CN116346549A - Underwater acoustic channel sparse estimation method adopting convolutional neural network channel cluster detection - Google Patents
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Abstract
The invention belongs to the technical field of underwater acoustic signal processing, and particularly relates to an underwater acoustic channel sparse estimation method adopting convolutional neural network channel cluster detection, which is used for an OFDM underwater acoustic communication system, and comprises the following steps: acquiring frequency domain signals corresponding to different data blocks and based on pilot frequency information; carrying out channel rough estimation on the frequency domain signal; inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection, so as to obtain channel cluster position information; and realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm. The invention utilizes the convolutional neural network to perform cluster detection on the underwater acoustic channel, further combines the cluster detection result with the sparse estimation method, limits the search space of the channel, reduces the influence of noise on channel estimation, improves the estimation precision, and has higher channel estimation precision, stability and robustness compared with the traditional method.
Description
Technical Field
The invention belongs to the technical field of underwater acoustic signal processing, and particularly relates to an underwater acoustic channel sparse estimation method adopting convolutional neural network channel cluster detection.
Background
The acoustic wave is an important carrier for underwater wireless communication, the characteristics of the underwater acoustic channel are complex and changeable, and the underwater acoustic communication device has the characteristics of strong multipath, strong noise, large Doppler frequency shift, obvious space and time fluctuation and the like, and brings great difficulty and challenge to the underwater acoustic communication. The underwater acoustic channel estimation is an important step for completing underwater information transmission, and the accurate estimation of channel parameters is an important means for improving communication performance.
The underwater acoustic channel typically exhibits a clustered sparse characteristic, i.e., most of the channel impulse response is zero or near zero, with channel energy concentrated primarily within the sparse unevenly distributed clustered structure. Traditional channel estimation methods, such as Least Squares (LS) algorithm and Minimum Mean Square Error (MMSE) algorithm, introduce noise estimation errors at zero tap, and the higher order estimator required by channel estimation has larger operation complexity.
For sparse characteristics of the underwater acoustic channel, a sparse estimation method is used for improving channel estimation performance, and in recent years, a channel estimation method based on compressed sensing has received extensive attention and research due to a good estimation effect. The Orthogonal Matching Pursuit (OMP) algorithm has obvious performance advantages compared with the traditional algorithm, and on the basis, the Synchronous Orthogonal Matching Pursuit (SOMP) algorithm is applied to solve the joint sparse reconstruction problem of the channel in a period of time by utilizing the stable sparse characteristic of the slowly-changing underwater acoustic channel. The method further improves the algorithm performance by utilizing the time gain, but the method does not fully utilize the characteristic of the sparse cluster structure of the underwater acoustic channel, and still has noise estimation errors outside a cluster area to influence the channel estimation precision.
How to detect the underwater acoustic channel cluster structure based on the sparse characteristic of the underwater acoustic channel and utilize the underwater acoustic channel cluster structure to improve the performance of the sparse estimation method is a key, some existing research methods have been proposed for detecting the channel cluster structure, such as judging whether each tap coefficient is greater than a channel mean value for clustered grouping by using a rough channel estimation result, but when larger noise interference exists, estimation errors easily occur in the method; the traditional Page detection method can also be applied to underwater acoustic channel cluster detection, but the algorithm needs to adjust parameters according to the environment, so that the stability and the robustness are poor.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a sparse estimation method for an underwater acoustic channel by adopting convolutional neural network channel cluster detection.
In order to achieve the above object, the present invention proposes a sparse estimation method for underwater acoustic channel using convolutional neural network channel cluster detection, for an Orthogonal Frequency Division Multiplexing (OFDM) underwater acoustic communication system, the method comprising:
step 1) obtaining frequency domain signals corresponding to different data blocks based on pilot frequency information;
step 2) carrying out channel coarse estimation on the frequency domain signal;
step 3) inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection, so as to obtain channel cluster position information;
and 4) realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm.
As an improvement of the above method, the frequency domain signal of the corresponding different data block of step 1) based on pilot information satisfies the following formula:
Y p,l =diag(X p,l )F p h l +W p,l
wherein Y is p,l For the frequency domain received signal of the first data block based on pilot information, l=1, 2, …, L,l is the total number of data blocks, diag (X) p,l ) For corresponding pilot symbol X p,l Diagonal matrix of components F p For the corresponding Fourier transform matrix, W p,l H is the corresponding frequency domain additive noise l E n×1 is the channel corresponding to the first data block, and N is the channel length.
As an improvement of the above method, the step 2) specifically includes:
frequency domain signal Y based on pilot information for different data blocks using p,l Performing channel rough estimation to obtain a channel rough estimation result of the first data block
As an improvement of the method, the input of the cluster detection model is a channel rough estimation result, and the output is channel cluster position information; the convolutional neural network adopting the 'U-net' architecture comprises a contracted path and an expanded path, wherein the two paths form a symmetrical structure,
the shrink path is used for extracting required features through feature dimension reduction;
the expansion path is used for decoding the extracted characteristics, comparing each numerical value in the decoded vector with a set threshold to obtain corresponding cluster position information ψ n ,n∈[1,N]Further obtaining channel cluster position information [ ψ ] with channel length N 1 ,…Ψ n ,…Ψ N ]。
As an improvement of the above method, the corresponding cluster position information is ψ n Satisfies the following formula:
wherein,,representing the probability of the intra-cluster channel impulse response of the corresponding position, wherein the probability is larger than a set threshold of 0.5, and considering that the intra-cluster channel impulse response exists in the position, otherwise, the intra-cluster channel impulse response does not exist in the position.
As an improvement of the above method, the step 4) specifically includes:
constructing a cluster area constraint matrix psi according to the obtained channel cluster position information:
Ψ=diag([Ψ 1 ,…Ψ n ,…Ψ N ]),Ψ n ∈{0,1}
wherein diag () represents a diagonal matrix;
solving a received signal Y of a frequency domain of a first data block based on pilot frequency information under a cluster constraint condition by adopting a compressed sensing sparse reconstruction algorithm p,l Simplified into the following form:
Y p,l =Φ l Ψh l +W p,l
wherein phi is l For the perception matrix, Φ l =diag(X p,l )F p ,l=1,2,…,L;
Based on the joint sparse model, the joint dictionary matrix Λ=diag (Φ) l ψ) the dictionary atoms with the corresponding cluster region constraint matrix position of 1 remain unchanged, the rest dictionary atoms are 0 vectors, and the corresponding optimization problem is expressed as:
wherein,,representing the estimation result matrix of L channels, +.>For a receiving matrix made up of pilot information of L data blocks, (-) T Representing a transpose; delta is the minimum residual allowed to exist;
and solving a channel joint sparse reconstruction problem by adopting a sparse channel estimation algorithm.
As an improvement of the above method, the method further comprises a training step of the cluster detection model; the method specifically comprises the following steps:
selecting historical data of a peripheral sea area to perform channel measurement and extracting a cluster structure to generate a training set;
inputting the training set into convolutional neural network, and outputting vector asN is the channel length, each numerical value in the vector represents the probability of the channel impulse response in the cluster at the corresponding position, two kinds of cross entropy are used as a loss function, training is carried out in a supervised learning mode until the training requirement is met, and a trained cluster detection model is obtained.
As an improvement of the method, the historical data of the peripheral sea area is selected for channel measurement, a cluster structure is extracted, and a training set is generated; the method specifically comprises the following steps:
and taking the channel rough estimation result and the known cluster position information as input data of a training set and training labels respectively, wherein the training labels are expressed by vectors, the position with impulse response is 1, and the rest positions are 0.
On the other hand, the invention also provides a sparse estimation system for the underwater acoustic channel, which adopts convolutional neural network channel cluster detection, and comprises the following steps:
the receiving module is used for acquiring frequency domain signals corresponding to different data blocks and based on pilot frequency information;
the channel coarse estimation module is used for carrying out channel coarse estimation on the frequency domain signals;
the cluster detection module is used for inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection so as to obtain channel cluster position information; and
and the channel estimation module is used for realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm.
Compared with the prior art, the invention has the advantages that:
the invention utilizes the characteristic that the slowly-varying underwater acoustic channel presents a relatively stable sparse cluster structure within a certain time, utilizes the convolutional neural network to detect the underwater acoustic channel cluster structure, realizes the accurate positioning of the channel cluster position, further combines cluster position information and a channel sparse estimation method, constructs a channel sparse estimation algorithm based on cluster constraint, reduces the influence of noise on channel estimation by limiting the search space of the channel, and simultaneously obtains time gain by adopting joint estimation, further improves the channel estimation precision, and has good stability and robustness.
Drawings
FIG. 1 is a schematic flow chart of a sparse estimation method of an underwater acoustic channel detected by a convolutional neural network channel cluster;
FIG. 2 is a schematic diagram of a convolutional neural network cluster detection model of example 1;
fig. 3 is a diagram of the channel estimation result of embodiment 1;
fig. 4 is a graph of simulated performance versus signal-to-noise ratio for example 1.
Detailed Description
The invention provides a sparse estimation method for an underwater acoustic channel by adopting convolutional neural network channel cluster detection, which utilizes the characteristics that the underwater acoustic channel presents a sparse cluster structure, a slowly-varying channel has stable sparse characteristics and the like, firstly carries out coarse estimation on a time-varying channel, then carries out cluster detection on a channel coarse estimation result by using the convolutional neural network, and further combines cluster position information and the channel sparse estimation method, so that the search space on channel estimation is limited, and the estimation precision is improved. The method is used for an OFDM underwater acoustic communication system, and comprises the following steps:
step 1) obtaining frequency domain signals corresponding to different data blocks based on pilot frequency information;
step 2) carrying out channel coarse estimation on the frequency domain signal;
step 3) inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection, so as to obtain channel cluster position information;
and 4) realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm.
The method specifically comprises the following steps:
and (one) selecting historical data of the surrounding sea area to perform channel measurement, extracting a cluster structure, and generating a training data set.
More specifically, the channel rough estimation result and the known cluster position information are respectively used as input data of a training data set and a training label. The training tag is specifically represented as a vector, the position with impulse response in the vector is 1, and the rest positions are 0.
And secondly, training the underwater sound channel cluster detection model by using the training data set obtained in the step one. The cluster detection model adopts a convolutional neural network with a U-net architecture, the network can be regarded as a contracted path and an expanded path, the contracted path extracts required characteristics through characteristic dimension reduction, and the symmetrical expanded path decodes the extracted characteristics to obtain channel cluster position information.
More specifically, the convolutional neural network has 14 layers in total, wherein 12 layers are hidden layers. Extending paths, wherein the convolution kernel size is 3 multiplied by 1, performing 1 multiplied by 1 boundary filling before each layer of convolution, performing ReLU activation operation and 2 multiplied by 1 maximum pooling operation, and doubling the number of channels after each layer of convolution except the first layer; the expansion path and the contraction path are in symmetrical structures, in the expansion path, the characteristic diagram is subjected to double up-sampling before each layer of convolution, then 1 multiplied by 1 boundary filling is performed, then the convolution of halving the number of characteristic channels is performed, then the characteristic diagram and the corresponding characteristic diagram in the contraction path are subjected to channel splicing, then the convolution of halving the number of channels with the size of 3 multiplied by 1 boundary filling and convolution kernel of 1 multiplied by 1 is performed, and then the ReLU function activation is performed; the last layer is convolution mapping the number of channels to 1, the convolution kernel size is 1×1, and the activation function is Sigmoid function.
The output vector of the network isN is the length of the channel, each value in the vector represents the probability of the channel impulse response in the cluster at the corresponding position, and the training is performed by using the two kinds of cross entropy as the loss function of the network and adopting a supervised learning mode. If the probability is greater than the threshold (threshold=0.5), the position is considered to have intra-cluster channel impulse response, and the corresponding cluster position information can be obtained as follows:
and thirdly, performing cluster detection on the channel by using the trained model, and estimating the channel by combining a sparse estimation algorithm. Specifically:
3.1 more specifically, in an Orthogonal Frequency Division Multiplexing (OFDM) underwater acoustic communication system, for an OFDM signal having L data blocks, a reception signal of a frequency domain based on pilot information can be obtained at a reception end
Y p,l =diag(X p,l )F p h l +W p,l (2)
Wherein l=1, 2, …, L, Y p,l Is the frequency domain received signal of the first data block based on pilot information, diag (X) p,l ) Is a corresponding diagonal matrix of pilot symbols, F p Is a corresponding Fourier transform matrix, W p,l Is the corresponding frequency domain additive noise, h l E n×1 is the channel corresponding to the first data block, and N is the channel length.
And respectively carrying out channel coarse estimation on different data blocks by adopting the following formula:
And 3.2, inputting each column of the channel estimation result obtained in the step 3.1 as different channels of a cluster detection model, and obtaining the channel cluster position information by outputting the model through a formula (1). Constructing a cluster region constraint matrix by using the obtained cluster position information, specifically defining ψ as the cluster region constraint matrix
Ψ=diag([Ψ 1 ,...,Ψ n ,...,Ψ N ]),Ψ n ∈{0,1} (4)
And 3.3, estimating the underwater sound channel by utilizing the cluster constraint matrix obtained in the step 3.2 and combining a sparse estimation method.
Specifically, a cluster-constrained joint channel sparse model is constructed according to a cluster constraint matrix by utilizing common sparse characteristics of different communication data blocks under a slowly-varying channel, and a joint dictionary matrix is deduced. More specifically, since the sparse characteristics of the channel can be seen that most of the values in h can be seen as 0, the problem of formula (3) can be solved by using a compressed sensing sparse reconstruction algorithm, and under the cluster constraint condition, the problem is further simplified into the following form
Y p,l =Φ l Ψh l +W p,l (5)
Wherein phi is l =diag(X p,l )F p Is a sensing matrix. Under the joint sparse model (JSM 2), the OFDM channel joint sparse reconstruction problem for L data blocks can be expressed as:
wherein,,is a receiving matrix composed of pilot information of L data blocks; Λ is a cluster constrained joint dictionary matrix; phi l ,l∈[1,L]The pilots on different data blocks may be different for the perceptual matrix of a single data block. Therefore, under the action of the cluster constraint matrix, dictionary atoms with the corresponding cluster region constraint matrix position of 1 in the joint dictionary matrix Λ are kept unchanged, and the rest dictionary atoms are 0 vectors. The corresponding optimization problem is expressed as:
where δ is the minimum residual allowed to exist.
And finally, solving a channel joint sparse reconstruction problem by adopting a sparse channel estimation algorithm.
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, embodiment 1 of the present invention proposes a sparse estimation method for an underwater acoustic channel using convolutional neural network channel cluster detection, in this embodiment, an OFDM underwater acoustic communication system is used as an application background, an SOMP algorithm is used as a sparse channel estimation method combined with cluster information, and the effectiveness of the present invention is illustrated through simulation verification.
The method specifically comprises the following steps:
1.1, preprocessing real sea test data, extracting a cluster structure from a channel estimation result, and taking the cluster structure as a channel for a simulation experiment.
1.2 the channel obtained in 1.1 is utilized to simulate the underwater acoustic communication process, and the time-varying channel rough estimation is carried out according to the received signal and the prior sequence.
Specifically, the simulation parameters are: the transmitting signal is an OFDM signal, the bandwidth is 100Hz, the total number of subcarriers is 256, the subcarrier interval is 0.39Hz, 64 pilots are inserted at equal intervals, the guard interval length is 0.44s, the modulation mode is 4-order QAM, and a complete OFDM signal comprises 10 data blocks. The training set simulation signal-to-noise ratio is [ -5,15] dB, and the test set simulation signal-to-noise ratio is [ -515] dB. The signal to noise ratio is defined herein as
At the receiving end of the OFDM underwater acoustic communication system, the rough estimation result of the channel is obtained by utilizing the received signal and pilot frequency information.
And 1.3, respectively taking the channel rough estimation result and the known cluster position information as input data of a training data set and training labels, wherein the training data is 400 groups in total.
And 2, performing model training on the convolutional neural network by using the training data set obtained in the step one, wherein model parameters and structures are shown in fig. 2.
And step 3, performing cluster detection on the channel by using the trained model, and estimating the channel by combining a sparse estimation algorithm.
Specifically, as shown in FIG. 3, the channel parameter h is set to [ -0.250+0.153i,0, 0.715+0.425i,0, -0.265+0.054i,0,0.92-0.389i,0, -0.223-0.230i, zeros (1, 78), -0.141-0.028 i,0, 0.361+0.41i,0, 0.201-0.169i,0, -0.103-0.04i, zeros (1, 60)]The method comprises the steps of carrying out a first treatment on the surface of the Simulation signal to noise ratio of [15 ]]dB (dB). Taking the channel rough estimation result as input, and outputting the channel cluster position information vector by the networkIs [ is ] 1, zeroes (1, 78), 1, zeroes (1, 60) (1, 60)]The method comprises the steps of carrying out a first treatment on the surface of the Channel estimation is carried out by adopting a cluster constraint SOMP algorithm, and a result is output +.>Is [ -0.236+0.200i,0.057-0.046i,0,0.740+0.378i,0, -0.253-0.0070 i,0, 0.88-0.279 j,0, -0.232-0.244i, zeros (1,79), -0.047-0.162i,0,0.272+0.357i,0-0.105+0.018i,0,0.132-0.127i,0, -0.019+0.098i, -0.030-0.015i, zeros (1, 60)]. In contrast, the error rate after equalization of the channel estimation result according to the LS algorithm, OMP algorithm, SOMP algorithm, and proposed SOMP (DL-SOMP) algorithm using deep learning convolutional neural network cluster detection and the error rate when the full Channel State Information (CSI) is known were calculated as 0.066,0.043,0.033,0.029 and 0.027, respectively. Further, in the signal to noise ratio [ -5,15]Simulations were performed in the dB range to obtain the bit error rate curve of fig. 4.
Example 2
The embodiment 2 of the invention provides an underwater sound channel sparse estimation system adopting convolutional neural network channel cluster detection, which is realized based on the method of the embodiment 1, and comprises the following steps:
the receiving module is used for acquiring frequency domain signals corresponding to different data blocks and based on pilot frequency information;
the channel coarse estimation module is used for carrying out channel coarse estimation on the frequency domain signals;
the cluster detection module is used for inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection so as to obtain channel cluster position information;
and the channel estimation module is used for realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm.
The invention provides a sparse estimation method for an underwater acoustic channel by adopting convolutional neural network channel cluster detection, which comprises the steps of firstly carrying out cluster detection on the underwater acoustic channel by using the convolutional neural network, further combining a cluster detection result with a sparse estimation method, limiting the search space of the channel, reducing the influence of noise on channel estimation, and improving the estimation precision.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (9)
1. A method for sparse estimation of an underwater acoustic channel using convolutional neural network channel cluster detection for an OFDM underwater acoustic communication system, the method comprising:
step 1) obtaining frequency domain signals corresponding to different data blocks based on pilot frequency information;
step 2) carrying out channel coarse estimation on the frequency domain signal;
step 3) inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection, so as to obtain channel cluster position information;
and 4) realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm.
2. The method for sparse estimation of underwater acoustic channels using convolutional neural network channel cluster detection as set forth in claim 1, wherein the corresponding different data blocks of step 1) satisfy the following equation based on the frequency domain signal of the pilot information:
Y p,l =diag(X p,l )F p h l +W p,l
wherein Y is p,l For the frequency domain received signal of the L data block based on pilot information, l=1, 2, …, L is the total number of data blocks, diag (X) p,l ) For corresponding pilot symbol X p,l Diagonal matrix of components F p For the corresponding Fourier transform matrix, W p,l H is the corresponding frequency domain additive noise l E n×1 is the channel corresponding to the first data block, and N is the channel length.
3. The method for sparse estimation of underwater acoustic channels using convolutional neural network channel cluster detection as set forth in claim 2, wherein said step 2) is specifically:
frequency domain signal Y based on pilot information for different data blocks using p,l Performing channel rough estimation to obtain a channel rough estimation result of the first data block
4. The underwater sound channel sparse estimation method adopting convolutional neural network channel cluster detection as claimed in claim 3, wherein the input of the cluster detection model is a channel rough estimation result, and the output is channel cluster position information; the convolutional neural network adopting the 'U-net' architecture comprises a contracted path and an expanded path, wherein the two paths form a symmetrical structure,
the shrink path is used for extracting required features through feature dimension reduction;
the expansion path is used for decoding the extracted characteristics, comparing each numerical value in the decoded vector with a set threshold to obtain corresponding cluster position information ψ n ,n∈[1,N]Further obtaining channel cluster position information [ ψ ] with channel length N 1 ,…Ψ n ,…Ψ N ]。
5. The method for sparse estimation of acoustic channels using convolutional neural network channel cluster detection of claim 4, wherein the corresponding cluster position information is ψ n Satisfies the following formula:
wherein,,representing the probability of the intra-cluster channel impulse response of the corresponding position, wherein the probability is larger than a set threshold of 0.5, and considering that the intra-cluster channel impulse response exists in the position, otherwise, the intra-cluster channel impulse response does not exist in the position.
6. The method for sparse estimation of underwater acoustic channels using convolutional neural network channel cluster detection as set forth in claim 5, wherein said step 4) specifically comprises:
constructing a cluster area constraint matrix psi according to the obtained channel cluster position information:
Ψ=diag([Ψ 1 ,…Ψ n ,…Ψ N ]),Ψ n ∈{0,1}
wherein diag () represents a diagonal matrix;
solving a received signal Y of a frequency domain of a first data block based on pilot frequency information under a cluster constraint condition by adopting a compressed sensing sparse reconstruction algorithm p,l Simplified into the following form:
Y p,l =Φ l Ψh l +W p,l
wherein phi is l For the perception matrix, Φ l =diag(X p,l )F p ,l=1,2,…,L;
Based on the joint sparse model, the joint dictionary matrix Λ=diag (Φ) l ψ) the dictionary atoms with the corresponding cluster region constraint matrix position of 1 remain unchanged, the rest dictionary atoms are 0 vectors, and the corresponding optimization problem is expressed as:
wherein,,representing the estimation result matrix of L channels, +.>For a receiving matrix made up of pilot information of L data blocks, (-) T Representing a transpose; delta is the minimum residual allowed to exist;
and solving a channel joint sparse reconstruction problem by adopting a sparse channel estimation algorithm.
7. The method for sparse estimation of underwater acoustic channels using convolutional neural network channel cluster detection of claim 5, further comprising a training step of a cluster detection model; the method specifically comprises the following steps:
selecting historical data of a peripheral sea area to perform channel measurement and extracting a cluster structure to generate a training set;
inputting the training set into convolutional neural network, and outputting vector asN is the channel length, each numerical value in the vector represents the probability of the channel impulse response in the cluster at the corresponding position, two kinds of cross entropy are used as a loss function, training is carried out in a supervised learning mode until the training requirement is met, and a trained cluster detection model is obtained.
8. The method for estimating underwater acoustic channel sparsity using convolutional neural network channel cluster detection as defined in claim 7, wherein the selecting the surrounding sea area history data performs channel measurement and extracts cluster structure, generating training set; the method specifically comprises the following steps:
and taking the channel rough estimation result and the known cluster position information as input data of a training set and training labels respectively, wherein the training labels are expressed by vectors, the position with impulse response is 1, and the rest positions are 0.
9. A system for sparse estimation of an underwater acoustic channel using convolutional neural network channel cluster detection, the system comprising:
the receiving module is used for acquiring frequency domain signals corresponding to different data blocks and based on pilot frequency information;
the channel coarse estimation module is used for carrying out channel coarse estimation on the frequency domain signals;
the cluster detection module is used for inputting the channel rough estimation result into a pre-established and trained cluster detection model to perform cluster detection so as to obtain channel cluster position information; and
and the channel estimation module is used for realizing channel estimation according to the channel cluster position information and a sparse estimation algorithm.
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CN116915555A (en) * | 2023-08-28 | 2023-10-20 | 中国科学院声学研究所 | Underwater acoustic channel estimation method and device based on self-supervision learning |
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