CN110099016B - Millimeter wave sparse array surface channel estimation method based on deep learning network - Google Patents

Millimeter wave sparse array surface channel estimation method based on deep learning network Download PDF

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CN110099016B
CN110099016B CN201910397076.5A CN201910397076A CN110099016B CN 110099016 B CN110099016 B CN 110099016B CN 201910397076 A CN201910397076 A CN 201910397076A CN 110099016 B CN110099016 B CN 110099016B
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许威
张雯惠
徐锦丹
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Southeast University
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    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0254—Channel estimation channel estimation algorithms using neural network algorithms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2626—Arrangements specific to the transmitter only
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Abstract

The invention discloses a millimeter wave sparse array surface channel estimation method based on a deep learning network. Firstly, a fully-connected phase shifter network is adopted, and an isotropic analog transceiver is designed by configuring the phase uniform distribution of each phase shifter; and then using the obtained channel sparse information and the designed optimal digital estimator as training data of the fully-connected deep learning network. And for the sparse channel under each signal-to-noise ratio, inputting the sparse information of the channel into a network to obtain a corresponding digital estimator so as to obtain a 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 realized by using a deep learning network, so that the channel estimation complexity is reduced.

Description

Millimeter wave sparse array surface channel estimation method based on deep learning network
Technical Field
The invention relates to the field of communication, in particular to a millimeter wave sparse array surface channel estimation method based on a deep learning network.
Background
In recent years, communication technology has been developed in a breakthrough manner and is becoming mature, and the mobile communication industry has been developed rapidly on a global scale. The Multiple Input Multiple Output (MIMO) technology is one of the key technologies for the development of communication technology, and improves the data transmission rate of the system. A plurality of antennas are arranged at a transmitting end and a receiving end of the system, and diversity is formed by the antennas at the transmitting end and the receiving end, so that the stability of the system can be improved. Meanwhile, the number of independent channels between the antennas at the transmitting end and the receiving end is greatly increased, so that the data volume transmitted by the system in unit time is improved, and the spectrum utilization efficiency of the system is improved.
Compared with the MIMO technology, the Massive MIMO technology has the advantages that the transmission rate, the energy efficiency, the transmission reliability and the like are greatly improved, the millimeter wave Massive MIMO technology greatly reduces the configuration difficulty of a Massive antenna array surface, and the Massive MIMO technology solves the problem that millimeter wave signals are high in loss and easy to block. In order to reduce power consumption and hardware complexity in the millimeter wave massive MIMO system, a digital-analog hybrid architecture of a small number of radio frequency links may be used.
In order to perform high performance transmission, channel estimation needs to be performed first. Channel estimation of a conventional large-scale multi-antenna technology system is a big challenge in itself, and the use of a low-precision analog-to-digital converter in a hybrid architecture makes channel estimation more difficult while reducing cost and power consumption. Meanwhile, it is also a challenge how to reduce the estimation complexity and pilot overhead while utilizing the sparsity of the millimeter wave channel, and obtain high-precision channel estimation.
Disclosure of Invention
In order to solve the problems, the invention provides a sparse channel estimation method which is used for a low-precision analog-to-digital converter and a broadband mmWave large-scale multi-antenna technology system with a hybrid framework. And training the designed full-connection deep neural network by taking the sparse characteristic of the millimeter wave channel as prior information and taking the selection matrix of the sparse channel and a digital estimator corresponding to the selection matrix as input to obtain the deep neural network suitable for different signal-to-noise ratios, and the deep neural network is used for estimating the communication channel of the millimeter wave array. Firstly, a fully-connected phase shifter network is adopted, and an isotropic analog transceiver is designed by configuring the phase uniform distribution of each phase shifter; and then, the obtained channel sparse information is used as priori knowledge, an optimal digital estimator is designed, and the channel sparse information and the optimal digital estimator are used as training data of the fully-connected deep learning network. For the sparse channel under each signal-to-noise ratio, inputting the sparse information of the channel into the network, and obtaining a corresponding digital estimator so as to obtain a 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 realized by using a deep learning network, so that the channel estimation complexity is reduced. In a mixed-frame multi-antenna system adopting a low-precision analog-to-digital converter, the performance of the method can approach the theoretically optimal channel estimation method.
In order to achieve the purpose, the invention provides the following technical scheme:
a millimeter wave sparse array surface channel estimation method based on a deep learning network comprises the following steps:
a transmitting end sends a pilot signal, a simulation precoder consisting of fully-connected phase shifters reaches a receiver through a channel, and a receiving end obtains channel estimation by using a simulation estimator, a low-precision analog-to-digital converter quantizer and a deep learning network;
the method is characterized in that: the channel estimation method based on the hardware architecture comprises the following steps:
the method comprises the following steps: the base station designs simulation pre-coding and sends pilot signals, the simulation pre-coding FAmDesigned according to the following formula:
Figure GDA0003296279380000021
wherein, the [ alpha ], [ beta ] -a]ijElements representing the ith row and the jth column of the matrix; fAmThe representation dimension is Nt×NRFtAnalog precoding matrix of, NtRepresenting the number of transmitting antennas, NRFtRepresenting the number of radio frequency links of a transmitting end;
Figure GDA0003296279380000022
representing the phase of the ith row and jth column element of the analog precoding matrix;
step two: receiving end optimization design simulation estimator WAm,WAmCalculated according to the following formula:
Figure GDA0003296279380000023
wherein, WAmWith a representation dimension of Nr×NRFrAnalog estimation matrix of, NrRepresenting the number of receiving antennas, NRFrRepresenting the number of radio frequency links of a receiving end;
Figure GDA0003296279380000024
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, namely the position of a non-zero element in a sparse channel matrix, through a compressed sensing technology, such as a classical Orthogonal Matching Pursuit (OMP) technology, 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 endv[k]Is stored and a selection matrix P is selected according to eachv[k]Designing corresponding digital estimation matrix
Figure GDA0003296279380000025
Step five: selecting the matrix Pv[k]And a digital estimation matrix corresponding thereto
Figure GDA0003296279380000026
And as a training set of the fully-connected neural network, obtaining the fully-connected feedforward network suitable for each signal-to-noise ratio through neural network training. Within the coherent time, the receiving end selects the matrix P according to the sparse channelv[k]Obtaining a digital estimation matrix of the network output using the network structure
Figure GDA0003296279380000027
Detecting the received signal by using the data estimation matrix to obtain a channel estimation value
Figure GDA0003296279380000031
Further, the matrix P is selected in the fourth stepv[k]Expressed by the following formula:
Figure GDA00032962793800000311
wherein e isπ(i)(π(i)∈{1,2,…,NrNt}) represents a dimension of NrNtThe pi (i) -th element of x 1 is a vector of 1 and the remaining elements are 0. N is a radical ofvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[k]Number of non-zero elements in (1).
For non-zero channel elements in the channel matrix, the selection matrix P of the channelv[k]Has N possible forms, for all possible sets Pv1[k],Pv2[k],…,PvN[k]Each Pvi[k]The possibility of occurrence of (i ═ 1, …, N) is all
Figure GDA0003296279380000032
Namely, it is
Figure GDA0003296279380000033
Wherein N is the total number of the possible numbers,
Figure GDA0003296279380000034
c represents a combination number formula. N is a radical ofvRepresents that the dimension on the k sub-carrier is NrNtVector component h of x 1 channel vector projected onto angular domainv[k]Number of medium non-zero elements.
Further, projecting the channel to the virtual angle domain to obtain a channel vector component hv[k]，hv[k]Calculated according to the following formula:
Figure GDA0003296279380000035
wherein A istThe representation dimension is Nt×NtA transmit dictionary matrix composed of transmit front response vectors,
Figure GDA0003296279380000036
representation matrix AtConjugation of (2);
Figure GDA0003296279380000037
represents the kronecker product; a. therWith a representation dimension of Nr×NrA receiving dictionary matrix composed of the receiving array surface response vectors; h [ k ]]Denotes the dimension N on the k sub-carrierr×NtVec (H [ k ]) of]) Representation matrix H [ k ]]Vectorization of (2).
Wherein A istExpressed by the following formula:
Figure GDA0003296279380000038
wherein the content of the first and second substances,
Figure GDA0003296279380000039
with a representation dimension of NtX 1 of the transmitted wavefront response vector, where
Figure GDA00032962793800000310
Wherein N istP × 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;
Arexpressed by the following formula:
Figure GDA0003296279380000041
wherein the content of the first and second substances,
Figure GDA0003296279380000042
with a representation dimension of NrX 1, where,
Figure GDA0003296279380000043
wherein N isrI denotes the number of antennas on the horizontal axis of the receiving antenna array, and J denotes the number of antennas on the vertical axis of the receiving antenna arrayThe number of lines;
further, the optimal number estimation matrix in the fourth step
Figure GDA0003296279380000044
Using the channel estimation minimum mean square error criterion,
Figure GDA0003296279380000045
it can be calculated as follows:
Figure GDA0003296279380000046
wherein K ∈ {1,2, …, K } denotes the kth subcarrier, K denotes the total number of subcarriers;
Figure GDA0003296279380000047
representing N on the k sub-carrierRFr×NvM represents the number of channel uses, i.e., the number of channel estimates, within the coherence time. EtabRepresents 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 MNRFr×NvThe measurement matrix of (2); omegaH[k]Represents the matrix omega k]The conjugate transpose of (1);
Figure GDA0003296279380000048
represents the large scale fading coefficient of the channel;
Figure GDA0003296279380000049
with a representation dimension of Nv×NvThe identity matrix of (1);
Figure GDA00032962793800000410
representing the variance of each element of the equivalent noise vector,
Figure GDA00032962793800000411
represents an Additive White Gaussian Noise (AWGN) variance; p denotes a transmit pilot power.
Further, the channel estimation times M are expressed by the following formula:
Figure GDA00032962793800000412
Figure GDA00032962793800000413
indicating rounding up.
The measurement matrix Ω [ k ] is represented by the following formula:
Ω[k]＝Φ[k]ΨPv[k],
wherein the dimension is NRFr×NrNtPilot correlation matrix of
Figure GDA00032962793800000414
sm[k](M ∈ {1,2, …, M }) denotes the dimension N at the mth trainingRFrX 1 transmit pilot vector.
Where Ψ represents the dimension NrNt×NrNtThe spatial transformation matrix, Ψ, is represented by the following equation:
Figure GDA00032962793800000415
wherein A istWith a representation dimension of Nt×NtA transmit dictionary matrix composed of transmit array surface response vectors, ArThe representation dimension is Nr×NrA receive dictionary matrix composed of receive front response vectors.
Wherein, Pv[k]With a representation dimension of NrNt×NvThe selection matrix of (2).
Further, in step five
Figure GDA0003296279380000051
The method is obtained through a full-connection deep learning network with forward feedback according to the following steps:
(1) for a known number of non-zero elements NvOf the sparse channel, the channel matrix H [ k ]]Denotes the dimension N on the k sub-carrierr×NtUnder each signal-to-noise ratio, the receiving end calculates all possible P according to the sparse characteristic informationv[k]Formed covariance matrix C k]＝ΩH[k]Ω[k]Wherein Ω [ k ]]＝Φ[k]ΨPv[k]. At the same time, calculate with each Pv[k]Formed covariance matrix C k]Corresponding to
Figure GDA0003296279380000052
Designing a new numerical estimation matrix
Figure GDA0003296279380000053
And will all possible C k]And corresponding
Figure GDA0003296279380000054
Stored in a database.
(2) Data are extracted from the database and divided into two groups, namely training data and testing data. Carrying out complex value splitting operation on the training data, and carrying out a training set C [ k ]]And WD′[k]Split into a real part matrix CR[k]、
Figure GDA0003296279380000055
And an imaginary matrix CI[k]、
Figure GDA0003296279380000056
Two parts.
(3) Then C is addedR[k]、
Figure GDA0003296279380000057
And CI[k]、
Figure GDA0003296279380000058
Performing matrix vectorization operation to obtain dimension Nv 2X 1 column vector cR[k]、
Figure GDA0003296279380000059
And cI[k]、
Figure GDA00032962793800000510
C is toR[k]、
Figure GDA00032962793800000511
As input and training targets of the real part deep learning network, cI[k]、
Figure GDA00032962793800000512
As input to the imaginary deep learning network and as a training target.
(4) Two deep learning fully-connected networks are constructed, and the network structures are the same. All are two layers of forward feedback fully-connected neural networks, the number of neurons in the first layer is N, wherein
Figure GDA00032962793800000513
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; the first layer output is connected to the second layer neurons, the number of neurons is N, and the bias (bias) connection is also set at the second layer.
The softmax function is defined as follows:
Figure 1
wherein, the output of each layer of fully-connected network is as follows:
Figure GDA00032962793800000515
wherein W and b represent parameters of a fully-connected neural network, yiAnd biThe i-th element, x, representing y and bjDenotes the j-th element of x, Wi,jRepresents an element with position (i, j) in W.
(5) The fully-connected neural network is trained, and the deep learning network is tested by taking complex value splitting and matrix vectorization of test data as input, so that a stable network structure under each signal-to-noise ratio is obtained.
(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
Figure GDA0003296279380000061
Further, the channel estimation value in step five
Figure GDA0003296279380000062
Obtained according to the following formula:
Figure GDA0003296279380000063
wherein (C)HA conjugate transpose operation representing a matrix; ()-1Representing the inversion operation of the matrix.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1) for the broadband channel estimation, OFDM modulation is adopted in the invention, so that frequency domain channel estimation is carried out on each narrowband subcarrier, the invention takes the millimeter wave channel sparse characteristic as prior information, and takes a selection matrix of a sparse channel and a digital estimator corresponding to the selection matrix as input to train a designed full-connection deep neural network, so as to obtain the deep neural network suitable for different signal-to-noise ratios and used for millimeter wave array surface communication channel estimation; 2) the scheme adopts a fully-connected phase shifter network, and designs an isotropic analog transceiver by configuring the phase uniform distribution of each phase shifter; and designing an optimal digital estimator by taking the obtained channel sparse characteristic information as prior knowledge, and taking the optimal digital estimator and the channel sparse characteristic information as training data of the fully-connected deep learning network. For the sparse channel under each signal-to-noise ratio, inputting the sparse information of the channel into a network, and obtaining a corresponding digital estimator so as to obtain a channel estimation result; 3) 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 realized by using a deep learning network, so that the channel estimation complexity is reduced. In a mixed-frame multi-antenna system adopting a low-precision analog-to-digital converter, the performance of the method can approach the theoretically optimal channel estimation method.
Drawings
FIG. 1 is a block diagram of the system of the present invention;
fig. 2 is a graph of Normalized Mean Square Error (NMSE) of channel estimation as a function of signal-to-noise ratio (SNR) for an 8 x 4 millimeter wave antenna array, quantized by a 4-bit analog-to-digital converter at the receiving end;
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention.
The invention provides a millimeter wave sparse array surface channel estimation method based on a deep learning network, which is characterized in that millimeter wave channel sparse characteristics are used as prior information, a selection matrix of a sparse channel and a corresponding digital estimator are used as input to train a designed full-connection deep neural network, and the deep neural network suitable for different signal-to-noise ratios is obtained and used for millimeter wave array surface communication channel estimation.
Firstly, a fully-connected phase shifter network is adopted, and an isotropic analog transceiver is designed by configuring the phase uniform distribution of each phase shifter; and then, the obtained channel sparse information is used as priori knowledge, an optimal digital estimator is designed, and the channel sparse information and the optimal digital estimator are used as training data of the fully-connected deep learning network. For the sparse channel under each signal-to-noise ratio, inputting the sparse information of the channel into the network, and obtaining a corresponding digital estimator so as to obtain a channel estimation result. The sparse channel estimator provided by the invention can reduce the error caused by the nonlinear quantization of a low-precision analog-to-digital converter (ADC), and is realized by using a deep learning network, so that the channel estimation complexity is reduced. In a mixed-frame multi-antenna system adopting a low-precision analog-to-digital converter, the performance of the method can approach the theoretically optimal channel estimation method.
As shown in fig. 1, under each signal-to-noise ratio, channel prior sparse information is obtained through a compressed sensing technology, and an optimal digital estimator under a corresponding minimum mean square error is designed according to all possible sparse channels and is used as a training input of a deep learning full-connection network. Through training and testing the deep learning network, the network which can be used under each signal-to-noise ratio is obtained and used for channel estimation. In a hybrid architecture, a transmitting end sends a pilot signal, an analog precoder consisting of fully-connected phase shifters reaches a receiver through a channel, and sparse information of the channel is input into a network for sparse channels under various signal-to-noise ratios through an analog estimator and a low-precision analog-to-digital converter quantizer, so that a corresponding digital estimator can be obtained, and a channel estimation result is obtained. 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 realized by using a deep learning network, so that the channel estimation complexity is reduced. In a mixed-frame multi-antenna system adopting a low-precision analog-to-digital converter, the performance of the method can approach the theoretically optimal channel estimation method.
The channel estimation method provided by the invention comprises the following steps:
the method comprises the following steps: base station design simulation pre-coding and sending pilot signal, simulation pre-coding FAmDesigned according to the following formula:
Figure GDA0003296279380000071
wherein [ 2 ], [ 2 ]]ijElements representing the ith row and the jth column of the matrix; fAmWith a representation dimension of Nt×NRFtAnalog precoding matrix of, NtRepresenting the number of transmitting antennas, NRFtRepresenting the number of radio frequency links of a transmitting end;
Figure GDA0003296279380000072
representing the phase of the ith row and jth column element of the analog precoding matrix;
step two: receiving end optimization design simulation estimator WAm,WAmCalculated according to the following formula:
Figure GDA0003296279380000073
wherein, WAmWith a representation dimension of Nr×NRFrAnalog estimation matrix of, NrRepresenting the number of receiving antennas, NRFrRepresenting the number of radio frequency links of a receiving end;
Figure GDA0003296279380000074
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, namely the position of a non-zero element in a sparse channel matrix, through a compressed sensing technology, such as a classical Orthogonal Matching Pursuit (OMP) technology, 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 endv[k]Is stored and a selection matrix P is selected according to eachv[k]Designing corresponding digital estimation matrix
Figure GDA0003296279380000081
Step five: selecting the matrix Pv[k]And a digital estimation matrix corresponding thereto
Figure GDA0003296279380000082
And as a training set of the fully-connected neural network, obtaining the fully-connected feedforward network suitable for each signal-to-noise ratio through neural network training. Within the coherent time, the receiving end selects the matrix P according to the corresponding selection matrix of the sparse channelv[k]Obtaining a digital estimation matrix of the network output using the network structure
Figure GDA0003296279380000083
Detecting the received signal by using the data estimation matrix to obtain a channel estimation value
Figure GDA0003296279380000084
Further, the matrix P is selected in the fourth stepv[k]Expressed by the following formula:
Figure GDA00032962793800000811
wherein e isπ(i)(π(i)∈{1,2,…,NrNt}) represents a dimension of NrNtThe pi (i) -th element of x 1 is a vector of 1 and the remaining elements are 0. N is a radical ofvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[k]Number of medium non-zero elements.
For non-zero channel elements in the channel matrix, the selection matrix P of the channelv[k]Has N possible forms, for all possible sets Pv1[k],Pv2[k],…,PvN[k]Each Pvi[k]The possibility of occurrence of (i ═ 1, …, N) is all
Figure GDA0003296279380000085
Namely, it is
Figure GDA0003296279380000086
Wherein N is the total number of the possible numbers,
Figure GDA0003296279380000087
c represents a combination number formula. N is a radical ofvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[k]Number of medium non-zero elements.
Further, projecting the channel to the virtual angle domain to obtain a channel vector component hv[k]，hv[k]Calculated according to the following formula:
Figure GDA0003296279380000088
wherein A istThe representation dimension is Nt×NtA transmit dictionary matrix composed of transmit front response vectors,
Figure GDA0003296279380000089
representation matrix AtConjugation of (1);
Figure GDA00032962793800000810
represents the kronecker product; a. therThe representation dimension is Nr×NrA receiving dictionary matrix composed of receiving array surface response vectors; h [ k ]]Denotes the dimension N on the k sub-carrierr×NtVec (H [ k ]) of]) Representation matrix H [ k ]]Vectorization of (2).
Wherein A istExpressed by the following formula:
Figure GDA0003296279380000091
wherein the content of the first and second substances,
Figure GDA0003296279380000092
(p∈{1,2,…,Nt}) represents a dimension of NtX 1 of the transmitted wavefront response vector, where
Figure GDA0003296279380000093
Wherein N istP 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.
ArExpressed by the following formula:
Figure GDA0003296279380000094
wherein the content of the first and second substances,
Figure GDA0003296279380000095
(q∈{1,2,…,Nrdenotes the dimension NrX 1 of received wavefront response vector, wherein，
Figure GDA0003296279380000096
Wherein N isrI 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.
Further, the optimal number estimation matrix in the fourth step
Figure GDA0003296279380000097
Using the channel estimation minimum mean square error criterion,
Figure GDA0003296279380000098
it can be calculated as follows:
Figure GDA0003296279380000099
wherein K ∈ {1,2, …, K } denotes the kth subcarrier, K denotes the total number of subcarriers;
Figure GDA00032962793800000910
representing N on the k sub-carrierRFr×NvM represents the number of channel uses within the coherence time, i.e., the number of channel estimates. EtabRepresents 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 MNRFr×NvThe measurement matrix of (2); omegaH[k]Represents the matrix omega k]The conjugate transpose of (1);
Figure GDA00032962793800000911
represents the large scale fading coefficient of the channel;
Figure GDA00032962793800000912
with a representation dimension of Nv×NvThe identity matrix of (1);
Figure GDA00032962793800000913
representing the variance of each element of the equivalent noise vector,
Figure GDA00032962793800000914
represents an Additive White Gaussian Noise (AWGN) variance; p denotes a transmit pilot power.
Further, the channel estimation times M is expressed by the following formula:
Figure GDA00032962793800000915
Figure GDA00032962793800000916
indicating rounding up.
The measurement matrix Ω [ k ] is represented by the following formula:
Ω[k]＝Φ[k]ΨPv[k],
wherein the dimension is NRFr×NrNtPilot correlation matrix of
Figure GDA0003296279380000101
sm[k](M ∈ {1,2, …, M }) denotes the dimension N at the mth trainingRFrX 1 transmit pilot vector.
Where Ψ represents the dimension NrNt×NrNtThe spatial transformation matrix, Ψ, is represented by the following equation:
Figure GDA0003296279380000102
wherein A istWith a representation dimension of Nt×NtA transmit dictionary matrix composed of transmit array surface response vectors, ArWith a representation dimension of Nr×NrA receive dictionary matrix composed of receive front response vectors.
Wherein, Pv[k]With a representation dimension of NrNt×NvThe selection matrix of (2).
Further, in step five
Figure GDA0003296279380000103
The method is obtained through a full-connection deep learning network with forward feedback according to the following steps:
(1) for a known number of non-zero elements NvOf the sparse channel, the channel matrix H [ k ]]Denotes the dimension N on the k sub-carrierr×NtUnder each signal-to-noise ratio, the receiving end calculates all possible P according to the sparse characteristic informationv[k]Formed covariance matrix C k]＝ΩH[k]Ω[k]Wherein Ω [ k ]]＝Φ[k]ΨPv[k]. At the same time, calculate with each Pv[k]Formed covariance matrix C k]Corresponding to
Figure GDA0003296279380000104
Designing a new numerical estimation matrix
Figure GDA0003296279380000105
And will all possible C [ k ]]And corresponding
Figure GDA0003296279380000106
Stored in a database.
(2) Data are extracted from a database and divided into two groups, namely training data and testing data. Carrying out complex value splitting operation on the training data, and carrying out training set C [ k ]]And WD′[k]Split into a real matrix CR[k]、
Figure GDA0003296279380000107
And an imaginary matrix CI[k]、
Figure GDA0003296279380000108
Two parts.
(3) Then C is addedR[k]、
Figure GDA0003296279380000109
And CI[k]、
Figure GDA00032962793800001010
Performing matrix vectorization operation to obtain dimension Nv 2X 1 column vector cR[k]、
Figure GDA00032962793800001011
And cI[k]、
Figure GDA00032962793800001012
C is toR[k]、
Figure GDA00032962793800001013
As input and training targets of the real part deep learning network, cI[k]、
Figure GDA00032962793800001014
As input to the imaginary deep learning network and as a training target.
(4) Two deep learning fully-connected networks are constructed, and the network structures are the same. The neural networks are all two layers of forward feedback full-connection neural networks, the number of neurons in the first layer is N, wherein
Figure GDA00032962793800001015
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; the first layer output is connected to the second layer neurons, the number of neurons is N, and the bias (bias) connection is also set at the second layer.
The softmax function is defined as follows:
Figure 2
wherein, the output of each layer of fully-connected network is as follows:
Figure GDA0003296279380000112
wherein W and b represent parameters of a fully-connected neural network, yiAnd biThe i-th element, x, representing y and bjDenotes the j-th element of x, Wi,jRepresents the position of the middle position of W(i, j) elements.
(5) The fully-connected neural network is trained, and the deep learning network is tested by taking complex value splitting and matrix vectorization of test data as input, so that a stable network structure under each signal-to-noise ratio is obtained.
(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
Figure GDA0003296279380000113
Further, the channel estimation value in step five
Figure GDA0003296279380000114
Obtained according to the following formula:
Figure GDA0003296279380000115
wherein (C)HA conjugate transpose operation representing a matrix; ()-1Representing the inversion operation of the matrix.
As shown in fig. 2, under sparse channel, the channel estimation method proposed by the present invention is extremely close to the theoretically optimal Minimum Mean Square Error (MMSE) estimator, especially under low signal-to-noise ratio (SNR). Under a sparse channel, the invention provides the deep learning network, so that the precision of channel estimation is further improved and the complexity is reduced.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and such improvements and modifications are also considered to be within the 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 FAmDesigned according to the following formula:
Figure FDA0003581383380000011
wherein, the [ alpha ], [ beta ] -a]ijElements representing the ith row and the jth column of the matrix; fAmWith a representation dimension of Nt×NRFtAnalog precoding matrix of, NtRepresenting the number of transmitting antennas, NRFtRepresenting the number of radio frequency links of a transmitting end;
Figure FDA0003581383380000012
representing the phase of the ith row and jth column element of the analog precoding matrix;
step two: receiving end optimization design simulation estimator WAm,WAmCalculated according to the following formula:
Figure FDA0003581383380000013
wherein, WAmWith a representation dimension of Nr×NRFrAnalog estimation matrix of, NrRepresenting the number of receiving antennas, NRFrRepresenting the number of radio frequency links of a receiving end;
Figure FDA00035813833800000111
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 endv[k]Is collected intoStoring the rows and selecting a matrix P according to eachv[k]Designing corresponding digital estimation matrix
Figure FDA0003581383380000014
Step five: selecting the matrix Pv[k]And a digital estimation matrix corresponding thereto
Figure FDA0003581383380000015
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 channelv[k]Obtaining a digital estimation matrix of the network output using the network structure
Figure FDA0003581383380000016
Detecting the received signal by using the data estimation matrix to obtain a channel estimation value
Figure FDA0003581383380000017
The step four middle digital estimation matrix
Figure FDA0003581383380000018
Using the channel estimation minimum mean square error criterion,
Figure FDA0003581383380000019
calculated according to the following formula:
Figure FDA00035813833800000110
wherein K ∈ {1,2, …, K } denotes the kth subcarrier, K denotes the total number of subcarriers;
Figure FDA0003581383380000021
representing the kth subcarrierN on waveRFr×NvM represents the number of channel uses within the coherence time, i.e., the number of channel estimates; etabRepresents 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 MNRFr×NvThe measurement matrix of (2); omegaH[k]Represents the matrix omega k]The conjugate transpose of (1);
Figure FDA0003581383380000022
represents the large scale fading coefficient of the channel;
Figure FDA0003581383380000023
with a representation dimension of Nv×NvThe identity matrix of (1);
Figure FDA0003581383380000024
representing the variance of each element of the equivalent noise vector,
Figure FDA0003581383380000025
represents an Additive White Gaussian Noise (AWGN) variance; p represents the transmit pilot power;
in step five
Figure FDA0003581383380000026
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 NvOf the sparse channel, the channel matrix H [ k ]]Denotes the dimension N on the k sub-carrierr×NtUnder each signal-to-noise ratio, the receiving end calculates all possible P according to the sparse characteristic informationv[k]Formed covariance matrix C k]＝ΩH[k]Ω[k]Wherein Ω [ k ]]＝Φ[k]ΨPv[k]，
The channel estimation times M are expressed by the following formula:
Figure FDA0003581383380000027
Figure FDA0003581383380000028
represents rounding up;
the measurement matrix Ω [ k ] is represented by the following formula:
Ω[k]＝Φ[k]ΨPv[k],
wherein the dimension is NRFr×NrNtPilot correlation matrix of
Figure FDA0003581383380000029
sm[k](M e {1,2, …, M }) represents that the dimension at the mth training time is NRFrA transmit pilot vector of x 1,
where Ψ represents the dimension NrNt×NrNtThe spatial transformation matrix, Ψ, is represented by the following equation:
Figure FDA00035813833800000210
wherein A istWith a representation dimension of Nt×NtA transmit dictionary matrix composed of transmit array surface response vectors, ArWith a representation dimension of Nr×NrA receiving dictionary matrix composed of the receiving array surface response vectors;
wherein, Pv[k]With a representation dimension of NrNt×NvThe selection matrix of (2);
at the same time, calculate with each Pv[k]Formed covariance matrix C k]Corresponding to
Figure FDA0003581383380000031
Designing a new numerical estimation matrix
Figure FDA0003581383380000032
And will all possible C [ k ]]And corresponding
Figure FDA0003581383380000033
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 CR[k]、
Figure FDA0003581383380000034
And an imaginary matrix CI[k]、
Figure FDA0003581383380000035
Two parts;
(3) then C is addedR[k]、
Figure FDA0003581383380000036
And CI[k]、
Figure FDA0003581383380000037
Performing matrix vectorization operation to obtain dimension Nv 2X 1 column vector cR[k]、
Figure FDA0003581383380000038
And cI[k]、
Figure FDA0003581383380000039
C is toR[k]、
Figure FDA00035813833800000310
As an input and training target of the real part deep learning network, cI[k]、
Figure FDA00035813833800000311
As input and training targets for the imaginary deep learning network; n is a radical ofvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[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
Figure FDA00035813833800000312
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:
Figure FDA00035813833800000313
wherein, the output of each layer of fully-connected network is as follows:
Figure FDA00035813833800000314
wherein W and b represent parameters of a fully-connected neural network, yiAnd biI-th element, x, representing y and bjDenotes the jth element of x, Wi,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
Figure FDA0003581383380000041
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 usedv[k]Expressed by the following formula:
Figure FDA0003581383380000042
wherein e isπ(i)(π(i)∈{1,2,…,NrNt}) represents a dimension of NrNtX 1. pi (i) th vector with 1 element and 0 elements, NvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[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 channelv[k]Has N possible forms, for all possible sets Pv1[k],Pv2[k],…,PvN[k]Each Pvi[k]The possibility of occurrence of (i ═ 1, …, N) is all
Figure FDA0003581383380000043
Namely, it is
Figure FDA0003581383380000044
Wherein N is the total number of the possible numbers,
Figure FDA0003581383380000045
c represents a combination number formula, NvRepresenting a dimension of N on the k-th subcarrierrNtVector component h of x 1 channel vector projected onto angular domainv[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 hv[k]，hv[k]Calculated according to the following formula:
Figure FDA0003581383380000046
wherein A istWith a representation dimension of Nt×NtA transmit dictionary matrix composed of transmit front response vectors,
Figure FDA0003581383380000047
representation matrix AtConjugation of (2);
Figure FDA0003581383380000048
represents the kronecker product; a. therWith a representation dimension of Nr×NrA receiving dictionary matrix composed of the receiving array surface response vectors; h [ k ]]Denotes the dimension N on the k sub-carrierr×NtVec (H [ k ]) of]) Representation matrix H [ k ]]Vectorization of (2);
wherein A istExpressed by the following formula:
Figure FDA0003581383380000049
Figure FDA0003581383380000051
wherein the content of the first and second substances,
Figure FDA0003581383380000052
with a representation dimension of NtX 1 of the transmitted wavefront response vector, where
Figure FDA0003581383380000053
Wherein N istP × 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;
Arexpressed by the following formula:
Figure FDA0003581383380000054
wherein the content of the first and second substances,
Figure FDA0003581383380000055
with a representation dimension of NrX 1, where,
Figure FDA0003581383380000056
wherein N isrI 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
Figure FDA0003581383380000057
Calculated according to the following formula:
Figure FDA0003581383380000058
wherein (C)HA conjugate transpose operation representing a matrix; ()-1Representing the inversion operation of the matrix.
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