CN116418633A - Depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics - Google Patents

Depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics Download PDF

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CN116418633A
CN116418633A CN202310174517.1A CN202310174517A CN116418633A CN 116418633 A CN116418633 A CN 116418633A CN 202310174517 A CN202310174517 A CN 202310174517A CN 116418633 A CN116418633 A CN 116418633A
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李�杰
黄婷婷
赵昊
季飞
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Abstract

The invention discloses a depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics, which comprises the following steps: the sparse and low-rank prior knowledge of the underwater sound double-expansion channel in the time delay-Doppler domain is combined, and the underwater sound channel is solved by adopting an alternate linearization minimization method through the sparse and low-rank two-part matrix. Meanwhile, a certain threshold value is set, so that the depth expansion algorithm network has self-adaptive iteration depth. In the invention, under the background of weak sparsity of a time delay-Doppler domain, the sparsity of underwater acoustic double expansion channels is not needed, and a depth expansion algorithm is adopted, so that the improved deep learning method has good interpretation based on a model method and stability of a classical deep learning network method, and the method has good estimation performance when being used for testing simulation data and real data.

Description

Depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics
Technical Field
The invention relates to the technical field of underwater acoustic channel estimation and deep learning, in particular to a deep expansion underwater acoustic channel estimation method based on sparse and low-rank features.
Background
In contrast to terrestrial wireless communication, four main features of the underwater acoustic channel are: severe multipath and long delays, frequency selective transmission loss, doppler spread, low sonic propagation, etc. Under multipath and time-varying conditions, the underwater acoustic channel exhibits typical delay-doppler double spread, i.e., delay spread caused by multipath propagation, and doppler shift spread caused by water body motion and transceiver side motion. To eliminate the channel effects, accurate estimation of multiple channel parameters such as multipath delay, doppler shift, and attenuation factor is required, which poses challenges for high-speed underwater acoustic communication.
The application of compressed sensing algorithms has significantly improved the speed and efficiency of channel estimation over the past decade, as it exploits the sparsity of the underwater acoustic channel to be able to reconstruct a high-dimensional channel from a low-dimensional undersampled signal. However, the performance of channel estimation based on compressed sensing algorithms is highly dependent on the sparsity of the channel. However, in practice, the sparsity assumption of the underwater acoustic channel is not always well satisfied due to scattering of the underwater acoustic channel, dense multipath propagation, and spectral leakage effects of signal processing. The performance of the compressed sensing algorithm based estimator may be significantly degraded due to the weak sparsity of the underwater acoustic channel. The existing method also provides some improvements to the problem. For example, improved base extensions are used to enhance channel sparsity (Yu H, song a, barkey M, et al, iterative estimation of doubly selective underwater acoustic channel using basis expansion models [ J ]. Ad Hoc Networks,2015, 34:52-61.); also, the channel cluster structure is processed using block sparsity constraints (Gong B, gui L, qin Q, et al Block distributed compressive sensing-based doubly selective channel estimation and pilot design for large-scale MIMO systems [ J ]. IEEE Transactions on Vehicular Technology,2017,66 (10): 9149-9161.). However, the above method essentially measures the one-dimensional sparsity of the dual-spread channel, and still does not fully utilize the inherent characteristics of the dual-spread channel in the delay-doppler two-dimensional domain.
In addition, many channel estimation algorithms exist that can be formulated as optimization problems that are typically solved using iterative numerical optimization algorithms. In practice, however, the specific iterative algorithm does not necessarily match the application scenario exactly. In recent years, there has been an increasing interest in the scientific and engineering communities due to deep learning. Deep learning achieves mapping of inputs to specific function outputs by training a network using a large amount of data. However, a purely data-driven deep learning algorithm, like a "black box", has no strict algorithm idea constraints. The model-driven neural network integrates a principle algorithm with performance guarantee with a deep learning tool, and aims to combine the advantages of the two ideas. Therefore, in the underwater acoustic channel estimation task, the sparse and low-rank model of the channel is combined with the data-driven neural network by using the deep expansion model-driven neural network method technology, so that the estimation of the double-expansion channel vector is realized.
Summarizing the existing underwater acoustic double-expansion channel estimation method, the following main problems are presented:
1. due to dense multipath, scattering and the like, the sparsity of the underwater acoustic channel in a delay-Doppler domain is weakened, and the performance of the traditional algorithm relying on the sparsity is degraded or even fails.
2. The existing deep learning method based on pure data driving depends on a large amount of training data to complete extraction and estimation of channel characteristics, and prior model characteristics of a channel are not fully utilized.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provide a depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics.
The aim of the invention can be achieved by adopting the following technical scheme:
a depth expansion underwater acoustic channel estimation method based on sparse and low rank features, the channel estimation method comprising the steps of:
s1, constructing a water sound double-expansion channel, and assuming that the water sound double-expansion channel has a delay and Doppler effect, the channel parameters of the water sound double-expansion channel in a delay-Doppler domain comprise: the time delay domain dimension M, the time sampling interval T, the Doppler domain dimension L, the frequency interval delta f, the Doppler resolution 1/(L.times.T) and the time delay resolution 1/(M.times.delta.f);
s2, according to the formula
Figure BDA0004100394160000031
Generating a double spread function U (m, l) of a delay-Doppler domain, wherein a is a channel gain, delta (·) is an impact function, m epsilon (0, M-1), l epsilon (0, L-1), m represents an mth dimension of the delay domain, and l represents a first dimension of the Doppler domain;
s3, generating a transmission signal x [ n ] of an input underwater acoustic double expansion channel, wherein n represents the moment;
s4, the double spread function of the delay-Doppler domain generated in the step S2 and the transmission signal x [ n ] generated in the step S3]By the formula:
Figure BDA0004100394160000032
obtaining a received signal y [ n ]]Wherein N is 0 Is the received signal dimension, N 0 =n+m-1, the transmit signal length is N, w [ N ]]Is gaussian noise;
input and output of the underwater sound double expansion channel are written in a vector form:
y＝Au+w
wherein y= [ y [0 ]],...,y[N 0 -1]] T ，w＝[w[0],...,w...，w[N[N 0 -1]] T ，
Figure BDA0004100394160000033
Is an observation matrix, a= [ phi ] 0 X,...,Φ l X,...,Φ L-1 X]Wherein->
Figure BDA0004100394160000034
Is a diagonal matrix defined as: />
Figure BDA0004100394160000035
Figure BDA0004100394160000036
Is->
Figure BDA0004100394160000037
Figure BDA0004100394160000038
Channel vectors, which are delay-doppler domains, are defined as u= [ U (0, 0), …, U (0, M-1), … U (L, 0), …, U (L, M-1), …, U (L-1, 0) …, U (L-1, M-1)] T When the measurement vector y is known, the channel vector u of the delay-doppler domain can be estimated;
s5, building a deep-expansion neural network;
s6, generating a data set for training the neural network
Figure BDA0004100394160000041
Data set->
Figure BDA0004100394160000042
Comprises a measurement vector y and a channel vector u of the delay-doppler domain;
s7, utilizing the data set
Figure BDA0004100394160000043
Performing iterative training on the neural network to enable the loss function to converge to the minimum value, thereby obtaining a model parameter set +.>
Figure BDA0004100394160000044
S8, using the model parameter set
Figure BDA0004100394160000045
Initializing a neural network, generating an analog signal or acquiring a real scene signal, and inputting the analog signal or the real scene signal into the neural network after data conversion and normalization to obtain an output +.>
Figure BDA0004100394160000046
Figure BDA0004100394160000047
Is the channel vector of the estimated delay-doppler domain.
Further, the step S5 is as follows:
the optimization problem to be solved is defined as follows:
Figure BDA0004100394160000048
middle| I 1 Represents the L1 norm w,* Representing a weighted kernel norm, L and S representing a low rank part and a sparse part of u respectively;
the deep-unfolding neural network consists of K iterative blocks, and each iterative block is respectively formed by a weighted low-rank module L k +1 Sparse module S k+1 And channel vector recovery module u k+1 The updating steps of the modules correspond to the formulas:
Figure BDA0004100394160000049
firstly, building a weighted low-rank module L k+1 Wherein
Figure BDA00041003941600000410
Sigma is a diagonal matrix containing singular values, for each diagonal element, sigma, in Sigma ii There is->
Figure BDA00041003941600000411
Figure BDA00041003941600000412
Represents the contraction of singular values with a weighted value omega, i.e. the recovery of the low rank part L of the (k+1) th iteration by a weighted kernel norm minimization method k+1 ；
Secondly, building a sparse module S k+1 The T (-) represents a sparse regularization function, constrained by an L1 norm, a sparse module S k+1 Will u k And L is equal to k+1 Splicing in the channel dimension, and inputting the spliced characteristics into a continuous systemThree convolution layers with the convolution kernel size of 3 multiplied by 3 are used for obtaining sparse priori knowledge, a PReLU activation function is adopted, and a sparse part S of the (k+1) th iteration is restored k+1 ；
Finally, a channel vector recovery module u is built k+1 Using low rank part L that has been restored k+1 And a sparse part S k+1 The learning step length gamma is used for solving the parameter selection problem, and the gradient term F is A + (A(L k+1 +S k+1 ) -y), wherein A + To observe the pseudo-inverse of the matrix, a residual vector (a (L k+1 +S k+1 ) Y) sequentially inputting two continuous full-connection layers, wherein the activation function of the full-connection layers is Sigmoid function, and obtaining a pause factor h by calculating the L2 norm of the residual vector k ，h k For comparison with a threshold parameter epsilon, which is set by man, when k=min (K: h k And less than or equal to epsilon), stopping iteration by the neural network, wherein K is the total number of iteration blocks operated by the neural network, and the obtained channel vector recovery module outputs u K Finally u is K Input into the fully connected layer of neurons, output estimated channel vector of delay-Doppler domain
Figure BDA0004100394160000051
Further, the step S6 generates a required data set
Figure BDA0004100394160000052
The process of (2) is as follows: the measurement vector y and the channel vector u of the estimated delay-doppler domain are first input into the following equation: />
Figure BDA0004100394160000053
Wherein real (-) and imag (-) respectively represent real part taking and imaginary part taking operation, then the real part and the imaginary part of complex data are spliced to form a real data set, and finally each group of data is normalized to obtain a data set->
Figure BDA0004100394160000054
Compared with the prior art, the invention has the following advantages and effects:
1. the traditional method for estimating the underwater sound double-expansion channel generally depends on the sparsity of the time delay-Doppler domain, the sparsity of the double-expansion channel is not strong and the number of paths is difficult to determine in a scattering underwater sound environment, the sparsity and the low rank of the time delay-Doppler domain are jointly utilized, the two-dimensional structural characteristics of the channel are fully excavated, the sparsity is not only relied, and the estimation effect is better.
2. The invention is based on the deep development technology, the traditional deep learning method is equivalent to a black box, only a large number of sample data training models are used, no specific algorithm thought is used for guaranteeing the performance, and no logic interpretability is provided. The method integrates the thought of iterative algorithm into deep learning, is divided into three iterative modules, and all parameters are learnable, so that better estimation performance can be obtained by using less training data.
3. Compared with the existing depth expansion algorithm, the invention combines the characteristics of the studied underwater acoustic double expansion channel to make two-point improvement: (1) By adjusting the supervised learning parameters and introducing the threshold parameters, the neural network iteration times are self-adaptive, the estimated running speed is accelerated, and the estimation effect is enhanced; (2) In order to strengthen priori knowledge of matrix singular values, a weighted kernel norm minimization method is adopted; through the improvement measures, the algorithm provided by the invention can obtain a better performance result compared with the existing compressed sensing algorithm and the deep learning algorithm in estimating the underwater acoustic double-expansion channel performance.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the invention and do not constitute a limitation on the invention. In the drawings:
fig. 1 is a network structure block diagram of a sparse and low rank feature-based deep expansion underwater acoustic dual expansion channel estimation method disclosed by the invention;
fig. 2 is a schematic diagram of a delay-doppler domain dual spread channel in a "weak sparse" and sparse background constructed in accordance with the present invention;
FIG. 3 is a graph of the results of the test of the invention using simulated data, performed in a "weak sparse" underwater acoustic dual expansion channel background, wherein FIG. 3 (a) is a schematic diagram of three deep learning methods, and FIG. 3 (b) is a schematic diagram of a comparison of estimated performance comprising two compressed sensing algorithms;
fig. 4 is a graph of test results using simulation data, which is performed in a sparse underwater acoustic dual expansion channel background, wherein fig. 4 (a) is a schematic diagram of three deep learning methods, and fig. 4 (b) is a schematic diagram of comparison of estimation performance including two compressed sensing algorithms.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
As shown in fig. 1, the embodiment discloses a specific implementation step of a depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics in a simulation signal scene:
s1, constructing a water sound double-expansion channel, and assuming that the water sound double-expansion channel has a delay and Doppler effect, the channel parameters of the water sound double-expansion channel in a delay-Doppler domain comprise: delay domain dimension m=16, doppler domain dimension l=16, frequency interval Δf=15 KHZ, time sampling interval t=1/Δf, doppler resolution 1/(l×t), delay resolution 1/(m×Δf);
s2, according to the formula
Figure BDA0004100394160000071
Generating a double spread function U (m, l) of the delay-Doppler domain, where a is the channel gain, delta(. Cndot.) is an impact function, m.epsilon. (0, M-1), l.epsilon. (0, L-1), m represents the m-th dimension of the delay domain, and l represents the first dimension of the Doppler domain;
s3, generating a transmission signal x [ n ] of an input underwater acoustic double expansion channel, wherein n represents the moment;
s4, the double spread function of the delay-Doppler domain generated in the step S2 and the transmission signal x [ n ] generated in the step S3]By the formula:
Figure BDA0004100394160000072
obtaining a received signal y [ n ]]Wherein N is 0 Is the received signal dimension, N 0 =n+m-1, the transmit signal length is N, w [ N ]]Is gaussian noise;
input and output of the underwater sound double expansion channel are written in a vector form:
y＝Au+w
wherein y= [ y [0 ]],...,y[N 0 -1]] T ，w＝[w[0],…,w[N 0 -1]] T ，
Figure BDA0004100394160000081
Is an observation matrix, a= [ phi ] 0 X,…,Φ l X,...,Φ L-1 X]Wherein->
Figure BDA0004100394160000082
Is a diagonal matrix defined as: />
Figure BDA0004100394160000083
Figure BDA0004100394160000084
Is->
Figure BDA0004100394160000085
Figure BDA0004100394160000086
Channel vectors, which are delay-doppler domains, are defined as u= [ U (0, 0), …, U (0, M-1), … U (L, 0), …, U (L, M-1), …, U (L-1, 0) …, U (L-1, M-1)] T When the measurement vector y is known, it can be estimatedChannel vector u of delay-doppler domain;
s5, building a deep-expansion neural network, which corresponds to the figure 1;
the deep-spread neural network consists of a plurality of iteration blocks, and each iteration block is respectively formed by a weighted low-rank module L k+1 Sparse module S k+1 And channel vector recovery module u k+1 The updating steps of the modules correspond to the formulas:
Figure BDA0004100394160000087
firstly, building a weighted low-rank module L k+1 Wherein
Figure BDA0004100394160000088
Sigma is a diagonal matrix containing singular values, for each diagonal element, sigma, in Sigma ii There is->
Figure BDA0004100394160000089
Figure BDA00041003941600000810
Represents the contraction of singular values with a weighted value omega, i.e. the recovery of the low rank part L of the (k+1) th iteration by a weighted kernel norm minimization method k+1 ；
Secondly, building a sparse module S k+1 The T (-) represents a sparse regularization function, constrained by an L1 norm, a sparse module S k+1 Will u k And L is equal to k+1 Splicing in channel dimension, inputting the spliced features into a convolution layer with 3×3 continuous three-layer convolution kernel size to obtain sparse priori knowledge, and recovering sparse part S of the (k+1) th iteration by adopting PReLU activation function k+1 ；
Finally, a channel vector recovery module u is built k+1 Using low rank part L that has been restored k+1 And a sparse part S k+1 The learning step length gamma is used for solving the parameter selection problem, and the gradient term F is A + (A(L k+1 +S k+1 ) -y), wherein A + Is the pseudo-inverse of the observation matrix. Residual error (A (L) k+1 +S k+1 ) -y) sequentially inputting two continuous full-connection layers, wherein the activation function is a Sigmoid function, and calculating the L2 norm of the residual vector to obtain the pause factor h k 。h k For comparison with a threshold parameter epsilon, which is set by man, when k=min (K: h k And less than or equal to epsilon), stopping iteration by the network, wherein K is the final layer number of network operation, and the obtained channel vector recovery module outputs u K . Finally u is K Input into the fully connected layer of neurons, output estimated channel vector of delay-Doppler domain
Figure BDA0004100394160000098
S6, generating a data set for training the neural network
Figure BDA0004100394160000091
Data set->
Figure BDA0004100394160000092
The data samples in (a) comprise a measurement vector y, a channel vector u of the delay-doppler domain;
s7, utilizing the data set
Figure BDA0004100394160000093
Performing iterative training on the neural network to enable the loss function to converge to the minimum value, thereby obtaining a model parameter set +.>
Figure BDA0004100394160000094
S8, using the model parameter set
Figure BDA0004100394160000095
Initializing a neural network, generating an analog signal, and inputting the analog signal into the neural network after data conversion and normalization to obtain an output +.>
Figure BDA0004100394160000096
Figure BDA0004100394160000097
Is the channel vector of the estimated delay-doppler domain.
The delay-doppler domain channels to be estimated in this embodiment are divided into two cases of "weak sparsity" and sparse, corresponding to fig. 2 (a) and fig. 2 (b), respectively, and it can be seen that, compared with the sparse case, the number of paths in the delay-doppler domain is "clustered", the number of paths is increased, and the accurate number of paths cannot be determined in the underwater acoustic double-spread channel under the "weak sparsity" background.
The test results of this embodiment are shown in fig. 3 and fig. 4, and fig. 3 is a result in a "weak sparse" background, and as can be seen from fig. 3 (a), the performance of the method disclosed in the present invention is superior to that of the end-to-end deep learning algorithm and the unmodified deep expansion algorithm. As can be seen from fig. 3 (b), the performance of the method disclosed by the invention is significantly better than that of the OMP and CoSaMP two compressed sensing algorithms, and the end-to-end deep learning algorithm and the unmodified deep expansion algorithm.
Where fig. 4 is a result in a sparse background, as can be seen from fig. 4 (a), the disclosed method performs better than the end-to-end deep learning algorithm and the unmodified deep-expansion algorithm. As can be seen in fig. 4 (b), by comparing the OMP and CoSaMP compressed sensing algorithms, it can be seen that the two compressed sensing algorithms can achieve good estimation performance even in the case of high signal-to-noise ratio, because the conventional iterative algorithm is also well matched to the sparse channel model in the delay-doppler domain under the sparse background. However, under the condition of low signal-to-noise ratio, the estimation performance of the deep expansion learning algorithm disclosed by the invention is better.
Example 2
The embodiment discloses a specific implementation step of a depth expansion underwater sound channel estimation method based on sparse and low-rank characteristics in a real signal scene.
S1, in our experiments, according to the actual underwater sound data set, the lengths of the signal and the CP are respectively set to 1024 and 128;
s2, after data processing, the length of the sending signal and the length of the receiving signal are both768 obtaining the channel vector u at the pilot by least square method P And a true channel vector u real ；
S3, generating a transmission signal x [ n ] of an input underwater acoustic double expansion channel, wherein n represents the moment;
s4, the double spread function of the delay-Doppler domain generated in the step S2 and the transmission signal x [ n ] generated in the step S3]By the formula:
Figure BDA0004100394160000101
obtaining a received signal y [ n ]]Wherein N is 0 Is the received signal dimension, N 0 =n+m-1, the transmit signal length is N, w [ N ]]Is gaussian noise;
input and output of the underwater sound double expansion channel are written in a vector form:
y＝Au+w
wherein y= [ y [0 ]],...,y[N 0 -1]] T ，w＝[w[0],...,w[N 0 -1]] T ，
Figure BDA0004100394160000111
Is an observation matrix, a= [ phi ] 0 X,...,Φ l X,...,Φ L-1 X]Wherein->
Figure BDA0004100394160000112
Is a diagonal matrix defined as: />
Figure BDA0004100394160000113
Figure BDA0004100394160000114
Is->
Figure BDA0004100394160000115
Figure BDA0004100394160000116
Channel vectors, which are delay-doppler domains, are defined as u= [ U (0, 0), …, U (0, M-1), … U (L, 0), …, U (L, M-1), …, U (L-1, 0) …, U (L-1, M-1)] T When the measurement vector y is known, the delay-Doppler domain can be estimatedChannel vector u of (a);
s5, building a deep-expansion neural network, which corresponds to the figure 1;
the deep-spread neural network consists of a plurality of iteration blocks, and each iteration block is respectively formed by a weighted low-rank module L k+1 Sparse module S k+1 And channel vector recovery module u k+1 The updating steps of the modules correspond to the formulas:
Figure BDA0004100394160000117
firstly, building a weighted low-rank module L k+1 Wherein
Figure BDA0004100394160000118
Sigma is a diagonal matrix containing singular values, for each diagonal element, sigma, in Sigma ii There is->
Figure BDA0004100394160000119
Figure BDA00041003941600001110
Represents the contraction of singular values with a weighted value omega, i.e. the recovery of the low rank part L of the (k+1) th iteration by a weighted kernel norm minimization method k+1 。
Secondly, building a sparse module S k+1 The T (-) represents a sparse regularization function, constrained by an L1 norm, a sparse module S k+1 Will u k And L is equal to k+1 Splicing in channel dimension, inputting the spliced features into a convolution layer with 3×3 continuous three-layer convolution kernel size to obtain sparse priori knowledge, and recovering sparse part S of the (k+1) th iteration by adopting PReLU activation function k+1 。
Finally, a channel vector recovery module u is built k+1 Using low rank part L that has been restored k+1 And a sparse part S k+1 The learning step length gamma is used for solving the parameter selection problem, and the gradient term F is A + (A(L k+1 +S k+1 ) -y), wherein A + For observing matrixIs a pseudo-inverse of the matrix of (a). Residual error (A (L) k+1 +S k+1 ) -y) sequentially inputting two continuous full-connection layers, wherein the activation function is a Sigmoid function, and calculating the L2 norm of the residual vector to obtain the pause factor h k 。h k For comparison with a threshold parameter epsilon, which is set by man, when k=min (K: h k And less than or equal to epsilon), stopping iteration by the network, wherein K is the final layer number of network operation, and the obtained channel vector recovery module outputs u K . Finally u is K Input into the full connection layer composed of neurons, output estimated underwater sound channel vector
Figure BDA0004100394160000128
S6, generating a data set for training the neural network
Figure BDA0004100394160000121
Data set->
Figure BDA0004100394160000122
Each set of data samples in (b) includes a channel vector u at the pilot P And a true channel vector u real ；
S7, utilizing the data set
Figure BDA0004100394160000123
Performing iterative training on the neural network to enable the loss function to converge to the minimum value, thereby obtaining a model parameter set +.>
Figure BDA0004100394160000124
S8, using the model parameter set
Figure BDA0004100394160000125
Initializing a neural network, collecting a real scene signal, inputting the real scene signal into the neural network after data conversion and normalization to obtain an output +.>
Figure BDA0004100394160000126
Figure BDA0004100394160000127
For the estimated channel vector.
The test results of this example are as follows: the estimation error of the end-to-end deep learning algorithm is 0.02902, the estimation error of the depth expansion algorithm is 0.01948, and the estimation error of the improved depth expansion algorithm is 0.01549. The deep expansion learning algorithm disclosed by the invention has better estimation performance.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.

Claims (3)

1. The depth expansion underwater sound channel estimation method based on the sparse and low-rank characteristics is characterized by comprising the following steps of:
s1, constructing a water sound double-expansion channel, and assuming that the water sound double-expansion channel has a delay and Doppler effect, the channel parameters of the water sound double-expansion channel in a delay-Doppler domain comprise: the time delay domain dimension M, the time sampling interval T, the Doppler domain dimension L, the frequency interval delta f, the Doppler resolution 1/(L.times.T) and the time delay resolution 1/(M.times.delta.f);
s2, according to the formula
Figure FDA0004100394140000011
Generating a double spread function U (m, l) of a delay-Doppler domain, wherein a is a channel gain, delta (·) is an impact function, m epsilon (0, M-1), l epsilon (0, L-1), m represents an mth dimension of the delay domain, and l represents a first dimension of the Doppler domain;
s3, generating a transmission signal x [ n ] of an input underwater acoustic double expansion channel, wherein n represents the moment;
s4, the double spread function of the delay-Doppler domain generated in the step S2 and the transmission signal x [ n ] generated in the step S3]By the formula:
Figure FDA0004100394140000012
obtaining a received signal y [ n ]]Wherein N is 0 Is the received signal dimension, N 0 =n+m-1, the transmit signal length is N, w [ N ]]Is gaussian noise;
input and output of the underwater sound double expansion channel are written in a vector form:
y＝Au+w
wherein y= [ y [0 ]],...,y[N 0 -1]] T ，w＝[w[0],...,w[N 0 -1]] T ，
Figure FDA0004100394140000013
Is an observation matrix, a= [ phi ] 0 X,,Φ l X,...,Φ L-1 X]Wherein->
Figure FDA0004100394140000014
Is a diagonal matrix defined as: />
Figure FDA0004100394140000015
Figure FDA0004100394140000021
Is->
Figure FDA0004100394140000022
Figure FDA0004100394140000023
Channel vectors, which are delay-doppler domains, are defined as
u＝[U(0,0),,U(0,M-1),U(l,0),,U(l,M-1),,U(L-1,0),U(L-1,M-1)] T ，
When the measurement vector y is known, the channel vector u of the delay-doppler domain can be estimated;
s5, building a deep-expansion neural network;
s6, generating a data set for training the neural network
Figure FDA0004100394140000024
Data set->
Figure FDA0004100394140000025
Comprises a measurement vector y and a channel vector u of the delay-doppler domain;
s7, utilizing the data set
Figure FDA0004100394140000026
Performing iterative training on the neural network to enable the loss function to converge to the minimum value, thereby obtaining a model parameter set +.>
Figure FDA0004100394140000027
S8, using the model parameter set
Figure FDA0004100394140000028
Initializing a neural network, generating an analog signal or acquiring a real scene signal, and inputting the analog signal or the real scene signal into the neural network after data conversion and normalization to obtain an output +.>
Figure FDA0004100394140000029
Is the channel vector of the estimated delay-doppler domain.
2. The depth expansion underwater sound channel estimation method based on sparse and low rank features of claim 1, wherein the step S5 process is as follows:
the optimization problem to be solved is defined as follows:
Figure FDA00041003941400000210
middle| I 1 Represents the L1 norm w,* Representing a weighted kernel norm, L and S representing a low rank part and a sparse part of u respectively;
the deep-unfolding neural network consists of K iterative blocks, and each iterative block is respectively formed by a weighted low-rank moduleL k+1 Sparse module S k+1 And channel vector recovery module u k+1 The updating process of each module corresponds to the following formula:
Figure FDA0004100394140000031
firstly, building a weighted low-rank module L k+1 Wherein
Figure FDA0004100394140000032
Sigma is a diagonal matrix containing singular values, for each diagonal element, sigma, in Sigma ii There is->
Figure FDA0004100394140000033
Represents the contraction of singular values with a weighted value omega, i.e. the recovery of the low rank part L of the (k+1) th iteration by a weighted kernel norm minimization method k+1 ；
Secondly, building a sparse module S k+1 The T (-) represents a sparse regularization function, constrained by an L1 norm, a sparse module S k+1 Will u k And L is equal to k+1 Splicing in channel dimension, inputting the spliced features into a convolution layer with 3×3 continuous three-layer convolution kernel size to obtain sparse priori knowledge, and recovering sparse part S of the (k+1) th iteration by adopting PReLU activation function k+1 ；
Finally, a channel vector recovery module u is built k+1 Using low rank part L that has been restored k+1 And a sparse part S k+1 Using a leachable step size gamma to solve the parameter selection problem, gradient terms
Figure FDA0004100394140000034
Is A + (A(L k+1 +S k+1 ) -y), wherein A + To observe the pseudo-inverse of the matrix, a residual vector (a (L k+1 +S k+1 ) -y) sequentially inputting two continuous full-connection layers, wherein the activation function of the full-connection layers is Sigmoid function, and the L2 norm of the residual vector is calculatedTo a pause factor h k ，h k For comparison with a threshold parameter epsilon, which is set by man, when k=min (K: h k And less than or equal to epsilon), stopping iteration by the neural network, wherein K is the total number of iteration blocks operated by the neural network, and the obtained channel vector recovery module outputs u K Finally u is K Input into the fully connected layer of neurons, output the estimated channel vector of delay-Doppler domain +.>
Figure FDA0004100394140000035
3. The sparse and low rank feature-based depth spread underwater acoustic dual spread channel estimation method according to claim 1, wherein the required data set is generated in the step S6
Figure FDA0004100394140000036
The process of (2) is as follows: the measurement vector y and the channel vector u of the estimated delay-doppler domain are first input into the following equation: />
Figure FDA0004100394140000041
Wherein real (-) and imag (-) respectively represent real part taking and imaginary part taking operation, then the real part and the imaginary part of complex data are spliced to form a real data set, and finally each group of data is normalized to obtain a data set->
Figure FDA0004100394140000042
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