Matrix recovery algorithm-based deep learning channel estimation method for massive MIMO in millimeter wave

Abstract

The application discloses a millimeter wave massive MIMO deep learning channel estimation method based on a matrix restoration algorithm. First, the channel estimation problem is converted into a low-rank matrix restoration problem by utilizing the sparse characteristics of the antenna angle domain of the millimeter wave channel. Then, a non-convex gamma-norm is used to replace the kernel norm to approximate the channel matrix rank function, thereby improving the accuracy of the channel matrix approximation. The application utilizes the adaptability and parallelism of a neural network to construct a Lagrange programming neural network model, so that the optimization problem can be solved quickly and an effective solution is obtained. Simulation results show that the Lagrange programming neural network algorithm has faster convergence than other channel estimation algorithms, i.e. the SVT algorithm.

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 (MIMO) technology used in the millimeter-wave frequency band (typically 30 GHz to 300 GHz). It combines the high bandwidth of millimeter-wave communications with the high energy efficiency of massive MIMO systems, aiming to achieve higher data rates and system capacity. In the millimeter-wave frequency band, communication requirements for higher speeds, lower latency, and greater connection density can be met. Channel estimation is a crucial step in millimeter-wave massive MIMO systems. The goal of channel estimation is to determine channel state information—the characteristics of the communication channel between the transmitter and receiver. This information helps the receiver perform better signal decoding and the transmitter perform key operations such as beamforming. Traditional channel estimation algorithms require significant pilot overhead and are computationally complex. Compressed sensing methods, however, leverage the sparsity of the millimeter-wave channel in the antenna angle domain to reconstruct channel coefficients using an observation matrix. Because of its sparsity, resulting in low rank, a matrix recovery algorithm is used to obtain the channel matrix by solving its rank function. However, since it is relatively difficult to directly obtain the rank function, it is currently necessary to solve the problem by approximating it through the deformation of the nuclear norm, such as the nuclear norm, the γ-norm, the truncated nuclear norm, or by approximating the rank function through a function, so as to convert the problem into an optimization problem that is easier to implement, and then use the optimization algorithm to solve it. Summary of the Invention

[0003] The present invention aims to address the shortcomings and deficiencies of the above-mentioned prior art and proposes a deep learning channel estimation method for millimeter-wave massive MIMO based on a matrix recovery algorithm. This method addresses the non-convex problem caused by the γ-norm approximation of the rank function. It uses a Lagrangian programming neural network, adds Lagrangian multipliers and a quadratic penalty term to convexify the objective function, and then uses the neural network to solve the non-convex problem. The present invention uses a Lagrangian programming neural network based on the Lagrangian multiplier method to solve general nonlinear constrained optimization problems. Instead of considering them numerically, an analog neural network is constructed and neural dynamics are defined to control the state transitions of neurons. When the network stabilizes at one of the equilibrium points, the solution is obtained by measuring the output of the neurons at this stable equilibrium point, and the channel matrix is ​​output. The neural network includes a recurrent neural network and a feedforward neural network. The feedforward neural network is used to solve the subgradient of the γ-norm of the channel matrix, while the recurrent neural network is responsible for iterative processing of variables and Lagrangian multipliers to output the channel matrix.

[0004] The technical scheme adopted by the present application to solve its technical problems is: a millimeter wave massive MIMO deep learning channel estimation method based on a matrix recovery algorithm, the method comprising the following steps:

[0005] Step S1, a millimeter wave massive MIMO system is constructed, and a system communication model is built;

[0006] Step S2, a matrix recovery algorithm combining a gamma-norm approximate rank function is used to solve the gamma-norm minimization problem by using a Lagrange programming neural network;

[0007] Step S3, after the receiving end receives the signal, the signal is transmitted to a neural network module, and channel estimation is performed in combination with a pilot signal, the neural network module is mainly composed of a recurrent neural network, and a feedforward neural network is used in cooperation, and a channel matrix is output;

[0008] Step S4, signal difference measurement is performed on the subsequently received signal, the network weight is adjusted, and an updated channel matrix is obtained.

[0009] Further, the present application introduces a Lagrange neuron and a variable neuron, and constructs a recurrent neural network based on a Lagrange multiplier method.

[0010] Further, the present application comprises:

[0011]

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

[0013] Further, the present application is suitable for Partly, a feedforward neural network is replaced, an input matrix is input, and a subgradient of a matrix gamma-norm is output, and other parts are solved by using an active summing circuit.

[0014] Further, the present application uses a Lagrange programming neural network to solve the approximate problem in the matrix recovery algorithm, the algorithm is applied to a millimeter wave massive MIMO, a deep learning module is constructed, the deep learning module is used in a channel estimation part in a millimeter wave massive MIMO system, a receiver analog combines and digitally combines the output signal of the received signal, and the signal is transmitted to the module as an input of the module system, and the pilot signal is also input as an input signal, and the system outputs a channel matrix.

[0015] Further, the present application combines the Lagrange programming neural network with the matrix restoration algorithm in the millimeter wave large-scale MIMO system, the pilot signal is sent multiple times at the sending end, and the receiving end is known, after receiving a plurality of signals, the pilot signal is transmitted into the neural network module at the same time, the neural network is iterated, then the signal is received again, the weight between neurons is adjusted according to the signal, and at this time, the channel matrix obtained last time is used as an initial value, the iteration number is reduced, the system can be stabilized faster, and the output is obtained.

[0016] The present application adopts a narrowband millimeter wave channel model, and a uniform linear antenna array (ULA) is used at the transceiving end:

[0017]

[0018] Wherein, ρ represents a transmission path loss, L represents a path number between the transceiving end of the system, and the path number is far less than the number of transceiving end antennas, τ t represents the time delay of the lth path. l g l represents the path gain of the lth path. α T and α R respectively represent the antenna array response vectors of the sending end and the receiving end.

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

[0020]

[0021] Because the number of antennas of the base station and the user end is far greater than the transceiving end path L, rank(H)≤L. Therefore, the channel matrix H to be estimated is a low-rank matrix, and the present application can use the low-rank matrix restoration method to perform channel estimation. Because the rank of the channel matrix H is relatively small, the present application converts the CSI estimation problem into a low-rank matrix restoration problem. However, the rank function is not derivable, so in order to facilitate solving, scholars have proposed to approximate the rank function of the channel matrix by using the kernel norm, so that the channel estimation problem is converted into a problem of minimizing the kernel 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 application, a non-convex gamma-norm is used to approximate the channel matrix rank function instead of the nuclear norm, and the channel estimation problem is converted into a low-rank matrix recovery problem based on the gamma-norm by taking advantage of the sparsity of the channel in the angle domain, so that the channel estimation problem is converted into:

[0025]

[0026] Further, the following problem is considered:

[0027]

[0028] Here, the scalar c>0, ||·||F F represents the Frobenius norm of a matrix. The 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 converted into an augmented Lagrangian function, which is specifically represented 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] where respectively represent ||H|| γ , the Clark generalized gradient of P(H), p(H), and ε>0 is a constant.

[0036] According to the above neural network model, the following neural network learning rule is established:

[0037]

[0038] The above neural network model gives the state equation of the improved neural network, i.e., the learning method of the network model. The hardware implementation and its working process corresponding to the model are shown in Figure 3 When the initial voltage is input to the hardware circuit, the current will oscillate in the circuit and eventually tend to be stable. The stable value in it is the optimal solution of the optimization problem to be solved.

[0039] The hardware implementation of the Lagrange neural network of the application comprises two parts: a feedforward neural network and a recurrent neural network. The recurrent neural network is the main body, and the feedforward neural network is auxiliary. Since the gradient of the matrix kernel norm is involved, it is difficult to implement using traditional hardware circuits, and the calculation complexity is high, so the feedforward neural network is used in advance to replace, 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 set as the output, and the loss function is used to train the neural network. The rest of the recurrent neural network uses active summing integration circuit to solve.

[0042] Beneficial effects:

[0043] 1. The Lagrange programming neural network algorithm constructed in the application has faster convergence than other channel estimation algorithms.

[0044] 2. The Lagrange neural network can improve the convergence performance of the neural network. The dynamic behavior of the neural network is simulated by using Matlab programming, and the neural dynamics are used to control the state transition of the neurons. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The application is a comparison diagram of the convergence speed of the Lagrange programming neural network and the SVT algorithm.

[0046] Figure 2 The application is a comparison diagram of the estimated CSI of the Lagrange programming neural network, the LS algorithm and the SVT algorithm.

[0047] Figure 3 The application is a hardware implementation and working process diagram of the neural network model corresponding to the optimization problem. DETAILED DESCRIPTION

[0048] The application will be further described in detail below in combination with the drawings of the specification.

[0049] As shown in the drawings, Figure 3 The application adopts a narrowband millimeter wave large-scale MIMO system, and considers a point-to-point communication system. The base station end is equipped with N T root antennas, RF links, the user end has N R root antennas, 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 a frequency division duplex (FDD) mode, and a training symbol vector s is transmitted from the base station end to the user end in consideration of a downlink channel T×L The precoding vector of the base station end is set as The training sequence is set The length of the precoding matrix After the base station end hybrid beamforming, the combined vector received by the user end after the channel is set as The user end combined matrix The signal received by the user end Can be expressed as:

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

[0052] Wherein is a noise matrix, which is subject to a complex Gaussian distribution with a mean of 0 and a variance of , that is

[0053] If a geometric channel is used as the channel modeling of the millimeter wave MIMO, then:

[0054]

[0055] In the formula, N T ,N R are the number of antennas of the system transceiver, ρ represents the transmission path loss, L represents the number of paths between the system transceiver, and the path number is much smaller than the transceiver antenna number, τ l represents the time delay of the lth path. β l represents the path gain of the lth path. θ l and represent the arrival angle and departure angle of the lth path. α T and α R respectively represent the antenna array response vectors of the sending end and the receiving end:

[0056]

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

[0058] Considering that the narrowband millimeter wave channel model is used in the application, in order to facilitate research, the multipath time delay in the formula (2) can be ignored, and the base station end and the user end adopt point-to-point communication, and the channel model is as follows:

[0059]

[0060] For convenience of calculation, let Then the received signal at the user end is represented as:

[0061]

[0062] The problem of estimating the downlink channel at the mmWave is described as a minimization problem of the rank function, i.e.

[0063]

[0064] Since the rank function is not derivable, in order to facilitate the solution, scholars have proposed to approximate the rank function of the channel matrix by using the nuclear norm, and thus the channel estimation problem is converted into a problem of minimizing the nuclear norm of the channel matrix, i.e.

[0065]

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

[0067] In order to improve the accuracy of the rank approximation, the γ-norm is closer to the rank function than the nuclear norm, which is represented as and Since the γ-norm formula is non-convex, the present application introduces a Lagrange neural network for the optimization method of non-convex problems according to the augmented Lagrange multiplier method to solve the problem of minimizing the γ-norm. Thus the channel estimation problem is converted into:

[0068]

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

[0070]

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

[0072] In order to solve the problem, define Obviously,

[0073]

[0074] The above formula is converted into an augmented Lagrange function, which is specifically represented as:

[0075]

[0076] where mu is a Lagrange multiplier, and c is a positive scalar.

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

[0078]

[0079] where respectively represent the Clark generalized gradient of , and epsilon is a constant.

[0080] According to the above neural network model, the following neural network learning rule is established:

[0081]

[0082] The role of parameter c in the above neural network model: (1) convex objective function, when the parameter c is large enough, the optimization problem can satisfy the local convexity; (2) accelerate the convergence speed of network trajectory. The larger the parameter is, the greater the punishment for violating the equality constraint. And when the parameter is large enough, it can force the network state to quickly approach the feasible region, so as to satisfy the equality constraint.

[0083] When the receiver receives the signal, first, the signal is simulated and merged, and then the output signal is down-converted to the baseband through the RF link, and the digital merging is carried out in the baseband. After that, the obtained channel is transmitted into the Lagrange neural network module.

[0084] The hardware implementation of the Lagrange neural network of the application includes two parts: a feedforward neural network and a recurrent neural network. The recurrent neural network is the main body, and the feedforward neural network is auxiliary. Since the gradient of the matrix kernel norm is involved, it is difficult to implement using traditional hardware circuit, and the calculation complexity is high, the application uses the feedforward neural network in advance to replace, during the offline training of the 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 gamma-norm of the data calculated by the simulation computer can be represented 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 real and imaginary parts. The rest of the recurrent neural network uses active summing integration circuit to solve, as shown in Figure 3 .

[0087] For the subsequent detection link, the channel state information can be continuously obtained. The receiving end compares the obtained signal with the previously received signal, adjusts the weight of the recurrent neural network model according to the degree of change, and takes the previously estimated channel matrix as the initial value, so as to reduce the iteration times and obtain the channel information more quickly.

[0088] In order to verify that the Lagrange neural network mentioned in the application can improve the convergence performance of the neural network, the dynamic behavior of the neural network is simulated by programming with Matlab, and the neural dynamics are defined to control the state transition of the neurons. In the experiment, the convergence speed and the CSI estimation performance of the algorithm and the traditional SVT algorithm are compared 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 of the transceiver is 100, the millimeter wave operating frequency band is 90GHz, the rank of the channel matrix is 6, the maximum iteration number is 100, and the CSI estimation error is the normalized mean square error Frobenuis norm error, that is,

[0089]

[0090] Figure 1 By comparing the convergence performance of the augmented Lagrange neural network model and the SVT algorithm, it can be seen that the SVT algorithm starts to stabilize after a long time, while the method used in the application starts to converge after ten iterations, and the accuracy is higher.

[0091] Figure 2 By comparing the CSI estimation performance of the LS, SVT and augmented Lagrange 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, and as the SNR increases, the CSI of each algorithm is improved accordingly. When the SNR is the same, the augmented Lagrange neural network algorithm is obviously better than other algorithms, and the estimation error is smaller.

Claims

1. A matrix recovery algorithm-based millimeter wave massive MIMO deep learning channel estimation method, characterized in that, The method comprises the following steps: Step S1, constructing a millimeter wave massive MIMO system, building a system communication model; Step S2, combining the matrix recovery algorithm of the gamma-norm approximate rank function, and using the Lagrange programming neural network to solve the gamma-norm minimization problem; Step S3, after the receiving end receives the signal, the signal is transmitted to the neural network module, and the channel estimation is performed in combination with the pilot signal, the neural network module is mainly composed of a recurrent neural network, cooperates with a feedforward neural network, and outputs a channel matrix; Step S4, signal difference measurement is performed on the subsequently received signal, the network weight is adjusted, and an updated channel matrix is obtained.

2. The method of claim 1, wherein the matrix recovery algorithm-based deep learning channel estimation method for massive MIMO in mmWave is characterized by: The method introduces Lagrange neurons and variable neurons, and constructs a recurrent neural network based on the Lagrange multiplier method.

3. The method of claim 1, wherein the matrix recovery algorithm is based on a deep learning method. The method comprises: wherein is a channel matrix variable, μ is a Lagrange multiplier, c is a scalar, W is a feasible region, S is a pilot signal, and Y is a received signal.

4. The method of claim 3, wherein the matrix recovery algorithm is based on: For Parts, instead of a feedforward neural network, input matrix, output matrix γ-norm of the sub-gradient, other parts with active summing circuit solution.

5. The method of claim 2, wherein the matrix recovery algorithm is based on: The method is applied to a millimeter wave massive MIMO, a deep learning module is constructed, in a millimeter wave massive MIMO system, a deep learning module is used in channel estimation, the receiver outputs the signal after analog combining and digital combining of the received signal to the module, as the input of the module system, and the pilot signal is also input as the input signal, and the system outputs a channel matrix.

6. The method of claim 1, wherein the matrix recovery algorithm-based deep learning channel estimation method for massive MIMO in mmWave is characterized by: In a millimeter wave massive MIMO system, the Lagrange programming neural network is combined with the matrix recovery algorithm, the sending end sends the pilot signal for multiple times, the receiving end is known, a plurality of signals are received, and the pilot signal is transmitted into the neural network module at the same time, the neural network is iterated, then the signal is received again, the weight between neurons is adjusted according to the signal, the channel matrix obtained last time is used as an initial value at this time, the number of iterations is reduced, the system is stabilized faster, and the output is obtained.

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