, and the number of paths is much smaller than the number of transceiver antennas, τ t represents the delay of the lth path. l θ represents the path gain of the lth path. l and represents the arrival angle and departure angle of the lth path. T and α R Represent the antenna array response vectors of the transmitting and receiving ends respectively.

[0019] Therefore, the downlink channel matrix H can be expressed as:

[0020]

[0021] Since the number of antennas at the base station and the user end is much larger than the transceiver path L, rank(H)≤L. It can be seen that the channel matrix H to be estimated is a low-rank matrix, and the present invention can use the low-rank matrix recovery method to perform channel estimation. Because the rank of the channel matrix H is relatively small, the present invention converts the CSI estimation problem into a low-rank matrix recovery problem. However, the rank function is not differentiable, so in order to facilitate the solution, some scholars have proposed using the nuclear norm to approximate the rank function of the channel matrix, so the channel estimation problem is converted into a problem of minimizing the nuclear norm of the channel matrix:

[0022]

[0023] In the formula, ||H|| * =Σ i σ i (H), σ i (H) is the i-th singular value of H.

[0024] As a further improvement of the present invention, a non-convex γ-norm is used instead of a nuclear norm to approximate the channel matrix rank function, and the sparse characteristics of the millimeter wave channel angle domain are utilized to convert the channel estimation problem into a low-rank matrix recovery problem based on the γ-norm. Therefore, the channel estimation problem is converted into:

[0025]

[0026] Further, consider the following questions:

[0027]

[0028] Here the scalar c>0, ||·|| F represents the Frobenius norm of the matrix. The restoration problem is equivalent to the original optimization problem.

[0029] To solve the problem, define Obviously, {H:P(H)=0}=W.

[0030] The above formula is transformed into the augmented Lagrangian function, which is specifically expressed as:

[0031]

[0032] Where μ is the Lagrange multiplier and the scalar c>0.

[0033] Based on the augmented Lagrangian function, the following neural network model is proposed to solve the optimization problem:

[0034]

[0035] in Respectively represent ||H|| γ ,P(H),Clark generalized gradient of p(H), ε>0 is a constant.

[0036] According to the above neural network model, the following neural network learning rules are established:

[0037]

[0038] The above neural network model gives the state equation of the neural network, that is, the learning method of the network model. The hardware implementation and working process of the model are shown in Figure 3 When the hardware circuit is input with the initial voltage, the current will oscillate in the circuit and eventually approach stability. The stable value is the optimal solution to the optimization problem.

[0039] The hardware implementation of the Lagrangian neural network of the present invention includes two parts: a feedforward neural network and a recursive neural network. The recursive neural network is the main body, supplemented by the feedforward neural network. Since it involves the gradient of the matrix nuclear norm, it is difficult to implement using traditional hardware circuits and the computational complexity is high. The present invention uses a feedforward neural network instead in advance. According to the millimeter wave channel vector model, the channel matrix is ​​simulated and generated as the input of the feedforward neural network, which can be expressed as:

[0040]

[0041] Secondly, the gradient is used as the output and the loss function is set to train the neural network. The rest of the recurrent neural network is solved using an active summation and integration circuit.

[0042] Beneficial effects:

[0043] 1. The Lagrangian planning neural network algorithm constructed by the present invention has faster convergence than other channel estimation algorithms.

[0044] 2. The Lagrangian neural network of the present invention can well improve the convergence performance of the neural network, simulate the dynamic behavior of the neural network by Matlab programming, and realize neural dynamics to control the state transfer of neurons. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram comparing the convergence speed of the Lagrangian programming neural network and the SVT algorithm of the present invention.

[0046] Figure 2 It is a schematic diagram comparing the CSI estimated by the Lagrangian programming neural network, LS algorithm and SVT algorithm according to the present invention.

[0047] Figure 3 It is a diagram of the hardware implementation and working process corresponding to the neural network model for optimization problems of the present invention. DETAILED DESCRIPTION

[0048] The invention will be further described in detail below in conjunction with the accompanying drawings.

[0049] like Figure 3 As shown, the present invention adopts a narrowband millimeter wave large-scale MIMO system, considering a point-to-point communication system. The base station is equipped with N T Antenna, RF links, the user end has N R Antenna, RF links, and The downlink channel matrix between the base station and the user is

[0050] The narrowband millimeter wave massive MIMO system operates in the frequency division duplex (FDD) mode. Considering the downlink channel, the base station sends a training symbol vector s∈R T×L , the precoding vector at the base station is set to Setting up the training sequence The length is T, the precoding matrix After hybrid beamforming at the base station, the combined vector received by the user end after passing through the channel is set to User-side merge matrix The signal received by the user It can be expressed as:

[0051] Y=SG T HQ+n (1)

[0052] in is a noise matrix with a mean of 0 and a variance of The complex Gaussian distribution of

[0053] If the geometric channel is used as the channel model for mmWave MIMO, then:

[0054]

[0055] Where N T ,N R are the number of antennas at the transmitting and receiving ends of the system, ρ represents the transmission path loss, L represents the number of paths between the transmitting and receiving ends of the system, and the number of paths is much smaller than the number of antennas at the transmitting and receiving ends, τ l represents the delay of the lth path. l θ represents the path gain of the lth path. l and represents the arrival angle and departure angle of the lth path. T and α R Represent the antenna array response vectors at the transmitting and receiving ends respectively:

[0056]

[0057] Where λ represents the millimeter wave wavelength, D represents the element spacing of the antenna array,

[0058] Considering that the present invention adopts a narrowband millimeter wave channel model, for the convenience of research, the multipath delay effect of formula (2) can be ignored. The base station and the user end adopt point-to-point communication, and the channel model is as follows:

[0059]

[0060] In order to facilitate calculation, The received signal at the user end is expressed as:

[0061]

[0062] The millimeter wave downlink channel estimation problem is described as a problem of minimizing the rank function, namely:

[0063]

[0064] Since the rank function is not differentiable, in order to facilitate the solution, some scholars have proposed using the nuclear norm to approximate the rank function of the channel matrix. Therefore, the channel estimation problem is transformed into the problem of minimizing the nuclear norm of the channel matrix, that is:

[0065]

[0066] In the formula, for The i-th singular value of .

[0067] In order to improve the accuracy of rank approximation, the γ-norm is closer to the rank function than the nuclear norm, expressed as and Since the γ-norm is non-convex, the present invention introduces the Lagrangian neural network optimization method for non-convex problems based on the augmented Lagrangian multiplier method to solve the problem of minimizing the γ-norm. Therefore, the channel estimation problem is transformed into:

[0068]

[0069] Before applying neural networks to solve non-convex optimization problems, consider the following optimization problem:

[0070]

[0071] Here the scalar c>0, ||·|| F represents the Frobenius norm of the matrix. It can be seen that if is the minimum point that satisfies the constraints of the above optimization problem, then So Therefore, this optimization problem is equivalent to the original optimization problem.

[0072] To solve the problem, define Obviously,

[0073]

[0074] The above formula is transformed into the augmented Lagrangian function, which is specifically expressed as:

[0075]

[0076] Where μ is the Lagrange multiplier and the scalar c>0.

[0077] Based on the augmented Lagrangian function, the following neural network model is proposed to solve the optimization problem:

[0078]

[0079] in Respectively represent Clark's generalized gradient, ε>0 is a constant.

[0080] According to the above neural network model, the following neural network learning rules are established:

[0081]

[0082] The role of parameter c in the above neural network model is: (1) convexifying the objective function. When parameter c is large enough, the optimization problem can satisfy local convexity; (2) accelerating the convergence of the network trajectory. The larger the parameter, the greater the penalty for violating the equality constraint. When the parameter is large enough, the network state can be forced to quickly approach the feasible domain, so that the equality constraint is satisfied.

[0083] When the receiver receives the signal, it first performs analog combination on the signal, then down-converts the output signal to baseband through the RF link, performs digital combination at the baseband, and then passes the obtained channel to the Lagrangian neural network module.

[0084] The hardware implementation of the Lagrangian neural network of the present invention includes two parts: a feedforward neural network and a recursive neural network. The recursive neural network is the main body, supplemented by the feedforward neural network. Since it involves the gradient of the matrix nuclear norm, it is difficult to implement using traditional hardware circuits and the calculation complexity is high. The present invention uses a feedforward neural network instead in advance. During the offline training of this network, according to the millimeter wave channel vector model (4), the channel matrix is ​​simulated and generated as the input of the feedforward neural network. The derivative of the γ-norm of the data calculated by the simulation computer can be expressed as:

[0085]

[0086] The training of the feedforward neural network aims to train the difference between the network output and the calculated data, and the mean square error of the difference between the two values ​​is used to calculate the loss function. Because the neural network can only process real numbers, the input is divided into two parts: the real part and the imaginary part. The rest of the recurrent neural network is solved using an active summing and integrating circuit, such as Figure 3 shown.

[0087] For the subsequent detection link, the channel state information can be continuously obtained. The receiving end compares the received signal with the previously received signal, adjusts the weight of the recursive neural network model according to the degree of change, and uses the previously estimated channel matrix as the initial value to reduce the number of iterations and obtain channel information faster.

[0088] In order to verify that the Lagrangian neural network mentioned in this invention can improve the convergence performance of the neural network, Matlab programming is used to simulate the dynamic behavior of the neural network, and neural dynamics are defined to control the state transition of the neurons. The experiment compares the convergence speed and CSI estimation performance between the algorithm and the traditional SVT algorithm for the channel estimation problem. In the simulation, the AoD angle of the antenna is L is the effective transmission path, the number of antennas at the transmitting and receiving ends is 100, the millimeter wave operating frequency band is 90 GHz, the rank of the channel matrix is ​​6, the maximum number of iterations is 100, and the CSI estimation error uses the normalized mean square error Frobenuis norm error, that is,

[0089]

[0090] Figure 1 By comparing the convergence performance of the augmented Lagrangian neural network model and the SVT algorithm, it can be seen that the SVT algorithm begins to stabilize after a long time, while the method used in the present invention begins to converge after dozens of iterations and has higher accuracy.

[0091] Figure 2 By comparing the CSI estimation performance of LS, SVT, and augmented Lagrangian neural network algorithms under different signal-to-noise ratios, it can be seen that when SNR=5dB, the estimation error of each algorithm is large. As the SNR increases, the CSI of each algorithm is improved accordingly. When the SNR is the same, the augmented Lagrangian neural network algorithm is significantly better than other algorithms and has a smaller estimation error.

Claims

1. A millimeter wave massive MIMO deep learning channel estimation method based on matrix recovery algorithm, characterized in that: The method comprises the following steps: Step S1, constructing a millimeter wave massive MIMO system and building a system communication model; Step S2, combining the matrix recovery algorithm of the γ-norm approximate rank function and using the Lagrangian programming neural network to solve the γ-norm minimization problem; Step S3, after receiving the signal, the receiving end transmits it to the neural network module, and performs channel estimation in combination with the pilot signal. The neural network module is mainly composed of a recursive neural network, which cooperates with a feedforward neural network to output a channel matrix; Step S4, performing signal difference measurement on the subsequently received signals, adjusting the network weights, and obtaining an updated channel matrix.

2. The method for deep learning channel estimation of millimeter wave massive MIMO based on matrix recovery algorithm according to claim 1, characterized in that: The method introduces Lagrangian neurons and variable neurons, and constructs a recursive neural network based on the Lagrangian multiplier method.

3. The method for deep learning channel estimation of millimeter wave massive MIMO based on matrix recovery algorithm according to claim 1, characterized in that: The method comprises: in is the channel matrix variable, μ is the Lagrange multiplier, c is a scalar, W is the feasible domain, S is the pilot signal, and Y is the received signal.

4. The method for millimeter wave massive MIMO deep learning channel estimation based on matrix recovery algorithm according to claim 3, characterized in that: for Part, is replaced by a feedforward neural network, the input matrix, the sub-gradient of the output matrix γ-norm, and the other parts are solved by active summation circuits.

5. The method for millimeter wave massive MIMO deep learning channel estimation based on matrix recovery algorithm according to claim 2, characterized in that: The method is applied to millimeter wave massive MIMO to construct a deep learning module. In the millimeter wave massive MIMO system, the deep learning module is used in the channel estimation part. The receiver performs analog and digital merging on the received signals and the output signal is passed into the module as the input of the module system. At the same time, the pilot signal is also used as the input signal, and the system outputs a channel matrix.

6. The method for millimeter wave massive MIMO deep learning channel estimation based on matrix recovery algorithm according to claim 1, characterized in that: In the millimeter wave massive MIMO system, the Lagrangian planning neural network is combined with the matrix recovery algorithm. The transmitter sends the pilot signal multiple times. The receiver knows that after receiving several signals, they are transmitted to the neural network module at the same time as the pilot signal. The neural network is iterated. After receiving the signal again, the weights between neurons are adjusted according to the signal. At this time, the channel matrix obtained last time is used as the initial value to reduce the number of iterations, stabilize the system faster, and obtain the output.

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