CN112737987B - Novel time-varying channel prediction method based on deep learning - Google Patents

Novel time-varying channel prediction method based on deep learning Download PDF

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CN112737987B
CN112737987B CN202011577593.XA CN202011577593A CN112737987B CN 112737987 B CN112737987 B CN 112737987B CN 202011577593 A CN202011577593 A CN 202011577593A CN 112737987 B CN112737987 B CN 112737987B
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杨丽花
张捷
聂倩
杨龙祥
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses a novel time-varying channel prediction method based on deep learning, which comprises the following steps: acquiring a time domain channel estimation value under the condition that both data and pilot frequency are known; constructing a pre-training sample set according to the time domain channel estimation value; randomly initializing network parameters, and pre-training the network by using a pre-training sample set to obtain the weight and threshold parameters of the pre-training network; under the condition that only the pilot frequency is known, acquiring a time domain channel estimation value, and constructing a training sample set according to the time domain channel estimation value; adopting the weight and threshold parameters of the pre-training network as initial parameters of the network in the training stage, and training the network again through a training sample set to obtain a channel prediction network model; and performing online channel prediction based on the channel prediction network model, and converting the online predicted value into a complex number to be used as a final channel predicted value. The time-varying channel prediction accuracy is remarkably improved, the calculation complexity is low, and the method is suitable for efficiently acquiring the time-varying channel information in a high-speed mobile environment.

Description

Novel time-varying channel prediction method based on deep learning
Technical Field
The invention relates to the technical field of wireless communication, in particular to a novel time-varying channel prediction method based on deep learning.
Background
In recent years, wireless communication technology has been rapidly developed, and results related to wireless channels have been diversified. With the large-scale deployment of High Speed Railways (HSRs) operating at speeds exceeding 300 km, wireless communication in the HSR environment is drawing more and more attention worldwide. In the HSR environment, high-speed running of a train may cause a large doppler shift, and the large doppler shift may cause a Channel to be rapidly time-varying, and it is critical to acquire Channel State Information (CSI) with high accuracy in this scenario. Although the CSI can be obtained through channel estimation, the CSI obtained is outdated due to fast time variation of the channel and processing delay of the channel estimation, and the channel condition at the current time cannot be reflected.
Disclosure of Invention
The invention aims to provide a novel time-varying channel prediction method based on deep learning, which can obviously improve the time-varying channel prediction precision, has lower calculation complexity and is suitable for efficiently acquiring time-varying channel information in a high-speed mobile environment.
The invention adopts the following technical scheme for realizing the aim of the invention:
the invention provides a novel time-varying channel prediction method based on deep learning, which comprises the following steps:
acquiring a time domain channel estimation value under the condition that both data and pilot frequency are known;
constructing a pre-training sample set according to the time domain channel estimation value;
randomly initializing network parameters, and pre-training the network by using a pre-training sample set to obtain a weight and a threshold parameter of the pre-training network;
under the condition that only the pilot frequency is known, acquiring a time domain channel estimation value, and constructing a training sample set according to the time domain channel estimation value;
adopting the weight and threshold parameters of the pre-training network as initial parameters of the network in the training stage, and training the network again through a training sample set to obtain a channel prediction network model;
and performing online channel prediction based on the channel prediction network model, and converting the online predicted value into a complex number to be used as a final channel predicted value.
Further, a formula for constructing a pre-training sample set according to the time domain channel estimation value is as follows:
Figure BDA0002863793450000011
in the formula: u represents the number of pre-training samples;
Figure BDA0002863793450000012
represents the u-th input/output sample set of the pre-training phase, wherein
Figure BDA0002863793450000013
Is an input sampleIt represents the estimated channel parameters
Figure BDA0002863793450000014
The channel state information of the u-th sampling instant and the next (D-1) sampling instant,
Figure BDA0002863793450000015
is an output sample representing the channel state information of the (u + D) th and the (P-1) th sampling instants following the ideal channel parameter h (n), i.e. the output sample
Figure BDA0002863793450000021
Figure BDA0002863793450000022
In the formula: h (n) is an ideal time domain channel parameter,
Figure BDA0002863793450000023
under the condition that data and pilot frequency are known, a time domain channel estimation value is obtained by utilizing a received signal and an LS method; Γ (-) is an operation to convert a complex number to a real number, i.e.
Γ(h(n))＝[Re(h(n)),Im(h(n))]
In the formula: re (-) and Im (-) are real and imaginary operations, respectively.
Further, the formula for constructing the training sample set according to the time domain channel estimation value is as follows:
Figure BDA0002863793450000024
in the formula: u represents the number of training samples;
Figure BDA0002863793450000025
the u-th input and output sample set of the training stage is represented and is structured as follows:
Figure BDA0002863793450000026
Figure BDA0002863793450000027
in the formula: inputting samples
Figure BDA0002863793450000028
Representing estimated channel parameters
Figure BDA0002863793450000029
Channel state information of the middle (u) th sampling instant and the next (D-1) sampling instant; outputting the sample
Figure BDA00028637934500000210
Channel state information representing the (u + D) th and (P-1) th sampling instants in an ideal channel parameter h (n), which is an ideal time domain channel parameter,
Figure BDA00028637934500000211
when only the pilot is known, the time domain channel estimation value is obtained by using the received signal r (n), the LS method and the linear interpolation method.
Further, the method for online channel prediction based on the channel prediction network model comprises the following steps:
on-line channel prediction is carried out based on a channel prediction network model, and channel parameter estimated values x at the previous D moments are input to the networkEObtaining the predicted value y of the channel at the next P momentsEWherein
Figure BDA00028637934500000212
yE＝[Γ(hpre(n)),Γ(hpre(n+1)),...,Γ(hpre(n+P-1))]。
Further, the on-line predicted value is converted into a complex number as the final channel predicted value, namely
hpre＝Γ-1(yE)
In the formula: gamma-shaped-1(. Cndot.) is the inverse operation of Γ (·), i.e., the operation of converting a real number into a complex number.
Further, the system model employed includes:
using the Leise channel as a channel model, i.e.
Figure BDA0002863793450000031
In the formula: alpha is alpha0(m, n) is the LOS path component of the channel, αl(m, n), L =1, L-1 being the scattering component path, which obeys rayleigh distribution, L being the number of paths of the multipath rice channel, τlIs the normalized time delay of the first path, and the Rice factor is defined as
Figure BDA0002863793450000032
If the length of the cyclic prefix is greater than the maximum delay of the wireless transmission channel and the receiving end considers the ideal timing synchronization, the received signal of the nth sampling point of the mth OFDM symbol is:
Figure BDA0002863793450000033
in the formula: z (m, n) is mean 0 and variance is
Figure BDA0002863793450000034
Additive White Gaussian Noise (AWGN).
Furthermore, the network adopts a three-layer BP neural network, which comprises an input layer, a hidden layer and an output layer;
if there are D neurons in the input layer, Q neurons in the hidden layer and P neurons in the output layer of the BP neural network, the training sample set of the BP neural network is defined as:
C＝{(x(1),y(1)),(x(2),y(2)),...,(x(U),y(U))}
in the formula: u represents the number of training samples;
Figure BDA0002863793450000035
is the u-th vector of input samples,
Figure BDA0002863793450000036
is the d-th element in the u-th input sample vector, i.e. the value on the d-th input neuron;
Figure BDA0002863793450000037
representing the u-th output sample vector,
Figure BDA0002863793450000038
is the value on the p-th element, i.e. the p-th output neuron, in the u-th output sample vector.
Further, the method for training the BP neural network according to the sample set comprises the following steps:
in the hidden layer of the BP neural network, the output of the qth hidden neuron is:
Figure BDA0002863793450000039
in the formula: g is a radical of formula1(. For hidden layer activation function) the Sigmoid function is chosen here, i.e. it is
Figure BDA00028637934500000310
Figure BDA00028637934500000311
The inputs for the qth hidden neuron are:
Figure BDA00028637934500000312
in the formula: x is a radical of a fluorine atomdDenotes the d-th input neuron, Wd,qRepresenting the weight, ξ, between the qth hidden neuron and the d input neuronqA threshold for the qth hidden neuron;
at the output layer of the BP neural network, the output of the pth output neuron is:
Figure BDA0002863793450000041
in the formula: g is a radical of formula2(. To) as an output layer activation function, where a ReLU function is selected, i.e.
Figure BDA0002863793450000042
Figure BDA0002863793450000043
Is the input to the pth output neuron:
Figure BDA0002863793450000044
in the formula: vq,pIs the weight between the qth hidden layer neuron and the pth output layer neuron, θpIs the threshold of the p-th output neuron.
The invention has the following beneficial effects:
offline training and online prediction are performed using a network:
in the on-line off-training stage, the better network weight and threshold parameter are obtained through pre-training treatment, and then the network is trained again based on the obtained network parameter, so that the performance loss caused by the random initialization of the BP neural network is reduced, and meanwhile, the convergence speed and the prediction accuracy of the network are improved;
in the online prediction stage, channel prediction at a future moment is carried out by utilizing a channel prediction network model obtained in the training stage;
in addition, the network is retrained by modifying the number of neurons in the output layer of the neural network, so that multi-time prediction of a time-varying channel can be realized;
the method reduces the complexity of calculation, improves the prediction efficiency of the system, effectively saves system resources, has higher convergence rate and high prediction performance, and has certain practical value.
Drawings
FIG. 1 is a flow chart provided in accordance with an embodiment of the present invention;
FIG. 2 is a block diagram of a 3-layer BP neural network provided in accordance with an embodiment of the present invention;
fig. 3 is a diagram comparing MSE performance of the channel prediction method provided in the embodiment of the present invention with that of the existing channel prediction method under different snr conditions;
fig. 4 is a diagram comparing MSE performance of a channel prediction method provided in an embodiment of the present invention with that of an existing channel prediction method based on a BP neural network, which realizes multi-time prediction under different signal-to-noise ratios;
fig. 5 is a diagram illustrating a comparison of MSE performance when channel prediction is implemented by using the channel prediction method according to the embodiment of the present invention and a conventional channel prediction method based on a BP neural network under different hidden layer structures.
Detailed Description
The invention is further described with reference to specific examples. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Referring to fig. 1 to 5, the technical scheme adopted by the invention is a time-varying channel prediction method based on deep learning and suitable for a high-speed moving scene, and aims to improve the prediction accuracy of a time-varying channel and reduce the calculation complexity of the time-varying channel. The method is based on BP neural network to carry out offline training and online prediction. In the off-line training stage, the method obtains an expected network initial value through a pre-training method, then trains the BP neural network again based on the initial value, and obtains a channel prediction network model to reduce the performance loss caused by the random initialization of the BP neural network; in an online prediction stage, the method fully utilizes a multi-input multi-output BP neural network and realizes the prediction of future single and multiple time channels based on a training network. The technical scheme adopted by the invention comprises the following steps:
step 1: obtaining time domain channel estimation value by using received signal and LS method under the condition that data and pilot frequency are known
Figure BDA0002863793450000051
And 2, step: based on time domain channel estimates
Figure BDA0002863793450000052
Construction of a Pre-training sample set CpI.e. by
Figure BDA0002863793450000053
Wherein U represents the number of pre-training samples,
Figure BDA0002863793450000054
represents the u-th input/output sample set of the pre-training phase, wherein
Figure BDA0002863793450000055
For input samples, representing estimated channel parameters
Figure BDA0002863793450000056
The channel state information of the u-th sampling instant and the next (D-1) sampling instant,
Figure BDA0002863793450000057
is an output sample representing the channel state information of the (u + D) th and the (P-1) th sampling instants following the ideal channel parameter h (n), i.e. the output sample
Figure BDA0002863793450000058
Figure BDA0002863793450000059
Where h (n) is an ideal time domain channel parameter. Γ (-) is an operation that converts a complex number into a real number, i.e., Γ (h (n)) = [ Re (h (n)), im (h (n)) ], where Re (-) and Im (-) are real and imaginary parts taking operations, respectively;
and step 3: utilizing a pre-training sample set C based on randomly initialized network parameterspPre-training a BP neural network;
and 4, step 4: obtaining the weight value as Wpre，VpreAnd a threshold parameter of ξpre，θpreA neural network of (a);
and 5: in the case where only the pilot is known, the time domain channel estimation value is acquired using the received signal r (n), the LS method, and the linear interpolation method
Figure BDA00028637934500000510
Step 6: according to the time domain channel estimated value in the step 5
Figure BDA00028637934500000511
Construction of training sample set CTI.e. by
Figure BDA00028637934500000512
Wherein U represents the number of training samples,
Figure BDA00028637934500000513
represents the u-th input/output sample set of the training phase and is constructed as
Figure BDA00028637934500000514
Figure BDA00028637934500000515
In the formula, input samples
Figure BDA0002863793450000061
Representing estimated channel parameters
Figure BDA0002863793450000062
The channel state information of the middle u sampling moment and the next (D-1) sampling moment, and outputs a sample
Figure BDA0002863793450000063
Channel state information representing the (u + D) th sampling instant and the (P-1) th sampling instant thereafter in an ideal channel parameter h (n), h (n) being an ideal time domain channel parameter;
and 7: adopting the weight parameter W obtained in the step 4pre，VpreAnd threshold parameter xipre，θpreAs initial parameters of the network in the training phase, a training sample set C is utilizedTTraining the network again;
and 8: obtaining the final weight value parameter Wtrain，VtrainAnd a threshold parameter of ξtrain，θtrainThe channel prediction network model of (a);
and step 9: performing on-line channel prediction based on the channel prediction network model obtained in step 8, and inputting channel parameter estimation values x of the previous D moments into the networkEObtaining the predicted value y of the channel at the next P momentsEWherein
Figure BDA0002863793450000064
yE＝[Γ(hpre(n)),Γ(hpre(n+1)),...,Γ(hpre(n+P-1))]
Step 10: converting the predicted value obtained in step 9 into complex number as the final channel predicted value, i.e. the final channel predicted value
hpre＝Ξ(yE)
In the formula, xi (xi) is an operation of converting a real number into a complex number, i.e. xi (y)E)＝Re(yE)+jIm(yE)。
Consider a single-input single-output OFDM system (i.e., SISO-OFDM system), assuming SmIs the m-th transmitted OFDM symbol of the frequency domain, and Sm＝[S(m,0),S(m,1),...,S(m,N-1)]TWhere S (m, k) denotes a transmission signal on the kth subcarrier of the mth OFDM symbol, and N is an OFDM symbol length. To SmThe IFFT is carried out to obtain a time domain sending signal of
Figure BDA0002863793450000065
In the HSR communication environment, since the base stations are all built near the rails, there will be a strong direct-of-sight (LOS) component, so the rice channel is usually used as the channel model in the HSR environment, i.e. the channel model is
Figure BDA0002863793450000066
In the formula, alpha0(m, n) is the LOS path component of the channel, αl(m, n), L =1, L-1 being the scattering component path, which obeys rayleigh distribution, L being the number of paths of the multipath rice channel, τlIs the normalized time delay of the first path, and the Rice factor is defined as
Figure BDA0002863793450000067
Assuming that the length of the cyclic prefix is greater than the maximum delay of the wireless transmission channel and the receiving end considers the ideal timing synchronization, the received signal of the nth sampling point of the mth OFDM symbol is
Figure BDA0002863793450000071
Wherein z (m, n) is a mean of 0 and a variance of
Figure BDA0002863793450000072
Additive White Gaussian Noise (AWGN). Since the channel prediction method for each OFDM symbol considered here is the same, the symbol index m will be omitted in the following discussion.
The invention adopts a multi-input multi-output three-layer BP neural network, which comprises an input layer, a hidden layer and an output layer. Suppose that the input layer of the BP neural network has D neurons, the hidden layer has Q neurons, and the output layer has P neurons. Here, the set of training samples defining the network is
C＝{(x(1),y(1)),(x(2),y(2)),...,(x(U),y(U))}
In the formula, U represents the number of training samples,
Figure BDA0002863793450000073
is the u-th vector of input samples,
Figure BDA0002863793450000074
is the value on the d-th element, i.e. the d-th input neuron, in the u-th input sample vector.
Figure BDA0002863793450000075
Representing the u-th output sample vector,
Figure BDA0002863793450000076
is the value on the p-th element, i.e. the p-th output neuron, in the u-th output sample vector.
Since the input value of any node in the neural network is the output of the neuron in the previous layer multiplied by the weight and added with the threshold value, and then the activation function activates the output value of the node, the output of the q hidden neuron is the output of any training sample
Figure BDA0002863793450000077
In the formula, g1(. For hidden layer activation function) the Sigmoid function is chosen here, i.e. it is
Figure BDA0002863793450000078
Figure BDA0002863793450000079
Input for the q hidden neuron
Figure BDA00028637934500000710
In the formula, xdDenotes the d-th input neuron, Wd,qRepresenting the weight, ξ, between the qth hidden neuron and the d input neuronqIs the threshold for the qth hidden neuron.
At the output layer of the BP neural network, the output of the p-th output neuron is
Figure BDA00028637934500000711
In the formula, g2(. Cndot.) is an output layer activation function, where the ReLU function is chosen, i.e.
Figure BDA00028637934500000712
Figure BDA00028637934500000713
Is the input of the p-th output neuron
Figure BDA0002863793450000081
In the formula, Vq,pFor the weight between the qth hidden layer neuron and the pth output layer neuron, θpIs the threshold of the p-th output neuron.
The technology of the invention takes the Mean Square Error (MSE) of the BP neural network output and an ideal channel value h (n) as a loss function, adopts a gradient descent method to update a weight and a threshold matrix, and trains the network through a sample so as to enable the error to meet the set precision.
Simulation result
The performance of the invention is analyzed in conjunction with simulations. In the simulation, the system is assumed to be a single-input single-output OFDM system, where the FFT/IFFT length is 128, the cyclic prefix length is 16, a comb-shaped pilot structure is adopted, the number of pilots is 32, and the pilots are uniformly distributed. Assuming that the moving speed of the train is 500km/h, the channel adopts a multipath Rice channel, and the Rice factor is 5. The carrier frequency was 3.5GHz and the subcarrier spacing was 15kHz. Sample interval Ts＝0.72×10-4And s. The number of input neurons of the network D =10 and the number of hidden layer neurons Q =5. Learning rate of network eta =0.001, target error of training epsilongoal＝1×10-4The maximum number of iterations is set to 1000. In the simulation, the number of training samples considered U =5000. In order to compare the performances of the invention, the performances of the AR model-based linear prediction method, the echo state network-based channel prediction method and the traditional BP neural network-based channel prediction method are also provided in the simulation.
Fig. 3 shows an MSE performance curve under different snr conditions for the present invention and the existing channel prediction method. In the figure, "ideal value" refers to the best performance that can be achieved by channel prediction under ideal conditions. It can be seen from the figure that, as the signal-to-noise ratio increases, the prediction performance of various prediction methods is improved, and compared with the conventional channel prediction method, the channel prediction method based on the BP neural network and the technology of the present invention can obtain better prediction performance, which is closer to an ideal value. However, the technology of the invention adds pre-training processing, which provides ideal network initial parameters for the training stage and avoids the random initialization of the parameters, so the invention has better performance than the traditional channel prediction method based on the BP neural network.
Fig. 4 shows an MSE performance curve for multi-time prediction implemented by the technique of the present invention and a conventional channel prediction method based on a BP neural network under different signal-to-noise ratios. In the figure, "P" indicates the number of neurons in the output layer, and indicates that the predicted channel value at the future "P" times is output. It can be seen from the figure that, no matter single-time prediction or multi-time prediction is performed, with the increase of the signal-to-noise ratio, the MSE performance of the channel prediction method based on the BP neural network and the conventional MSE performance of the channel prediction method based on the BP neural network both become better, and when the signal-to-noise ratio increases to a certain extent, the prediction performance of the channel prediction method tends to be stable, and the MSE performance curve of the channel prediction method based on the channel prediction method of the invention slightly fluctuates within the allowable range of errors, but generally keeps at a stable level. However, as the number of prediction instants increases, the MSE performance of both methods deteriorates because the correlation of the channel gradually decreases with increasing time interval, and thus the MSE performance of multi-instant prediction deteriorates with increasing number of prediction instants. However, the performance of the technology of the invention is always superior to that of the traditional BP neural network, which also shows that the technology of the invention can better realize the multi-time prediction function of the channel compared with the prior method.
Fig. 5 shows an MSE performance curve for implementing channel prediction under different hidden layer structures by using the technique of the present invention and a conventional channel prediction method based on a BP neural network. In the figure, "Q" means the number of neurons in the hidden layer. It can be seen from the figure that, no matter what hidden layer structure is based on, the MSE performance of the channel prediction method based on the BP neural network becomes better as the signal-to-noise ratio increases. However, increasing the number of hidden layers does not have as much effect as increasing the number of hidden layer neurons in the channel prediction performance, and thus the prediction performance can be improved by appropriately increasing the number of hidden layer neurons. However, under the same hidden layer structure, the MSE performance of the technology of the present invention is always superior to that of the conventional channel prediction method based on the BP neural network, which shows that the technology of the present invention has superiority in implementing channel prediction.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, it is possible to make various improvements and modifications without departing from the technical principle of the present invention, and those improvements and modifications should be considered as the protection scope of the present invention.

Claims (1)

1. A novel time-varying channel prediction method based on deep learning is characterized by comprising the following steps:
obtaining time domain channel estimation value by using received signal and LS method under the condition that data and pilot frequency are known
Figure FDA0003839524460000011
In the case where only the pilot is known, the time domain channel estimation value is acquired using the received signal r (n), the LS method, and the linear interpolation method
Figure FDA0003839524460000012
Based on time domain channel estimates
Figure FDA0003839524460000013
Construction of a Pre-training sample set Cp(ii) a Based on time domain channel estimates
Figure FDA0003839524460000014
Construction of training sample set CT；
Randomly initializing network parameters, and pre-training the network by using a pre-training sample set to obtain the weight and threshold parameters of the pre-training network; under the condition that only the pilot frequency is known, acquiring a time domain channel estimation value, and constructing a training sample set according to the time domain channel estimation value;
adopting the weight and threshold parameters of the pre-training network as initial parameters of the network in the training stage, and training the network again through a training sample set to obtain a channel prediction network model;
performing online channel prediction based on a channel prediction network model, and converting an online predicted value into a complex number to be used as a final channel predicted value;
based on time domain channel estimates
Figure FDA0003839524460000015
Construction of a Pre-training sample set CpThe formula of (1) is as follows:
Figure FDA0003839524460000016
in the formula: u represents the number of pre-training samples;
Figure FDA0003839524460000017
represents the u-th input/output sample set of the pre-training phase, wherein
Figure FDA0003839524460000018
Is input samples representing estimated channel parameters
Figure FDA0003839524460000019
The channel state information of the u-th sampling instant and the next (D-1) sampling instant,
Figure FDA00038395244600000110
is an output sample representing the channel state information of the (u + D) th and the (P-1) th sampling instants following the ideal channel parameter h (n), i.e. the output sample
Figure FDA00038395244600000111
Figure FDA00038395244600000112
In the formula: h (n) is an ideal time domain channel parameter,
Figure FDA00038395244600000113
is obtained by using a received signal and an LS method under the condition that data and pilot frequency are knownTaking a time domain channel estimation value; Γ (-) is an operation to convert a complex number to a real number, i.e.
Γ(h(n))＝[Re(h(n)),Im(h(n))]
In the formula: re (-) and Im (-) are real part and imaginary part operations respectively;
based on time domain channel estimates
Figure FDA00038395244600000114
Construction of training sample set CTThe formula of (1) is as follows:
Figure FDA00038395244600000115
in the formula: u represents the number of training samples;
Figure FDA00038395244600000116
the u-th input and output sample set of the training stage is represented and is structured as follows:
Figure FDA00038395244600000117
Figure FDA00038395244600000118
in the formula: inputting samples
Figure FDA00038395244600000119
Representing estimated channel parameters
Figure FDA00038395244600000120
Channel state information of the middle (u) th sampling instant and the next (D-1) sampling instant; outputting the sample
Figure FDA0003839524460000021
Representing the (u + D) th sample in the ideal channel parameter h (n)Channel state information at and after (P-1) sample instants, h (n) is an ideal time domain channel parameter,
Figure FDA0003839524460000022
under the condition that only pilot frequency is known, a time domain channel estimation value is obtained by utilizing a received signal r (n), an LS method and a linear interpolation method;
the method for online channel prediction based on the channel prediction network model comprises the following steps:
on-line channel prediction is carried out based on a channel prediction network model, and channel parameter estimated values x at the previous D moments are input to the networkEObtaining the predicted value y of the channel at the next P momentsEWherein
Figure FDA0003839524460000023
Converting the on-line predicted value into complex number as the final channel predicted value
hpre＝Γ-1(yE)
In the formula: gamma-shaped-1(. Cndot.) is the inverse operation of Γ (·), i.e., the operation of converting a real number into a complex number;
the system model employed includes:
using the Leise channel as a channel model, i.e.
Figure FDA0003839524460000024
In the formula: alpha is alpha0(m, n) is the LOS path component of the channel, αl(m, n), L =1, L-1 being the scattering component path, which obeys rayleigh distribution, L being the number of paths of the multipath rice channel, τlIs the normalized time delay of the first path, and the Rice factor is defined as
Figure FDA0003839524460000025
If the length of the cyclic prefix is greater than the maximum delay of the wireless transmission channel and the receiving end considers the ideal timing synchronization, the received signal of the nth sampling point of the mth OFDM symbol is:
Figure FDA0003839524460000026
in the formula: z (m, n) is mean 0 and variance is
Figure FDA0003839524460000027
Additive White Gaussian Noise (AWGN);
the network adopts a three-layer BP neural network and comprises an input layer, a hidden layer and an output layer;
if there are D neurons in the input layer, Q neurons in the hidden layer and P neurons in the output layer of the BP neural network, the training sample set of the BP neural network is defined as:
C＝{(x(1),y(1)),(x(2),y(2)),...,(x(U),y(U))}
in the formula: u represents the number of training samples;
Figure FDA0003839524460000031
is the vector of the u-th input sample,
Figure FDA0003839524460000032
is the d-th element in the u-th input sample vector, i.e. the value on the d-th input neuron;
Figure FDA0003839524460000033
representing the u-th output sample vector,
Figure FDA0003839524460000034
is the p-th element in the u-th output sample vector, i.e. the value on the p-th output neuron;
the method for training the BP neural network according to the sample set comprises the following steps:
in the hidden layer of the BP neural network, the output of the qth hidden neuron is:
Figure FDA0003839524460000035
in the formula: g1(. For hidden layer activation function) the Sigmoid function is chosen here, i.e. it is
Figure FDA0003839524460000036
Figure FDA0003839524460000037
The inputs for the qth hidden neuron are:
Figure FDA0003839524460000038
in the formula: x is the number ofdDenotes the d-th input neuron, Wd,qRepresents the weight between the qth hidden neuron and the d input neuron, ξqA threshold for the qth hidden neuron;
at the output layer of the BP neural network, the output of the pth output neuron is:
Figure FDA0003839524460000039
in the formula: g2(. To) as an output layer activation function, where a ReLU function is selected, i.e.
Figure FDA00038395244600000310
Figure FDA00038395244600000311
Is the input to the pth output neuron:
Figure FDA00038395244600000312
in the formula: vq,pIs the weight between the qth hidden layer neuron and the pth output layer neuron, θpIs the threshold of the p-th output neuron.
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