CN109617847B - OFDM receiving method without cyclic prefix based on model-driven deep learning - Google Patents

OFDM receiving method without cyclic prefix based on model-driven deep learning Download PDF

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CN109617847B
CN109617847B CN201811417172.3A CN201811417172A CN109617847B CN 109617847 B CN109617847 B CN 109617847B CN 201811417172 A CN201811417172 A CN 201811417172A CN 109617847 B CN109617847 B CN 109617847B
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CN109617847A (en
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金石
张静
何恒涛
高璇璇
温朝凯
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Southeast University
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    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2695—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation with channel estimation, e.g. determination of delay spread, derivative or peak tracking
    • 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
    • H04L27/2627—Modulators
    • H04L27/2628—Inverse Fourier transform modulators, e.g. inverse fast Fourier transform [IFFT] or inverse discrete Fourier transform [IDFT] modulators
    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2668—Details of algorithms
    • H04L27/2669—Details of algorithms characterised by the domain of operation
    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2668—Details of algorithms
    • H04L27/2673—Details of algorithms characterised by synchronisation parameters
    • H04L27/2676—Blind, i.e. without using known symbols
    • H04L27/2678—Blind, i.e. without using known symbols using cyclostationarities, e.g. cyclic prefix or postfix
    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2691—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation involving interference determination or cancellation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2201/00—Algorithms used for the adjustment of time-domain equalizers
    • H04L2201/02—Algorithms used for the adjustment of time-domain equalizers minimizing an error signal, e.g. least squares, minimum square error

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Abstract

The invention discloses a cyclic prefix-free OFDM receiving method based on model-driven deep learning, which comprises the following steps: (1) receiving a pilot signal y in a signal ypTransforming to obtain frequency domain pilot signal, performing least square estimation initialization with local frequency domain pilot signal to obtain least square channel estimation result, inputting to fully-connected first deep neural network for improvement, and performing Fourier inversion on the improved result to obtain time domain channel estimation signal
Figure DDA0001879754570000011
(2) The received signal y is converted into a real number domain received signal after eliminating intersymbol interference
Figure DDA0001879754570000016
(3) Receiving a signal in the real number domain
Figure DDA0001879754570000012
As input, a signal is estimated from a time domain channel
Figure DDA0001879754570000017
Iterative solution is carried out by adopting a second deep neural network to obtain a finally estimated modulation signal
Figure DDA0001879754570000015
(4) Will modulate the signal
Figure DDA0001879754570000014
Obtaining transmitted information bits after demodulation
Figure DDA0001879754570000013
The invention has the advantages of less time consumption and high detection performance.

Description

OFDM receiving method without cyclic prefix based on model-driven deep learning
Technical Field
The invention relates to a communication technology, in particular to a cyclic prefix-free OFDM receiving method based on model-driven deep learning.
Background
In recent years, deep learning has been a fundamental technique in artificial intelligence, and has been a great success in subjects such as computer vision and natural language processing. Deep learning is a branch of the field of machine learning, and is a supervised learning method, and a group of optimal neural network parameters are obtained by minimizing a loss function between a predicted value and a true value of a deep neural network, so that the deep neural network can perform accurate prediction.
Deep learning has been studied in the wireless communication physical layer, including channel estimation, signal detection, encoder, decoder, channel feedback information reconstruction, and end-to-end deep learning communication system. However, the examples of integrating the algorithm knowledge in the field of wireless communication into the neural network design are few at present, most of the functions of the existing neural network regard a wireless communication system or a module as a black box, the training of the neural network completely depends on a large amount of data driving, the parameter number of the neural network is large, and the training speed is slow. In OFDM without cyclic prefix, inter-symbol interference and inter-carrier interference caused by multipath channels make channel estimation and channel detection very challenging. The bit error rate of the data-driven neural network is high under high-order modulation, and the performance is expected to be further improved by using the model-driven neural network.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a cyclic prefix-free OFDM receiving method based on model-driven deep learning.
The technical scheme is as follows: the OFDM receiving method without the cyclic prefix based on the model-driven deep learning comprises the following steps:
(1) receiving a pilot signal y in a signal ypTransforming to obtain frequency domain pilot signal, performing least square estimation initialization with local frequency domain pilot signal to obtain least square channel estimation result, inputting to fully-connected first deep neural network for improvement, and performing Fourier inversion on the improved result to obtain time domain channel estimation signal
Figure GDA0002891968410000011
(2) The received signal y is converted into a real number domain received signal after eliminating intersymbol interference
Figure GDA0002891968410000012
(3) Receiving a signal in the real number domain
Figure GDA0002891968410000013
As input, a signal is estimated from a time domain channel
Figure GDA0002891968410000014
Iterative solution is carried out by adopting a second deep neural network expanded by the OAMP algorithm to obtain a finally estimated modulation signal
Figure GDA0002891968410000015
(4) Will modulate the signal
Figure GDA0002891968410000016
Obtaining transmitted information bits after demodulation
Figure GDA0002891968410000017
Further, the step (1) specifically comprises:
(1.1) receiving the signaly pilot signal ypFourier transform is carried out to obtain a frequency domain pilot signal Yp；
(1.2) mixing the frequency domain pilot signal YpAnd a local frequency domain pilot signal XpPerforming least square estimation initialization to obtain least square channel estimation result
Figure GDA0002891968410000021
Wherein, the least square channel estimation result of the k sub-carrier
Figure GDA0002891968410000022
Comprises the following steps:
Figure GDA0002891968410000023
in the formula, Yp(k)、Xp(k) Receiving frequency domain pilot signals and local frequency domain pilot signals of the kth subcarrier respectively, wherein N is the number of the subcarriers;
(1.3) estimating the result of least squares channel
Figure GDA0002891968410000024
The real part and the imaginary part of the vector are connected in series to form a vector
Figure GDA0002891968410000025
Improving a first deep neural network input to a full connection, wherein the first deep neural network comprises a layer network for performing the following calculations:
Figure GDA0002891968410000026
in the formula, WLMMSETo use the weight matrix for linear minimum mean square error channel estimation,
Figure GDA0002891968410000027
is WLMMSEA real-valued matrix of, and
Figure GDA0002891968410000028
re { }, Im { } denote taking a real part and an imaginary part respectively,
Figure GDA0002891968410000029
improving the result for the output of the first deep neural network;
(1.4) will improve the results
Figure GDA00028919684100000210
Performing inverse Fourier transform to obtain a time domain channel estimation signal
Figure GDA00028919684100000211
Further, the weight matrix WLMMSEObtained through training, the training process is as follows:
obtaining a plurality of samples, each sample comprising a true frequency domain channel H and a corresponding least squares channel estimation result
Figure GDA00028919684100000212
Will be provided with
Figure GDA00028919684100000213
As parameters to be trained, an Adam optimizer and a small-batch gradient descent method are adopted to perform multi-round training, and the learning rate is dynamically adjusted to obtain parameters
Figure GDA00028919684100000214
The optimum value of (d); loss function using squared error loss
Figure GDA00028919684100000215
Further, the step (2) specifically comprises:
(2.1) eliminating intersymbol interference from the received signal y according to the following formula:
Figure GDA0002891968410000031
in the formula (I), the compound is shown in the specification,
Figure GDA0002891968410000032
for eliminating the received signal of intersymbol interference, A is an intersymbol interference and intersymbol interference matrix, and the expression is
Figure GDA0002891968410000033
Figure GDA0002891968410000034
Is an estimate of A, qi-1Is a pilot OFDM symbol;
(2.2) received Signal to be interference cancelled between symbols
Figure GDA0002891968410000035
Conversion to a real number domain received signal according to
Figure GDA0002891968410000036
Figure GDA0002891968410000037
Further, in the step (3), the second deep neural network is formed by connecting LS layer network layers in series, the structures of all the layers are the same, and the input of the l layer network layer is the output of the l-1 layer
Figure GDA0002891968410000038
And receiving signals in real number domain
Figure GDA0002891968410000039
Output is as
Figure GDA00028919684100000310
The operations performed are:
Figure GDA00028919684100000311
Figure GDA00028919684100000312
Figure GDA00028919684100000313
Figure GDA00028919684100000314
Figure GDA00028919684100000315
Figure GDA00028919684100000316
in the formula (I), the compound is shown in the specification,
Figure GDA00028919684100000317
is a linear MMSE matrix and is a linear MMSE matrix,
Figure GDA00028919684100000318
Figure GDA00028919684100000319
estimating a signal for a time domain channel
Figure GDA00028919684100000320
F is a normalized fourier transform matrix,
Figure GDA0002891968410000041
is the noise variance, I is the identity matrix, β is the update parameter, λl、γlFor training parameters, N is the number of carriers, and ε isPositive number less than preset threshold, modulation symbol u from real modulation set
Figure GDA0002891968410000042
Figure GDA0002891968410000043
Indicates that the modulation symbol is judged as amProbability of (u)nA symbol is modulated for the nth sub-carrier,
Figure GDA0002891968410000044
is the nth subcarrier symbol received for the l layer.
Further, the training parameter λl、γlObtained through training, the training process is as follows:
obtaining a plurality of samples, each sample comprising a modulated signal u and a corresponding real number domain received signal
Figure GDA0002891968410000045
Will be lambdal、γlAs a parameter to be trained, an Adam optimizer and a small batch gradient descent method are adopted to perform multi-round training, and the learning rate is dynamically adjusted to obtain a parameter lambdal、γlThe optimum value of (d); loss function using squared error loss
Figure GDA0002891968410000046
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention reasonably integrates the OAMP algorithm into the neural network design, and the performance of the bit error rate is obviously improved in the OFDM without the cyclic prefix, the number of network training parameters is greatly reduced, and the training time is greatly shortened. The invention trains the neural network by the OFDM receiver in modules, and inputs the result of the traditional communication algorithm as an initial value into the neural network for optimization and improvement, thereby having less time consumption of network training and high detection performance.
Drawings
FIG. 1 is a schematic flow diagram of one embodiment of the present invention;
FIG. 2 is a flow chart of channel estimation of the present invention;
fig. 3 is a schematic flow chart of signal detection according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples of 64-subcarrier cyclic prefix-free OFDM systems.
First, the channel model suitable for this embodiment
In an OFDM system with 64 sub-carriers, the data frame format is one pilot OFDM symbol and one data OFDM symbol, with the pilot and data occupying 64 sub-carriers. The constellation modulation mode of the pilot frequency is QPSK, and the constellation modulation mode of the data adopts 64QAM of the LTE standard. At a transmitting end, data bits are 64 multiplied by 6 to 384 bits, and are converted into time domain sending signals through 64QAM constellation modulation, pilot frequency adding framing and IFFT; after passing through a multipath channel, time domain receiving pilot frequency and data are obtained at a receiving end and are sent to the OFDM system receiver without the cyclic prefix based on the model-driven deep learning, and 384-bit recovery is obtained.
Assuming that white gaussian noise w exists in the channel, the time domain signal y obtained at the receiving end is as follows:
Figure GDA0002891968410000051
where N denotes the number of subcarriers, u is the modulated signal, q and q-1Respectively representing a current OFDM symbol and a previous OFDM symbol. F is an N × N normalized fourier transform matrix and H is an N × N cyclic channel matrix, represented as follows:
Figure GDA0002891968410000052
a represents the channel matrix of the inter-carrier interference and the inter-symbol interference, and the expression is
Figure GDA0002891968410000053
The formula (1) can be further converted into
Figure GDA0002891968410000054
The transmitted signal received in the time domain is denoted as s ═ H1FHu, then SNR is expressed as
Figure GDA0002891968410000055
Wherein the content of the first and second substances,
Figure GDA0002891968410000056
Figure GDA0002891968410000057
is the variance of the noise w.
Second, the detailed steps of this embodiment
As shown in fig. 1, the neural network is applied to a wireless communication receiver, instead of the functions of two modules of channel estimation and signal equalization of the original OFDM system, and specifically includes two sub-modules of channel estimation and signal detection, the network is trained by a supervised learning method on line, the trained network is used for forward prediction in actual application, the receiver specifically includes four steps of channel estimation, signal calculation, signal detection and signal demodulation, a first deep neural network in the channel estimation step is trained first and then a second deep neural network in the signal detection step is trained in the training, and a channel estimation result output in the channel estimation step is obtained first and then signal detection is performed in the application.
(1) Channel estimation
As shown in fig. 2, the pilot signal y in the signal y is receivedpFourier transform is carried out to obtain a frequency domain pilot signal YpThe frequency domain pilot signal YpAnd a local frequency domain pilot signal XpPerforming least squares estimation initialization, wherein the least squares channel estimation result of the k sub-carrier
Figure GDA0002891968410000061
Comprises the following steps:
Figure GDA0002891968410000062
then, the real part and the imaginary part of the least square estimation result are connected in series to form a vector with the length of 128, the vector is input into a first neural network which is fully connected for improvement, and a channel estimation result with the length of 128 is output
Figure GDA0002891968410000063
Will improve the results
Figure GDA0002891968410000064
Performing inverse Fourier transform to obtain a time domain channel estimation signal
Figure GDA0002891968410000065
The deep neural network is a one-layer fully-connected network, an activation function is not adopted, multiplicative parameters of the layer network are initialized by adopting real values of a weight matrix of linear minimum mean square error channel estimation, initial values of additive parameters are set to be all zero, and all the parameters are set to be trainable. Wherein the minimum mean square error channel estimate
Figure GDA0002891968410000066
Weight matrix WLMMSEReal value matrix of
Figure GDA0002891968410000067
Is composed of
Figure GDA0002891968410000068
The dimension is 128 × 128. The deep neural network training process comprises the steps of obtaining a plurality of samples, wherein each sample comprises a real frequency domain channel H and a corresponding least square channel estimation result
Figure GDA0002891968410000069
The loss function is the loss of squared error
Figure GDA00028919684100000610
The optimizer is an Adam optimizer, small-batch gradient descent is adopted during training, 50 batches are adopted in each round, the size of each batch is 1000 samples, the training is carried out for 2000 rounds, the learning rate of the first 1000 rounds is 0.001, and the learning rate of the last 1000 rounds is 0.0001.
(2) Signal calculation
Firstly, the received signal y is eliminated with intersymbol interference according to the following formula:
Figure GDA00028919684100000611
in the formula (I), the compound is shown in the specification,
Figure GDA00028919684100000612
in order to cancel the received signal of the inter-symbol interference,
Figure GDA00028919684100000613
is an estimate of A, qi-1Is a pilot OFDM symbol; secondly, the received signal with intersymbol interference eliminated
Figure GDA00028919684100000614
Conversion to a real number domain received signal according to
Figure GDA00028919684100000615
(3) Signal detection
Iterative solution is carried out by adopting a second deep neural network to obtain a finally estimated modulation signal
Figure GDA00028919684100000616
And the second deep neural network expands the iterative OAMP algorithm and introduces trainable parameters to further improve the signal detection performance. To apply the OAMP algorithm, the second term in equation (2) needs to be removed. Since the data frame format is one pilot OFDM symbol and one data OFDM symbolThe previous OFDM symbol qi-1Are pilot OFDM symbols. The pilot symbols are known to the receiving end and thus the inter-symbol interference can be removed. As shown in fig. 2, the receiver obtains the time domain channel estimate by channel estimation
Figure GDA0002891968410000071
The received signal after removal of the intersymbol interference is then
Figure GDA0002891968410000072
Wherein the content of the first and second substances,
Figure GDA0002891968410000073
Figure GDA0002891968410000074
are all estimated by time domain channel
Figure GDA0002891968410000075
And (4) obtaining.
In order to increase the computation speed and reduce the complexity, the complex domain OFDM system needs to be converted into the real domain before signal detection. The equivalent real number domain of equation (4) is expressed as follows
Figure GDA0002891968410000076
Wherein
Figure GDA0002891968410000077
Figure GDA0002891968410000078
Figure GDA0002891968410000079
Figure GDA00028919684100000710
A set of numbers representing the real and imaginary parts of 64 QAM.
As shown in FIG. 3, the second deep neural network is formed by connecting LS layer network layers in series, each layer has the same structure, and the input of the l-layer network layer is the output of the l-1 layer
Figure GDA00028919684100000711
And receiving signals in real number domain
Figure GDA00028919684100000712
Output is as
Figure GDA00028919684100000713
The operations performed are:
Figure GDA00028919684100000714
Figure GDA00028919684100000715
Figure GDA00028919684100000716
Figure GDA00028919684100000717
Figure GDA00028919684100000718
Figure GDA00028919684100000719
in the formula (I), the compound is shown in the specification,
Figure GDA0002891968410000081
is a linear MMSE matrix and is a linear MMSE matrix,
Figure GDA0002891968410000082
i is the identity matrix, beta is the update parameter, set to 0.5, lambdal、γlFor training parameters, epsilon is a positive number smaller than a preset threshold, and modulation symbols u are from a real number modulation set
Figure GDA0002891968410000083
For a 64QAM, the number of bits in the symbol is,
Figure GDA0002891968410000084
Figure GDA0002891968410000085
indicates that the modulation symbol is judged as amProbability of (u)nA symbol is modulated for the nth sub-carrier,
Figure GDA0002891968410000086
is the nth subcarrier symbol received for the l layer. r islAnd
Figure GDA0002891968410000087
respectively, affecting the modulation symbol estimates
Figure GDA0002891968410000088
A priori mean and variance of precision.
As can be seen from FIG. 3, in the second neural network, each layer involves 2 trainable variables (λ)l,γl) The total amount of training parameters is 2 LS. Moreover, the number of training parameters is independent of the number of subcarriers, and is only related to the number of network layers. For large-scale OFDM, this structure shows great advantages.
The deep neural network is trained by obtaining a plurality of samples, each sample comprising a modulation signal u and a corresponding real number domain received signal
Figure GDA0002891968410000089
The loss function is the loss of squared error
Figure GDA00028919684100000810
The optimizer is an Adam optimizer, batch gradient descent is adopted during training, the size of each batch is 1000 samples, namely 1000 data are adopted in each round of training together, 10000 rounds of training are performed, and the learning rate is 0.001.
(4) Signal demodulation
Obtaining an estimate of the modulated signal by forward propagation after signal detection is complete
Figure GDA00028919684100000811
Then demodulating to obtain estimated bit data
Figure GDA00028919684100000812
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (6)

1. A cyclic prefix-free OFDM receiving method based on model-driven deep learning is characterized by comprising the following steps:
(1) receiving a pilot signal y in a signal ypTransforming to obtain frequency domain pilot signal, performing least square estimation initialization with local frequency domain pilot signal to obtain least square channel estimation result, inputting to fully-connected first deep neural network for improvement, and performing Fourier inversion on the improved result to obtain time domain channel estimation signal
Figure FDA0002891968400000011
(2) The received signal y is converted into a real number domain received signal after eliminating intersymbol interference
Figure FDA0002891968400000012
(3) Receiving a signal in the real number domain
Figure FDA0002891968400000013
As input, a signal is estimated from a time domain channel
Figure FDA0002891968400000014
Iterative solution is carried out by adopting a second deep neural network expanded by the OAMP algorithm to obtain a finally estimated modulation signal
Figure FDA0002891968400000015
(4) Will modulate the signal
Figure FDA0002891968400000016
Obtaining transmitted information bits after demodulation
Figure FDA0002891968400000017
2. The OFDM receiving method without cyclic prefix based on model-driven deep learning of claim 1, wherein: the step (1) specifically comprises the following steps:
(1.1) receiving a pilot signal y in a signal ypFourier transform is carried out to obtain a frequency domain pilot signal Yp；
(1.2) mixing the frequency domain pilot signal YpAnd a local frequency domain pilot signal XpPerforming least square estimation initialization to obtain least square channel estimation result
Figure FDA0002891968400000018
Wherein, the least square channel estimation result of the k sub-carrier
Figure FDA0002891968400000019
Comprises the following steps:
Figure FDA00028919684000000110
in the formula, Yp(k)、Xp(k) Receiving frequency domain pilot signals and local frequency domain pilot signals of the kth subcarrier respectively, wherein N is the number of the subcarriers;
(1.3) estimating the result of least squares channel
Figure FDA00028919684000000111
The real part and the imaginary part of the vector are connected in series to form a vector
Figure FDA00028919684000000112
Improving a first deep neural network input to a full connection, wherein the first deep neural network comprises a layer network for performing the following calculations:
Figure FDA00028919684000000113
in the formula, WLMMSETo use the weight matrix for linear minimum mean square error channel estimation,
Figure FDA00028919684000000114
is WLMMSEA real-valued matrix of, and
Figure FDA00028919684000000115
re { }, Im { } denote taking a real part and an imaginary part respectively,
Figure FDA00028919684000000116
improving the result for the output of the first deep neural network;
(1.4) will improve the results
Figure FDA0002891968400000021
Performing inverse Fourier transform to obtain a time domain channel estimation signal
Figure FDA0002891968400000022
3. The OFDM receiving method without cyclic prefix based on model-driven deep learning of claim 2, wherein: the weight matrix WLMMSEObtained through training, the training process is as follows:
obtaining a plurality of samples, each sample comprising a true frequency domain channel H and a corresponding least squares channel estimation result
Figure FDA0002891968400000023
Will be provided with
Figure FDA0002891968400000024
As parameters to be trained, an Adam optimizer and a small-batch gradient descent method are adopted to perform multi-round training, and the learning rate is dynamically adjusted to obtain parameters
Figure FDA0002891968400000025
The optimum value of (d); loss function using squared error loss
Figure FDA0002891968400000026
H (k) denotes the H value of k subcarriers,
Figure FDA0002891968400000027
representing k sub-carriers
Figure FDA0002891968400000028
The value is obtained.
4. The OFDM receiving method without cyclic prefix based on model-driven deep learning of claim 1, wherein: the step (2) specifically comprises the following steps:
(2.1) eliminating intersymbol interference from the received signal y according to the following formula:
Figure FDA0002891968400000029
in the formula (I), the compound is shown in the specification,
Figure FDA00028919684000000210
for eliminating the received signal of intersymbol interference, A is an intersymbol interference and intersymbol interference matrix, and the expression is
Figure FDA00028919684000000211
Figure FDA00028919684000000212
Is an estimate of A, q-1Is a pilot frequency OFDM symbol, and N is the number of subcarriers; h isiRepresenting the ith time domain impulse response forming an N × N cyclic channel matrix H;
(2.2) received Signal to be interference cancelled between symbols
Figure FDA00028919684000000213
Conversion to a real number domain received signal according to
Figure FDA00028919684000000214
Figure FDA00028919684000000215
5. The OFDM receiving method without cyclic prefix based on model-driven deep learning of claim 1, wherein: the second deep neural net in step (3)The network is formed by connecting LS layer network layers in series, each layer has the same structure, and the input of the l-th layer network layer is the output of the l-1 th layer
Figure FDA00028919684000000216
And receiving signals in real number domain
Figure FDA00028919684000000217
Output is as
Figure FDA00028919684000000218
The operations performed are:
Figure FDA0002891968400000031
Figure FDA0002891968400000032
Figure FDA0002891968400000033
Figure FDA0002891968400000034
Figure FDA0002891968400000035
Figure FDA0002891968400000036
in the formula (I), the compound is shown in the specification,
Figure FDA0002891968400000037
is a linear MMSE matrix and is a linear MMSE matrix,
Figure FDA0002891968400000038
a is the intercarrier interference and intersymbol interference matrix,
Figure FDA0002891968400000039
is an estimated value of a and is,
Figure FDA00028919684000000310
estimating a signal for a time domain channel
Figure FDA00028919684000000311
F is a normalized fourier transform matrix,
Figure FDA00028919684000000312
is the noise variance, I is the identity matrix, β is the update parameter, λl、γlInitializing u for training parameters, wherein N is the number of carriers, and epsilon is a positive number smaller than a preset threshold value10, the modulation signal u is from the real modulation set
Figure FDA00028919684000000313
Figure FDA00028919684000000314
Indicates that the modulation symbol is judged as amProbability of (u)nA symbol is modulated for the nth sub-carrier,
Figure FDA00028919684000000315
is the nth subcarrier symbol received for the l layer.
6. The OFDM reception method without cyclic prefix based on model-driven deep learning according to claim 5, wherein: the training parameter lambdal、γlObtained by training, a training processComprises the following steps:
obtaining a plurality of samples, each sample comprising a modulated signal u and a corresponding real number domain received signal
Figure FDA00028919684000000316
Will be lambdal、γlAs a parameter to be trained, an Adam optimizer and a small batch gradient descent method are adopted to perform multi-round training, and the learning rate is dynamically adjusted to obtain a parameter lambdal、γlThe optimum value of (d); loss function using squared error loss
Figure FDA00028919684000000317
u (k) denotes the u value of k subcarriers,
Figure FDA00028919684000000318
representing k sub-carriers
Figure FDA00028919684000000319
The value is obtained.
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