CN111614584B - Transform domain adaptive filtering channel estimation method based on neural network - Google Patents

Transform domain adaptive filtering channel estimation method based on neural network Download PDF

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CN111614584B
CN111614584B CN202010429993.XA CN202010429993A CN111614584B CN 111614584 B CN111614584 B CN 111614584B CN 202010429993 A CN202010429993 A CN 202010429993A CN 111614584 B CN111614584 B CN 111614584B
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CN111614584A (en
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李靖
韩竞宇
葛建华
任德锋
李慧芳
高明
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Xidian University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0254—Channel estimation channel estimation algorithms using neural network algorithms
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    • G06N3/045—Combinations of networks
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/022—Channel estimation of frequency response
    • 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
    • H04L27/2649—Demodulators
    • H04L27/265—Fourier transform demodulators, e.g. fast Fourier transform [FFT] or discrete Fourier transform [DFT] demodulators

Abstract

The invention discloses a transform domain self-adaptive filtering channel estimation method based on a neural network, which mainly solves the problem that the traditional transform domain filtering method uses a filtering window with fixed size and has less filtering noise. The implementation scheme is as follows: 1) constructing a neural network; 2) collecting a training data set for a neural network; 3) performing offline training on the neural network by using a training data set; 4) inputting the time domain estimation vector of the receiving end into a trained neural network to obtain the size of a filtering window; 5) filtering noise according to the size of a filtering window; 6) and performing discrete Fourier transform on the time domain estimation vector after the noise is filtered to obtain a frequency domain estimation vector, and finishing channel estimation. The invention introduces neural network based on traditional method, to obtain optimal filter window size, compared with traditional algorithm, to increase the amount of noise, to improve the channel estimation precision, to be used in channel estimation of OFDM technique.

Description

Transform domain adaptive filtering channel estimation method based on neural network
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a self-adaptive filtering channel estimation method which can be used for channel estimation of an Orthogonal Frequency Division Multiplexing (OFDM) technology.
Background
With the arrival of the 5G era, application scenarios of wireless communication are more and more diversified, besides traditional communication services, smart homes, smart cities, automatic driving, cloud office and the like, the diversified application scenarios bring higher performance index requirements, and the traditional communication technology is difficult to meet the increasing requirements in the aspects of transmission rate, transmission performance and the like.
The rapid development of artificial intelligence brings a new research direction to the field of communication technology, the basis of the artificial intelligence technology is a neural network technology, the neural network can effectively approach and fit any complex function, and can extract and process implicit characteristics, so that the neural network technology has great application potential in the physical layer of communication. The paper "Power of Deep Learning for Channel Estimation and Signal Detection in OFDM systems" published by Hao Ye et al in IEEE Wireless Communications Letters,2018,7(1): 114-.
The channel in the wireless communication field is relatively complex, the performance can be improved by the efficient channel estimation Technology, and a DFT-based channel estimation in 2D-pilot-system-estimated OFDM wireless system published in IEEE VTS 53rd Vehicular Technology Conference by scholars of m.julia et al uses a channel estimation scheme of transform domain filtering and denoising, and the scheme is provided with a filtering window to filter the noise of the channel in the time domain and improve the accuracy of channel estimation, but the filtering window of the algorithm is fixed and cannot be changed along with the change of the channel, and the amount of filtered noise is less.
In the present phase, many schemes for channel estimation using neural networks have been developed. The paper "Deep Learning-Based Channel Estimation and Equalization Scheme for FBMC/OQAM Systems" published by Xing Cheng et al in "IEEE Wireless Communications Letters,2019,8(3): 881-884" combines the Channel Estimation and Equalization modules and replaces them with a neural network, resulting in better performance than the conventional method, but the algorithm does not separate the Channel Estimation module separately, which is not beneficial to the modularization of the communication system.
Disclosure of Invention
The present invention aims to provide a transform domain adaptive filtering channel estimation scheme based on a neural network to change the size of a filtering window according to the change of a channel, filter more noise, and improve the accuracy of channel estimation, aiming at the defects of the prior art.
The technical idea of the invention is as follows: combining a neural network with a traditional transform domain filtering and denoising channel estimation scheme, namely in the process of the traditional transform domain filtering and denoising channel estimation scheme, adaptively selecting the size of a filtering window by using the neural network so as to filter more noise, wherein the implementation steps comprise the following steps:
1) building a neural network model comprising an input layer, two hidden layers and an output layer, wherein the two adjacent layers are connected in a full connection mode;
2) setting a random multi-path channel and recording the maximum time delay T of the channel;
3) after the transmitted signal passes through the multipath channel, least square estimation LS is firstly carried out at the receiving end to obtain a frequency domain estimation vector
Figure BDA0002500194700000021
Then to
Figure BDA0002500194700000022
Performing Inverse Discrete Fourier Transform (IDFT) to obtain time domain estimation vector of multipath channel
Figure BDA0002500194700000023
Wherein n is 0,1, 2.., 255;
4) estimating vectors over a time domain
Figure BDA0002500194700000024
Preprocessing data with the maximum time delay T of the multipath channel to form a training sample;
5) repetition of 2) to 4) of N in totaldataThen, obtaining a mixture containing NdataTraining data sets of the group training samples;
6) substituting the training data set into the built neural network to perform off-line training to obtain a trained neural network;
7) at the receiving endPerforming least square estimation and inverse discrete Fourier transform to obtain time domain channel estimation vector
Figure BDA0002500194700000025
Inputting the preprocessed signal into the trained neural network in 6) to obtain the size of an output filtering window
Figure BDA0002500194700000026
8) By filtering window size
Figure BDA0002500194700000027
Filtering out time domain channel estimation vectors
Figure BDA0002500194700000028
To obtain a time domain channel estimation vector after noise filtering
Figure BDA0002500194700000029
Then to
Figure BDA00025001947000000210
Performing Discrete Fourier Transform (DFT) to obtain frequency domain channel estimation vector
Figure BDA00025001947000000211
Compared with the prior art, the invention has the following advantages:
1. on the basis of the traditional transform domain filtering and denoising channel estimation scheme, the invention uses the neural network to adaptively identify the size of the filtering window aiming at different multipath channels, and can filter more noise, thereby improving the performance of channel estimation.
2. The invention independently applies the neural network to the channel estimation process, and is beneficial to the modular design of the communication system.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a neural network constructed in accordance with the present invention;
fig. 3 is a graph comparing the bit error rate performance of the present invention with that of the conventional transform domain filtering channel estimation method.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the implementation steps of this example are as follows:
step 1, constructing a neural network.
1.1) neural network architecture:
referring to fig. 2, the neural network model constructed in this step includes a 4-layer structure, which is sequentially: the input layer → the first hidden layer → the second hidden layer → the output layer, the two adjacent layers are connected by using a full connection mode, namely the output end of the input layer neuron is connected with the input end of the first hidden layer neuron in a pairwise manner, the output end of the first hidden layer neuron is connected with the input end of the second hidden layer neuron in a pairwise manner, and the output end of the second hidden layer neuron is connected with the input end of the output layer neuron in a pairwise manner.
1.2) parameters of each layer:
the input layer comprises 256 neurons, and the output value of each neuron is sequentially represented as
Figure BDA0002500194700000031
Wherein i is 1,2,31，n1＝256。
The first hidden layer comprises 1000 neurons, and the output value of each neuron is sequentially expressed as
Figure BDA0002500194700000032
The calculation formula is as follows:
Figure BDA0002500194700000033
wherein j is 1,2,32，n2＝1000；σ2(. to) as an activation function, the first hidden layer uses the ReLU function, formula σ2(x)＝max(x,0)；
Figure BDA0002500194700000034
A weight parameter for the first hidden layer;
Figure BDA0002500194700000035
is the bias parameter of the first hidden layer.
The second hidden layer comprises 250 neurons, and the output value of each neuron is sequentially expressed as
Figure BDA0002500194700000036
The calculation formula is as follows:
Figure BDA0002500194700000037
wherein, l is 1,2,33，n3＝250；σ3(. to) as an activation function, the second hidden layer uses the ReLU function, formula is σ3(x)＝max(x,0)；
Figure BDA0002500194700000038
A weight parameter for the second hidden layer;
Figure BDA0002500194700000039
is the bias parameter of the second hidden layer.
The output layer comprises 64 neurons, and the output value of each neuron is sequentially expressed as
Figure BDA00025001947000000310
The calculation formula is as follows:
Figure BDA0002500194700000041
wherein, m is 1,2,34，n4＝64；
Figure BDA0002500194700000042
Is the right of the output layerA weight parameter;
Figure BDA0002500194700000043
is the bias parameter of the output layer; sigma4(. to) is the activation function, the output layer uses the softmax function, expressed as:
Figure BDA0002500194700000044
σ4(x)mrepresenting the activation function used by the output layer in computing the mth neuron value.
1.3) two parameter sets of the neural network:
using weight parameters in neural networks
Figure BDA0002500194700000045
Constituting a weight parameter set W.
Using bias parameters in neural networks
Figure BDA0002500194700000046
Constituting a bias parameter set B.
And 2, acquiring a training data set.
2.1) setting a multipath channel model:
randomly setting the path number of a multipath channel model to be 2-10 paths, wherein the attenuation range of each path is 0-20 dB at random; then randomly generating multipath time delay of 0-0.62 microseconds, wherein the maximum multipath time delay is represented as T by the number of symbols, the range of T is [1,64], and recording T;
then, selecting a signal-to-noise ratio to represent the amount of Gaussian white noise added into the multipath channel, wherein the signal-to-noise ratio selected in the step is 20 dB;
2.2) after the transmitted signal passes through the multipath channel, the receiving end firstly carries out least square estimation LS to obtain the frequency domain channel estimation vector
Figure BDA0002500194700000047
The formula is as follows:
Figure BDA0002500194700000048
wherein x ispilot(n) is a known transmit pilot, ypilot(n) is a received pilot;
2.3) vector of channel estimation in frequency domain
Figure BDA0002500194700000049
Performing inverse discrete Fourier transform to obtain a time domain estimation vector
Figure BDA00025001947000000410
The formula is as follows:
Figure BDA00025001947000000411
wherein, N is 256;
2.4) estimating vector for time domain channel
Figure BDA00025001947000000412
Pretreatment, i.e. taking
Figure BDA00025001947000000413
Amplitude of
Figure BDA00025001947000000414
2.5) processing the maximum multipath delay T of the channel into one-hot type data, namely changing T into a 64-dimensional vector T (p), wherein the formula is as follows:
Figure BDA0002500194700000051
2.6) in amplitude
Figure BDA0002500194700000052
Vector T (p) is a label, and a training sample is formed;
2.7) repetition of 2.1) to 2.6) with NdataThen, obtaining a mixture containing NdataA training data set of training samples is set.
And 3, substituting the data set into a neural network for off-line training.
3.1) will contain NdataThe training data set of the set of training samples is separated into two parts, a training set and a test set, where NtrainGroup as training set, N remainstestGroup as test set, Ndata＝Ntrain+NtestIn this example Ntrain＝300000，Ntest＝100000；
3.2) selecting a loss function J, wherein the loss function selected in the example is a cross entropy function, and the formula is as follows:
Figure BDA0002500194700000053
wherein, ymIs the output of the neural network and is,
Figure BDA0002500194700000054
labels that are training samples;
3.3) training the neural network by adopting a random gradient descent method:
3.3.1) initializing neural networks: from [0,1 ]]Selecting a weight parameter set W and a bias parameter set B from uniformly distributed random numbers, and setting a threshold value J of a loss function0；
3.3.2) randomly selecting 200 samples in the training set, respectively substituting the samples into an input layer of the neural network, and calculating to obtain 200 output values;
3.3.3) respectively substituting 200 output values in 3.3.2) and labels in the training set into a loss function to calculate a loss function value, and averaging the loss function values to obtain an average value
Figure BDA0002500194700000055
3.3.4) average value
Figure BDA0002500194700000056
And a threshold value J0Make a comparison if
Figure BDA0002500194700000057
Training is completed, otherwise, 3.3.5) is executed;
3.3.5) performing back propagation operation, namely respectively solving partial derivatives of all parameters in the weight parameter set W and the bias parameter set B by using a loss function J to obtain a weight gradient set delta W and a bias gradient set delta B, wherein elements in the weight gradient set delta W correspond to elements in the weight parameter set W one by one, and elements in the bias gradient set delta B correspond to elements in the bias parameter set B one by one;
3.3.6) updating the set of weight parameters W and the set of bias parameters B according to the set of weight gradients Δ W and the set of bias gradients Δ B as:
Figure BDA0002500194700000061
w' is the updated weight parameter set; b' is the updated bias parameter set; η is the learning rate, η (0) is taken as the initial value to be 0.1, and then the number of rounds following training is attenuated, and the attenuation formula is:
Figure BDA0002500194700000062
in the formula, q is the number of times of updating the parameters, decay is an attenuation factor, and the value is 0.0001;
3.3.7) repeating 3.3.2) to 3.3.6) until the data in the training set is completely extracted, completing a training round;
3.3.8) repeating 3.3.2) to 3.3.7) until the loss function value meets the requirement of 3.3.4), stopping training;
3.3.9) substituting the test set into the neural network, judging the output accuracy, if the accuracy exceeds 99%, obtaining the trained neural network, otherwise, adjusting any parameter in 3.2) and 3.3), and retraining.
And 4, using the neural network trained in the step 3 at a receiving end.
4.1) obtaining a frequency domain receiving signal at a receiving end, and performing least square channel estimation to obtain a frequency domain estimation vector
Figure BDA00025001947000000618
The formula is as follows:
Figure BDA0002500194700000063
in the formula xpilot(n) is a known transmit pilot, ypilot(n) is a received pilot;
4.2) vector of channel estimation in frequency domain
Figure BDA0002500194700000064
Performing inverse discrete Fourier transform to obtain time domain estimation vector
Figure BDA0002500194700000065
Figure BDA0002500194700000066
Wherein N is 256;
4.3) taking time domain estimation vector
Figure BDA0002500194700000067
Amplitude of
Figure BDA0002500194700000068
Will amplitude value
Figure BDA0002500194700000069
Inputting the input into the trained neural network to obtain the output of the neural network, i.e. the size of the filtering window
Figure BDA00025001947000000610
4.4) preserving the estimate vector
Figure BDA00025001947000000611
Front of
Figure BDA00025001947000000612
Bit, left over
Figure BDA00025001947000000613
The bit is noise; setting the noise to 0 to obtain the time domain channel estimation vector after noise filtering
Figure BDA00025001947000000614
4.5) estimating vector for time domain channel after noise filtering
Figure BDA00025001947000000615
Performing discrete Fourier transform to obtain frequency domain channel estimation vector with noise filtered
Figure BDA00025001947000000616
Figure BDA00025001947000000617
Wherein N is 256;
at this point, channel estimation is completed.
The effects of the present invention can be further illustrated by the following simulations:
1. simulation conditions
The transmission system used for simulation is an Orthogonal Frequency Division Multiplexing (OFDM) system; the sampling rate of the system is 50MHz, the number of subcarriers is 256, and the length of a cyclic prefix is 64; the channel is an extended pedestrian channel model EPA, the channel comprises 7 paths, the power attenuation is respectively 0.0, -1.0, -2.0, -3.0, -8.0, -17.2 and-20.8 dB, and the multipath time delay is respectively 0, 30, 70, 90, 110, 190 and 410 nanoseconds; the standard for measuring the simulation result is the bit error rate, i.e. the ratio of the number of bits of system transmission errors to the total number of bits of transmission.
2. Emulated content
The bit error rate simulation is performed by using the method of the invention and two traditional channel estimation methods respectively, and the result is shown in figure 3.
The abscissa of fig. 3 is the signal-to-noise ratio and the ordinate is the bit error rate of the system. Wherein:
the IDEAL curve refers to the performance of an IDEAL channel estimate, which represents the ultimate performance of the system when the channel estimate is completely error free;
the LS curve is a bit error rate curve using the existing least square algorithm and represents the bit error rate performance when noise is not filtered;
the LS-DFT curve is the error rate of the existing traditional transform filtering algorithm, and the size of a filtering window of the algorithm is 64;
the NN-LS-DFT curve is the error rate curve of the invention;
comparing the error rate performance of the invention and the traditional transform filtering algorithm, it can be found that the invention shows better system performance than the traditional transform domain filtering channel estimation method when the signal-to-noise ratio is more than 10dB, and the performance is close to the limit performance under the ideal condition.

Claims (9)

1. A transform domain adaptive filtering channel estimation method based on a neural network comprises the following steps:
1) building a neural network model comprising 1 input layer, two hidden layers and 1 output layer, wherein the two adjacent layers are connected in a full connection mode;
2) setting a random multi-path channel and recording the maximum time delay T of the channel;
3) after the transmitted signal passes through the multipath channel, least square estimation LS is firstly carried out at the receiving end to obtain a frequency domain estimation vector
Figure FDA0003121841450000011
Then to
Figure FDA0003121841450000012
Performing Inverse Discrete Fourier Transform (IDFT) to obtain time domain estimation vector of multipath channel
Figure FDA0003121841450000013
Wherein n is 0,1, 2.., 255;
4) estimating vectors over a time domain
Figure FDA0003121841450000014
Preprocessing data with the maximum time delay T of the multipath channel to form a training sample;
5) repetition of 2) to 4) of N in totaldataThen, obtaining a mixture containing NdataTraining data sets of the group training samples;
6) substituting the training data set into the built neural network to perform off-line training to obtain a trained neural network;
7) performing least square estimation and inverse discrete Fourier transform at a receiving end to obtain a time domain estimation vector
Figure FDA0003121841450000015
Inputting the preprocessed signal into the trained neural network in 6) to obtain the size of an output filtering window
Figure FDA0003121841450000016
8) By filtering window size
Figure FDA0003121841450000017
Filtering out time domain estimation vectors
Figure FDA0003121841450000018
To obtain a time domain estimation vector after noise filtering
Figure FDA0003121841450000019
Then to
Figure FDA00031218414500000110
Performing Discrete Fourier Transform (DFT) to obtain frequency domain channel estimation vector
Figure FDA00031218414500000111
2. The method of claim 1, wherein the neural network model constructed in 1) has the following parameters for each layer:
the input layer contains 256 neurons;
the first hidden layer comprises 1000 neurons, and the used activation function is a ReLU function;
a second hidden layer, which contains 250 neurons and uses the ReLU function as the activation function;
the output layer contains 64 neurons, and the activation function used is the softmax function.
3. The method of claim 1, wherein the 2) is implemented by randomly setting the number of paths of the multipath channel model to 2 to 10 paths, wherein the attenuation range of each path is randomly 0-20 dB; then randomly generating 0-0.62 microsecond multipath time delay, wherein the maximum multipath time delay is represented as T by the number of symbols, and the range of T is [1,64 ]; then, a signal-to-noise ratio is selected, which represents the amount of white gaussian noise added by the multipath channel.
4. The method of claim 1, wherein the frequency domain estimation vector obtained in 3)
Figure FDA0003121841450000021
Is represented as follows:
Figure FDA0003121841450000022
wherein xpilot(n) is a known transmit pilot, ypilotAnd (n) is the pilot portion of the received signal.
5. The method of claim 1, wherein the time domain estimation vector obtained in 3)
Figure FDA0003121841450000023
Is represented as follows:
Figure FDA0003121841450000024
where N is 256.
6. The method of claim 1, wherein 4) the time domain estimation vector
Figure FDA0003121841450000025
And the maximum time delay T of the multipath channel is used for data preprocessing, and the following steps are realized:
4a) estimating vectors over a time domain
Figure FDA0003121841450000026
Pretreatment, i.e. taking
Figure FDA0003121841450000027
Amplitude of
Figure FDA0003121841450000028
4b) Processing the maximum multipath delay T of the channel into one-hot type data, namely changing the T into a 64-dimensional vector T (m), wherein the formula is as follows:
Figure FDA0003121841450000029
4c) by amplitude
Figure FDA00031218414500000210
For data, vector t (p) is a label, constituting a training sample.
7. The method of claim 1, wherein the neural network is trained offline in 6) by:
6a) will contain NdataThe training data set of the set of training samples is separated into two parts, where NtrainGroup as training set, N remainstestGroup as test set, Ndata＝Ntrain+Ntest；
6b) Selecting a cross entropy function as a loss function J;
6c) training the neural network by adopting a random gradient descent method:
6c1) initializing a neural network: from [0,1 ]]Selecting a weight parameter set W and a bias parameter set B from uniformly distributed random numbers, and setting a threshold value J of a loss function0；
6c2) Randomly selecting 200 samples in a training set, respectively substituting the samples into an input layer of a neural network, and performing operation to obtain 200 output values;
6c3) respectively substituting 200 output values in 6c2) and labels in the training set into a loss function to calculate loss function values, and averaging the loss function values to obtain an average value
Figure FDA0003121841450000031
6c4) Average value
Figure FDA0003121841450000032
And a threshold value J0Make a comparison if
Figure FDA0003121841450000033
Training is complete, otherwise, 6c5 is executed);
6c5) performing back propagation operation, namely solving partial derivatives of all parameters in the weight parameter set W and the bias parameter set B by using a loss function J to obtain a weight gradient set delta W and a bias gradient set delta B, wherein elements in the weight gradient set delta W correspond to elements in the weight parameter set W one by one, and elements in the bias gradient set delta B correspond to elements in the bias parameter set B one by one;
6c6) according to the weight gradient set Δ W and the bias gradient set Δ B, the weight parameter set W and the bias parameter set B are updated as follows:
Figure FDA0003121841450000034
w' is the updated weight parameter set; b' is the updated bias parameter set; η is a learning rate, and η (0) is an initial value of 0.1, and then as the number of rounds of training is attenuated, the attenuation formula is:
Figure FDA0003121841450000035
in the formula, escape is an attenuation factor, 0.0001 is taken, and q represents the number of times that parameter updating is carried out;
6c7) repeating 6c2) to 6c6) until the data in the training set is completely taken, and completing a round of training;
6c8) repeat 6c2) to 6c7) until the loss function value meets the requirement in 6c4), stop training;
6c9) substituting the test set into a neural network, judging the output accuracy, and if the accuracy meets the requirement, obtaining a trained neural network; otherwise, any parameter in 6b) and 6c) is adjusted, and the training is carried out again.
8. The method of claim 1, wherein 8) the time domain estimate vector is filtered out
Figure FDA0003121841450000036
Is to first retain the estimated vector
Figure FDA0003121841450000037
Front of
Figure FDA0003121841450000038
Bit, left over
Figure FDA0003121841450000039
The bit is noise; setting the noise to 0 to obtain the time domain estimation vector after noise filtering
Figure FDA00031218414500000310
Wherein
Figure FDA00031218414500000311
Is a value of the filter window size.
9. The method of claim 1, wherein 8) the frequency domain channel estimate vector after filtering the noise
Figure FDA00031218414500000312
Is represented as follows:
Figure FDA00031218414500000313
where N is 256.
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