A sparse underwater acoustic channel estimation method based on N2N-SAMP algorithm

Abstract

The application discloses a sparse underwater acoustic channel estimation method based on an N2N-SAMP algorithm, which comprises the following steps: firstly, obtaining a time-domain underwater acoustic channel response, and adding two zero-mean noises with the same dimension to the time-domain underwater acoustic channel response to obtain two pilot matrices containing noises; secondly, using the pilot matrices containing noises to obtain a pilot matrix without noise through an N2N algorithm and a U-net network; and finally, using the pilot matrix without noise and a SAMP algorithm to perform channel estimation. The application converts the de-noising problem of the pilot signal into an image de-noising problem, considers the statistical characteristics of ocean noise, combines the N2N algorithm, and improves the underwater acoustic channel estimation performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of channel estimation, and particularly relates to a sparse underwater acoustic channel estimation method combining an N2N-SAMP algorithm and a U-net network model. BACKGROUND

[0002] At present, among numerous reconstruction algorithms, a sparse degree adaptive matching pursuit (SAMP) algorithm approximates a real sparse degree by adaptively adjusting the step of selecting an atom and setting a suitable iteration stopping threshold, and has certain advantages in processing signals with unknown sparse degrees. However, in underwater acoustic channel estimation, due to the existence of ocean noise, the SAMP algorithm may select a large number of wrong atoms when selecting atoms, which leads to a serious loss of accuracy. In addition, the SAMP algorithm is very sensitive to noise, and the setting of the iteration stopping condition is closely related to the noise energy, and the iteration stopping threshold needs to be carefully adjusted according to the noise.

[0003] The existence of ocean noise can seriously interfere with the sparsity of the underwater acoustic channel, and bring difficulties to the setting of the iteration termination condition of the SAMP algorithm, thereby greatly affecting the performance of the underwater acoustic channel estimation. In this case, the most direct and effective method is to filter out these noise interference, that is, to filter out the noise interference in the pilot signal. Therefore, the N2N denoising method is applied to the pilot matrix denoising problem. SUMMARY

[0004] In view of the problems and defects existing in the prior art, the technical problem to be solved by the present application is to provide a sparse underwater acoustic channel estimation method based on an N2N-SAMP algorithm. The N2N algorithm in the image denoising theory is combined to further improve the performance of the underwater acoustic channel estimation.

[0005] To achieve the above-mentioned purpose, the present application provides a sparse underwater acoustic channel estimation method based on an N2N-SAMP algorithm, comprising the following steps:

[0006] Step one, obtaining a time-domain underwater acoustic channel response, and adding two zero-mean noises (with different noise powers) with the same dimension as the time-domain underwater acoustic channel response to obtain two pilot matrices containing noises.

[0007] Step two, using the pilot matrices containing noises to obtain a pilot matrix without noise through the N2N algorithm and the U-net network. The U-net network is trained using the pilot matrices containing noises, and after the model is trained, the network is evaluated using a test set. The pilot matrix without noise is obtained by using the U-net network output.

[0008] Step three, using the denoised pilot matrix and the SAMP algorithm to perform channel estimation. The performance of the N2N-SAMP is verified, and the threshold of the SAMP algorithm is dynamically adjusted according to the SNR, so that the optimal performance is achieved under different SNRs.

[0009] Advantages of the present application:

[0010] The N2N-SAMP algorithm-based sparse underwater acoustic channel estimation method of the present application is based on the actual demand and the current product status, technical problems and technical availability, and proposes an N2N-SAMP sparse underwater acoustic channel estimation method without SNR prior information and with constant iteration stopping threshold, which can solve the problems of difficult setting of iteration termination condition of the current SAMP algorithm and significant difference of selection of optimal threshold under different noise power conditions, convert the denoising problem of pilot signals into an image denoising problem, consider the statistical characteristics of ocean noise, combine the N2N algorithm, and design a U-net neural network suitable for pilot signal input, thereby improving the performance of underwater acoustic channel estimation. BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 Structure diagram of N2N-SAMP algorithm;

[0012] Figure 2 Schematic diagram of the U-Net network structure used;

[0013] Figure 3 Denoising performance analysis of N2N-SAMP algorithm;

[0014] Figure 4 Comparison chart of SMAP algorithm and N2N-SAMP algorithm MSE;

[0015] Figure 5 Comparison chart of SMAP algorithm and N2N-SAMP algorithm BER. DETAILED DESCRIPTION

[0016] The technical solutions of the present application will be further described in detail below with reference to the drawings and examples.

[0017] To address the challenge of pilot signal denoising, an innovative Noise2Noise (N2N) denoising method was adopted in this study. This method does not require a noise-free reference signal, but instead trains on pairs of noisy images, thereby achieving effective suppression of noise. Given the difficulty of obtaining noise-free pilot signals in underwater acoustic communication systems and the zero-mean characteristic of ocean noise, the N2N denoising technique provides a practical solution for denoising of pilot matrices.

[0018] Embodiment:

[0019] A N2N-SAMP algorithm-based sparse underwater acoustic channel estimation method, comprising the following steps:

[0020] Step one, in orthogonal frequency division multiplexing (OFDM) underwater acoustic communication, each frame of signal received by the receiving end can be regarded as a two-dimensional matrix, corresponding to each OFDM symbol in the signal in the time domain, and corresponding to each subcarrier frequency in the frequency domain. Correspondingly, the pilot signal also presents as a matrix form, therefore, the denoising process of the pilot signal can be regarded as a matrix denoising problem. The essence of image denoising is also to process the pixel values in the two-dimensional matrix to remove or reduce the influence of noise, so as to restore the original noise-free image. In view of the correlation between image denoising and pilot signal denoising in essence, the denoising process of the pilot signal can be equivalent to image denoising.

[0021] In order to obtain the pilot matrix containing noise, the time domain underwater acoustic channel response can be simulated by using the OFDM underwater acoustic channel simulator, and then the noise-free received pilot signal is:

[0022] Y c =X P F P h

[0023] Where Y c represents the noise-free received pilot signal, X P represents the transmitted pilot signal matrix, F P represents the DFT matrix corresponding to the pilot, and h is the sparse time domain underwater acoustic channel response. With the noise-free pilot signal, two zero-mean noises with the same dimension as Y c are added respectively, that is, two noise-containing pilot matrices Y and Y' are obtained. In addition to constructing the noise-containing pilot matrix by the above method, the pilot signal can also be transmitted multiple times within the coherence time of the channel (the maximum time range in which the channel state remains relatively stable). Then, the received pilot signal at the receiving end can be regarded as multiple independent noisy samples, and these samples all come from the same noise-free pilot signal, but due to the randomness of noise, each sample will be different. For example Figure 1 is the N2N-SAMP algorithm structure diagram.

[0024] Step two, the N2N algorithm divides a single noisy feature image into multiple small blocks, and regards the small blocks as independent noisy feature images under similar scenes; then, by constructing a U-net network, the small blocks are taken as input to learn the process of recovering the noise-free feature image from the noisy feature image. In the training process, the U-net network continuously optimizes its parameters to minimize the difference between the predicted noise-free feature image and the actual noise-free feature image.

[0025] With the training required noisy pilot data, the U-net network can be trained. In the N2N-SAMP method designed in the application, the U-net network model is selected, the input of which is the noisy pilot matrix in the previous step, and the output is the noise-free pilot matrix. Figure 2 The structure of the model can be divided into four core parts: down-sampling, up-sampling, skip connection and output part. The down-sampling part is composed of consecutive convolutional layers and pooling layers, which is responsible for extracting key features from the input image. The up-sampling part enlarges the size of the feature map through deconvolution, and then restores the original size of the image. The skip connection connects the corresponding layers of the down-sampling and up-sampling parts to realize the transmission of features. The U-net network can understand the image content more deeply with powerful feature extraction capability, and accurately restore the image part contaminated by noise. The loss function used by the network is L2 loss function, that is:

[0026]

[0027] Where f θ represents the U-net network with parameters θ, Y and Y' represent two pilot matrices containing noise.

[0028] After the model is trained, the network is evaluated using the test set, and the denoised pilot matrix is obtained. The SAMP algorithm is used for channel estimation using the denoised pilot signal. At this time, the SAMP reconstructed channel is the equivalent time-domain underwater acoustic channel response after denoising, which is more sparse than the original noisy channel, and the reconstruction accuracy can be effectively improved. Since the denoising process reduces noise, a smaller iteration termination threshold can be set, and dynamic adjustment according to noise power is not necessary.

[0029] The specific process of SAMP algorithm is as follows:

[0030] Input parameters: sensing matrix A, observation vector (pilot signal) y, step size S (default is 1 in this paper)

[0031] 1. Pilot denoising y→y'.

[0032] 2. Initialization: residual vector r0=y', iteration number t=1, step size L=S, support set Λ t represents the index set (column vector number of A) when the algorithm is iterated to the t-th time, A t represents the column vector set of the selected sensing matrix A according to Λ t .

[0033] 3. Calculate u=abs(A T r t-1) Pick the largest L values in u and construct the corresponding L index values as a set and denote it as J.

[0034] 4. Update the support set, i.e. Λ t = Λ t-1 ∪J, A t = A t-1 ∪{a j},j∈J.

[0035] 5. Solve the least square solution, i.e.

[0036] 6. Calculate the norm of , pick the corresponding K index values according to the norm size (from large to small), and then pick the corresponding L items from A and Λ t , and denote them as A tL and Λ tL , respectively, and set F = Λ tL .

[0037] 7. Update the residual, i.e. r tnew = y-A tL (A tL T A tL ) -1 A tL T y.

[0038] 8. If r t < σ, stop iteration and output the result, if ||r tnew ||2≥||r t-1 ||2, update the step size L = L + S, and return to step 2; if neither of the above two conditions is met, set Λ t = F, r t = r tnew , t = t + 1, and return to step 2.

[0039] Output: Sparse signal

[0040] Step three, in order to verify whether the denoiser can effectively remove noise, the noise energy contained in the pilot matrix before and after denoising is counted. Figure 3 The noise energy comparison chart before and after denoising of the pilot matrix when SNR = [0 5 10 15 20] dB is shown. It can be seen from the figure that the denoiser can effectively reduce the noise in the received pilot matrix.

[0041] After calculation, the noise energy is reduced by more than 50% in the SNR range of [0 5 10 15 20]. Among them, when SNR=20, the noise reduction is the least, which is 52.66%, and when SNR=15, the noise energy reduction is the most, which is 69.82%, and the denoising effect is the best.

[0042] Step four, in order to verify the channel estimation performance of N2N-SAMP algorithm and the influence of iteration threshold on the algorithm, SAMP and N2N-SAMP under different thresholds σ are used for channel estimation. In the experiment, the threshold σ is 0.5:0.5:10. Figure 4 The MSE comparison chart of SAMP algorithm and N2N-SAMP algorithm in selecting different σ for channel estimation is shown when SNR changes from 0 dB to 20 dB. Among them, the value of SAMP algorithm σ is 6, 4.5, 0.5, which corresponds to the selection of 0, 10, 20 respectively when the channel estimation performance is optimal. The value of N2N-SAMP algorithm σ is the smallest three values 1.5, 1, 0.5.

[0043] From Figure 4 It can be seen from the above that the SAMP algorithm is very unstable, and the selection of threshold σ has a great influence on the performance. When SNR is small, the threshold σ should be relatively large, and when SNR is large, the threshold σ should be relatively small. That is, in order to obtain better channel estimation performance, it is necessary to carefully adjust according to different noise levels. In contrast, the channel estimation performance of N2N-SAMP algorithm is relatively stable when the threshold σ is small, which shows that N2N-SAMP algorithm has certain robustness to noise changes, and can maintain good performance without frequent adjustment of parameters. In addition, it can be seen from the figure that in most cases, the MSE performance of N2N-SAMP algorithm is significantly better than that of SAMP algorithm. Figure 5 The comparison of the two algorithms in system BER is shown. It can be seen from the figure that N2N-SAMP algorithm also performs better in system BER.

[0044] The above detailed description of the specific design embodiments of the present application. It should be understood that those skilled in the art can make many modifications and changes without creative labor according to the concept of the present application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment on the basis of the prior art according to the concept of the present application shall be within the protection scope determined by the claims.

Claims

1. A sparse underwater acoustic channel estimation method based on the N2N-SAMP algorithm, characterized in that, Includes the following steps: Step 1: Obtain the time-domain underwater acoustic channel response and add two zero-mean noises of the same dimension to obtain two noisy pilot matrices. Step 2: Using the noisy pilot matrix, obtain the noise-free pilot matrix through the N2N algorithm and U-net network. The specific process is as follows: The N2N algorithm divides a single noisy feature image into multiple small blocks and treats each small block as an independent noisy feature image under similar scenes; then, by constructing a U-net network, the small blocks are used as input to learn the process of recovering the noise-free feature image from the noisy feature image. During the training process, the U-net network continuously optimizes its own parameters to minimize the difference between the predicted noise-free feature image and the actual noise-free feature image. Step 3: Channel estimation is performed using the denoised pilot matrix and the SAMP algorithm.

2. The sparse underwater acoustic channel estimation method based on the N2N-SAMP algorithm according to claim 1, characterized in that, The two zero-mean noises added have different power levels.

3. The sparse underwater acoustic channel estimation method based on the N2N-SAMP algorithm according to claim 1, characterized in that, The noise-free received pilot signal obtained from the underwater acoustic channel response is: ； in, This indicates a noise-free received pilot signal. This represents the transmitted pilot signal matrix. This represents the DFT matrix corresponding to the pilot signal. It is a sparse time-domain underwater acoustic channel response.

4. The sparse underwater acoustic channel estimation method based on the N2N-SAMP algorithm according to claim 3, characterized in that, The loss function used in the training of the U-net network is The loss function is: ； in, The parameter is The U-net network, and This represents two pilot matrices containing noise.

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