Underwater sound OFDM (Orthogonal Frequency Division Multiplexing) impulse noise estimation enhancement method based on distributed compressed sensing

Abstract

The invention discloses an underwater acoustic OFDM impulse noise estimation enhancement method based on distributed compressed sensing, and relates to the technical field of underwater acoustic communication. Carrying out frequency offset correction on the received OFDM signal by adopting a plurality of carrier frequency offset compensation values to obtain a plurality of groups of related signals; constructing an orthogonal projection matrix, projecting a received signal to a specific orthogonal subspace to eliminate channel components, and separating impulse noise; constructing a joint observation matrix by using the time domain sparsity of the impulse noise and the strong correlation under different carrier frequency offset compensation; and carrying out joint sparse reconstruction on the multiple groups of observation signals by adopting a distributed compressed sensing algorithm, and estimating an impulse noise time domain signal. A distributed compressed sensing algorithm is adopted, two characteristics of impulse noise are utilized, impulse noise estimation accuracy is improved, an impulse noise estimation effect is enhanced, and the problem that impulse noise estimation accuracy is limited under the condition of limited pilot frequency quantity is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic communication, and more specifically, to an enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing applicable to the shallow - water underwater acoustic channel environment. Background Art

[0002] The complex underwater acoustic channel poses great challenges to underwater acoustic communication. Currently, due to its high spectral efficiency and high robustness against multipath effects, the OFDM system is widely used in the field of underwater acoustic communication. However, different from terrestrial communication, there are complex noise interferences in the underwater environment. Since OFDM uses multiple carriers for information transmission, and impulse noise has the characteristics of short duration, high amplitude, and wide frequency band, it will contaminate all sub - carriers. Therefore, accurate estimation of impulse noise is necessary in underwater acoustic OFDM communication.

[0003] The distributed compressive sensing algorithm is widely applied to channel estimation in underwater acoustic communication receivers. By utilizing the sparsity of the channel and the time - domain correlation of the multipath structure, the performance of channel estimation is improved, and the problems of multipath effects, time - varying characteristics, and low signal - to - noise ratio brought by the complex underwater acoustic channel are overcome. It has a very large application prospect in underwater acoustic communication sparse reconstruction. However, it has not been applied to enhance impulse noise estimation yet.

[0004] The current mainstream method for underwater acoustic OFDM impulse noise estimation utilizes the sparse characteristics of impulse noise in the time domain in the underwater acoustic environment, and adopts the compressive sensing algorithm for sparse recovery, so as to eliminate the interference of impulse noise on the demodulation of OFDM signals. However, the sparse recovery of the compressive sensing algorithm for impulse noise is limited by the number of pilots, that is, the number of observation values. Increasing the number of pilots improves the estimation accuracy of impulse noise but reduces the spectral utilization rate, and reducing the number of pilots reduces the estimation accuracy of impulse noise but increases the spectral utilization rate.

[0005] Chinese Patent CN202311566816.6 discloses a distributed compressive sensing sparse time-varying channel estimation method. Based on the structural characteristics of the high-dimensional channel matrix, a system model and a time-varying channel evolution model under a Markov random switching topology are constructed; the sparse random input signal is compressed into a low-dimensional vector through a compressive sensing matrix, and a distributed adaptive algorithm of compression-estimation-decompression is constructed. This method uses distributed technology to fuse information from different data sources, solves the problem that existing channel estimation methods are all based on estimating single or homogeneous data sources, overcomes difficulties such as insufficient excitation of the original high-dimensional sparse regression vector, and does not require the regression vector to satisfy strict statistical assumptions such as independence, and has characteristics such as strong real-time performance and high accuracy. Chinese Patent CN202211586036.3 discloses a channel impulse noise estimation method based on variational Bayesian learning. Based on the received data model with impulse noise introduced, the expectations of the likelihood functions of the received data of the forward and backward EM algorithms of this model are derived, and based on this expectation, the update formulas of the hidden variables of the model are derived, and the forward channel impulse response, forward impulse noise, backward channel impulse response, and backward impulse noise are accurately estimated.

[0006] Existing OFDM underwater acoustic impulse noise estimation methods utilize the time-domain sparse characteristics of impulse noise and adopt compressive sensing algorithms for sparse recovery of impulse noise. However, since the compressive sensing algorithm requires sufficient observation values to ensure the accuracy of impulse noise estimation, the need to increase the number of observation values means an increase in the number of pilots, resulting in a decrease in the spectral efficiency of OFDM; conversely, reducing the number of pilots reduces the estimation accuracy of impulse noise but increases the spectral utilization rate. Therefore, to solve the problem of improving the accuracy of impulse noise estimation with a limited number of pilots, the present invention proposes an enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing, which overcomes the requirement for the number of pilots for high-accuracy impulse noise estimation. Summary of the Invention

[0007] The purpose of the present invention is to provide an enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing to effectively solve the key problem that the performance of the underwater acoustic OFDM communication system deteriorates due to limited accuracy of impulse noise estimation with a limited number of pilots in the existing underwater acoustic OFDM system, which is contradictory to the spectral efficiency. The present invention utilizes the sparse characteristics of impulse noise in the time domain and the strong correlation under different carrier frequency offset compensations, that is, the impulse index positions are the same and the amplitudes are different, and adopts a distributed compressive sensing algorithm to replace the traditional compressive sensing algorithm for sparse reconstruction of impulse noise, greatly improving the robustness of the system.

[0008] To achieve the above-mentioned invention purpose, the present invention provides the following technical solutions.

[0009] An enhanced method for estimating underwater acoustic OFDM impulse noise based on distributed compressive sensing. By performing different carrier frequency offset compensations on the received signal, impulse noise signals with extremely strong correlation are obtained, that is, the index positions of the impulse noise signals after compensation are the same while the amplitudes are different. Using this characteristic to construct a joint observation matrix, combined with the time-domain sparsity of impulse noise, a distributed compressive sensing algorithm is used for joint sparse reconstruction to achieve accurate estimation of impulse noise. The method of the present invention specifically includes the following steps:

[0010] 1) Perform multiple groups of carrier frequency offset compensations on the received OFDM signal, and extract the corresponding pilot information to obtain multiple groups of frequency-domain pilot information;

[0011] 2) Construct an orthogonal projection matrix, project the multiple groups of frequency-domain pilot information obtained in step 1) into an orthogonal subspace to eliminate the channel component and separate the impulse noise;

[0012] 3) Based on the time-domain sparsity of impulse noise and the strong correlation of impulse noise signals in multiple different orthogonal subspaces, construct a joint observation value and a joint observation matrix;

[0013] 4) Use the distributed compressive sensing algorithm to perform joint sparse reconstruction on multiple groups of observation signals, estimate the impulse noise time-domain signal, and achieve impulse noise estimation.

[0014] In step 1), the frequency offset correction is performed on the received OFDM signal with multiple carrier frequency offset compensation values to obtain multiple groups of frequency-domain pilot information. The specific steps may be:

[0015] Considering the combined effects of multipath effect, Doppler effect, impulse noise, and Gaussian noise in a complex underwater acoustic channel, an OFDM symbol with a total number of subcarriers of K is expressed as:

[0016]

[0017] where r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by the narrowband Doppler effect, represents the inverse Fourier transform matrix of size K×K, X = diag(X1, X2,..., X K ) represents the data matrix modulated at the transmitting end, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2,..., h L ) represents the channel impulse response of length L, w = (w1, w2,..., w K ) represents the impulse noise, g = (g1, g2,..., g K ) represents the Gaussian noise;

[0018] Therefore, the frequency-domain pilot information under different carrier frequency offsets compensation can be expressed as:

[0019]

[0020] Wherein, represents the OFDM time-domain baseband signal after carrier frequency offset compensation, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, w K ) represents the impulse noise, g = (g1, g2, …, g K ) represents the Gaussian noise.

[0021] In step 2), the specific steps of constructing the orthogonal projection matrix to project the received signal into a specific orthogonal subspace to eliminate the channel component and separate the impulse noise can be:

[0022] For the nth frequency-domain pilot signal under carrier frequency offset compensation, construct the orthogonal projection matrix O n , and its expression is as follows: Wherein, I represents the identity matrix, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, (·) -1Represent matrix inversion; use the constructed orthogonal projection matrix O n Project into a specific orthogonal subspace to eliminate the channel components, leaving only impulse noise in the orthogonal subspace. The nth orthogonal subspace signal is expressed as:

[0023]

[0024] Where O n represents the orthogonal projection matrix of the nth frequency-domain pilot signal, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h=(h1,h2,…,h L ) represents the channel impulse response of length L, w=(w1,w2,…,w K ) represents the impulse noise, g=(g1,g2,…,g K ) represents the Gaussian noise.

[0025] In step 3), the joint observation matrix is:

[0026]

[0027] Where

[0028]

[0029]

[0030] Where represents the joint observation matrix, represents the joint impulse noise to be estimated, represents the joint Gaussian noise, (·) T represents the transpose operation, N represents the number of joint sparse reconstructions.

[0031] The strong correlation can be reflected in the same impulse index position but different amplitudes.

[0032] In step 4), the optimization objective function of the distributed compressive sensing is:

[0033]

[0034] Among them, χ represents the pulse noise sparsity, ⊙ represents the Hadamard product, represents the joint observation value, represents the joint observation matrix, represents the joint pulse noise to be estimated, w n =(w n,1 , w n,2 , …, w n,K ) represents the nth pulse noise represents the square of the l2 norm, ||·||0 represents the l0 norm; the constraint condition of the above formula indicates that the pulse noise index positions in N different orthogonal subspaces are the same, but the amplitudes are different. The present invention uses the synchronous orthogonal matching pursuit algorithm to solve this optimization problem; the index position determined in the α-th round of iteration of the SOMP algorithm can be expressed as:

[0035]

[0036] Among them, Ω α represents the candidate set in the α-th round, <·, ·> represents the correlation operation, |·| represents the absolute value operation, Φ n represents the nth observation matrix, υ n represents the nth residual; it can be seen from the above formula that compared with the traditional orthogonal matching pursuit algorithm, the synchronous orthogonal matching pursuit algorithm uses N data blocks to determine the index; after determining the index position in the α-th round delete it from the index set Ω α to obtain the candidate set Ω α+1 for the next round, and add it to the determined index set Υ α and update the residual for use in the next iteration;

[0037]

[0038] Among them, represents the nth pulse noise estimated in the α-th round, represents the Υ α column of the nth observation matrix, y n represents the nth orthogonal subspace pulse noise signal observation value, the nth residual estimated in the (α + 1)-th round; it can be seen that by simultaneously using N data blocks to recover the strongly correlated pulse noise, the accuracy of the pulse noise sparse recovery index position is guaranteed, and the accuracy of pulse noise estimation is significantly improved.

[0039] The present invention utilizes the fact that there is a strong candidate correlation between pulse signals with different carrier frequency offset compensations. To visually illustrate that the sparse structure has a strong correlation, the atomic candidate correlation is defined as follows:

[0040]

[0041] where and respectively represent the candidate sets of known pulse noise and estimated pulse noise, ∩ and ||·||0 represent the union and l0 norm respectively; the simulation experiment results show that the candidate correlation of pulse noise is between 0.90 and 0.95.

[0042] The method of the present invention is applicable to shallow water acoustic OFDM communication systems, and the proportion of pilot numbers in the total number of subcarriers is not higher than 10%.

[0043] To improve the estimation accuracy of underwater acoustic OFDM pulse noise with a limited number of pilots, the present invention proposes an enhanced method for underwater acoustic OFDM pulse noise estimation based on distributed compressive sensing. Under the condition of the same number of pilots, the sparse characteristics of pulse noise in the time domain and the extremely strong correlation under different carrier frequency offset compensations are utilized, that is, the pulse index positions are the same but the amplitudes are different, and the distributed compressive sensing algorithm is adopted to improve the estimation accuracy of pulse noise.

[0044] The present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the enhanced method for underwater acoustic OFDM pulse noise estimation based on distributed compressive sensing are implemented.

[0045] The present invention provides an electronic device, including:

[0046] a processor;

[0047] a memory for storing instructions executable by the processor;

[0048] wherein, the processor is configured to execute the steps of the enhanced method for underwater acoustic OFDM pulse noise estimation based on distributed compressive sensing.

[0049] Compared with the prior art, the present invention has the following prominent advantages:

[0050] 1. The present invention verifies through simulation experiments that pulse noise has an extremely strong correlation under different carrier frequency offset compensations, that is, the pulse index positions are the same but the amplitudes are different, providing a theoretical basis for the subsequent application of the distributed compressive sensing algorithm.

[0051] 2. Make full use of the characteristics of impulse noise: Through research, the present invention finds that impulse noise has strong correlation under different carrier frequency offset compensations. By making full use of this characteristic and combining the distributed compressive sensing algorithm to replace the traditional compressive sensing algorithm, the performance of impulse noise estimation is enhanced.

[0052] 3. Improve the spectrum utilization rate: The present invention utilizes the time-domain sparsity characteristic of impulse noise and the strong correlation under different carrier frequency offset compensations. Based on the distributed theory, a joint observation value and a joint observation matrix are constructed, and the distributed compressive sensing algorithm is used for joint sparse recovery of impulse noise, reducing pilot consumption to achieve a higher spectrum utilization rate.

[0053] 4. Improve the accuracy of impulse noise estimation: Aiming at the problem that the existing underwater acoustic OFDM impulse noise estimation method using the compressive sensing algorithm is limited by the number of pilots, the present invention utilizes the sparsity characteristic of impulse noise in the time domain and the strong correlation under different carrier frequency offset compensations, that is, the impulse index positions are the same but the amplitudes are different. Therefore, the distributed compressive sensing algorithm is used to utilize the two characteristics of impulse noise, improve the accuracy of impulse noise estimation, enhance the impulse noise estimation effect, solve the problem that the accuracy of impulse noise estimation is limited under a limited number of pilots, and improve the robustness of the OFDM underwater acoustic system in an impulse noise interference environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow schematic diagram of the method proposed by the present invention.

[0055] Figure 2 It is a schematic diagram of sparse impulse noise.

[0056] Figure 3 It is a schematic diagram of the time-domain correlation of impulse noise after different carrier frequency offset compensations.

[0057] Figure 4 It is a simulation experimental diagram of the time-domain signal correlation of impulse noise after different carrier frequency offset compensations.

[0058] Figure 5 It is a channel schematic diagram of the comparison experiment of underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing and traditional compressive sensing.

[0059] Figure 6 It is the mean square error of impulse noise estimation under different signal-to-noise ratios.

[0060] Figure 7 It is the mean square error of channel estimation under different signal-to-noise ratios.

[0061] Figure 8 It is the output signal-to-noise ratio under different signal-to-noise ratios.

[0062] Figure 9The mean square error of pulse noise estimation at different signal-to-pulse ratios.

[0063] Figure 10 The mean square error of channel estimation at different signal-to-pulse ratios.

[0064] Figure 11 The output signal-to-noise ratio at different signal-to-pulse ratios.

[0065] Figure 12 The mean square error of pulse noise estimation with different numbers of pilots.

[0066] Figure 13 The mean square error of channel estimation with different numbers of pilots.

[0067] Figure 14 The output signal-to-noise ratio with different numbers of pilots. Detailed implementation manner

[0068] The following embodiments will further illustrate the present invention in conjunction with the accompanying drawings.

[0069] An embodiment of the present invention relates to an enhanced method for underwater acoustic OFDM pulse noise estimation based on distributed compressive sensing. The specific process is as Figure 1 shown. First, multiple carrier frequency offsets of the received time-domain baseband signal are compensated to obtain multiple groups of signals. Then, an orthogonal projection matrix is constructed to project the signals into a specific orthogonal subspace to eliminate the channel components. Utilizing the time-domain sparse characteristics of the pulse noise and the strong correlation of the pulse signals after multiple carrier frequency offsets compensation, a joint observation matrix and joint observations are constructed, and sparse reconstruction is performed through the distributed compressive sensing algorithm to achieve accurate estimation of the pulse noise.

[0070] 1 Pulse noise sparse correlation characteristics under different carrier frequency offsets

[0071] In a complex shallow sea environment, since the pulse noise generated naturally or artificially usually has sparse characteristics, it shows as short high-amplitude and high-energy spikes in the time domain, existing only at a few time points, corresponding to affecting all subcarriers in the frequency domain, as Figure 2 shown. The characteristics of high amplitude and wide frequency band seriously restrict the performance of the OFDM underwater acoustic communication system. Define the signal-to-noise ratio and signal-to-pulse ratio as:

[0072]

[0073] where represents the signal variance, and represent the additive Gaussian noise variance and the pulse noise variance respectively.

[0074] In addition, there is a significant strong correlation between the pulse noise time-domain signals after different carrier frequency offset compensations, that is, they have the same position index and different amplitudes, such as Figure 3 shown in the schematic diagram of pulse noise signals with the same index position but different amplitudes, Figure 3 it can be seen from the black circled parts in a and b of

[0075] that the pulse positions are the same but the amplitudes are different. Due to the sparse characteristics of pulse noise and the strong correlation characteristics after different carrier frequency offset compensations, the idea of distributed compressive sensing can be used to construct a joint sparse recovery equation for joint reconstruction.

[0076]

[0077] where and represent the candidate sets of known pulse noise and estimated pulse noise respectively, ∩ and ||·||0 represent the union and l0 norm respectively. Set the carrier frequency offset of the experiment to range from -5 Hz to 5 Hz and the signal-to-noise ratio to range from 10 dB to 40 dB. The simulation experimental results of the correlation of pulse noise time-domain signals after different carrier frequency offset compensations are as shown in Figure 4 shown. It can be seen from Figure 4 that the candidate correlation of pulse noise is between 0.90 and 0.95, showing a strong correlation. Therefore, the distributed compressive sensing algorithm can be applied.

[0078] 2 Enhanced Method for Underwater Acoustic OFDM Pulse Noise Estimation Based on Distributed Compressive Sensing

[0079] Considering the combined effects of multipath effect, Doppler effect, pulse noise, and Gaussian noise in a complex underwater acoustic channel, an OFDM symbol with a total number of subcarriers K can be expressed as:

[0080]

[0081] where r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by the narrowband Doppler effect, represents the inverse Fourier transform matrix of size K×K, X = diag(X1, X2, …, X K ) represents the data matrix modulated at the transmitter, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, wK ) represents impulse noise, g = (g1, g2, …, g K ) represents Gaussian noise.

[0082] Therefore, in different The frequency-domain pilot information under carrier frequency offset compensation can be expressed as:

[0083]

[0084] Among them, represents the OFDM time-domain baseband signal after carrier frequency offset compensation, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with carrier frequency offset θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, w K ) represents impulse noise, g = (g1, g2, …, g K ) represents Gaussian noise.

[0085] For the nth frequency-domain pilot signal under carrier frequency offset compensation, construct the orthogonal projection matrix O n , and its expression is as follows:

[0086]

[0087] Among them, I represents the identity matrix, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with carrier frequency offset θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, hL ) represents the channel impulse response of length L, (·) -1 represents matrix inversion.

[0088] The constructed orthogonal projection matrix O is adopted n to project into a specific orthogonal subspace to eliminate the channel component. Only impulse noise remains in the orthogonal subspace. The nth orthogonal subspace signal is expressed as:

[0089]

[0090] where O n represents the orthogonal projection matrix of the nth frequency-domain pilot signal, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, w K ) represents the impulse noise, g = (g1, g2, …, g K ) represents the Gaussian noise.

[0091] Therefore, the compressive sensing algorithm can be used to solve the above formula. As known from the foregoing, there is a strong sparse correlation between the impulse noise time-domain signals after different carrier frequency offset compensations. In order to apply the distributed compressive sensing algorithm, formula (6) is transformed to construct the joint observation value and the joint observation matrix, and joint sparse estimation is performed based on N observation vectors. Formula (6) is rewritten as:

[0092]

[0093] where

[0094]

[0095] where represents the joint observation matrix, represents the joint impulse noise to be estimated, represents the joint Gaussian noise, (·) T represents the transpose operation, and N represents the number of joint sparse reconstructions.

[0096] Therefore, the optimization equation for pulse estimation can be expressed as:

[0097]

[0098] where χ represents the pulse noise sparsity, ⊙ represents the Hadamard product, represents the joint observation value, represents the joint observation matrix, represents the joint pulse noise to be estimated, w n = (w n,1 , w n,2 , …, w n,K ) represents the nth pulse noise represents the square of the l2 norm, ||·||0 represents the l0 norm. The constraint condition of the above formula indicates that the pulse noise index positions in N different orthogonal subspaces are the same, but the amplitudes are different. The present invention uses the synchronous orthogonal matching pursuit algorithm to solve this optimization problem. The index position determined in the α-th iteration of the SOMP algorithm can be expressed as

[0099]

[0100] where Ω α represents the candidate set in the α-th round, <·, ·> represents the correlation operation, |·| represents the absolute value operation, Φ n represents the nth observation matrix, υ n represents the nth residual. It can be seen from the above formula that compared with the traditional orthogonal matching pursuit algorithm, the synchronous orthogonal matching pursuit algorithm uses N data blocks to determine the index. After determining the index position in the α-th round, it is deleted from the index set Ω α to obtain the candidate set Ω α+1 for the next round, and added to the determined index set Υ α , and the residual is updated for use in the next iteration;

[0101]

[0102] where, represents the nth pulse noise estimated in the α-th round, represents the Υ α column of the nth observation matrix, y n represents the nth orthogonal subspace pulse noise signal observation value, the nth residual estimated in the (α + 1)-th round.

[0103] It can be seen that compared with the traditional compressive sensing algorithm, by simultaneously using N data blocks to recover strongly correlated impulse noise, the accuracy of the sparse recovery index position of impulse noise is ensured, and the accuracy of impulse noise estimation is significantly improved.

[0104] To prove that the enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing proposed in the present invention has better effects than the traditional compressive sensing impulse estimation method, simulation experiments were carried out. In the simulation experiments, a single-input single-output OFDM system was used. The total number of subcarriers of the OFDM signal was 1024, the bandwidth was 4800 Hz, the sampling rate was 96 kHz, the QPSK constellation mapping method was adopted, the sparsity of impulse noise was set to 15, the sparsity of the traditional compressive sensing algorithm for impulse noise estimation was set to 20, the sparsity of the distributed compressive sensing algorithm adopted in the present invention for impulse noise estimation was set to 20, the carrier frequency offset search compensation range was set to -4.5 Hz to 4.5 Hz with an interval of 0.1 Hz, linear zero-forcing equalizers were used for all equalizers, and the orthogonal matching pursuit algorithm with a sparsity of 10 was used for channel estimation. The channel is as Figure 5 shown.

[0105] The defined evaluation parameters include the mean square error of impulse noise estimation, the mean square error of channel estimation, and the output signal-to-noise ratio:

[0106]

[0107] Among them, respectively represent the estimated channel, the estimated impulse noise, and the equalized symbol, represents the square of the l2 norm. To comprehensively evaluate the performance of the proposed enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing, simulation experiments were carried out and verified under different signal-to-noise ratios, signal-to-impulse ratios, and pilot numbers. The experimental results are as Figures 5 to 13 shown.

[0108] Figures 6 to 14 In, CS represents Compressive Sensing, which is an algorithm used for sparse recovery of underwater acoustic OFDM impulse noise in the prior art. It estimates using the time-domain sparsity of impulse noise, but is limited by the number of pilots (number of observation values), and the accuracy of impulse noise estimation is insufficient under limited pilots. DCS represents the Distributed Compressive Sensing adopted in the present invention. It not only utilizes the time-domain sparsity of impulse noise, but also combines the strong correlation of impulse noise with "the same index position and different amplitudes" after different carrier frequency offset compensations. By jointly sparse reconstruction, the accuracy of impulse noise estimation is improved, effectively solving the problem that the accuracy of the traditional CS algorithm is limited under limited pilot numbers. From Figures 5 to 13It can be seen that, whether it is in terms of different signal-to-noise ratios, different signal-to-pulse ratios, or different numbers of pilots, the enhanced underwater acoustic OFDM impulse noise estimation method based on distributed compressive sensing proposed by the present invention can achieve better system performance compared with the traditional compressive sensing estimation method, obtain better impulse noise estimation accuracy, and thus obtain better channel estimation mean square error and output signal-to-noise ratio, comprehensively verifying the effectiveness of the enhanced underwater acoustic OFDM impulse noise estimation method based on distributed compressive sensing proposed by the present invention.

[0109] Aiming at the problem that the existing underwater acoustic OFDM impulse noise estimation method using the compressive sensing algorithm is limited by the number of pilots, the present invention utilizes the sparse characteristic of impulse noise in the time domain and its strong correlation under different carrier frequency offset compensations, that is, the pulse index positions are the same but the amplitudes are different. Therefore, the distributed compressive sensing algorithm is adopted to utilize the two characteristics of impulse noise to improve the impulse noise estimation accuracy, enhance the impulse noise estimation effect, solve the problem of limited impulse noise estimation accuracy under a limited number of pilots, and ensure the spectrum utilization rate of the OFDM system.

[0110] The present invention overcomes the requirement of high accuracy of impulse noise estimation for the number of pilots. Utilizing the sparse characteristic of impulse noise in the time domain and its strong correlation under different carrier frequency offset compensations, that is, the pulse index positions are the same but the amplitudes are different. Therefore, the distributed compressive sensing algorithm is adopted to utilize the two characteristics of impulse noise to improve the impulse noise estimation accuracy, enhance the impulse noise estimation effect, and solve the problem of limited impulse noise estimation accuracy under a limited number of pilots.

[0111] The above embodiments are only preferred embodiments of the present invention and cannot be considered as limiting the scope of implementation of the present invention. All equivalent changes and improvements made in accordance with the scope of the present invention application shall still fall within the scope covered by the patent of the present invention.

Claims

1. An enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing, characterized in that It includes the following steps: 1) Perform multi-group carrier frequency offset compensation on the received OFDM signal, and extract the corresponding pilot information to obtain multi-group frequency-domain pilot information; 2) Construct an orthogonal projection matrix, project the multi-group frequency-domain pilot information obtained in step 1) into the orthogonal subspace to eliminate the channel component and separate the impulse noise; 3) Based on the time-domain sparsity of the impulse noise and the strong correlation of the impulse noise signals in multiple different orthogonal subspaces, construct a joint observation value and a joint observation matrix; 4) Use the distributed compressive sensing algorithm to perform joint sparse reconstruction on multiple groups of observation signals, estimate the time-domain signal of the impulse noise, and realize the impulse noise estimation.

2. The enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing according to claim 1, wherein In step 1), the specific steps of performing multi-group carrier frequency offset compensation on the received OFDM signal, extracting the corresponding pilot information, and obtaining multi-group frequency-domain pilot information are as follows: Considering the combined effects of multipath effect, Doppler effect, impulse noise, and Gaussian noise in the complex underwater acoustic channel, an OFDM symbol with a total number of subcarriers of K is expressed as: where r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with carrier frequency offset θ caused by narrowband Doppler effect, represents the inverse Fourier transform matrix of size K×K, X = diag(X1, X2, …, X K ) represents the data matrix modulated at the transmitter, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, w K ) represents the impulse noise, g = (g1, g2, …, g K ) represents the Gaussian noise; The frequency-domain pilot information under carrier frequency offset is expressed as follows: Among them, represents the OFDM time-domain baseband signal after carrier frequency offset compensation, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, w K ) represents the impulse noise, g = (g1, g2, …, g K ) represents the Gaussian noise.

3. The method for enhancing underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing according to claim 1, wherein In step 2), the specific steps of constructing an orthogonal projection matrix and projecting the received signal into a specific orthogonal subspace to eliminate the channel component and separate the impulse noise are as follows: For Construct an orthogonal projection matrix O for the nth frequency-domain pilot signal under carrier frequency offset compensation n , and its expression is as follows: Wherein, I represents the identity matrix, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2,..., h L ) represents the channel impulse response of length L, (·) -1 represents matrix inversion; Using the constructed orthogonal projection matrix O n Project onto a specific orthogonal subspace to eliminate the channel component. Only impulse noise remains in the orthogonal subspace. The nth orthogonal subspace signal is expressed as: Among them, O n represents the orthogonal projection matrix of the nth frequency-domain pilot signal, P p represents the pilot selection matrix, F K represents the Fourier transform matrix of size K×K, represents the corresponding carrier frequency offset matrix, r represents the received OFDM time-domain baseband signal, represents the carrier frequency offset matrix with a carrier frequency offset of θ caused by narrowband Doppler effect, represents the inverse Fourier matrix of size K×K, X p represents the pilot data diagonal matrix, F [:,1:L] represents the first L columns of the Fourier matrix, L is the channel length, h = (h1, h2, …, h L ) represents the channel impulse response of length L, w = (w1, w2, …, w K ) represents the impulse noise, g = (g1, g2, …, g K ) represents the Gaussian noise.

4. The method for enhancing underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing according to claim 1, characterized in that In step 3), the joint observation matrix is: where, Among them, represents the joint observation matrix, represents the joint impulse noise to be estimated, represents the joint Gaussian noise, (·) T represents the transpose operation, and N represents the number of joint sparse reconstructions.

5. The enhanced method for estimating underwater acoustic OFDM impulse noise based on distributed compressive sensing according to claim 1, characterized in that In step 4), the optimization objective function of the distributed compressive sensing is: where χ represents the pulse noise sparsity, ⊙ represents the Hadamard product, represents the joint observation value, represents the joint observation matrix, represents the joint pulse noise to be estimated, w n =(w n,1 , w n,2 , …, w n,K ) represents the nth pulse noise represents the square of the l2 norm, ||·||0 represents the l0 norm; the constraint condition of the above formula indicates that the pulse noise index positions in N different orthogonal subspaces are the same, but the amplitudes are different. The synchronous orthogonal matching pursuit algorithm is used to solve this optimization problem; the index position θ determined by the αth iteration of the SOMP algorithm α is expressed as: Among them, Ω α represents the candidate set in the α-th round, <·,·> represents the relevant operation, |·| represents the absolute value operation, and Φ n represents the n-th observation matrix, and υ n represents the n-th residual; it can be seen from the above formula that compared with the traditional orthogonal matching pursuit algorithm, the synchronous orthogonal matching pursuit algorithm uses N data blocks to determine the index; after determining the index position θ α in the α-th round, delete it from the index set Ω α to obtain the candidate set Ω α+1 in the next round, and add it to the determined index set Υ α and update the residual for use in the next iteration; Among them, represents the nth impulse noise in the αth round of estimation, represents Υ of the nth observation matrix α column, y n represents the nth orthogonal subspace impulse noise signal observation value, the nth residual in the (α + 1)th round of estimation; by simultaneously using N data blocks to recover impulse noise with strong correlation, the accuracy of the sparse recovery index position of impulse noise is guaranteed, and the accuracy of impulse noise estimation is improved.

6. The enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing according to any one of claims 1 to 5, characterized in that Utilize the strong candidate correlation between the impulse signals with different carrier frequency offsets to define the atomic candidate correlation: wherein, and respectively represent the candidate sets of known impulse noise and estimated impulse noise, ∩ and ||·||0 respectively represent the union and the l0 norm.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it realizes the steps of the enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing described in any one of claims 1 to 6.

8. An electronic device, characterized in that, It includes: a processor; a memory for storing instructions executable by the processor; wherein, the processor is configured to execute the steps of the enhanced method for underwater acoustic OFDM impulse noise estimation based on distributed compressive sensing described in any one of claims 1 to 6.

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