Underwater acoustic channel estimation method based on improved temporal multiple sparse Bayesian learning

Abstract

The present invention discloses an underwater acoustic channel estimation method based on improved time-series multiple sparse Bayesian learning. The method comprises: firstly, the underwater acoustic channel model is expressed as a sparse form including multipath delay and multipath fading factor, and the initial dictionary matrix is ​​obtained; then, the received broadband signal is subjected to multiple denoising to obtain the reconstructed time-domain denoised signal matrix; then, the weighted minimum l1 norm regularization algorithm is used to perform channel estimation on the reconstructed frequency-domain denoised signal matrix to obtain the channel estimation matrix, and then the modified dictionary matrix and the initialization hyperparameters are calculated; then, the time-domain underwater acoustic channel estimation is performed using the time-series multiple sparse Bayesian learning method based on time correlation to obtain the multipath delay estimation result; finally, the multipath fading factor of the underwater acoustic channel at a fixed frequency is optimized and solved to obtain the optimized multipath fading factor. The present invention can effectively obtain the estimation result of the multipath channel under the condition of narrow transmission signal bandwidth or low signal-to-noise ratio.

Description

Technical Field

[0001] The invention belongs to the field of signal processing and is a method for estimating an underwater acoustic channel under multipath interference, and specifically relates to a method for estimating an underwater acoustic channel based on weighted minimum L1 norm and time series multiple sparse Bayesian learning. Background Art

[0002] With the advent of the information age, science and technology have developed rapidly. Human beings are not satisfied with the development of land resources and have begun to explore the marine environment and continuously strengthen the exploitation and utilization of marine resources. In addition, the military of various countries have increasingly attached importance to the special strategic position of the ocean and have applied various underwater technologies to compete in this field.

[0003] Underwater information transmission is an important part of underwater technology, and underwater communication faces a more complex channel than land communication - the underwater acoustic channel. Since sound waves will experience multiple reflections from the water surface, the bottom of the water, and other objects in the water during propagation, and the sound speed changes due to uneven temperature and salinity in the water, the underwater acoustic channel has the following characteristics: (1) Narrow available bandwidth: The commonly used bandwidth of the transmitted signal is in the range of several kilohertz to tens of kilohertz; (2) Severe multipath interference: The channel multipath signals received by the receiving end cannot be directly separated in the time domain; (3) Doppler frequency shift: There is a relative displacement between the transmitting end and the receiving end, which causes the pulse width of the received signal to change and produce a frequency offset. In addition, there are also characteristics such as large transmission attenuation, extended propagation time, and rapid changes in time and space, which bring severe challenges to underwater communication. Therefore, underwater acoustic channel estimation is an important part of underwater acoustic communication and is the key to ensuring high-quality underwater communication.

[0004] The underwater acoustic channel model has a sparse characteristic, that is, the number of multipath signals is sparse in the time domain. Therefore, the sparse channel estimation method fully considers the sparsity of the channel compared to the traditional non-sparse channel estimation method, and achieves channel reconstruction with a high probability based on fewer observations.

[0005] At present, most of the sparse Bayesian learning algorithms are applied in the field of underwater acoustic channel estimation. According to the Bayesian formula, parameterized prior distribution is adopted, without the input and configuration of any model parameters, and the prior information and sparsity of the solution are fully considered. Compared with other sparse channel algorithms, it has better channel reconstruction performance. Summary of the invention

[0006] The purpose of the present invention is to provide an underwater acoustic channel estimation method based on weighted minimum L1 norm and temporal multiple sparse Bayesian learning to address the situation where underwater acoustic channel estimation is inaccurate when the transmission signal bandwidth is narrow. The present invention can improve the accuracy of channel estimation results at lower bandwidths and improve the overall stability of the system under low signal-to-noise ratios.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] 1) According to the transmitted signal and the received broadband signal, the underwater acoustic channel model is expressed as a sparse form including multipath delay and multipath fading factor, and the initial dictionary matrix is ​​obtained;

[0009] 2) After performing time domain multiple denoising and Fourier transform on the received broadband signal, a reconstructed frequency domain denoised signal matrix is ​​obtained;

[0010] 3) Using a weighted minimum l1 norm regularization algorithm to perform channel estimation on the reconstructed frequency domain denoised signal matrix, obtaining a channel estimation matrix, and calculating a modified dictionary matrix and initialization hyperparameters of a temporal multiple sparse Bayesian learning method based on time correlation according to the channel estimation matrix and the initial dictionary matrix;

[0011] 4) Based on the reconstructed frequency domain denoised signal matrix, the modified dictionary matrix and the initialized hyperparameters, the time domain underwater acoustic channel estimation is performed using the time-series multiple sparse Bayesian learning method based on time correlation to obtain the multipath delay estimation result;

[0012] 5) Taking the multipath delay estimation result as prior information, the least squares estimation method is used to optimize the multipath fading factor of the underwater acoustic channel at a fixed frequency to obtain the optimized multipath fading factor.

[0013] The 2) is specifically:

[0014] Firstly, wavelet denoising is performed on multiple groups of single observation data of received broadband signals respectively to obtain the corresponding denoised single observation data, and multi-observation data are composed of multiple groups of denoised single observation data. Then, singular value decomposition is performed on the multi-observation data to obtain a reconstructed time domain denoised signal matrix. Finally, the reconstructed time domain denoised signal matrix is ​​Fourier transformed to obtain a reconstructed frequency domain denoised signal matrix.

[0015] In the above 3), the modified dictionary matrix and the initialization hyperparameters of the temporal multiple sparse Bayesian learning method based on time correlation are calculated according to the channel estimation matrix and the initial dictionary matrix, which are specifically:

[0016] First, according to the channel estimation matrix Calculate the average energy E of the channel, the calculation formula is as follows:

[0017]

[0018] in, represents the channel estimation matrix The i-th column of is the channel estimation result of the signal received by the i-th receiving array element, and L represents the total number of receiving array elements;

[0019] Next, the index positions whose average energy E of the channel is greater than the energy threshold T1 are screened and form an index position set s;

[0020] Then, the boundary threshold T2 is set, the average energy superposition value corresponding to each index position in the index position set s is calculated and then compared with the boundary threshold T2, the search range corresponding to each index position is adjusted, and the index set after the expanded range corresponding to each index position is obtained, thereby obtaining the initialization hyperparameters in the time series multiple sparse Bayesian learning method based on time correlation Then get the initialization hyperparameter matrix

[0021] Finally, remove the elements in the initial dictionary matrix Φ that are not in the corresponding search range of each index position in the index position set s, and obtain the modified dictionary matrix The specific formula is as follows:

[0022]

[0023] in, represents the j-th column in the modified dictionary matrix, Φ(j) represents the j-th column in the initial dictionary matrix, and E(i) represents the channel energy at the i-th index position.

[0024] In 3), the search range of index position i is adjusted by the following formula:

[0025]

[0026] in, represents the hyperparameter value at the j-th index position, E(i) represents the channel energy at the ith index position, r1 and r2 are the first boundary adjustment value and the second boundary adjustment value respectively.

[0027] In 3), initialize the hyperparameter matrix The calculation formula is as follows:

[0028]

[0029] Where diag(·) represents the matrix diagonalization operation.

[0030] The energy threshold T1 satisfies T1=α1max(E), where α1 is the first energy coefficient.

[0031] The boundary threshold T2 satisfies T2=α2max(E), where α2 is the second energy coefficient.

[0032] The present invention has the following beneficial effects:

[0033] In order to reduce the influence of the transmission signal bandwidth and signal-to-noise ratio on the reconstruction performance of sparse channels, the present invention reduces the influence of noise on the channel estimation accuracy by performing multi-level denoising and reconstruction on the received broadband signal matrix, and combines the prior information of the weighted minimum l1 norm regularization algorithm in the case of low signal bandwidth and the high precision advantage of the TMSBL algorithm based on time correlation for channel estimation. After making full use of the spatiotemporal correlation structure between multiple observation models, a more accurate multipath estimation result can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the underwater acoustic channel estimation method based on weighted minimum l1 norm and TMSBL proposed by the present invention.

[0035] Figure 2 It is a joint sparse model of underwater acoustic channel under multi-observation.

[0036] Figure 3 It is based on the noise suppression effect of different wavelet transform algorithms on broadband signals.

[0037] Figure 4 It is the multipath estimation result of each algorithm under different signal-to-noise ratios of the present invention.

[0038] Figure 5 It is the multipath estimation result of each algorithm under different bandwidths of the present invention. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solution and advantages of the implementation of the present invention clearer, the technical solution in the embodiment of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiment of the present invention.

[0040] like Figure 1 As shown, the present invention comprises the following steps:

[0041] 1) The channel multipath caused by the sample cannot be separated in the time domain, but the actual number of multipaths is much smaller than the possible number of multipaths. In order to estimate the underwater acoustic channel, the original underwater acoustic channel model is discretized according to the known transmitted signal and received broadband signal, and the original underwater acoustic channel model is expressed as a sparse form containing multipath delay and multipath fading factor after discrete Fourier transform, and the initial dictionary matrix is ​​obtained;

[0042] The original underwater acoustic channel model can be expressed as

[0043]

[0044] Where y(t) represents the signal received at the hydrophone position at time t, s(t-τ l) is the transmitting signal generated at the transmitting transducer position, 0≤t≤T0, T0 represents the signal transmission duration, e(t) represents the noise signal, α l and τ l Respectively represent the channel attenuation and delay factor generated by the lth underwater acoustic channel. By discretizing and performing DFT on the model, the corresponding sparse form including multipath delay and multipath fading factor can be obtained, and the formula is as follows:

[0045]

[0046] Where y represents the signal reception item, Φ represents the initial dictionary matrix, and x represents the sparse vector containing multipath delay and multipath fading factor. represents the noise term, and the vector x is a sparse vector containing L non-zero elements, corresponding to the amplitudes of the L multipaths. The above formula is an underdetermined system of equations. By solving the underdetermined system of equations, the multipath delay of the underwater acoustic channel can be obtained: and multipath amplitude

[0047] 2) After performing time domain multiple denoising and Fourier transform on the received broadband signal, a reconstructed frequency domain denoised signal matrix is ​​obtained;

[0048] 2) Specifically:

[0049] In order to reduce the impact of noise on the accuracy of channel estimation, firstly, wavelet denoising is performed on multiple groups of single observation data of received broadband signals to obtain the corresponding denoised single observation data, and multi-observation data are composed of multiple groups of denoised single observation data. Then, singular value decomposition is performed on the multi-observation data to obtain a reconstructed time domain denoised signal matrix. Finally, the reconstructed time domain denoised signal matrix is ​​Fourier transformed to obtain a reconstructed frequency domain denoised signal matrix.

[0050] 3) Using a weighted minimum l1 norm regularization algorithm to perform channel estimation on the reconstructed frequency domain denoised signal matrix, obtaining a channel estimation matrix, and calculating a modified dictionary matrix and initialization hyperparameters of a temporal multiple sparse Bayesian learning method (TMSBL) based on the channel estimation matrix and the initial dictionary matrix;

[0051] The calculation formula of the channel estimation matrix is ​​as follows:

[0052]

[0053] Where Y represents the frequency domain denoising signal matrix after Fourier transform, X represents the matrix composed of sparse vectors containing multipath delay and multipath fading factors, ||·||2 represents the second norm, ||·||1 represents the first norm, λ is the Lagrange multiplier, W is the weighted diagonal matrix, and the weight is inversely proportional to the size of the sparse signal;

[0054]

[0055] in, represents the weighting coefficient, mean(·) represents the average value function, |·| represents the absolute value function, is the row vector of the channel estimation matrix after the nth iteration, Indicates additional items. is a small positive constant. In order to avoid The presence of zero-valued components in the solution leads to pathological changes.

[0056] 3), the modified dictionary matrix and the initialization hyperparameters of the temporal multiple sparse Bayesian learning method based on time correlation are calculated according to the channel estimation matrix and the initial dictionary matrix, which are specifically:

[0057] First, according to the channel estimation matrix Calculate the average energy E of the channel, the calculation formula is as follows:

[0058]

[0059] in, represents the channel estimation matrix The i-th column of is the channel estimation result of the signal received by the i-th receiving array element, and L represents the total number of receiving array elements;

[0060] Next, the index positions whose average energy E of the channel is greater than the energy threshold T1 are screened and form an index position set s; the energy threshold T1 satisfies T1=α1max(E), and α1 is the first energy coefficient.

[0061] Then, a boundary threshold T2 is set, and the boundary threshold T2 satisfies T2 = α2max (E), where α2 is the second energy coefficient. The average energy superposition value corresponding to each index position in the index position set s is calculated and then compared with the boundary threshold T2, and the search range corresponding to each index position is adjusted, that is, the index value within the adjusted search range is set to 1, and the index value outside the adjusted search range is set to 0, and the index set after the expanded range corresponding to each index position is obtained, thereby obtaining the initialization hyperparameters in the temporal multiple sparse Bayesian learning method based on time correlation Then get the initialization hyperparameter matrix

[0062] The search range for index position i is adjusted by the following formula:

[0063]

[0064] in, represents the hyperparameter value at the jth index position, and E(i) represents the channel energy at the ith index position. r1 and r2 are the first boundary adjustment value and the second boundary adjustment value respectively; that is, if the average energy superposition value E(i) of the current index position i(i∈s) is greater than or equal to the boundary threshold T2, then all the superposition values ​​in the range [i-r1:i+r1] are adjusted. The value is set to 1, and the others are similar. This setting is because the weighted l1 norm minimization channel estimation method is more accurate for multipaths with larger amplitudes, so a smaller search range is retained; while for multipaths with smaller amplitudes, the estimation deviation may be larger, so the search range is also appropriately relaxed.

[0065] Initialize the hyperparameter matrix The calculation formula is as follows:

[0066]

[0067] Where diag(·) represents the matrix diagonalization operation.

[0068] Eliminate the elements in the initial dictionary matrix Φ that are not in the search range corresponding to each index position in the index position set s to obtain the modified dictionary matrix The specific formula is as follows:

[0069]

[0070] in, represents the j-th column in the modified dictionary matrix, Φ(j) represents the j-th column in the initialized dictionary matrix, and E(i) represents the channel energy at the i-th index position.

[0071] 4) According to the spatiotemporal correlation structure of the reconstructed frequency domain denoised signal matrix, the modified dictionary matrix and the initialized hyperparameters, the time domain underwater acoustic channel estimation is performed using the time-series multiple sparse Bayesian learning method based on time correlation to obtain the multipath delay estimation result;

[0072] 5) The multipath delay estimation result is used as prior information and set in the discrete expression of the received signal. The multipath fading factor of the underwater acoustic channel at a fixed frequency is optimized and solved using the least squares estimation method to obtain the optimized multipath fading factor.

[0073] Specifically:

[0074] The discrete expression of the received signal is:

[0075]

[0076] in, It represents the transmission signal matrix composed of the first J multipaths after different delays, satisfying Represents the vector composed of the first J multipath amplitudes, satisfying and Respectively represent the frequency f pcw The received signal under the condition that the jth multipath passes through τ j The delayed transmitted signal and the amplitude of the j-th multipath, n represents the comprehensive noise term.

[0077] Using the multipath delay results of the previous J Based on the least squares, the final multipath fading factor can be obtained:

[0078]

[0079]

[0080] In the formula, represents the estimation result of the first J multipath amplitudes, represents the first J multipath amplitude vectors, represents the transmission signal matrix composed of the remaining negligible (LJ) multipaths after different time delays, represents the remaining negligible (LJ) multipath amplitude vectors, and β is the possible number of multipaths.

[0081] like Figure 2 The figure shows the joint sparse model of underwater acoustic channel under multi-observation, that is, multi-observation data composed of single observation data. For slow time-varying channels, the multipath structure of the channel is stable, and the signals received by multiple array elements have consistent sparsity in the time domain and strong correlation in time. Therefore, the spatial and temporal correlation structure between the signals received by multiple array elements can effectively improve the accuracy of channel estimation.

[0082] like Figure 3 The following are the simulation results of four broadband signal noise suppression algorithms based on wavelet transform, with a signal input signal-to-noise ratio of 10dB and a bandwidth of 1000Hz. It can be seen that the translation invariant and modulus maximum have the best noise suppression effect, which can improve the overall signal-to-noise ratio by about 9dB, the wavelet threshold noise suppression effect is second, and the wavelet weight noise suppression effect is the worst.

[0083] like Figure 4The figure shows the multipath estimation results of multiple sparse Bayesian learning (MSBL), TMSBL and the present invention under different signal-to-noise ratios. The initial transmission signal of the simulation is a linear frequency modulation signal (LFM), the initial frequency of the signal is 500 Hz, and the signal sampling frequency is f s =50kHz, the signal pulse width is 200ms, the number of hydrophones receiving the signal is 2, and the number of multipaths k is set to 6. The simulation signal bandwidth (Bandwidth, BW) is 2000Hz, and Gaussian white noise is added to the incident signal to make the signal-to-noise ratio range of the noise 5~20dB. Figure 3 It can be seen that the method of the present invention has the best overall performance and can obtain effective multipath delay and amplitude estimation results under low signal-to-noise ratio conditions, which fully demonstrates the effectiveness of the method.

[0084] like Figure 5 The figure shows the multipath estimation results of MSBL, TMSBL, weighted minimum l1 norm regularization and the present invention under different bandwidths obtained by simulation. The signal transmission and reception configurations are consistent with the above. The simulation signal bandwidth (Bandwidth, BW) is [1200 1400 1600 1800] Hz, and the incident signal noise ratio is set to SNR = 15dB. The overall performance of the method of the present invention is the best. In the case of low signal bandwidth, effective multipath delay and amplitude estimation results can be obtained, which reduces the sensitivity to signal bandwidth.

[0085] In general, the sparse channel estimation method of the present invention can effectively obtain channel estimation information in an underwater acoustic channel under multipath interference, especially in the case of low bandwidth signals and low signal ratios, which is beneficial for obtaining multipath signals that cannot be separated in the time domain.

[0086] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for underwater acoustic channel estimation based on improved temporal multiple sparse Bayesian learning, characterized in that: The steps include: 1) According to the transmitted signal and the received broadband signal, the underwater acoustic channel model is expressed as a sparse form including multipath delay and multipath fading factor, and the initial dictionary matrix is ​​obtained; 2) After performing time domain multiple denoising and Fourier transform on the received broadband signal, a reconstructed frequency domain denoised signal matrix is ​​obtained; 3) Using a weighted minimum l1 norm regularization algorithm to perform channel estimation on the reconstructed frequency domain denoised signal matrix, obtaining a channel estimation matrix, and calculating a modified dictionary matrix and initialization hyperparameters of a temporal multiple sparse Bayesian learning method based on time correlation according to the channel estimation matrix and the initial dictionary matrix; 4) Based on the reconstructed frequency domain denoised signal matrix, the modified dictionary matrix and the initialized hyperparameters, the time domain underwater acoustic channel estimation is performed using the time-series multiple sparse Bayesian learning method based on time correlation to obtain the multipath delay estimation result; 5) Taking the multipath delay estimation result as the prior information, the multipath fading factor of the underwater acoustic channel at a fixed frequency is optimized and solved by the least squares estimation method to obtain the optimized multipath fading factor; The 2) is specifically: Firstly, wavelet denoising is performed on multiple groups of single observation data of the received broadband signal respectively to obtain the corresponding denoised single observation data, and the multiple groups of denoised single observation data are used to form multi-observation data, and then singular value decomposition is performed on the multi-observation data to obtain a reconstructed time domain denoised signal matrix, and finally the reconstructed time domain denoised signal matrix is ​​Fourier transformed to obtain a reconstructed frequency domain denoised signal matrix; In the above 3), the modified dictionary matrix and the initialization hyperparameters of the temporal multiple sparse Bayesian learning method based on time correlation are calculated according to the channel estimation matrix and the initial dictionary matrix, which are specifically: First, according to the channel estimation matrix Calculate the average energy E of the channel, the calculation formula is as follows: in, represents the channel estimation matrix The i-th column of is the channel estimation result of the signal received by the i-th receiving array element, and L represents the total number of receiving array elements; Next, the index positions whose average energy E of the channel is greater than the energy threshold T1 are screened and form an index position set s; Then, the boundary threshold T2 is set, the average energy superposition value corresponding to each index position in the index position set s is calculated and then compared with the boundary threshold T2, the search range corresponding to each index position is adjusted, and the index set after the expanded range corresponding to each index position is obtained, thereby obtaining the initialization hyperparameters in the time series multiple sparse Bayesian learning method based on time correlation Then get the initialization hyperparameter matrix Finally, remove the elements in the initial dictionary matrix Φ that are not in the search range corresponding to each index position in the index position set s, and obtain the modified dictionary matrix The specific formula is as follows: in, represents the j-th column in the modified dictionary matrix, Φ(j) represents the j-th column in the initial dictionary matrix, and E(i) represents the channel energy at the i-th index position; In 3), the search range of index position i is adjusted by the following formula: in, represents the hyperparameter value at the j-th index position, E(i) represents the channel energy at the i-th index position, r1 and r2 are the first boundary adjustment value and the second boundary adjustment value respectively; In 3), initialize the hyperparameter matrix The calculation formula is as follows: Where diag(·) represents the matrix diagonalization operation; The energy threshold T1 satisfies T1=α1 max(E), where α1 is the first energy coefficient; The boundary threshold T2 satisfies T2=α2 max(E), where α2 is the second energy coefficient.

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