CN110099016B - A channel estimation method for millimeter-wave sparse fronts based on deep learning networks - Google Patents

Abstract

Translated fromChinese

本发明公开了一种基于深度学习网络的毫米波稀疏阵面信道估计方法，以毫米波信道稀疏特性为先验信息，训练设计的全连接深度神经网络，用于毫米波阵面通信信道估计。首先采用全连接移相器网络，通过配置各移相器相位均匀分布来设计各向同性的模拟收发器；然后将获得的信道稀疏信息和设计的最优数字估计器作为全连接深度学习网络的训练数据。对于各信噪比下的稀疏信道，将信道的稀疏信息输入网络，得到相应的数字估计器，进而得到信道估计结果。本发明给出的稀疏信道估计器可以减小低精度模数转换器非线性量化带来的误差，并使用深度学习网络实现，从而降低信道估计复杂度，本发明性能能够逼近理论上最优的信道估计方法。

The invention discloses a millimeter wave sparse front channel estimation method based on a deep learning network. Taking the sparse characteristics of the millimeter wave channel as prior information, a fully connected deep neural network designed for training is used for millimeter wave front communication channel estimation. First, a fully connected phase shifter network is used, and an isotropic analog transceiver is designed by configuring the phase distribution of each phase shifter to be uniform; then the obtained channel sparse information and the designed optimal digital estimator are used as the fully connected deep learning network. training data. For the sparse channels under each signal-to-noise ratio, the sparse information of the channel is input into the network to obtain the corresponding digital estimator, and then the channel estimation result is obtained. The sparse channel estimator provided by the present invention can reduce the error caused by the nonlinear quantization of the low-precision analog-to-digital converter, and is implemented by using a deep learning network, thereby reducing the complexity of channel estimation, and the performance of the present invention can approach the theoretical optimal Channel estimation method.

Description

Translated fromChinese

一种基于深度学习网络的毫米波稀疏阵面信道估计方法A channel estimation method for millimeter wave sparse front based on deep learning network

技术领域technical field

本发明涉及通信领域，涉及信道估计方法，更为具体的说是涉及一种基于深度学习网络的毫米波稀疏阵面信道估计方法。The invention relates to the field of communications, to a channel estimation method, and more particularly to a millimeter wave sparse front channel estimation method based on a deep learning network.

背景技术Background technique

近年来，通信技术取得了突破性的进展并逐步趋于成熟，全球范围内的移动通信产业已经得到了迅猛的发展。多输入多输出(MIMO)技术是通信技术发展的关键技术之一，提高了系统的数据传输速率。通过系统的发送端以及接收端配备多根天线，利用收发两端的多天线形成分集，可以提高系统稳定性。与此同时，由于收发两端天线间的独立信道数目的大大增加，单位时间内系统发送的数据量也得以提升，进而提高了系统的频谱利用效率。In recent years, the communication technology has made breakthrough progress and gradually matured, and the mobile communication industry has developed rapidly around the world. Multiple-input multiple-output (MIMO) technology is one of the key technologies in the development of communication technology, which improves the data transmission rate of the system. By equipping the transmitting end and the receiving end of the system with multiple antennas, and utilizing the multiple antennas at the transmitting and receiving ends to form diversity, the system stability can be improved. At the same time, due to the large increase in the number of independent channels between the antennas at both ends of the transceiver, the amount of data sent by the system per unit time is also increased, thereby improving the spectrum utilization efficiency of the system.

Massive MIMO(即大规模天线)技术在传输速率，能量效率，传输可靠性等方面相较于MIMO技术有了大幅改进，而毫米波大规模MIMO技术大大减小了大规模天线阵面的配置难度，而大规模MIMO技术则解决了毫米波信号高损耗易被阻挡的问题。为了减小毫米波大规模MIMO系统中的功耗和硬件复杂度，可以使用少量射频链路的数模混合架构。Massive MIMO (ie massive antenna) technology has greatly improved in terms of transmission rate, energy efficiency, transmission reliability, etc. compared with MIMO technology, and millimeter-wave massive MIMO technology greatly reduces the difficulty of configuring massive antenna arrays , while Massive MIMO technology solves the problem that millimeter wave signals are easily blocked due to high loss. To reduce power consumption and hardware complexity in mmWave massive MIMO systems, a digital-analog hybrid architecture with few RF links can be used.

为了进行高性能传输，需要首先进行信道估计。传统的大规模多天线技术系统的信道估计本身就是一大挑战，混合架构下低精度模数转换器的使用在降低成本和功耗的同时让信道估计变得更加困难。同时，如何在利用毫米波信道稀疏性的同时降低估计复杂度和导频开销，并获得高精度信道估计也是一大挑战。For high-performance transmission, channel estimation needs to be performed first. The channel estimation of traditional large-scale multi-antenna technology systems is a challenge in itself. The use of low-precision analog-to-digital converters in hybrid architectures makes channel estimation more difficult while reducing cost and power consumption. At the same time, how to reduce the estimation complexity and pilot overhead while taking advantage of the millimeter wave channel sparsity, and obtain high-precision channel estimation is also a big challenge.

发明内容SUMMARY OF THE INVENTION

为解决上述问题，本发明提出一种的稀疏信道估计方法，用于低精度模数转换器以及混合构架的宽带mmWave大规模多天线技术系统中。以毫米波信道稀疏特性为先验信息，将稀疏信道的选择矩阵及其对应的数字估计器作为输入对设计的全连接深度神经网络进行训练，得到适用于不同信噪比的深度神经网络，用于毫米波阵面通信信道估计。首先采用全连接移相器网络，通过配置各移相器相位均匀分布来设计各向同性的模拟收发器；然后将获得的信道稀疏信息作为先验知识，设计最优的数字估计器，将二者作为全连接深度学习网络的训练数据。对于各信噪比下的稀疏信道，将信道的稀疏信息输入网络，可以获得相应的数字估计器，从而得到信道估计结果。本发明给出的稀疏信道估计器可以减小低精度模数转换器非线性量化带来的误差，并使用深度学习网络实现从而降低信道估计复杂度。在采用低精度模数转换器的混合构架多天线系统中，本发明性能能够逼近理论上最优的信道估计方法。In order to solve the above problems, the present invention proposes a sparse channel estimation method, which is used in a low-precision analog-to-digital converter and a broadband mmWave large-scale multi-antenna technology system with a hybrid architecture. Taking the sparse characteristics of millimeter-wave channels as prior information, the selection matrix of sparse channels and their corresponding digital estimators are used as inputs to train the designed fully connected deep neural network, and a deep neural network suitable for different signal-to-noise ratios is obtained. Communication channel estimation on mmWave fronts. First, a fully-connected phase shifter network is used to design an isotropic analog transceiver by configuring the phase of each phase shifter to be uniformly distributed; then, the obtained channel sparse information is used as prior knowledge to design an optimal digital estimator. It is used as the training data of the fully connected deep learning network. For sparse channels under each signal-to-noise ratio, the sparse information of the channel is input into the network, and the corresponding digital estimator can be obtained, thereby obtaining the channel estimation result. The sparse channel estimator provided by the invention can reduce the error caused by the nonlinear quantization of the low-precision analog-to-digital converter, and is implemented by using a deep learning network to reduce the complexity of channel estimation. In a hybrid architecture multi-antenna system using a low-precision analog-to-digital converter, the performance of the present invention can approach the theoretically optimal channel estimation method.

为了达到上述目的，本发明提供如下技术方案：In order to achieve the above object, the present invention provides the following technical solutions:

一种基于深度学习网络的毫米波稀疏阵面信道估计方法，包括：A millimeter wave sparse front channel estimation method based on deep learning network, comprising:

发射端发送导频信号，经过全连接的移相器组成的模拟预编码器经由信道到达接收机，接收端使用模拟估计器、低精度模数转换器量化器和深度学习网络获得信道估计；The transmitter sends a pilot signal, and the analog precoder composed of fully connected phase shifters reaches the receiver through the channel, and the receiver uses an analog estimator, a low-precision analog-to-digital converter quantizer and a deep learning network to obtain channel estimation;

其特征在于：在所述硬件架构基础上的信道估计方法包括以下步骤：It is characterized in that: the channel estimation method based on the hardware architecture comprises the following steps:

步骤一：基站设计模拟预编码并发送导频信号，模拟预编码F_Am根据以下公式设计：Step 1: The base station designs analog precoding and sends pilot signals, and the analog precoding F_Am is designed according to the following formula:

其中，[]_ij表示矩阵的第i行、第j列的元素；F_Am表示维度为N_t×N_RFt的模拟预编码矩阵，N_t表示发射天线数，N_RFt表示发射端射频链路数；

表示模拟预编码矩阵的第i行、第j列元素的相位；Among them, []_ij represents the elements of the i-th row and j-th column of the matrix; F_Am represents the analog precoding matrix with dimension N_t ×N_RFt , N_t represents the number of transmitting antennas, and N_RFt represents the number of radio frequency chains at the transmitting end ;

Represents the phase of the elements in the i-th row and the j-th column of the analog precoding matrix;

步骤二：接收端优化设计模拟估计器W_Am,W_Am根据以下公式计算：Step 2: The receiver is optimally designed to simulate the estimator W_Am , and W_Am is calculated according to the following formula:

其中，W_Am表示维度为N_r×N_RFr的模拟估计矩阵，N_r表示接收天线数，N_RFr表示接收端射频链路数；

表示模拟估计矩阵的第i行、第j列元素的相位；Among them, W_Am represents an analog estimation matrix with dimension N_r ×N_RFr , N_r represents the number of receiving antennas, and N_RFr represents the number of radio frequency chains at the receiving end;

Represents the phase of the i-th row and j-th column element of the simulation estimation matrix;

步骤三：接收端通过压缩感知技术，如经典正交匹配追踪(OMP)技术，获得信道的稀疏特征信息，即稀疏信道矩阵中的非零元素位置，并以此作为后续信道估计的先验信息；Step 3: The receiving end obtains the sparse feature information of the channel through compressed sensing technology, such as the classical Orthogonal Matching Pursuit (OMP) technology, that is, the position of the non-zero elements in the sparse channel matrix, and uses this as the prior information for subsequent channel estimation ;

步骤四：接收端对于稀疏信道特征信息所对应的所有可能的选择矩阵P_v[k]的集合进行存储，并根据每一个选择矩阵P_v[k]设计相应的数字估计矩阵

Step 4: The receiver stores the set of all possible selection matrices P_v [k] corresponding to the sparse channel feature information, and designs a corresponding digital estimation matrix according to each selection matrix P_v [k]

步骤五：把上述选择矩阵P_v[k]的集合和与此对应的数字估计矩阵

作为全连接神经网络的训练集，经过神经网络训练得到适用于各信噪比下的全连接的前向反馈网络。相干时间内，接收端根据稀疏信道相应的选择矩阵P_v[k]，应用网络结构，得到网络输出的数字估计矩阵

用此数据估计矩阵对接收信号进行检测，从而得到信道估计值

Step 5: Combine the set of the above selection matrix P_v [k] and the corresponding digital estimation matrix

As the training set of the fully connected neural network, a fully connected forward feedback network suitable for each signal-to-noise ratio is obtained after the neural network training. During the coherence time, the receiving end applies the network structure according to the corresponding selection matrix P_v [k] of the sparse channel, and obtains the digital estimation matrix output by the network

Use this data estimation matrix to detect the received signal to obtain the channel estimation value

进一步的，所述步骤四中选择矩阵P_v[k]用下面公式表示：Further, in thestep 4, the selection matrix P_v [k] is represented by the following formula:

其中,e_π(i)(π(i)∈{1,2,…,N_rN_t})表示维度为N_rN_t×1的第π(i)个元素为1、其余元素为 0的矢量。N_v表示第k个子载波上维度为N_rN_t×1的信道矢量投影到角度域上的矢量分量 h_v[k]中非零元素的个数。Among them, e_π(i) (π(i)∈{1,2,…,N_r N_t }) indicates that the π(i)th element of dimension N_r N_t ×1 is 1, and the rest of the elements are 0 vector. N_v represents the number of non-zero elements in the vector component h_v [k] of the channel vector with dimension N_r N_t ×1 on the kth subcarrier projected onto the angle domain.

对于信道矩阵中的非零信道元素，信道的选择矩阵P_v[k]的形式有N种可能，对于所有可能的集合{P_v1[k],P_v2[k],…,P_vN[k]}，每一种P_vi[k](i＝1,…,N)出现的可能性均为

即For non-zero channel elements in the channel matrix, there are N possibilities in the form of the channel selection matrix P_v [k], for all possible sets {P_v1 [k], P_v2 [k],...,P_vN [k ]}, the probability of occurrence of each P_vi [k] (i=1,...,N) is

which is

其中，N为所有可能的个数，

C表示组合数公式。N_v表示第k个子载波上维度为N_rN_t×1的信道矢量投影到角度域上的矢量分量h_v[k]中非零元素的个数。where N is all possible numbers,

C represents the formula for the number of combinations. N_v represents the number of non-zero elements in the vector component h_v [k] of the channel vector with dimension N_r N_t ×1 on the kth subcarrier projected onto the angle domain.

进一步的，将信道投影到虚拟角度域上得到信道矢量分量h_v[k]，h_v[k]按以下公式计算：Further, the channel vector component h_v [k] is obtained by projecting the channel onto the virtual angle domain, and h_v [k] is calculated according to the following formula:

其中，A_t表示维度为N_t×N_t的发射阵面响应矢量组成的发射字典矩阵，

表示矩阵A_t的共轭；

表示克罗内克积；A_r表示维度为N_r×N_r的接收阵面响应矢量组成的接收字典矩阵；H[k]表示第k个子载波上的维度为N_r×N_t的物理信道矩阵，vec(H[k])表示矩阵H[k]的矢量化。Among them, A_t represents the emission dictionary matrix composed of the emission front response vectors with dimension N_t ×N_t ,

represents the conjugate of matrix_At ;

Represents the Kronecker product; Ar represents the reception dictionary matrix composed of the receiving front response vector with dimension N_r ×N_r ; H[_{k] represents the physical channel with dimension N r ×N tonthe} kth subcarrier matrix, vec(H[k]) represents the vectorization of matrix H[k].

其中，A_t按以下公式表示：Among them, At is_expressed by the following formula:

其中,

表示维度为N_t×1的发射阵面响应矢量，其中

其中，N_t＝P×Q,P表示发射天线阵面的横轴天线数，Q表示发射天线阵面的纵轴天线数；in,

represents the emission front response vector of dimension N_t × 1, where

Among them, N_t =P×Q, P represents the number of antennas on the horizontal axis of the transmitting antenna front, and Q represents the number of antennas on the vertical axis of the transmitting antenna front;

A_r按以下公式表示：A_r is expressed by the following formula:

其中，

表示维度为N_r×1的接收阵面响应矢量，其中，

其中，N_r＝I×J,I表示接收天线阵面的横轴天线数，J表示接收天线阵面的纵轴天线数；in,

represents the receive front response vector of dimension N_r ×1, where,

Among them, N_r =I×J, I represents the number of antennas on the horizontal axis of the receiving antenna front, and J represents the number of antennas on the vertical axis of the receiving antenna front;

进一步的，所述步骤四中最优数字估计矩阵

使用信道估计最小均方误差准则，

可以按如下公式计算：Further, the optimal digital estimation matrix in thestep 4

Using the channel estimation minimum mean square error criterion,

It can be calculated as follows:

其中，k∈{1,2,…,K}表示第k个子载波，K表示子载波总数；

表示第k个子载波上N_RFr×N_v的最优数字估计矩阵，M表示相干时间内信道使用次数，即信道估计次数。η_b表示与模数转换器(ADC)量化比特数b有关的失真因子；Ω[k]表示第k个子载波上的维度为MN_RFr×N_v的测量矩阵；Ω^H[k]表示矩阵Ω[k]的共轭转置；

表示信道的大尺度衰落系数；

表示维度为N_v×N_v的单位矩阵；

表示等效噪声矢量每个元素的方差，

表示加性高斯白噪声(AWGN)方差；P表示发射导频功率。Among them, k∈{1,2,…,K} represents the kth subcarrier, and K represents the total number of subcarriers;

Represents the optimal digital estimation matrix of N_RFr ×N_v on the kth subcarrier, and M represents the number of channel usages within the coherence time, that is, the number of channel estimations. η_b represents the distortion factor related to the number of quantized bits b of the analog-to-digital converter (ADC); Ω[k] represents the measurement matrix of dimension MN_RFr ×N_v on the kth subcarrier; Ω^H [k] represents the matrix Ω Conjugate transpose of [k];

represents the large-scale fading coefficient of the channel;

represents the identity matrix of dimension N_v ×N_v ;

represents the variance of each element of the equivalent noise vector,

represents the additive white Gaussian noise (AWGN) variance; P represents the transmit pilot power.

进一步的，信道估计次数M用下面公式表示：Further, the channel estimation times M is expressed by the following formula:

表示向上取整。

Indicates rounded up.

所述测量矩阵Ω[k]用下面的公式表示：The measurement matrix Ω[k] is represented by the following formula:

Ω[k]＝Φ[k]ΨP_v[k],Ω[k]＝Φ[k]ΨP_v [k],

其中,维度为N_RFr×N_rN_t的导频相关矩阵

s_m[k](m∈{1,2,…,M})表示第m次训练时的维度为N_RFr×1的发射导频向量。Among them, the pilot correlation matrix of dimension N_RFr ×N_r N_t

s_m [k](m∈{1,2,…,M}) represents the transmit pilot vector with dimension N_RFr ×1 during the mth training.

其中，Ψ表示维度为N_rN_t×N_rN_t空间转换矩阵，Ψ按以下公式表示：Among them, Ψ represents the dimension of N_r N_t ×N_r N_t space transformation matrix, and Ψ is expressed by the following formula:

其中，A_t表示维度为N_t×N_t的发射阵面响应矢量组成的发射字典矩阵，A_r表示维度为N_r×N_r的接收阵面响应矢量组成的接收字典矩阵。Among them, At represents the transmit dictionary matrix composed of the response vectors of the transmitting front with dimension N_t ×N_t , and_Ar represents the receiving dictionary matrix composed of the response vectors of the receiving_front with dimension N_r ×N_r .

其中，P_v[k]表示维度为N_rN_t×N_v的选择矩阵。where P_v [k] represents a selection matrix of dimension N_r N_t ×N_v .

进一步的，步骤五中的

按如下步骤通过前向反馈的全连接深度学习网络得到：Further, in step five

Obtained through a fully connected deep learning network with forward feedback as follows:

(1)对于一个已知非零元素个数N_v的稀疏信道，信道矩阵H[k]表示第k个子载波上的维度为N_r×N_t的物理信道矩阵，在各个信噪比下，接收端根据稀疏特征信息计算所有可能的P_v[k]组成的协方差矩阵C[k]＝Ω^H[k]Ω[k]，其中Ω[k]＝Φ[k]ΨP_v[k]。同时，计算与每一个P_v[k]组成的协方差矩阵C[k]对应的

设计新的数字估计矩阵

并将所有可能的C[k]以及对应的

存储到数据库中。(1) For a sparse channel with a known number of non-zero elements N_v , the channel matrix H[k] represents the physical channel matrix of dimension N_r ×N_t on the kth subcarrier. Under each signal-to-noise ratio, The receiver calculates the covariance matrix C[k]=Ω^H [k]Ω[k] composed of all possible P_v [k] according to the sparse feature information, where Ω[k]=Φ[k]ΨP_v [k] . At the same time, calculate the covariance matrix C[k] corresponding to each P_v [k]

Design a new numerical estimation matrix

and put all possible C[k] and the corresponding

stored in the database.

(2)从数据库中提取数据，分为训练数据和测试数据两组。将训练数据进行复值拆分操作，将训练集合C[k]和W_D′[k]拆分为实部矩阵C_R[k]、

和虚部矩阵C_I[k]、

两部分。(2) Extract data from the database and divide it into two groups: training data and test data. Perform complex-valued splitting operation on the training data, and split the training set C[k] and W_D '[k] into real part matrices C_R [k],

and the imaginary part matrix C_I [k],

two parts.

(3)接着将C_R[k]、

和C_I[k]、

进行矩阵矢量化操作，得到维度为N_v²×1的列向量c_R[k]、

以及c_I[k]、

将c_R[k]、

作为实部深度学习网络的输入和训练目标，将c_I[k]、

作为虚部深度学习网络的输入和训练目标。(3) Then_CR [k],

and C_I [k],

Perform matrix vectorization operation to obtain column vector c_R [k] with dimension N_v² ×1,

and c_I [k],

Set c_R [k],

As the input and training target of the real deep learning network, c_I [k],

as the input and training target of the imaginary deep learning network.

(4)构造两个深度学习的全连接网络，网络结构相同。皆为两层前向反馈的全连接神经网络，第一层神经元个数为N，其中

同时在第一层设置偏置(bias) 连接，且第一层的传输函数设置为softmax函数；将第一层输出与第二层神经元连接，神经元个数为N，并且在第二层同样设置偏置(bias)连接。(4) Construct two fully connected deep learning networks with the same network structure. Both are fully connected neural networks with two layers of forward feedback, and the number of neurons in the first layer is N, where

At the same time, the bias connection is set in the first layer, and the transfer function of the first layer is set to the softmax function; the output of the first layer is connected with the neurons of the second layer, the number of neurons is N, and the second layer Also set the bias (bias) connection.

softmax函数定义如下：The softmax function is defined as follows:

其中，每一层全连接网络的输出如下式：Among them, the output of each layer of fully connected network is as follows:

其中，W和b表示全连接神经网络的参数，y_i和b_i表示y和b的第i个元素，x_j表示x的第j个元素，W_i,j表示W中位置为(i,j)的元素。Among them, W and b represent the parameters of the fully connected neural network,_yi and b_i represent the i-th element of y and b, x_j represents the j-th element of x, and Wi_,j represent the position in W of (i, j) elements.

(5)对这样的全连接神经网络进行训练，并通过测试数据的复值拆分以及矩阵矢量化作为输入对该深度学习网络进行测试，从而得到各信噪比下的稳定网络结构。(5) Train such a fully connected neural network, and test the deep learning network through complex-valued splitting of the test data and matrix vectorization as input, so as to obtain a stable network structure under each signal-to-noise ratio.

(6)相干时间内，对于各信噪比下的稀疏信道，将含有信道的稀疏信息的信道协方差矩阵C[k]输入网络，可以获得相应的数字估计器

(6) In the coherence time, for the sparse channels under each signal-to-noise ratio, the channel covariance matrix C[k] containing the sparse information of the channel is input into the network, and the corresponding digital estimator can be obtained.

进一步的，步骤五中的信道估计值

按如下公式得到：Further, the channel estimation value instep 5

Obtained by the following formula:

其中,()^H表示矩阵的共轭转置操作；()^-1表示矩阵的求逆操作。Among them, ()^H represents the conjugate transpose operation of the matrix; ()^-1 represents the inversion operation of the matrix.

与现有技术相比，本发明具有如下优点和有益效果：Compared with the prior art, the present invention has the following advantages and beneficial effects:

1)该对于宽带信道估计，本发明采用OFDM调制，从而对各窄带子载波进行频域信道估计，本发明以毫米波信道稀疏特性为先验信息，将稀疏信道的选择矩阵及其对应的数字估计器作为输入对设计的全连接深度神经网络进行训练，得到适用于不同信噪比的深度神经网络，用于毫米波阵面通信信道估计；2)该方案采用全连接移相器网络，通过配置各移相器相位均匀分布来设计各向同性的模拟收发器；将获得的信道稀疏特征信息作为先验知识，设计最优的数字估计器，将二者作为全连接深度学习网络的训练数据。对于各信噪比下的稀疏信道，将信道的稀疏信息输入网络，可以获得相应的数字估计器，从而得到信道估计结果；3)本发明给出的稀疏信道估计器可以减小低精度模数转换器非线性量化带来的误差，并使用深度学习网络实现从而降低信道估计复杂度。在采用低精度模数转换器的混合构架多天线系统中，本发明性能能够逼近理论上最优的信道估计方法。1) For wideband channel estimation, the present invention adopts OFDM modulation to perform frequency domain channel estimation on each narrowband subcarrier. The present invention takes the sparse characteristics of millimeter-wave channels as prior information, and uses the selection matrix of the sparse channel and its corresponding digital The estimator is used as an input to train the designed fully connected deep neural network, and a deep neural network suitable for different signal-to-noise ratios is obtained for millimeter-wave front communication channel estimation; 2) The scheme uses a fully connected phase shifter network, which is Configure the phase of each phase shifter to be evenly distributed to design an isotropic analog transceiver; take the obtained channel sparse feature information as prior knowledge, design an optimal digital estimator, and use the two as the training data of the fully connected deep learning network . For sparse channels under each signal-to-noise ratio, the sparse information of the channel is input into the network, and the corresponding digital estimator can be obtained, thereby obtaining the channel estimation result; 3) The sparse channel estimator provided by the present invention can reduce the low-precision modulus The error caused by the nonlinear quantization of the converter is realized by using a deep learning network to reduce the complexity of channel estimation. In a hybrid architecture multi-antenna system using a low-precision analog-to-digital converter, the performance of the present invention can approach the theoretically optimal channel estimation method.

附图说明Description of drawings

图1是本发明系统框图；Fig. 1 is the system block diagram of the present invention;

图2是8*4的毫米波天线阵面，接收端4比特的模数转换器量化下，信道估计归一化均方误差(NMSE)随信噪比(SNR)变化的曲线图；Figure 2 is a graph of the normalized mean square error (NMSE) of channel estimation versus signal-to-noise ratio (SNR) under the quantization of a 4-bit analog-to-digital converter at the receiving end with an 8*4 millimeter-wave antenna front;

具体实施方式Detailed ways

以下将结合具体实施例对本发明提供的技术方案进行详细说明，应理解下述具体实施方式仅用于说明本发明而不用于限制本发明的范围。The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

本发明提出了一种基于深度学习网络的毫米波稀疏阵面信道估计方法，以毫米波信道稀疏特性为先验信息，将稀疏信道的选择矩阵及其对应的数字估计器作为输入对设计的全连接深度神经网络进行训练，得到适用于不同信噪比的深度神经网络，用于毫米波阵面通信信道估计。The invention proposes a millimeter wave sparse front channel estimation method based on a deep learning network, which takes the sparse characteristics of the millimeter wave channel as a priori information, and takes the selection matrix of the sparse channel and its corresponding digital estimator as the input to the designed full-scale channel. The deep neural network is connected for training, and the deep neural network suitable for different signal-to-noise ratios is obtained for millimeter wave front communication channel estimation.

首先采用全连接移相器网络，通过配置各移相器相位均匀分布来设计各向同性的模拟收发器；然后将获得的信道稀疏信息作为先验知识，设计最优的数字估计器，将二者作为全连接深度学习网络的训练数据。对于各信噪比下的稀疏信道，将信道的稀疏信息输入网络，可以获得相应的数字估计器，从而得到信道估计结果。本发明给出的稀疏信道估计器可以减小低精度模数转换器(ADC)非线性量化带来的误差，并使用深度学习网络实现从而降低信道估计复杂度。在采用低精度模数转换器的混合构架多天线系统中，本发明性能能够逼近理论上最优的信道估计方法。First, a fully-connected phase shifter network is used to design an isotropic analog transceiver by configuring the phase of each phase shifter to be uniformly distributed; then, the obtained channel sparse information is used as prior knowledge to design an optimal digital estimator. It is used as the training data of the fully connected deep learning network. For sparse channels under each signal-to-noise ratio, the sparse information of the channel is input into the network, and the corresponding digital estimator can be obtained, thereby obtaining the channel estimation result. The sparse channel estimator provided by the present invention can reduce the error caused by the nonlinear quantization of the low-precision analog-to-digital converter (ADC), and is implemented by using a deep learning network to reduce the complexity of channel estimation. In a hybrid architecture multi-antenna system using a low-precision analog-to-digital converter, the performance of the present invention can approach the theoretically optimal channel estimation method.

如图1所示，在各个信噪比下，通过压缩感知技术获得信道先验稀疏信息，并根据所有的可能的稀疏信道设计相应最小均方误差下的最优数字估计器，作为深度学习全连接网络的训练输入。通过对深度学习网络进行训练和测试，得到可以用于各信噪比下的网络，用于信道估计。在混合构架下，发射端发送导频信号，经过全连接的移相器组成的模拟预编码器经由信道到达接收机，经过模拟估计器、低精度模数转换器量化器，对于各信噪比下的稀疏信道，将信道的稀疏信息输入网络，可以获得相应的数字估计器，从而获得信道估计结果。本发明给出的稀疏信道估计器可以减小低精度模数转换器非线性量化带来的误差，并使用深度学习网络实现从而降低信道估计复杂度。在采用低精度模数转换器的混合构架多天线系统中，本发明性能能够逼近理论上最优的信道估计方法。As shown in Figure 1, under each signal-to-noise ratio, the channel prior sparse information is obtained through compressed sensing technology, and the optimal digital estimator under the corresponding minimum mean square error is designed according to all possible sparse channels, which is used as a full-scale deep learning system. Connect the training input of the network. By training and testing the deep learning network, a network that can be used for various signal-to-noise ratios is obtained for channel estimation. In the hybrid architecture, the transmitter sends a pilot signal, and the analog precoder composed of fully connected phase shifters reaches the receiver through the channel, and goes through the analog estimator and low-precision analog-to-digital converter quantizer. The sparse channel under , the sparse information of the channel is input into the network, and the corresponding digital estimator can be obtained, thereby obtaining the channel estimation result. The sparse channel estimator provided by the invention can reduce the error caused by the nonlinear quantization of the low-precision analog-to-digital converter, and is implemented by using a deep learning network to reduce the complexity of channel estimation. In a hybrid architecture multi-antenna system using a low-precision analog-to-digital converter, the performance of the present invention can approach the theoretically optimal channel estimation method.

本发明提出的信道估计方法包括如下步骤：The channel estimation method proposed by the present invention includes the following steps:

步骤一：基站设计模拟预编码并发送导频信号，模拟预编码F_Am根据以下公式设计：Step 1: The base station designs analog precoding and sends pilot signals, and the analog precoding F_Am is designed according to the following formula:

其中，[]_ij表示矩阵的第i行、第j列的元素；F_Am表示维度为N_t×N_RFt的模拟预编码矩阵，N_t表示发射天线数，N_RFt表示发射端射频链路数；

表示模拟预编码矩阵的第i行、第j列元素的相位；Among them, []_ij represents the elements of the i-th row and j-th column of the matrix; F_Am represents the analog precoding matrix with dimension N_t ×N_RFt , N_t represents the number of transmitting antennas, and N_RFt represents the number of radio frequency chains at the transmitting end ;

Represents the phase of the elements in the i-th row and the j-th column of the analog precoding matrix;

步骤二：接收端优化设计模拟估计器W_Am,W_Am根据以下公式计算：Step 2: The receiver is optimally designed to simulate the estimator W_Am , and W_Am is calculated according to the following formula:

其中，W_Am表示维度为N_r×N_RFr的模拟估计矩阵，N_r表示接收天线数，N_RFr表示接收端射频链路数；

表示模拟估计矩阵的第i行、第j列元素的相位；Among them, W_Am represents an analog estimation matrix with dimension N_r ×N_RFr , N_r represents the number of receiving antennas, and N_RFr represents the number of radio frequency chains at the receiving end;

Represents the phase of the i-th row and j-th column element of the simulation estimation matrix;

步骤三：接收端通过压缩感知技术，如经典正交匹配追踪(OMP)技术，获得信道的稀疏特征信息，即稀疏信道矩阵中的非零元素位置，并以此作为后续信道估计的先验信息。Step 3: The receiving end obtains the sparse feature information of the channel through compressed sensing technology, such as the classical Orthogonal Matching Pursuit (OMP) technology, that is, the position of the non-zero elements in the sparse channel matrix, and uses this as the prior information for subsequent channel estimation .

步骤四：接收端对于稀疏信道特征信息所对应的所有可能的选择矩阵P_v[k]的集合进行存储，并根据每一个选择矩阵P_v[k]设计相应的数字估计矩阵

Step 4: The receiver stores the set of all possible selection matrices P_v [k] corresponding to the sparse channel feature information, and designs a corresponding digital estimation matrix according to each selection matrix P_v [k]

步骤五：把上述选择矩阵P_v[k]的集合和与此对应的数字估计矩阵

作为全连接神经网络的训练集，经过神经网络训练得到适用于各信噪比下的全连接的前向反馈网络。相干时间内，接收端根据稀疏信道相应的选择矩阵P_v[k]，应用网络结构，得到网络输出的数字估计矩阵

用此数据估计矩阵对接收信号进行检测，从而得到信道估计值

Step 5: Combine the set of the above selection matrix P_v [k] and the corresponding digital estimation matrix

As the training set of the fully connected neural network, a fully connected forward feedback network suitable for each signal-to-noise ratio is obtained after the neural network training. During the coherence time, the receiving end applies the network structure according to the corresponding selection matrix P_v [k] of the sparse channel, and obtains the digital estimation matrix output by the network

Use this data estimation matrix to detect the received signal to obtain the channel estimation value

进一步的，所述步骤四中选择矩阵P_v[k]用下面公式表示：Further, in thestep 4, the selection matrix P_v [k] is represented by the following formula:

其中,e_π(i)(π(i)∈{1,2,…,N_rN_t})表示维度为N_rN_t×1的第π(i)个元素为1、其余元素为 0的矢量。N_v表示第k个子载波上维度为N_rN_t×1的信道矢量投影到角度域上的矢量分量 h_v[k]中非零元素的个数。Among them, e_π(i) (π(i)∈{1,2,…,N_r N_t }) indicates that the π(i)th element of dimension N_r N_t ×1 is 1, and the rest of the elements are 0 vector. N_v represents the number of non-zero elements in the vector component h_v [k] of the channel vector with dimension N_r N_t ×1 on the kth subcarrier projected onto the angle domain.

对于信道矩阵中的非零信道元素，信道的选择矩阵P_v[k]的形式有N种可能，对于所有可能的集合{P_v1[k],P_v2[k],…,P_vN[k]}，每一种P_vi[k](i＝1,…,N)出现的可能性均为

即For non-zero channel elements in the channel matrix, there are N possibilities in the form of the channel selection matrix P_v [k], for all possible sets {P_v1 [k], P_v2 [k],...,P_vN [k ]}, the probability of occurrence of each P_vi [k] (i=1,...,N) is

which is

其中，N为所有可能的个数，

C表示组合数公式。N_v表示第k个子载波上维度为N_rN_t×1的信道矢量投影到角度域上的矢量分量h_v[k]中非零元素的个数。where N is all possible numbers,

C represents the formula for the number of combinations. N_v represents the number of non-zero elements in the vector component h_v [k] of the channel vector with dimension N_r N_t ×1 on the kth subcarrier projected onto the angle domain.

进一步的，将信道投影到虚拟角度域上得到信道矢量分量h_v[k]，h_v[k]按以下公式计算：Further, the channel vector component h_v [k] is obtained by projecting the channel onto the virtual angle domain, and h_v [k] is calculated according to the following formula:

其中，A_t表示维度为N_t×N_t的发射阵面响应矢量组成的发射字典矩阵，

表示矩阵A_t的共轭；

表示克罗内克积；A_r表示维度为N_r×N_r的接收阵面响应矢量组成的接收字典矩阵；H[k]表示第k个子载波上的维度为N_r×N_t的物理信道矩阵，vec(H[k])表示矩阵H[k]的矢量化。Among them, A_t represents the emission dictionary matrix composed of the emission front response vectors with dimension N_t ×N_t ,

represents the conjugate of matrix_At ;

Represents the Kronecker product; Ar represents the reception dictionary matrix composed of the receiving front response vector with dimension N_r ×N_r ; H[_{k] represents the physical channel with dimension N r ×N tonthe} kth subcarrier matrix, vec(H[k]) represents the vectorization of matrix H[k].

其中，A_t按以下公式表示：Among them, At is_expressed by the following formula:

其中,

(p∈{1,2,…,N_t})表示维度为N_t×1的发射阵面响应矢量，其中

其中，N_t＝P×Q,P表示发射天线阵面的横轴天线数，Q表示发射天线阵面的纵轴天线数。in,

(p∈{1,2,…,N_t }) denotes the emission front response vector of dimension N_t ×1, where

Among them, N_t =P×Q, P represents the number of antennas on the horizontal axis of the transmitting antenna front, and Q represents the number of antennas on the vertical axis of the transmitting antenna front.

A_r按以下公式表示：A_r is expressed by the following formula:

其中，

(q∈{1,2,…,N_r}表示维度为N_r×1的接收阵面响应矢量，其中，

其中，N_r＝I×J,I表示接收天线阵面的横轴天线数，J表示接收天线阵面的纵轴天线数。in,

(q∈{1,2,…,N_r } denotes the receiving front response vector with dimension N_r ×1, where,

Wherein, N_r =I×J, I represents the number of antennas on the horizontal axis of the receiving antenna front, and J represents the number of antennas on the vertical axis of the receiving antenna front.

进一步的，所述步骤四中最优数字估计矩阵

使用信道估计最小均方误差准则，

可以按如下公式计算：Further, the optimal digital estimation matrix in thestep 4

Using the channel estimation minimum mean square error criterion,

It can be calculated as follows:

其中，k∈{1,2,…,K}表示第k个子载波，K表示子载波总数；

表示第k个子载波上N_RFr×N_v的最优数字估计矩阵，M表示相干时间内信道使用次数，即信道估计次数。η_b表示与模数转换器(ADC)量化比特数b有关的失真因子；Ω[k]表示第k个子载波上的维度为MN_RFr×N_v的测量矩阵；Ω^H[k]表示矩阵Ω[k]的共轭转置；

表示信道的大尺度衰落系数；

表示维度为N_v×N_v的单位矩阵；

表示等效噪声矢量每个元素的方差，

表示加性高斯白噪声(AWGN)方差；P表示发射导频功率。Among them, k∈{1,2,…,K} represents the kth subcarrier, and K represents the total number of subcarriers;

Represents the optimal digital estimation matrix of N_RFr ×N_v on the kth subcarrier, and M represents the number of channel usages within the coherence time, that is, the number of channel estimations. η_b represents the distortion factor related to the number of quantized bits b of the analog-to-digital converter (ADC); Ω[k] represents the measurement matrix of dimension MN_RFr ×N_v on the kth subcarrier; Ω^H [k] represents the matrix Ω Conjugate transpose of [k];

represents the large-scale fading coefficient of the channel;

represents the identity matrix of dimension N_v ×N_v ;

represents the variance of each element of the equivalent noise vector,

represents the additive white Gaussian noise (AWGN) variance; P represents the transmit pilot power.

进一步的，信道估计次数M用下面公式表示：Further, the channel estimation times M is expressed by the following formula:

表示向上取整。

Indicates rounded up.

所述测量矩阵Ω[k]用下面的公式表示：The measurement matrix Ω[k] is represented by the following formula:

Ω[k]＝Φ[k]ΨP_v[k],Ω[k]＝Φ[k]ΨP_v [k],

其中,维度为N_RFr×N_rN_t的导频相关矩阵

s_m[k](m∈{1,2,…,M})表示第m次训练时的维度为N_RFr×1的发射导频向量。Among them, the pilot correlation matrix of dimension N_RFr ×N_r N_t

s_m [k](m∈{1,2,…,M}) represents the transmit pilot vector with dimension N_RFr ×1 during the mth training.

其中，Ψ表示维度为N_rN_t×N_rN_t空间转换矩阵，Ψ按以下公式表示：Among them, Ψ represents the dimension of N_r N_t ×N_r N_t space transformation matrix, and Ψ is expressed by the following formula:

其中，A_t表示维度为N_t×N_t的发射阵面响应矢量组成的发射字典矩阵，A_r表示维度为N_r×N_r的接收阵面响应矢量组成的接收字典矩阵。Among them, At represents the transmit dictionary matrix composed of the response vectors of the transmitting front with dimension N_t ×N_t , and_Ar represents the receiving dictionary matrix composed of the response vectors of the receiving_front with dimension N_r ×N_r .

其中，P_v[k]表示维度为N_rN_t×N_v的选择矩阵。where P_v [k] represents a selection matrix of dimension N_r N_t ×N_v .

进一步的，步骤五中的

按如下步骤通过前向反馈的全连接深度学习网络得到：Further, in step five

Obtained through a fully connected deep learning network with forward feedback as follows:

(1)对于一个已知非零元素个数N_v的稀疏信道，信道矩阵H[k]表示第k个子载波上的维度为N_r×N_t的物理信道矩阵，在各个信噪比下，接收端根据稀疏特征信息计算所有可能的P_v[k]组成的协方差矩阵C[k]＝Ω^H[k]Ω[k]，其中Ω[k]＝Φ[k]ΨP_v[k]。同时，计算与每一个P_v[k]组成的协方差矩阵C[k]对应的

设计新的数字估计矩阵

并将所有可能的C[k]以及对应的

存储到数据库中。(1) For a sparse channel with a known number of non-zero elements N_v , the channel matrix H[k] represents the physical channel matrix of dimension N_r ×N_t on the kth subcarrier. Under each signal-to-noise ratio, The receiver calculates the covariance matrix C[k]=Ω^H [k]Ω[k] composed of all possible P_v [k] according to the sparse feature information, where Ω[k]=Φ[k]ΨP_v [k] . At the same time, calculate the covariance matrix C[k] corresponding to each P_v [k]

Design a new numerical estimation matrix

and put all possible C[k] and the corresponding

stored in the database.

(2)从数据库中提取数据，分为训练数据和测试数据两组。将训练数据进行复值拆分操作，将训练集合C[k]和W_D′[k]拆分为实部矩阵C_R[k]、

和虚部矩阵C_I[k]、

两部分。(2) Extract data from the database and divide it into two groups: training data and test data. Perform complex-valued splitting operation on the training data, and split the training set C[k] and W_D '[k] into real part matrices C_R [k],

and the imaginary part matrix C_I [k],

two parts.

(3)接着将C_R[k]、

和C_I[k]、

进行矩阵矢量化操作，得到维度为N_v²×1的列向量c_R[k]、

以及c_I[k]、

将c_R[k]、

作为实部深度学习网络的输入和训练目标，将c_I[k]、

作为虚部深度学习网络的输入和训练目标。(3) Then_CR [k],

and C_I [k],

Perform matrix vectorization operation to obtain column vector c_R [k] with dimension N_v² ×1,

and c_I [k],

Set c_R [k],

As the input and training target of the real deep learning network, c_I [k],

as the input and training target of the imaginary deep learning network.

(4)构造两个深度学习的全连接网络，网络结构相同。皆为两层前向反馈的全连接神经网络，第一层神经元个数为N，其中

同时在第一层设置偏置(bias) 连接，且第一层的传输函数设置为softmax函数；将第一层输出与第二层神经元连接，神经元个数为N，并且在第二层同样设置偏置(bias)连接。(4) Construct two fully connected deep learning networks with the same network structure. Both are fully connected neural networks with two layers of forward feedback, and the number of neurons in the first layer is N, where

At the same time, the bias connection is set in the first layer, and the transfer function of the first layer is set to the softmax function; the output of the first layer is connected with the neurons of the second layer, the number of neurons is N, and the second layer Also set the bias (bias) connection.

softmax函数定义如下：The softmax function is defined as follows:

其中，每一层全连接网络的输出如下式：Among them, the output of each layer of fully connected network is as follows:

其中，W和b表示全连接神经网络的参数，y_i和b_i表示y和b的第i个元素，x_j表示x的第j个元素，W_i,j表示W中位置为(i,j)的元素。Among them, W and b represent the parameters of the fully connected neural network,_yi and b_i represent the i-th element of y and b, x_j represents the j-th element of x, and Wi_,j represent the position in W of (i, j) elements.

(5)对这样的全连接神经网络进行训练，并通过测试数据的复值拆分以及矩阵矢量化作为输入对该深度学习网络进行测试，从而得到各信噪比下的稳定网络结构。(5) Train such a fully connected neural network, and test the deep learning network through complex-valued splitting of the test data and matrix vectorization as input, so as to obtain a stable network structure under each signal-to-noise ratio.

(6)相干时间内，对于各信噪比下的稀疏信道，将含有信道的稀疏信息的信道协方差矩阵C[k]输入网络，可以获得相应的数字估计器

(6) In the coherence time, for the sparse channels under each signal-to-noise ratio, the channel covariance matrix C[k] containing the sparse information of the channel is input into the network, and the corresponding digital estimator can be obtained.

进一步的，步骤五中的信道估计值

按如下公式得到：Further, the channel estimation value instep 5

Obtained by the following formula:

其中,()^H表示矩阵的共轭转置操作；()^-1表示矩阵的求逆操作。Among them, ()^H represents the conjugate transpose operation of the matrix; ()^-1 represents the inversion operation of the matrix.

如图2所示，在稀疏信道下，本发明提出的信道估计方法极其接近理论最优的最小均方误差(MMSE)估计器，特别是在低信噪比(SNR)下。在稀疏信道下，本发明提出使用深度学习网络，进一步提高了信道估计的精度以及降低复杂度。As shown in Fig. 2, under sparse channels, the channel estimation method proposed in the present invention is very close to the theoretically optimal minimum mean square error (MMSE) estimator, especially under low signal-to-noise ratio (SNR). Under sparse channels, the present invention proposes to use a deep learning network, which further improves the accuracy of channel estimation and reduces the complexity.

本发明方案所公开的技术手段不仅限于上述实施方式所公开的技术手段，还包括由以上技术特征任意组合所组成的技术方案。应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也视为本发明的保护范围。The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can also be made, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims (4)

1. A millimeter wave sparse array surface channel estimation method based on a deep learning network is characterized by comprising the following steps:

the method comprises the following steps: base station design simulation pre-coding and sending pilot signal, simulation pre-coding F_AmDesigned according to the following formula:

wherein, the [ alpha ], [ beta ] -a]_ijElements representing the ith row and the jth column of the matrix; f_AmWith a representation dimension of N_t×N_RFtAnalog precoding matrix of, N_tRepresenting the number of transmitting antennas, N_RFtRepresenting the number of radio frequency links of a transmitting end;

representing the phase of the ith row and jth column element of the analog precoding matrix;

step two: receiving end optimization design simulation estimator W_Am,W_AmCalculated according to the following formula:

wherein, W_AmWith a representation dimension of N_r×N_RFrAnalog estimation matrix of, N_rRepresenting the number of receiving antennas, N_RFrRepresenting the number of radio frequency links of a receiving end;

representing the phase of the ith row and jth column element of the simulation estimation matrix;

step three: the receiving end obtains sparse characteristic information of the channel through a compressed sensing technology, namely the position of a non-zero element in a sparse channel matrix, and the sparse characteristic information is used as prior information of subsequent channel estimation;

step four: all possible selection matrixes P corresponding to sparse channel characteristic information by the receiving end_v[k]Is collected intoStoring the rows and selecting a matrix P according to each_v[k]Designing corresponding digital estimation matrix

Step five: selecting the matrix P_v[k]And a digital estimation matrix corresponding thereto

As the training set of the fully-connected neural network, the fully-connected feedforward network suitable for each signal-to-noise ratio is obtained through the training of the neural network, and the receiving end selects the matrix P according to the sparse channel_v[k]Obtaining a digital estimation matrix of the network output using the network structure

Detecting the received signal by using the data estimation matrix to obtain a channel estimation value

The step four middle digital estimation matrix

Using the channel estimation minimum mean square error criterion,

calculated according to the following formula:

wherein K ∈ {1,2, …, K } denotes the kth subcarrier, K denotes the total number of subcarriers;

representing the kth subcarrierN on wave_RFr×N_vM represents the number of channel uses within the coherence time, i.e., the number of channel estimates; eta_bRepresents a distortion factor related to the quantization bit number b of an analog-to-digital converter (ADC); omega k]Denotes the dimension on the k sub-carrier as MN_RFr×N_vThe measurement matrix of (2); omega^H[k]Represents the matrix omega k]The conjugate transpose of (1);

represents the large scale fading coefficient of the channel;

with a representation dimension of N_v×N_vThe identity matrix of (1);

representing the variance of each element of the equivalent noise vector,

represents an Additive White Gaussian Noise (AWGN) variance; p represents the transmit pilot power;

in step five

The method is obtained through a full-connection network with forward feedback, and comprises the following steps:

(1) for a known number of non-zero elements N_vOf the sparse channel, the channel matrix H [ k ]]Denotes the dimension N on the k sub-carrier_r×N_tUnder each signal-to-noise ratio, the receiving end calculates all possible P according to the sparse characteristic information_v[k]Formed covariance matrix C k]＝Ω^H[k]Ω[k]Wherein Ω [ k ]]＝Φ[k]ΨP_v[k]，

The channel estimation times M are expressed by the following formula:

represents rounding up;

the measurement matrix Ω [ k ] is represented by the following formula:

Ω[k]＝Φ[k]ΨP_v[k],

wherein the dimension is N_RFr×N_rN_tPilot correlation matrix of

s_m[k](M e {1,2, …, M }) represents that the dimension at the mth training time is N_RFrA transmit pilot vector of x 1,

where Ψ represents the dimension N_rN_t×N_rN_tThe spatial transformation matrix, Ψ, is represented by the following equation:

wherein A is_tWith a representation dimension of N_t×N_tA transmit dictionary matrix composed of transmit array surface response vectors, A_rWith a representation dimension of N_r×N_rA receiving dictionary matrix composed of the receiving array surface response vectors;

wherein, P_v[k]With a representation dimension of N_rN_t×N_vThe selection matrix of (2);

at the same time, calculate with each P_v[k]Formed covariance matrix C k]Corresponding to

Designing a new numerical estimation matrix

And will all possible C [ k ]]And corresponding

Storing the data in a database;

(2) extracting data from database, dividing the data into two groups of training data and test data, carrying out complex value splitting operation on the training data, and collecting training set C [ k ]]And W'_D[k]Split into a real matrix C_R[k]、

And an imaginary matrix C_I[k]、

Two parts;

(3) then C is added_R[k]、

And C_I[k]、

Performing matrix vectorization operation to obtain dimension N_v²X 1 column vector c_R[k]、

And c_I[k]、

C is to_R[k]、

As an input and training target of the real part deep learning network, c_I[k]、

As input and training targets for the imaginary deep learning network; n is a radical of_vRepresenting a dimension of N on the k-th subcarrier_rN_tVector component h of x 1 channel vector projected onto angular domain_v[k]The number of the non-zero elements in the group,

(4) two deep learning fully-connected networks are constructed, the network structures are the same, the two deep learning fully-connected networks are both two layers of forward feedback fully-connected neural networks, the number of neurons in the first layer is N, wherein

Meanwhile, a bias (bias) connection is set in the first layer, and the transfer function of the first layer is set as a softmax function; connecting the first layer output with the second layer neuron, wherein the number of the neurons is N, and setting bias (bias) connection on the second layer;

the softmax function is defined as follows:

wherein, the output of each layer of fully-connected network is as follows:

wherein W and b represent parameters of a fully-connected neural network, y_iAnd b_iI-th element, x, representing y and b_jDenotes the jth element of x, W_i,jRepresents an element with (i, j) in W;

(5) training the fully-connected neural network, and testing the deep learning network by taking complex value splitting and matrix vectorization of test data as input, thereby obtaining a stable network structure under each signal-to-noise ratio;

(6) in the coherent time, for the sparse channel under each signal-to-noise ratio, a channel covariance matrix C [ k ] containing sparse information of the channel]Input network to obtain corresponding digital estimator

2. The millimeter wave sparse front channel estimation method based on the deep learning network as claimed in claim 1, wherein in the fourth step, a compressed sensing technique is used to obtain sparse feature information of the channel, and a corresponding selection matrix P is used_v[k]Expressed by the following formula:

wherein e is_π(i)(π(i)∈{1,2,…,N_rN_t}) represents a dimension of N_rN_tX 1. pi (i) th vector with 1 element and 0 elements, N_vRepresenting a dimension of N on the k-th subcarrier_rN_tVector component h of x 1 channel vector projected onto angular domain_v[k]The number of the non-zero elements in the group,

for non-zero channel elements in the channel matrix, the selection matrix P of the channel_v[k]Has N possible forms, for all possible sets P_v1[k],P_v2[k],…,P_vN[k]Each P_vi[k]The possibility of occurrence of (i ═ 1, …, N) is all

Namely, it is

Wherein N is the total number of the possible numbers,

c represents a combination number formula, N_vRepresenting a dimension of N on the k-th subcarrier_rN_tVector component h of x 1 channel vector projected onto angular domain_v[k]Number of medium non-zero elements.

3. The deep based of claim 2The millimeter wave sparse array surface channel estimation method of the degree learning network is characterized in that a channel is projected to a virtual angle domain to obtain a channel vector component h_v[k]，h_v[k]Calculated according to the following formula:

wherein A is_tWith a representation dimension of N_t×N_tA transmit dictionary matrix composed of transmit front response vectors,

representation matrix A_tConjugation of (2);

represents the kronecker product; a. the_rWith a representation dimension of N_r×N_rA receiving dictionary matrix composed of the receiving array surface response vectors; h [ k ]]Denotes the dimension N on the k sub-carrier_r×N_tVec (H [ k ]) of]) Representation matrix H [ k ]]Vectorization of (2);

wherein A is_tExpressed by the following formula:

wherein,

with a representation dimension of N_tX 1 of the transmitted wavefront response vector, where

Wherein N is_tP × Q, P denotes the number of antennas on the horizontal axis of the transmitting antenna array, and Q denotes the number of antennas on the vertical axis of the transmitting antenna array;

A_rexpressed by the following formula:

wherein,

with a representation dimension of N_rX 1, where,

wherein N is_rI denotes the number of antennas on the horizontal axis of the reception antenna array, and J denotes the number of antennas on the vertical axis of the reception antenna array.

4. The deep learning network-based millimeter wave sparse front channel estimation method according to claim 3, wherein the channel estimation value in step five is

Calculated according to the following formula:

wherein (C)^HA conjugate transpose operation representing a matrix; ()^-1Representing the inversion operation of the matrix.

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