Channel estimation method for millimeter wave frequency division duplex massive MIMO system based on compressed sensing and deep learning

Abstract

The application discloses a channel estimation method for a millimeter wave frequency division duplex massive MIMO system based on compressed sensing and deep learning, and belongs to the technical field of wireless communication.The technical scheme is as follows: a received pilot signal is processed by using a compressed sensing method to extract a preliminary CSI matrix; a convolutional neural network and a long short-term memory network are combined to extract spatial features and capture time correlation; the preliminary estimated CSI matrix is input into a ConvLSTM layer, and the ConvLSTM network fuses time correlation information to improve the estimation accuracy of the CSI; the same padding, ReLU activation function and filter with appropriate size are used to obtain the same size as the input data; and dimension transformation and inverse normalization are used to obtain the final CSI estimation result.The application has the beneficial effects that the method for channel estimation by using compressed sensing and deep learning aims at reducing the overhead of channel estimation and improving the estimation accuracy in a time-varying channel, reduces the overhead of downlink training and uplink feedback, and improves the channel estimation accuracy in the time-varying channel.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and specifically relates to a method for channel estimation by using compressive sensing and deep learning in a massive multiple-input multiple-output (MIMO) system in a millimeter wave frequency-division duplex (FDD) mode. The present application aims to reduce the overhead of channel estimation and improve the estimation accuracy in time-varying channels. BACKGROUND

[0002] Massive multiple-input multiple-output (MIMO) technology has always been considered as a key technology for the fifth generation of wireless communication systems due to its huge performance advantages in capacity and reliability [1] . In order to achieve these performance gains of massive MIMO, it is necessary to obtain the downlink channel state information (CSI) at the base station (BS) [2] . In a time-division duplex system, the downlink CSI is usually obtained by using channel reciprocity, but the requirement for accurate calibration of hardware circuits is high and the cost is high [3] . In a frequency-division duplex (FDD) system, the reciprocity of uplink and downlink channels does not hold, so it is necessary to estimate the downlink channel CSI first and then feed it back to the BS [4] . Therefore, it does not require complex hardware calibration. At the same time, traditional cellular systems mainly work in FDD mode. Therefore, FDD massive MIMO systems are currently also very popular topics in academia and industry. However, due to the use of massive antennas on the antenna array, FDD massive MIMO will result in huge channel acquisition overhead and channel time-varying fading will further increase the complexity of channel acquisition. For traditional pilot algorithms such as least squares or least mean square error algorithms, the number of pilots required is always linearly related to the number of antennas, so it will result in huge computational complexity [5] . To solve this problem, compressive sensing (CS) is widely used in channel estimation in massive MIMO to recover the sparse channel state information from the reduced received pilots [6][7]However, they cannot play a greater advantage in time-varying channels considering the cost of channel estimation and feedback. Therefore, it is necessary to study the channel training and feedback scheme of FDD large-scale time-varying MIMO system. Although the channel is time-varying, its statistical properties are often stable, so the information of previous estimation can be used to track the time-varying characteristics of the channel in the current estimation. In particular, the stable statistical properties will lead to the sparsity of the channel in some areas, so the compressed sensing technology can be used to estimate the channel. A CS recovery method for estimating time-varying channels using prior support is proposed in [8], and it is shown that the use of time correlation can further reduce the training signal. In [9], a differential-based structured compressed sampling matching pursuit (S-CoSaMP) algorithm is proposed to obtain CSI by further utilizing the time correlation of time-varying channels. The above methods rely on the prior knowledge of the channel, i.e. the correlation and sparsity of the channel. A distributed compressed sensing aided channel estimation method is proposed in

[10] , which fully utilizes the slow change of channel statistics in consecutive time slots and the spatial common sparsity of multiple subchannels in the frequency domain. A feasible downlink training sequence design method based on partial CSI estimation is proposed in

[11] . However, the channel estimation schemes in the above documents have strict requirements for prior channel information. In

[12] -

[16] , several channel estimation schemes without prior channel information are proposed. In

[12] and

[13] , adaptive step sparsity adaptive matching pursuit (AS-SAMP) and unknown sparsity orthogonal matching pursuit algorithm (OMP-US) are proposed for sparse channel estimation when the number of non-zero coefficients is unknown. In

[14] , a low-overhead adaptive channel estimation and feedback algorithm for OFDM systems is proposed, which can adaptively adjust the training overhead and pilot design to achieve reliable CSI estimation. Compared with the method in [8], an adaptive M-SP method is proposed in

[15] , which can adaptively adjust the prior channel support quality parameter to a suitable value in the case of model mismatch. In

[16] , an approximate message passing algorithm based on expectation maximization and Gaussian mixture distribution is proposed, which can simultaneously learn the signal distribution and recover the signal. However, all CS-based methods have a disadvantage that the noise added on non-zero elements is difficult to eliminate. In recent years, deep learning (DL) methods have been successfully applied to wireless communication, especially in channel estimation and feedback. In

[17] and

[18] , two RNN networks are proposed to improve the feedback accuracy of CSI in large-scale MIMO systems. In

[19] , a method based on convolutional long-short-term memory (LSTM) network is proposed to predict downlink CSI from uplink CSI.By exploiting the correlation of time-varying channels, the convolutional neural network (CNN) and recurrent neural network (RNN) are used to extract spatial features and inter-frame correlation, respectively, in

[20] . In

[21] , a framework named CS-ReNet is proposed by combining the CS-based and DL-based methods, which compresses the perfect CSI at the user side and then reconstructs the CSI at the BS side using a deep neural network. From the perspective of bit-level quantization performance, the joint convolution residual network in

[22] is beneficial to the extraction and recovery of MIMO channel features. For high mobility environments, a channel estimation network is developed in

[23] , which consists of a CNN simulating the frequency domain interpolation process and a bidirectional LSTM network for time domain channel prediction. In addition to the aforementioned data-driven methods, there are some model-driven deep learning methods to obtain CSI. In

[24] , a full convolutional denoising approximate message passing (FCDAMP) algorithm is proposed by combining the full convolutional denoising network (FCDNet) with the learned approximate message passing network (LAMP).

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[24] H. He, C.-K. Wen, S. Jin, and G. Y. Li, "Deep learning-based channel estimation for beamspace mmwave massive MIMO systems," IEEE Wireless Commun. Lett., vol. 7, no. 5, pp. 852-855, Oct. 2018. SUMMARY

[0027] In order to solve the above problems existing in the prior art, the application provides a channel estimation scheme for an FDD massive MIMO system based on CS and DL, which reduces the overhead of downlink training and uplink feedback, and improves the channel estimation accuracy in a time-varying channel; the scheme first feeds back the pilot received by the user to the base station, and then adopts an adaptive structured orthogonal matching pursuit (AS-JOMP) method, which can adaptively reconstruct the channel by using the structural sparsity of the channel without knowing the number of non-zero elements in the CSI; the structural sparsity is caused by the close arrangement of antennas on the base station, which makes the signal experience similar paths; after obtaining the initial estimation of the CSI, the DL-based DCNN-LSTM method is developed to reconstruct the channel matrix to further improve the accuracy of the final CSI estimation, aiming at the problem that the initial CSI cannot effectively eliminate the noise addition of the non-zero element position and does not fully utilize the effective information between time-varying channels.

[0028] To achieve the above purpose, the application provides the following technical scheme:

[0029] A channel estimation method for a millimeter wave frequency division duplex massive MIMO system based on compressed sensing and deep learning, comprising the following steps:

[0030] S1, compressed sensing preliminary estimation: using compressed sensing method to process the received pilot signal, and extracting the preliminary CSI matrix therefrom;

[0031] S2, deep learning network structure: adopting a combined structure of convolutional neural network and long short-term memory network, extracting spatial features through the convolutional neural network, and capturing time correlation through the long short-term memory network;

[0032] S3, ConvLSTM network processing: inputting the preliminary estimated CSI matrix into the ConvLSTM layer in time sequence, and the ConvLSTM network fuses time correlation information to improve the accuracy of CSI estimation;

[0033] S4, CSI reconstruction: using the same padding, ReLU activation function and filter of appropriate size to obtain the same size as the input data; through dimension transformation and inverse normalization to obtain the final CSI estimation result.

[0034] Further, by performing in a massive MIMO-OFDM system in a millimeter wave frequency division duplex mode, in which the base station and a plurality of single antenna users communicate, a comb pilot method is used, the pilot interval in each OFDM symbol is equal, and the pilot symbol is randomly selected.

[0035] Further, in the massive MIMO-OFDM system, the following steps are performed:

[0036] D1, pilot symbol generation: randomly selecting a pilot symbol at each antenna from the OFDM symbol, and obtaining a time domain transmission symbol through inverse discrete Fourier transform;

[0037] D2, signal reception: at the receiving end, the received signal is represented in the frequency domain through Fourier transform;

[0038] D3, channel state information extraction: the user extracts the pilot symbol from the received signal, and restores the sparse CSI matrix through the compressive sensing method.

[0039] Further, the pilot of the i-th transmitting antenna of the k-th user is C ik ∈C P×1 , wherein P is the number of pilot, the pilot symbol at the i-th antenna is C i ∈C P×1 , wherein C i The elements in are randomly selected from the OFDM symbol ; through inverse discrete Fourier transform, the time domain transmission symbol is:

[0040]

[0041] Wherein is the DFT matrix, (.) H is the complex conjugate transpose, N c is the number of subcarriers; the i-th antenna at the BS transmits the time domain signal X i ; then the received signal y in the time domain has the following expression:

[0042]

[0043] Wherein h i ∈C L×1 is the channel state information from the i-th antenna of the BS to the user, and L is the channel length, denotes independent and identically distributed (i.i.d.) additive white complex Gaussian noise, * denotes convolution operation, and also denotes matrix multiplication;

[0044] If the OFDM system has a proper length of cyclic prefix, the linear convolution in equation (2) becomes a circular convolution after removing the cyclic prefix at the receiver; for h i Using zero padding, the convolution operation will be as follows:

[0045]

[0046] where the Lth to Nth elements of c are all zeros, the convolution in equation (3) can also be represented as a matrix multiplication as follows:

[0047]

[0048] where is a Toeplitze matrix; as follows:

[0049]

[0050] In equation (4), is the cumulative sum of the sequence from y o to N c ; and the circular convolution in equation (3) is represented by matrix convolution;

[0051] By DFT transform, the received symbol in frequency domain can be represented as

[0052]

[0053] where is a matrix with diagonal elements being ; and

[0054] To estimate the channel state information h i , the user has to extract the pilot symbol f from the received signal y The received signal can be written as follows:

[0055]

[0056] where is selected from in the index set Ω, F Ω,L ∈ C P×L corresponds to a partial Fourier matrix, the row is selected from the index of the pilot, and the column is selected from the first L columns of F; obviously, is equal to c i;therefore

[0057]

[0058] in is the CSI from the ith base station antenna to the user, It means the mean is zero and the variance is Additive Gaussian white noise; if the pilot intervals within the OFDM symbol are equal and the pilot symbols are randomly selected, the pilot received from a certain user is

[0059]

[0060] in

[0061] Formula (10) is regarded as a compressed sensing problem, Φ is the sensing matrix, and h is the sparse signal; therefore, the reconstruction algorithm based on compressed sensing is used to calculate the value of Φ and y. c In this channel model, the uplink channel and the downlink channel have the same signal-to-noise ratio, and the noise parameter represents the total noise power of the downlink and uplink channels; for block fading time-varying MIMO channels, the CSI varies from one time slot to another but remains unchanged within a time slot; the dynamic channel is modeled by the change of CSI support and the evolution of the amplitude of non-zero elements:

[0062]

[0063] Among them, h t is the CSI at time t, s t (l)∈{0,1} represents s t Whether the lth support index of g is zero, t (l)∈C is g t The amplitude at the lth support index of Represents the Hadamard product; specifically, a first-order Markov process is used to model the change of support, that is, two transition probabilities are defined as:

[0064]

[0065] Among them, In order to achieve a steady-state sparsity rate p∈(0,1), the amplitude adopts a first-order autoregressive model, which is expressed as follows:

[0066]

[0067] The correlation coefficient ρ=J0(2πf d τ) is given by the zero-order Bessel function of the first kind, f d is the maximum Doppler frequency, τ is the duration, and the parameter is a complex Gaussian variable iid.

[0068] Furthermore, the method further includes the following steps: using the AS-JOMP algorithm based on compressed sensing to recover CSI from the received signal; the AS-JOMP algorithm combines the sensing matrix Φ with the remaining observation vector r according to the structural sparsity. i The cross-correlation vector of the product is divided into N BS vectors and sum them, and then select the maximum indicator like OMP; in the second observation, two threshold parameters are used to stop the iteration under high SNR and low SNR.

[0069] Furthermore, the method further includes the following steps: using the estimated CSI as the input of DCNN-LSTM to remove noise and learn the characteristics between time-varying channels; the DCNN-LSTM is a joint network based on CNN and LSTM, in which the CSI channel group is used as the input of DCNN-LSTM to remove noise and learn the characteristics between time-varying channels; As input, where T is the number of CSI in the channel group i = 1, 2, ..., N sample , where N sample is the number of samples; the output of the network is expressed as Obtained by AS-JOMP algorithm Is a size of LN BS ×1 complex vector; therefore, separate the real and imaginary parts of the complex vector into two LN BS ×1 real vector, and then transformed into two vectors of size The real matrix of Therefore, the data of each layer of the network is a four-dimensional tensor. The sum of the products on the left side of each layer represents the size of the CSI channel group; the number above is the number of feature maps.

[0070] Furthermore, the DCNN-LSTM includes a channel feature extraction module, a time-varying channel correlation extraction module and a CSI reconstruction module.

[0071] Furthermore, the channel feature extraction module is completed by the CNN network in the first layer. In this process, the matrix of each time dimension can be convolved separately to extract features. The convolution layer contains 64 3×3 convolution kernels with a sliding step of 1. The same zeros are used to pad the input during convolution so that the feature map output by each layer of the network remains the same size as the original channel matrix, and ReLU is used as the activation function.

[0072] Furthermore, the time-varying channel correlation extraction module: the extraction of time correlation is mainly completed by the second layer LSTM network; the ConvLSTM network consists of an input gate i t and an output gate O tThe composition, the input gate is used for recording the information of the current state, the output gate is used for controlling how much information of the current state can be seen by the external network; the forgetting gate f t Controlling the quantity of the history state information flow allowed to enter the current state, the memory unit C t The information of the previous time; as shown in formula 16, wherein W xi , W hi , W ci , W ho , W xo , W co , W xf Indicate a weight matrix, b i , b o , b f , b c Indicate a bias, shape a number representing information transmission in the range [0, 1], 0 represents no transmission, and 1 represents full transmission;

[0073] The preliminary estimated CSI matrix is sequentially input into the ConvLSTM layer; at each time step, the ConvLSTM network can fuse the time-related information learned at the previous time point into the input at the current time step, and the related information is updated with the time step;

[0074]

[0075] Further, the CSI reconstruction module: using the same padding, ReLU activation function and 3*3*2 size filter to obtain the same size as the input data; through dimension transformation and inverse normalization to obtain the final CSI estimation result

[0076] The beneficial effects of the present application are:

[0077] Compared with the prior art, the millimeter wave frequency division duplex massive MIMO system channel estimation method based on compressed sensing and deep learning provided by the application utilizes compressed sensing and deep learning to perform channel estimation, aims to reduce the overhead of channel estimation and improve the estimation accuracy in the time-varying channel, reduces the overhead of downlink training and uplink feedback, and improves the channel estimation accuracy in the time-varying channel; the scheme first feeds back the pilot received by the user to the base station, and then adopts an adaptive structured orthogonal matching pursuit (AS-JOMP) method, which can adaptively reconstruct the channel by utilizing the structural sparsity of the channel without knowing the number of non-zero elements in the CSI; the structural sparsity is caused by the close arrangement of the antennas on the base station, so that the signals experience similar paths; after obtaining the initial estimation of the CSI, the DL-based DCNN-LSTM method is developed to reconstruct the channel matrix to further improve the accuracy of the final CSI estimation, aiming at the problem that the initial CSI cannot effectively eliminate the noise addition of the non-zero element position and does not fully utilize the effective information between the time-varying channels. BRIEF DESCRIPTION OF DRAWINGS

[0078] In order to more clearly illustrate the technical solutions of the embodiments of the application, the application will be described in detail below with reference to the drawings and specific embodiments. Obviously, the drawings described below are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor. Among them:

[0079] Figure 1 The comb pilot pattern of the application;

[0080] Figure 2 The D CNN -LSTM network architecture diagram;

[0081] Figure 3 The basic unit structure diagram of the ConvLSTM network of the application. DETAILED DESCRIPTION

[0082] In order to make the purpose, technical scheme and advantages of the application more clear and obvious, the application will be further described in detail below with reference to the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application, and are not used to limit the application. The application will be described below with reference to the drawings Figures 1-3 The millimeter wave frequency division duplex massive MIMO system channel estimation method based on compressed sensing and deep learning is further described.

[0083] Example 1

[0084] The application provides a millimeter wave frequency division duplex massive MIMO system channel estimation method based on compressed sensing and deep learning. The specific embodiments of the application will be described in detail below, enabling those skilled in the art to implement the application without creative labor.

[0085] 1. System model

[0086] The method described in the application is applicable to a massive MIMO-OFDM system in a millimeter wave frequency division duplex (FDD) mode. In this system, communication is carried out between a base station (BS) and a plurality of single-antenna users. The application adopts a comb pilot scheme, as shown in FIG. 1. In this scheme, the pilot interval within each OFDM symbol is equal, and the pilot symbol is randomly selected. Figure 1

[0087] - Pilot symbol generation: The pilot symbol at each antenna is randomly selected from the OFDM symbol, and the time-domain transmission symbol is obtained by inverse discrete Fourier transform (IDFT).

[0088] - Signal reception: At the receiving end, considering the cyclic prefix and zero padding technology of the OFDM system,

[0089] The received signal is represented in the frequency domain by Fourier transform.

[0090] - Channel state information (CSI) extraction: The user extracts the pilot symbol from the received signal,

[0091] The sparse CSI matrix is recovered by compressed sensing technology.

[0092] 2. Channel estimation

[0093] The application adopts a method combining compressed sensing and deep learning for channel estimation. The specific steps are as follows:

[0094] a) Compressed sensing preliminary estimation: The received pilot signal is processed by using compressed sensing technology, and a preliminary CSI matrix is extracted therefrom.

[0095] b) Deep learning network structure: A combined structure of convolutional neural network (DCNN) and long short-term memory network (LSTM) is adopted, as shown in FIG. 2. The DCNN is used to extract spatial features, and the LSTM is used to capture time correlation. Figure 2

[0096] c) ConvLSTM network processing: The preliminary estimated CSI matrix is input into the ConvLSTM layer in time sequence, and the ConvLSTM network can fuse time correlation information, further improving the accuracy of CSI estimation. The basic unit structure of ConvLSTM is shown in FIG. 3. Figure 3 ​​​

[0097] d) CSI reconstruction: To obtain the same size as the input data, the same padding, ReLU activation function and filter of appropriate size are used. Finally, the final CSI estimation result is obtained by dimension transformation and inverse normalization.

[0098] Embodiment 2

[0099] 1.1 System model

[0100] The present application considers a millimeter wave massive MIMO-OFDM system in frequency division duplex mode. In this system, N BS antennas are installed in both the BS and K single-antenna users. Figure 1

[0101] In this scheme, the pilot interval within each OFDM symbol is equal, and each circle represents a resource unit in the time and frequency domains. Users working in non-overlapping frequency bands. The pilot of the i-th transmit antenna of the k-th user is C ik ∈C P×1 , where P is the number of pilots. In order not to lose generality, the present application omits the subscript k in the following discussion. The pilot symbol at the i-th antenna is C i ∈C P×1 , where the elements in C i are randomly selected from the OFDM symbol . Through inverse discrete Fourier transform (IDFT), the time-domain transmission symbol can be obtained as

[0102]

[0103] where is the DFT matrix, (·) H is the complex conjugate transpose, and N c is the number of subcarriers. The i-th antenna at the BS transmits the time-domain signal X i . Then the received signal y in the time domain has the following representation

[0104]

[0105] where h i ∈C L×1 is the channel state information from the i-th antenna of the BS to the user, L is the channel length, represents independent and identically distributed (i.i.d.) additive white complex Gaussian noise (AWGN), * represents convolution operation, which can also be represented as matrix multiplication.

[0106] If the OFDM system has a suitable length of cyclic prefix, the linear convolution in (2) becomes a circular convolution after removing the cyclic prefix at the receiving end.​i Using proper zero padding (ZP), the convolution operation will be as follows

[0107]

[0108] where the Lth to Nth element of c is 0, the convolution in (3) can also be represented as a matrix multiplication as follows

[0109]

[0110] where is a Toeplitze matrix. The following equation

[0111]

[0112] In (4), is the cumulative sum of the sequence from y o to N c . And the circular convolution in (3) can be represented as a matrix convolution.

[0113] By DFT transform, the received symbol in frequency domain can be represented as

[0114]

[0115] where is a matrix with diagonal elements .

[0116] To estimate the channel state information h i , the user must extract the pilot symbol f from the received signal y The received signal can be written as follows

[0117]

[0118] where is selected from in the index set Ω, F Ω,L ∈ C P×L corresponds to a partial Fourier matrix, the row is selected from the index of the pilot, and the column is selected from the first L columns of F.

[0119] Obviously, is equal to c i . Therefore

[0120]

[0121] where is the CSI of the ith base station antenna to the user, represents an additive white Gaussian noise with zero mean and variance If the comb pilot shown in Fig. 2 is adopted, the received pilot of a certain user is Figure 1

[0122]

[0123] where

[0124] Based on a large amount of experimental data and theoretical analysis, it is known that the number of non-zero elements of the CSI h i is much smaller than its length, so that the channel can be compressed in the time domain. Therefore, (10) can be regarded as a compressed sensing problem, and Φ is the sensing matrix, and h is the sparse signal. Therefore, the present application can reconstruct h by Φ and y c using the reconstruction algorithm based on compressed sensing. Under this channel model, the uplink channel and the downlink channel have the same signal-to-noise ratio, and the noise parameter represents the total noise power of the downlink and uplink channels

[25] . For block-fading time-varying MIMO channels, the CSI changes from one time slot to another, but remains unchanged within one time slot. The dynamic channel can be modeled by the change of the support of the CSI and the evolution of the amplitude of the non-zero elements:

[0125]

[0126] where h t is the CSI at time t, s t (l)∈{0,1} indicates whether the lth support index of s t is zero, g t (l)∈C is the amplitude at the lth support index of g t , and represents the Hadamard product. Specifically, a first-order Markov process is used to model the change of the support, i.e., two transition probabilities are defined as

[0127]

[0128] where it is assumed that reaches a steady-state sparsity p∈(0,1). The amplitude adopts a first-order autoregressive model, which is expressed as

[0129]

[0130] where the correlation coefficient ρ=J0(2πf d τ) is given by the first kind of zero-order Bessel function, f d is the maximum Doppler frequency, τ is the duration, and the parameter​ The complex Gaussian variables i.i.d. Some classic Cy algorithms require to know the number of non-zero elements in the channel matrix in advance, which is not suitable for time-varying channel systems, because it is difficult to obtain prior knowledge at each time slot. Therefore, the present application designs a new method that does not require channel prior knowledge and is more suitable for millimeter wave FDD large-scale MIMO systems.

[0131] 1.2 Joint channel training and feedback

[0132] 1.2.1 AS-JOMP algorithm based on compressed sensing

[0133] In this section, a joint training and feedback plan will be proposed, which includes two steps. First, the AS-JOMP algorithm based on compressed sensing is used to recover the CSI from the received signal. Second, the estimated CSI is used as the input of the DCNN-LSTM to remove noise and learn the features between time-varying channels.

[0134] For simplicity, the superscript t is omitted in the above equation, and for the FDD system, the CSI knowledge at the BS is obtained by the step of estimating the CSI of the i-th user and then feeding it back to the BS. Using the traditional LS-based CSI estimation technique, the channel can be estimated by:

[0135]

[0136] where, is the Moore-Penrose pseudo-inverse. However, this LS-based method requires P ≥ LN BS When N BS is large, this will increase the pilot training and CSI feedback overhead. When P < LN BS , formula (7) is an underdetermined problem, which can be solved by using the sparsity of the CSI through CS technology. For the general CS model, and Φ are called measurement and measurement matrix respectively. Obviously, due to the reduction of the number of pilots, the overhead of downlink training is also reduced. In addition, the user feeds back the received pilot to the BS, so that the uplink feedback can also be reduced LN BS to P.

[0137] Among many compressed sensing reconstruction algorithms, the orthogonal matching pursuit (OMP) algorithm is a classic algorithm that has been used and improved many times

[26] . OMP reconstructs the channel by iteratively identifying the support set, which contains the index of the column of Φ that is closest to the measurement associated. In each iteration, it selects an index according to the maximum correlation test and subtracts the contribution of the corresponding column from the current metric. The iteration process continues until the indices of all non-zero elements are identified. However, sparsity S is not available in general practical applications. Therefore, the present application adopts an improved adaptive structured orthogonal matching pursuit algorithm based on OMP algorithm, namely AS-JOMP algorithm. According to the structural sparsity, AS-JOMP algorithm divides the cross-correlation vector of the product of the sensing matrix Φ and the residual observation vector r i into N BS vectors and sums them up, and then selects the maximum value index as OMP. This method can more accurately select the non-zero element index of CSI. In the second observation, two threshold parameters are used to stop the iteration under high and low signal-to-noise ratios. Therefore, the AS-JOMP algorithm can adaptively recover the CSI without any prior sparsity information. Compared with the current most advanced CS-based channel estimation scheme, the AS-JOMP algorithm has the following remarkable features:

[0138] (1) The proposed AS-JOMP algorithm can adaptively obtain the sparsity of the millimeter wave massive MIMO channel, avoiding the unrealistic assumption of using channel sparsity as prior information for channel estimation. The proposed stopping criterion enables the AS-JOMP algorithm to obtain good channel estimation performance under high and low signal-to-noise ratios.

[0139] (2) The AS-JOMP algorithm considers the structural sparsity of h, provides more accurate support updates, and updates the support of each CSI recovery performance can be greatly improved.

[0140] 1.2.2 DCNN-LSTM based on deep learning

[0141] Although the AS-JOMP algorithm can select the non-zero element index of the sparse channel, the noise is not eliminated, and the time-varying characteristics of the channel are not well utilized. Based on these needs, the present application proposes a network architecture based on deep learning, namely DCNN-LSTM. DCNN-LSTM is a joint network based on CNN and LSTM. This network not only reduces noise by extracting channel structure information through CNN, but also learns the correlation of time-domain channels through the LSTM network. This can effectively learn the space-time features of the channel, thereby improving the final CSI estimation accuracy. The network architecture is shown in Figure 2 .

[0142] In this network, the CSI channel group is taken as input, where T is the number of CSI in the channel group i = 1, 2,..., N sample , where N sampleis the number of samples. The output of the network is expressed as For the sake of convenience, the present invention omits the subscript i and and Expressed as and At present, the input data of deep neural networks are all real numbers. Therefore, two real number matrices are used to represent the real and imaginary parts of the input channel matrix. Then all elements in the matrix are normalized to [0, 1], which is equivalent to the image data of two channels, which is convenient for training. Is a size of LN Bs × 1 complex vector. Therefore, the real and imaginary parts of the complex vector are separated into two parts of size LN BS ×1 real vector, and then transformed into two vectors of size The real matrix of Therefore, the data of each layer of the network is a four-dimensional tensor, and the sum of the products on the left side of each layer represents the size of the CSI channel group. The number above is the number of feature maps.

[0143] In fact, the D CNN The LSTM network consists of three layers, mainly including channel feature extraction, time-varying channel correlation extraction, and CSI reconstruction. The main components are as follows:

[0144] (1) Channel feature extraction: This is mainly performed by the first layer of the CNN network. In this process, each time dimension matrix can be convolved separately to extract features. The convolution layer contains 64 3×3 convolution kernels with a sliding step of l. The same zero padding around the input is used during convolution to keep the feature map output by each layer of the network the same size as the original channel matrix, and ReLU is used as the activation function.

[0145] (2) Time-varying channel correlation extraction: The extraction of time correlation is mainly completed by the second layer LSTM network. At present, most LSTM networks that predict time states use a fully connected structure, but the input of the fully connected network is one-dimensional and does not consider spatial correlation. Compared with traditional methods, the convolution operation used in the ConvLSTM network can obtain better space-time relationship because ConvLSTM, like LSTM, uses the output of the previous layer as the input of the next layer. ConvLSTM network is as follows: Figure 3 As shown, the network consists of an input gate i t and an output gate O t The input gate is used to record the current state information, and the output gate is used to control how much current state information can be seen by the external network. t Control the number of historical state information flows to the current state after the entry, memory unit Ct The information at the moment before the book is stored. As shown in equation 16, wherein W xi , W hi , W ci , W ho , W xo , W co , W xf represents the weight matrix, b i , b o , b f , b c represents the bias, and the number in the range [0, 1] is shaped to represent the proportion of information transmission, 0 represents no transmission, and 1 represents full transmission.

[0146] The preliminary estimated CSI matrix is sequentially input into the ConvLSTM layer. At each time step, the ConvLSTM network can fuse the time-related information learned at the previous time point into the input at the current time step, and the related information is updated with the time step.

[0147]

[0148] (3) CSI reconstruction: In order to obtain the same size as the input data, the same padding, ReLU activation function and 3x3x2 size filter are considered. Finally, the final CSI estimation result is obtained by dimension transformation and inverse normalization

[0149] From the detailed description of the above specific embodiments, it can be seen that the present application can effectively perform channel estimation of the millimeter wave FDD large-scale MIMO system. Those skilled in the art can adjust and optimize the above steps and structures according to the actual application to realize all or part of the technical effects of the present application.

[0150] The above is only the preferred specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any skilled person in the art can make equivalent replacement or change according to the technical solution and the inventive concept of the present application within the technical range disclosed by the present application, and all of them should be covered within the protection scope of the present application.

Claims

1. A channel estimation method for millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning, characterized in that: Here are the steps: S1. Compressed sensing preliminary estimation: The received pilot signal is processed using the compressed sensing method to extract the preliminary CSI matrix; S2. Deep learning network structure: ConvLSTM network is used. The ConvLSTM network is a combination of convolutional neural network and long short-term memory network. The convolutional neural network extracts spatial features and the long short-term memory network captures temporal correlations. S3, ConvLSTM network processing: The initially estimated CSI matrix is ​​input into the ConvLSTM network in chronological order. The ConvLSTM network integrates time-related information to improve the accuracy of CSI estimation; S4, CSI reconstruction: Use the same padding, ReLU activation function and appropriately sized filters to obtain the same size as the input data; obtain the final CSI estimation result through dimensionality transformation and denormalization.

2. The method for channel estimation of a millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 1, wherein: It is performed through a massive MIMO-OFDM system in millimeter-wave frequency division duplex mode. In the massive MIMO-OFDM system, communication is carried out between the base station and multiple single-antenna users, using a comb pilot method. The pilot intervals within each OFDM symbol are equal, and the pilot symbols are randomly selected.

3. The method for channel estimation of a millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 2, wherein: In the massive MIMO-OFDM system, the following steps are performed: D1. Pilot symbol generation: Randomly select the pilot symbol at each antenna from the OFDM symbol and obtain the time domain transmission symbol through inverse discrete Fourier transform; D2. Signal Reception: At the receiving end, the received signal is represented in the frequency domain through Fourier transform; D3. Channel State Information Extraction: The user extracts pilot symbols from the received signal and recovers the sparse CSI matrix through compressed sensing.

4. The method for channel estimation of a millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 2, wherein: The pilot C of the i-th transmitting antenna of the k-th user ik ∈C P×1 , where C px1 It is a standard mathematical symbol representing a complex vector, C represents a complex set, and px1 represents a matrix with p rows and 1 column, that is, a column vector, where P is the number of pilots, and the pilot symbol at the i-th antenna is C i ∈C P×1 , where C i The elements in are from OFDM symbols randomly selected from; through inverse discrete Fourier transform, the transmission symbol in the time domain is obtained as: in is the DFT matrix, (·) H is the complex conjugate transpose, N c is the number of subcarriers; the i-th antenna at the BS transmits the time domain signal X i ; Then the signal y received in the time domain is expressed as follows: where h i ∈C L×1 is the channel state information from the ith antenna of the BS to the user, L is the channel length, represents independent and identically distributed (iid) complex additive Gaussian white noise, * represents convolution operation, also expressed as matrix multiplication, N BS Indicates the number of base station antennas; If the OFDM system has a cyclic prefix of appropriate length, the linear convolution in Equation (2) becomes a cyclic convolution after the cyclic prefix is ​​removed at the receiving end; i Using zero padding, the convolution operation will be expressed as follows: in L to N c The elements are all 0, and the convolution in formula (3) can also be expressed as the matrix multiplication as follows: in Is a Toeplitze matrix; as follows: In formula (4), From y o to N c The cumulative sum of the sequence; and the circular convolution in formula (3) is represented by matrix convolution; Through DFT transformation, the symbol received in the frequency domain can be expressed as in The diagonal elements are The matrix, y f Represents the received signal in the frequency domain, Fy c Indicates the DFT transformation of the time domain cyclic convolution received signal, Fx i represents the frequency domain representation of the signal transmitted by the i-th antenna of the base station, and Fn represents the frequency domain representation of the time domain noise; In order to estimate the channel state information h i , the user must receive the signal y f Extract pilot symbols The received signal can be written as follows: Among them F Ω,L is the measurement matrix for sparse channels, F Ω is the DFT transform matrix for non-sparse noise, is from the index set Ω The selected Ω，L ∈C P×L The corresponding is a partial Fourier matrix, the rows are selected from the index of the pilot, and the columns are selected from the first L columns of F; obviously, Equal to c i ;therefore in h i =[h i (1), h i (2), ..., h i (L)] T is the CSI from the ith base station antenna to the user, It means the mean is zero and the variance is Additive Gaussian white noise; If the pilot intervals within the OFDM symbol are equal and the pilot symbols are randomly selected, the pilot received from a certain user is in and Formula (10) is regarded as a compressed sensing problem, Φ is the sensing matrix, j is the sparse signal; therefore, the reconstruction algorithm based on compressed sensing is used to calculate the value of Φ and y. c Reconstruct h, where y c It is the input data of the entire compressed sensing problem and the starting point of the channel reconstruction algorithm. Under this channel model, the uplink channel and the downlink channel have the same signal-to-noise ratio, and the noise parameter represents the total noise power of the downlink and uplink channels; for block fading time-varying MIMO channels, the CSI varies from one time slot to another but remains unchanged within a time slot; the dynamic channel is modeled by the change of CSI support and the evolution of the amplitude of non-zero elements: Among them, h t is the CSI at time t, s t (l)∈{0,1} represents s t Whether the lth support index of g is zero, t (l)∈C is g t The amplitude at the lth support index of Represents the Hadamard product; specifically, a first-order Markov process is used to model the change of support, that is, two transition probabilities are defined as: Among them, In order to achieve a steady-state sparsity rate p∈(0,1), the amplitude adopts a first-order autoregressive model, which is expressed as follows: The correlation coefficient ρ=J0(2πf d τ) is given by the zero-order Bessel function of the first kind, f d is the maximum Doppler frequency, τ is the duration, and the parameter is an iid complex Gaussian variable.

5. The method for channel estimation of a millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 1, wherein: The following steps are also included: The AS-JOMP algorithm based on compressed sensing is used to recover CSI from the received signal. According to the structural sparsity, the AS-JOMP algorithm combines the sensor matrix Φ with the residual observation vector r i The cross-correlation vector of the product is divided into N BS vectors and sum them, N BS represents the number of base station antennas, and then selects the maximum indicator like OMP; in the second observation, two threshold parameters are used to stop the iteration under high SNR and low SNR.

6. The method for channel estimation of a millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 5, wherein: The following steps are also included: Use the estimated CSI as the input of the DCNN-LSTM network to remove noise and learn the features between time-varying channels; in the DCNN-LSTM network, the CSI channel group As input, where T is the number of CSI in the channel group i = 1, 2, ..., N sample , where N sample is the number of samples; the output of the network is expressed as Obtained by AS-JOMP algorithm Is a size of LN BS ×1 complex vector, Represents a three-dimensional complex tensor, which represents a channel group, including N base stations in T consecutive time slots BS The channel information between the root antenna and the user, the first dimension L represents the length of each channel vector, the second dimension N BS represents the number of base station antennas, and the third dimension T represents the time dimension. represents the output of AS-JOMP, i.e. the initial channel estimate; therefore, the real and imaginary parts of the complex vector are separated into two LN BS ×1 real vector, and then transformed into two vectors of size The real matrix of Therefore, the data of each layer of the network is a four-dimensional tensor, and the sum of the products on the left side of each layer represents the size of the CSI channel group.

7. The method for channel estimation of a millimeter-wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 6, wherein: The DCNN-LSTM network includes a channel feature extraction module, a time-varying channel correlation extraction module and a CSI reconstruction module.

8. The method for channel estimation of a millimeter wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 7, wherein: The channel feature extraction module is completed by the CNN network in the first layer. In this process, the matrix of each time dimension can be convolved separately to extract features. The convolution layer contains 64 3×3 convolution kernels with a sliding step of 1. The same zero padding around the input is used during convolution to ensure that the feature map output by each layer of the network remains the same size as the original channel matrix, and ReLU is used as the activation function.

9. The method for channel estimation of a millimeter wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 7, wherein: The time-varying channel correlation extraction module: the extraction of time correlation is mainly completed by the second layer LSTM network; the ConvLSTM network is composed of input gate i t , output gate O t 、Forget Gate t and memory unit C t The input gate is used to record the current state information, and the output gate is used to control how much current state information can be seen by the external network; the forget gate f t Control the number of historical state information flows to the current state after the entry, memory unit C t Store the information of the previous moment; As shown in formula 16, where W xi , W hi , W ci , W xo , W ho , W co , W xf , w hf , w cf , w xc , w hc , represents the weight matrix, b i , b o , b f , b c , represents the bias, the output value of these gate control units is between [0,1], which is used to represent the proportion of information passing through, 0 means no transmission, and 1 means all transmission; The initially estimated CSI matrix is ​​used as the input of the ConvLSTM network in chronological order. At each time step, the ConvLSTM network can integrate the time-related information learned at the previous time point into the input of the current time step, and the relevant information is updated with the time step. Where * represents the convolution operation, which is used to extract the spatial features of the data. Represents the Hadamard product, which is used in the gating mechanism to control the ratio of information flow, x t Represents the input data at the current time step t.

10. The method for channel estimation of a millimeter wave frequency division duplex massive MIMO system based on compressed sensing and deep learning according to claim 7, wherein: The CSI reconstruction module uses the same padding, ReLU activation function, and 3×3×2 filter size to obtain the same size as the input data; the final CSI estimation result is obtained through dimensionality transformation and denormalization.

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