CN113676431A - Model-driven MIMO-OFDM receiving method without cyclic prefix - Google Patents

Model-driven MIMO-OFDM receiving method without cyclic prefix Download PDF

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CN113676431A
CN113676431A CN202110771439.4A CN202110771439A CN113676431A CN 113676431 A CN113676431 A CN 113676431A CN 202110771439 A CN202110771439 A CN 202110771439A CN 113676431 A CN113676431 A CN 113676431A
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金石
周星宇
张静
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Abstract

The invention discloses a model-driven MIMO-OFDM receiving method without cyclic prefix. First, the received symbol vector is eliminated
Figure DDA0003153630780000011
Calculating a channel matrix C at the same time of the inter-symbol interference of the medium redundancy, and converting the channel matrix C into a real number domain; then, the real-valued received symbol vector is processed
Figure DDA0003153630780000012
And a real-valued channel matrix
Figure DDA0003153630780000013
Inputting the signal into a signal detection network developed by an orthogonal approximate message transfer algorithm improved by conjugate gradient, and outputting an estimated frequency domain symbol vector through a plurality of series layers
Figure DDA0003153630780000014
Finally, the frequency domain symbol vector is processed
Figure DDA0003153630780000015
Demodulating to obtain an estimated transmitted bit stream
Figure DDA0003153630780000016
After buffering, the symbol vector is sent to a feedback loop, and the estimated time domain symbol vector is obtained by operation in the feedback loop
Figure DDA0003153630780000017
For canceling intersymbol interference in the next round of reception. The invention has the advantages of excellent detection performance and short operation time, and simultaneously, the frequency spectrum efficiency of the system is obviously improved.

Description

Model-driven MIMO-OFDM receiving method without cyclic prefix
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a model-driven MIMO-OFDM receiving method without cyclic prefix.
Background
As an important branch of artificial intelligence technology, deep learning has been applied to improve physical layer transmission performance in recent years. In this application, the construction of neural network models presents two paradigms, data-driven and model-driven. The data-driven neural network treats the wireless communication system as a black box, and end-to-end training is completed by means of a large amount of labeled data. The model driven neural network does not change the model structure of the wireless communication system, and the network topology is constructed based on the domain knowledge acquired in the deep research of the wireless communication field for decades, so that the computing resources and time required by training are obviously reduced, and the neural network has environmental adaptivity and generalization, so that the system performance level is improved with more potential.
The MIMO-OFDM has high spectrum efficiency and strong frequency selective fading resistance, and is a technology with the greatest prospect for improving the throughput of a wireless link. However, there is a redundant cyclic prefix in the conventional MIMO-OFDM system, which limits the spectral efficiency of the system. On the other hand, the MIMO-OFDM system without cyclic prefix suffers from severe inter-carrier interference and inter-symbol interference, and the signal detection performance is seriously deteriorated. How to design a cyclic prefix-free MIMO-OFDM receiving method with low complexity and excellent performance by utilizing a model-driven neural network is a problem which needs to be solved urgently at present.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a model-driven MIMO-OFDM receiving method without cyclic prefix, aiming at overcoming the interference caused by the lack of the cyclic prefix by utilizing a model-driven neural network, improving the receiving performance, and introducing a conjugate gradient algorithm to reduce the computational complexity and reduce the running time.
The technical scheme is as follows: the technical scheme adopted by the invention specifically comprises the following steps:
(1) transmitting time domain symbol vectors based on the estimated symbol time
Figure BDA0003153630760000011
Cancelling a received symbol vector
Figure BDA0003153630760000012
Inter-symbol interference of medium redundancy to obtain symbol vector
Figure BDA0003153630760000013
Calculating a channel matrix C by using the channel state information; then vector the symbols to
Figure BDA0003153630760000014
Converting the sum channel matrix C into a real number domain equivalently to obtain a real value receiving symbol vector
Figure BDA0003153630760000015
And a real-valued channel matrix
Figure BDA0003153630760000016
(2) Receiving a real-valued symbol vector
Figure BDA0003153630760000017
And a real-valued channel matrix
Figure BDA0003153630760000018
Inputting the symbol vector into a signal detection network, expanding the network by an orthogonal approximate message transfer algorithm with improved conjugate gradient, and finally outputting an estimated frequency domain symbol vector
Figure BDA0003153630760000019
(3) Symbol vector of frequency domain to be estimated
Figure BDA0003153630760000021
Demodulating to obtain an estimated transmitted bit stream
Figure BDA0003153630760000022
Bit stream
Figure BDA0003153630760000023
Storing the bit stream in a buffer to obtain a delayed bit stream
Figure BDA0003153630760000024
After modulation and inverse Fourier transform, estimates of symbol vectors of a transmission frequency domain and a transmission time domain are obtained in sequence
Figure BDA0003153630760000025
And
Figure BDA0003153630760000026
for the next round of receiving process.
Further, the step (1) specifically comprises:
(1.1) canceling the received symbol vector according to
Figure BDA0003153630760000027
To obtain a symbol vector
Figure BDA0003153630760000028
Figure BDA0003153630760000029
In the formula (I), the compound is shown in the specification,
Figure BDA00031536307600000210
for the transmitted time-domain symbol vector estimated in the last symbol time, A-1Truncating the channel matrix for the blocks in the last symbol time, wherein the expression is as follows:
Figure BDA00031536307600000211
Ncis the number of OFDM subcarriers, NtFor the number of transmitting antennas, NrFor the number of receive antennas, L is the time domain channel length, 0 is the all-zero matrix, h-1,lL ∈ { 0.,.., L-1} is a MIMO channel matrix formed by the L-th path between the transmitting and receiving antenna arrays in the last symbol time, and the expression is:
Figure BDA00031536307600000212
wherein the content of the first and second substances,
Figure BDA00031536307600000213
is the time domain multipath channel between the p-th transmitting antenna and the q-th receiving antenna in the last symbol time;
(1.2) calculating a channel matrix C according to the channel state information, as follows:
Figure BDA00031536307600000214
wherein H is a block cyclic channel matrix in the current symbol time, A is a block truncation channel matrix in the current symbol time, and the matrix
Figure BDA00031536307600000215
Wherein F is a normalized Fourier transform matrix (·)HA conjugate transpose of the matrix is represented,
Figure BDA00031536307600000216
which represents the kronecker product of,
Figure BDA00031536307600000217
is Nt×NtAn identity matrix of dimensions.
(1.3) vector the symbols according to
Figure BDA0003153630760000031
Converting to real number domain equivalent to channel matrix C to obtain real value receiving symbol vector
Figure BDA0003153630760000032
And a real-valued channel matrix
Figure BDA0003153630760000033
Figure BDA0003153630760000034
Re (-) and Im (-) denote the real and imaginary parts of the complex number, respectively (.)TRepresenting the transpose of the matrix.
Further, the signal detection network in step (2) is a deep neural network having T layers of the same series connection layer. The input to the t-th network comprises a real-valued received symbol vector
Figure BDA0003153630760000035
Real-valued channel matrix
Figure BDA0003153630760000036
And an estimated signal output from the (t-1) th layer
Figure BDA0003153630760000037
Wherein, T is 1, 2. The t-th network can be divided into a preprocessing module, a linear estimation module and a nonlinear estimation module and comprises four adjustable parameters (gamma)t,θt,φt,ξt}. The preprocessing module first calculates the matrix
Figure BDA0003153630760000038
Characteristic value λ ofi(i＝1,...,2NcNr) For finding a decorrelation coefficient ζtThen, a conjugate gradient algorithm is used for iteratively solving a linear system mapped by the linear minimum mean square error estimation to obtain a solution vector st(ii) a The linear estimation module uses the solution vector stAnd error variance of (t-1) th layer output
Figure BDA0003153630760000039
Calculating the mean vector rtSum-out error variance
Figure BDA00031536307600000310
The non-linear estimation module then uses the mean vector rtSum-out error variance
Figure BDA00031536307600000311
By non-dispersive non-linear functions etat(. to) calculate the posterior mean
Figure BDA00031536307600000312
As output of the layer, and updates the error variance
Figure BDA00031536307600000313
The final output of the signal detection network is the estimated frequency domain symbol vector
Figure BDA00031536307600000314
Further, for the preprocessing module of the t-th network, the decorrelation coefficient zetatThe calculation formula of (2) is as follows:
Figure BDA00031536307600000315
wherein the content of the first and second substances,
Figure BDA00031536307600000316
is the noise variance. The linear system to which the linear minimum mean square error estimate is mapped can be expressed as:
Ξtst＝yt
wherein, the matrix
Figure BDA00031536307600000317
I is an identity matrix, vector
Figure BDA00031536307600000318
stIs the solution vector of the linear system, iteratively refined using a conjugate gradient algorithm.
Further, for a linear estimation module of the t-th network, the mean vector rtSum-out error variance
Figure BDA00031536307600000319
The calculation formula of (a) is:
Figure BDA0003153630760000041
Figure BDA0003153630760000042
wherein, γtAnd thetatFor the adjustable parameter, ε is a preset small positive number.
Further, for the non-linear estimation module of the t-th network, the posterior mean value
Figure BDA0003153630760000043
Sum error variance
Figure BDA0003153630760000044
The calculation formula of (a) is:
Figure BDA0003153630760000045
Figure RE-GDA0003313931550000046
wherein eta ist(. is a non-divergence non-linear function, phi)tAnd xitIn order to be able to adjust the parameters,
Figure BDA0003153630760000047
for transmitting the true values of the frequency-domain symbol vectors, the elements thereof
Figure BDA0003153630760000048
The minimum mean square error estimate of (d) is:
Figure BDA0003153630760000049
rt nis rtThe nth component of amFinite character set formed by real parts of modulation symbols
Figure BDA00031536307600000410
The m-th element of (a) is,
Figure BDA00031536307600000411
further, the adjustable parameter { gamma }t,θt,φt,ξtThe training is optimized, a small batch of training and a random gradient descent algorithm are used, an optimizer is selected as Adam, the learning rate is initialized to 0.001, 1000 rounds of signal detection network training are performed totally, a training set of each round comprises 500 samples, and each sample is formed by a randomly generated tuple
Figure BDA00031536307600000412
Is formed therein
Figure BDA00031536307600000413
Is the transmitted real-valued frequency-domain symbol vector, as supervisory information,
Figure BDA00031536307600000414
is a real-valued received symbol vector. The loss function is the squared loss L2：
Figure BDA00031536307600000415
Wherein S is the number of samples contained in a small batch,
Figure BDA00031536307600000416
is a predicted value of the network output.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects:
the invention constructs the neural network driven by the model by taking the orthogonal approximate message transfer algorithm as a prototype, can effectively inhibit the interference of the receiving end of the MIMO-OFDM system without the cyclic prefix through training a small number of key parameters in the network, and obtains remarkable performance gain compared with the prior scheme. Meanwhile, the conjugate gradient algorithm is used for replacing complex direct matrix inversion in the prototype algorithm, and the running time is effectively reduced. The invention reasonably combines the traditional communication algorithm with the neural network design, has only a small amount of adjustable parameters in the network, greatly reduces the training overhead, and has the advantages of strong generalization and rapid deployment. In addition, the invention removes redundant cyclic prefix in MIMO-OFDM without causing obvious performance loss, thereby greatly improving the spectrum efficiency of the system.
Drawings
FIG. 1 is a block diagram of the architecture of one embodiment of the present invention;
fig. 2 is a schematic diagram of a signal detection network according to the present invention.
Detailed Description
The present invention will be specifically explained below with reference to the accompanying drawings and an example of a MIMO-OFDM system without cyclic prefix.
First, the system model adopted in this embodiment
In a group having NtRoot of heavenLine, NrMIMO-OFDM system with multiple receive antennas using N per antennacThe sub-carriers transmit information, in this embodiment, the number of antennas Nt＝NrNumber of subcarriers N equal to 8c64. The modulation mode adopts QPSK square constellation modulation, and a constellation symbol set
Figure BDA0003153630760000051
The information bit number transmitted by the transmitter in one symbol time is 64 × 8 × 2 ═ 1024 bits, firstly serial bit stream is converted into multi-channel parallel sub data stream by serial-to-parallel conversion, each channel is modulated by independent OFDM (without inserting cyclic prefix), then the time domain transmission symbol vector is obtained, and at the same time, the time domain transmission symbol vector is sent from multi-antenna and sent into multi-path channel. In this embodiment, the channel is quasi-static, i.e. remains unchanged for one symbol time, p (p e {1t}) root transmit antennas and the q (q e { 1., N) }r}) time domain multipath channel between receiving antennas can be characterized by FIR filter of (L-1) order with tap coefficient of filter
Figure BDA0003153630760000052
In this embodiment, the length L of the time domain channel is taken as 16.
After passing through a multipath channel, a received MIMO-OFDM time domain symbol vector
Figure BDA0003153630760000057
Can be expressed as:
Figure BDA0003153630760000053
wherein the content of the first and second substances,
Figure BDA0003153630760000054
for the currently transmitted frequency-domain symbol vector,
Figure BDA0003153630760000055
and
Figure BDA0003153630760000056
respectively representing a currently transmitted time domain symbol vector and a time domain symbol vector transmitted in a previous symbol time,
Figure BDA0003153630760000061
is an additive white Gaussian noise vector with a noise variance of
Figure BDA0003153630760000062
Matrix array
Figure BDA0003153630760000063
Wherein F is Nc×NcDimension normalization Fourier transform matrix, (.)HThe conjugate transpose of the matrix is represented,
Figure BDA0003153630760000064
which represents the kronecker product of,
Figure BDA0003153630760000065
is Nt×NtAn identity matrix of dimensions. H is the block cyclic channel matrix in the current symbol time, and the expression is:
Figure BDA0003153630760000066
a and A-1The block truncated channel matrices in the current symbol time and the last symbol time, respectively, where the expression of a is:
Figure BDA0003153630760000067
H. a and A-1All are 512 × 512-dimensional block matrixes, wherein block 0 represents an 8 × 8-dimensional all-zero matrix, and block hlL ∈ { 0.,.., L-1} is an 8 × 8-dimensional MIMO channel matrix formed by the L-th path between the transmitting and receiving antenna arrays in the current symbol time, and the expression is:
Figure BDA0003153630760000068
second, the detailed steps of this embodiment
As shown in fig. 1, the receiver comprises a module for eliminating intersymbol interference, a deep neural network for signal detection, a demodulation module, and a feedback loop. The complete receiving process comprises three steps of eliminating intersymbol interference, decomposing a real value, detecting a signal, demodulating and buffering:
(1) intersymbol interference cancellation and real-valued decomposition
Firstly, a sending time domain symbol vector estimated in the last symbol time output by a feedback loop is utilized
Figure BDA0003153630760000069
Cancelling a received symbol vector
Figure BDA00031536307600000610
The redundant intersymbol interference in (1), and the symbol vector obtained after the process
Figure BDA00031536307600000611
Can be expressed as:
Figure BDA0003153630760000071
in the formula, a channel matrix
Figure BDA0003153630760000072
Calculated from the known channel state information.
To facilitate algebraic manipulation and the use of deep learning methods, the system represented by equation (1) is subjected to a real-valued decomposition as follows:
Figure BDA0003153630760000073
Figure BDA0003153630760000074
re (-) and Im (-) denote the real and imaginary parts of the complex number, respectively (.)TRepresenting the transpose of the matrix. The real decomposition yields the equivalent real form of the system represented by equation (1) as follows:
Figure BDA0003153630760000075
(2) signal detection
Receiving the real-valued received symbol vector calculated in step (1)
Figure BDA0003153630760000076
And a real-valued channel matrix
Figure BDA0003153630760000077
Inputting the signal into a signal detection network which is a deep neural network developed by an orthogonal approximate message transfer algorithm with improved conjugate gradient and is used for solving the system represented by the formula (2), and finally outputting an estimated frequency domain symbol vector
Figure BDA0003153630760000078
As shown in FIG. 2, the signal detection network is a deep neural network with T layers of identical series layers, and key adjustable parameters [ gamma ] are introduced into each layert,θt,φt,ξtAnd (4) greatly improving the detection performance. The input to the t-th network comprises a real-valued received symbol vector
Figure BDA0003153630760000079
Real-valued channel matrix
Figure BDA00031536307600000710
And an estimated signal output from the (t-1) th layer
Figure BDA00031536307600000711
Wherein, T is 1, 2.Considering that each layer of network has the same structure, the following takes the t-th layer of network as an example to describe the specific steps executed by each layer of network:
(2.1) layer t network is first preprocessed to form a matrix
Figure BDA00031536307600000712
Decomposing the characteristic value to obtain the characteristic value lambdai(i＝1,...,2NcNr) Then, the decorrelation coefficient ζ is calculated using these characteristic valuestThe expression employed in the present embodiment is:
Figure BDA00031536307600000713
wherein the content of the first and second substances,
Figure BDA00031536307600000714
is an estimated signal output from the (t-1) th layer
Figure BDA00031536307600000715
In combination with a real-valued received symbol vector
Figure BDA00031536307600000716
Real-valued channel matrix
Figure BDA0003153630760000081
Sum noise variance
Figure BDA0003153630760000082
The following formula is used for calculation in the present embodiment
Figure BDA0003153630760000083
Figure RE-GDA0003313931550000084
And then solving a linear system mapped by the linear minimum mean square error estimation by using a conjugate gradient algorithm to avoid complex matrix inversion, wherein the linear system can be expressed as:
Ξtst＝yt
wherein, the matrix
Figure BDA0003153630760000085
I is an identity matrix, vector
Figure BDA0003153630760000086
stIs the solution vector of the linear system, and the vector s is solved iteratively using a conjugate gradient algorithmtAssuming the maximum number of iterations to be 50, the initial approximate solution vector x00, initial residual vector ρ0＝ytInitial conjugate direction vector p0＝ρ0The specific steps of the ith iteration are shown below:
a. computing an approximate solution x for the ith iterationi：
Figure BDA0003153630760000087
xi＝xi-1+αi-1pi-1
Where ρ isi-1And pi-1The residual and conjugate direction vectors, alpha, of the (i-1) th iteration output, respectivelyi-1Is a scalar search step;
b. updating residual vector ρiAnd a conjugate direction vector pi：
ρi＝ρi-1-αi-1Ξtpi-1
Figure BDA0003153630760000088
pi＝ρi+βi-1pi-1
Wherein, betai-1Is a gram-schmitt orthogonalization constant;
c. computing residual vectorsNorm | ρiIf less than 10 | |, the ratio-4Then the iteration is terminated and the approximate solution vector x is outputiAs a counter vector st(ii) an estimate of (d); otherwise, returning to the step a and continuously executing iteration.
(2.2) combining the decorrelation coefficients ζ obtained in step (2.1)tSum vector stComputing the mean vector r using a linear estimatortSum-out error variance
Figure BDA0003153630760000089
The expression used in this embodiment is:
Figure BDA00031536307600000810
Figure BDA0003153630760000091
wherein the parameter gamma is adjustabletIs the mean vector rtUpdate step length of (2), adjustable parameter thetatIs the variance of the outward error
Figure BDA0003153630760000092
The two adjustable parameters affect the accuracy of the estimation of the transmitted symbol vector, and epsilon is a preset positive threshold, which is 10 in this embodiment-10To avoid
Figure BDA0003153630760000093
The result of calculation of (c) is a negative value.
(2.3) combining the mean vector r obtained in step (2.2)tSum-out error variance
Figure BDA0003153630760000094
Computing posterior means using a non-linear estimator
Figure BDA0003153630760000095
As the estimated symbol vector of the t-th network output, in this embodimentComputing
Figure BDA0003153630760000096
The expression of (A) is:
Figure BDA0003153630760000097
wherein eta ist(. to) is a non-linear estimation function without divergence, the adjustable parameter phitAnd xitFor maintaining ηtThe non-divergence characteristic of the (-) ensures the stability of the network,
Figure BDA0003153630760000098
to transmit the true values of the frequency domain symbol vectors,
Figure BDA0003153630760000099
is to
Figure BDA00031536307600000910
Is estimated. In the present embodiment, it is preferred that,
Figure BDA00031536307600000911
each component of (a) is from a finite character set consisting of the real parts of QPSK modulation symbols
Figure BDA00031536307600000912
Therefore, it is
Figure BDA00031536307600000913
The expression for each component of (a) is:
Figure BDA00031536307600000914
wherein the content of the first and second substances,
Figure BDA00031536307600000915
and
Figure BDA00031536307600000916
are respectively as
Figure BDA00031536307600000917
And rtThe (n) th component of (a),
Figure BDA00031536307600000918
Figure BDA00031536307600000919
representing components
Figure BDA00031536307600000920
Is taken as amThe probability of (c) is:
Figure BDA00031536307600000921
obtaining the posterior mean value
Figure BDA00031536307600000922
Then, the error variance is updated using the following equation
Figure BDA00031536307600000923
Figure RE-GDA00033139315500000922
The same serial layer of the T layers executes the steps (2.1) - (2.3) and finally outputs an estimated frequency domain symbol vector
Figure BDA00031536307600000925
As shown in FIG. 2, there are only 4 adjustable parameters { γ } for each layer of the signal detection neural networkt,θt,φt,ξtAnd the total quantity of the adjustable parameters is 4T, and is irrelevant to the number of the antennas and the number of the subcarriers, so that the framework is favorable for reducing the training overhead and can realize quick deployment. The adjustable parameters of each layer are determined by training optimization, and the specific training process is：
Using a small batch training and a random gradient descent algorithm, selecting Adam as an optimizer, initializing the learning rate to be 0.001, training the signal detection network for 1000 times in total, wherein the training set of each time contains 500 samples, and each sample consists of a randomly generated tuple
Figure BDA0003153630760000101
Is formed therein
Figure BDA0003153630760000102
Is the transmitted real-valued frequency-domain symbol vector, as supervisory information,
Figure BDA0003153630760000103
is the real valued received symbol vector and k is the sample number. The loss function is the squared loss L2：
Figure BDA0003153630760000104
Wherein S is the number of samples contained in a small batch, which is taken as 100 in this embodiment, that is, 100 samples are sent to the network for forward propagation each time in training,
Figure BDA0003153630760000105
the method is a predicted value of network output, and the loss function is calculated and then is propagated reversely for optimizing adjustable parameters.
After the training is completed according to the above process, the network can be rapidly deployed on line, and forward signal detection is realized.
(3) Demodulation and buffering
Frequency domain symbol vector to be estimated after signal detection
Figure BDA0003153630760000106
Restoration to the complex field followed by demodulation to obtain an estimated transmitted bit stream
Figure BDA0003153630760000107
Bit stream
Figure BDA0003153630760000108
Storing the bit stream in a buffer to obtain a delayed bit stream
Figure BDA0003153630760000109
Sending the symbol vectors to a feedback loop, and sequentially obtaining the estimation of the symbol vectors of the sending frequency domain and the time domain through modulation and inverse Fourier transform
Figure BDA00031536307600001010
And
Figure BDA00031536307600001011
for eliminating redundant intersymbol interference in the next round of reception.
The above description of the preferred embodiment of the invention with reference to the accompanying drawings is only one of the preferred embodiments of the invention and should not be taken as limiting the scope of the invention, which is defined in the appended claims, and all equivalent modifications made by the principles of the invention are intended to be covered by the claims.

Claims (7)

1. A model-driven MIMO-OFDM receiving method without cyclic prefix is characterized by comprising the following steps:
(1) transmitting time domain symbol vectors based on the estimated symbol time
Figure FDA0003153630750000011
Cancelling a received symbol vector
Figure FDA0003153630750000012
Inter-symbol interference of medium redundancy to obtain symbol vector
Figure FDA0003153630750000013
Calculating a channel matrix C by using the channel state information; then the symbol vector is transformed
Figure FDA0003153630750000014
Converting the sum channel matrix C into a real number domain equivalently to obtain a real value receiving symbol vector
Figure FDA0003153630750000015
And a real-valued channel matrix
Figure FDA0003153630750000016
(2) Receiving a real-valued symbol vector
Figure FDA0003153630750000017
And a real-valued channel matrix
Figure FDA0003153630750000018
Inputting the signal into a signal detection network, expanding the network by an orthogonal approximate message transfer algorithm with improved conjugate gradient, and finally outputting an estimated frequency domain symbol vector
Figure FDA0003153630750000019
(3) Symbol vector of frequency domain to be estimated
Figure FDA00031536307500000110
Demodulating to obtain an estimated transmitted bit stream
Figure FDA00031536307500000111
Bit stream
Figure FDA00031536307500000112
Storing the bit stream in a buffer to obtain a delayed bit stream
Figure FDA00031536307500000113
After modulation and inverse Fourier transform, estimates of symbol vectors of a transmission frequency domain and a transmission time domain are obtained in sequence
Figure FDA00031536307500000114
And
Figure FDA00031536307500000115
for the next round of receiving process.
2. The model-driven MIMO-OFDM receiving method without cyclic prefix according to claim 1, wherein: the step (1) specifically comprises the following steps:
(1.1) canceling the received symbol vector according to
Figure FDA00031536307500000116
To obtain a symbol vector
Figure FDA00031536307500000117
Figure FDA00031536307500000118
In the formula (I), the compound is shown in the specification,
Figure FDA00031536307500000119
for the transmitted time-domain symbol vector estimated in the last symbol time, A-1Truncating the channel matrix for the blocks in the last symbol time, wherein the expression is as follows:
Figure FDA00031536307500000120
Ncis the number of OFDM subcarriers, NtFor the number of transmitting antennas, NrFor the number of receive antennas, L is the time domain channel length, 0 is the all-zero matrix, h-1,lAnd L belongs to {0, …, L-1} is a MIMO channel matrix formed by the L-th path between the transmitting antenna array and the receiving antenna array in the last symbol time, and the expression is as follows:
Figure FDA0003153630750000021
wherein the content of the first and second substances,
Figure FDA0003153630750000022
is the time domain multipath channel between the p-th transmitting antenna and the q-th receiving antenna in the last symbol time;
(1.2) calculating a channel matrix C according to the channel state information, as follows:
Figure FDA0003153630750000023
wherein H is a block cyclic channel matrix in the current symbol time, A is a block truncation channel matrix in the current symbol time, and the matrix
Figure FDA0003153630750000024
Wherein F is a normalized Fourier transform matrix (·)HRepresents the conjugate transpose of the matrix and,
Figure FDA0003153630750000025
which represents the kronecker product of,
Figure FDA0003153630750000026
is Nt×NtAn identity matrix of dimensions;
(1.3) vector the symbols according to
Figure FDA0003153630750000027
Converting to real number domain equivalent to channel matrix C to obtain real value receiving symbol vector
Figure FDA0003153630750000028
And a real-valued channel matrix
Figure FDA0003153630750000029
Figure FDA00031536307500000210
Re (-) and Im (-) denote the real and imaginary parts of the complex number, respectively (.)TRepresenting the transpose of the matrix.
3. The model-driven MIMO-OFDM receiving method without cyclic prefix according to claim 1, wherein: the signal detection network in the step (2) is a deep neural network with T layers of same series layers; the input to the t-th network comprises a real-valued received symbol vector
Figure FDA00031536307500000211
Real-valued channel matrix
Figure FDA00031536307500000212
And an estimated signal output from the (t-1) th layer
Figure FDA00031536307500000213
Wherein, T is 1, 2.. times.t; the t-th network is divided into a preprocessing module, a linear estimation module and a nonlinear estimation module and comprises four adjustable parameters (gamma)t,θt,φt,ξt}; the preprocessing module first calculates the matrix
Figure FDA00031536307500000214
Characteristic value λ ofi(i＝1,...,2NcNr) For finding a decorrelation coefficient ζtThen, a conjugate gradient algorithm is used for iteratively solving a linear system mapped by the linear minimum mean square error estimation to obtain a solution vector st(ii) a The linear estimation module uses the solution vector stAnd error variance of (t-1) th layer output
Figure FDA00031536307500000215
Calculating the mean vector rtSum-out error variance
Figure FDA00031536307500000216
The non-linear estimation module then uses the mean vector rtSum-out error variance
Figure FDA00031536307500000217
By non-dispersive non-linear functions etat(. to) calculate the posterior mean
Figure FDA00031536307500000218
As output of the layer, and updates the error variance
Figure FDA00031536307500000219
The final output of the signal detection network is an estimated frequency domain symbol vector
Figure FDA0003153630750000031
4. The model-driven MIMO-OFDM receiving method without cyclic prefix according to claim 3, wherein: preprocessing module of t-th network, decorrelation coefficient ζtThe calculation formula of (2) is as follows:
Figure FDA0003153630750000032
wherein the content of the first and second substances,
Figure FDA0003153630750000033
is the noise variance; the linear system to which the linear minimum mean square error estimate is mapped is represented as:
Ξtst＝yt
wherein, the matrix
Figure FDA0003153630750000034
I is an identity matrix, vector
Figure FDA0003153630750000035
stIs the solution vector of the linear system, iteratively solved using a conjugate gradient algorithm.
5. The model-driven MIMO-OFDM receiving method without cyclic prefix according to claim 3, wherein: linear estimation module of t-th network, mean vector rtSum-out error variance
Figure FDA0003153630750000036
The calculation formula of (2) is as follows:
Figure FDA0003153630750000037
Figure FDA0003153630750000038
wherein, γtAnd thetatFor the adjustable parameter, ε is a preset small positive number.
6. The model-driven MIMO-OFDM receiving method without cyclic prefix according to claim 3, wherein: non-linear estimation module of t-th network, posterior mean
Figure RE-FDA0003313931540000039
Sum error variance
Figure RE-FDA00033139315400000310
The calculation formula of (2) is as follows:
Figure RE-FDA00033139315400000311
Figure RE-FDA00033139315400000312
wherein eta ist(. is a non-divergence non-linear function, phi)tAnd xitIn order to be able to adjust the parameters,
Figure RE-FDA00033139315400000313
for transmitting the true values of the frequency-domain symbol vectors, the elements thereof
Figure RE-FDA00033139315400000314
The minimum mean square error estimate of (d) is:
Figure RE-FDA00033139315400000315
rt nis rtThe nth component of amFinite character set formed by real parts of modulation symbols
Figure RE-FDA00033139315400000316
The m-th element of (a) is,
Figure RE-FDA0003313931540000041
7. the model-driven MIMO-OFDM receiving method without cyclic prefix according to claim 3, wherein: adjustable parameter [ gamma ]t,θt,φt,ξtThe training is optimized, a small batch of training and a random gradient descent algorithm are used, an optimizer is selected as Adam, the learning rate is initialized to 0.001, 1000 rounds of signal detection network training are performed totally, a training set of each round comprises 500 samples, and each sample is formed by a randomly generated tuple
Figure FDA0003153630750000042
Is formed therein
Figure FDA0003153630750000043
Is the transmitted real-valued frequency-domain symbol vector, as supervisory information,
Figure FDA0003153630750000044
is a real-valued received symbol vector. The loss function is the squared loss L2：
Figure FDA0003153630750000045
Wherein S is the number of samples contained in a small batch,
Figure FDA0003153630750000046
is a predicted value of the network output.
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