Underwater acoustic channel estimation method based on adaptive sparse domain inverse power standardization

Abstract

The adaptive sparse domain inverse power standardized underwater acoustic channel estimation method provided by the invention is used for improving the convergence speed and the calculation efficiency of a filtering algorithm, and has the beneficial effects that a discrete cosine transform (DCT) mechanism is combined with an adaptive normalized step length LMS method, and power estimation of an input signal is dynamically updated, so that the adaptive sparse domain inverse power standardized underwater acoustic channel estimation method is realized. According to the method, adaptive step length adjustment is realized, the convergence speed and stability of the algorithm are effectively improved, and relatively low calculation complexity can still be kept under the condition of relatively large input signal power change, so that the adaptivity and robustness of the filter are improved; adaptive adjustment can be carried out more quickly and accurately in different underwater acoustic channel environments, so that the real-time tracking capability and accurate estimation of the underwater acoustic channel are enhanced.

Description

Technical Field

[0001] The invention relates to the fields of underwater communication and ocean monitoring, and in particular to an underwater acoustic channel estimation method with adaptive sparse domain inverse power standardization. Background Art

[0002] Problems such as channel estimation and noise suppression in underwater acoustic communications can be reduced to the optimization problem of sparse channel responses. Through optimal estimation, the estimation methods of underwater acoustic channels include the classic regularized minimum mean square error (NLMS) and the data reuse recursive least squares algorithm (DRRLS). For details of the normalized subband adaptive filter method, please refer to the article "Sparsity-aware normalized subband adaptive filters with jointly optimized parameters", published in the Journal of the Franklin Institute, Vol. 357, No. 17, 2020, with the article start and end pages 13144-13157. For details of the data reuse recursive least squares algorithm, please refer to the article "Data-Reuse Recursive Least-Squares Algorithms", published in the IEEE Signal Processing Letters, Vol. 29, 2022, with the article start and end pages 752-756. These studies provide a theoretical basis for channel estimation in the sparse domain, but there are still many challenges when facing complex underwater environments.

[0003] Due to the complexity and non-stationary characteristics of the underwater acoustic channel, it is extremely difficult to accurately and effectively model and estimate it. In addition, the underwater acoustic channel may be affected by many factors, such as noise, multipath effects, etc. The traditional adaptive filtering method based on fixed step size often loses the ability to accurately estimate the channel response in a complex and dynamically changing underwater environment. Therefore, considering the time-varying characteristics of the underwater acoustic channel, it is necessary to perform fine adaptive adjustment and power estimation of the channel coefficients to improve the channel description ability and enhance robustness.

[0004] However, the convergence accuracy and convergence speed of traditional adaptive filtering methods cannot meet the requirements of fast convergence and accurate estimation at the same time, which makes it difficult to balance the estimation accuracy and convergence performance. To solve this problem, the present invention proposes an underwater acoustic channel estimation method based on adaptive sparse domain inverse power normalization, which uses discrete cosine transform (DCT) to map the channel response to the sparse domain, and continuously and adaptively adjusts the step size to achieve accurate channel estimation in a complex and changeable underwater acoustic environment. In addition, by introducing an inverse power normalization strategy, power estimation is used to adjust the filter gain in order to achieve a stable estimation of the channel response, thereby significantly improving the robustness and overall performance of channel estimation.

[0005] Purpose of the Invention

[0006] In order to effectively solve the problem of complex and changeable underwater acoustic channels, the present invention proposes an underwater acoustic channel estimation method based on adaptive sparse domain inverse power normalization. The invention utilizes the discrete cosine transform (DCT) framework, combined with an adaptive power normalization mechanism, to continuously adjust the step size and power estimation, thereby achieving high-precision channel estimation in complex underwater environments. By introducing a sparse domain channel representation strategy and adopting an inverse power normalization method, the convergence speed and stability of channel estimation are effectively balanced, and ultimately the underwater acoustic channel response is accurately reconstructed, thereby improving the robustness and performance of the overall communication system.

[0007] Technical Solution

[0008] In order to solve the problem that the classical algorithm calculation amount, convergence speed and accuracy are difficult to balance under dynamic conditions, the specific implementation steps of the present invention are as follows:

[0009] (1) Set the parameter μ0 as the initial value of the learning rate, set λ as the forgetting factor, initialize the weight vector w to an all-zero vector, and initialize the mean square error vector MSD to an all-zero vector;

[0010] (2) Given the input signal x, the expected signal d, and the initial weight h, repeat the following i-th iteration until the number of iterations reaches the signal length N:

[0011] Update the input vector x v , where xv = [x i ,x i-1 ,...,x i-L+1 ];

[0012] Calculate the transformed input Where D is the discrete cosine transform matrix (DCT matrix);

[0013] Update the power estimate p, where p = λp + (1-λ) |u| 2 ,|u| 2 represents the square modulus of each element in u;

[0014] Compute the inverse diagonal matrix H inv =diag(1 / p);

[0015] Calculate the output y i =u T w and calculate the error e = d i -y i ;

[0016] Calculate the normalized step size factor μ = μ0 / (u T H inv u+10 -6 );

[0017] Update weight vector w = w + μH inv ue * ;

[0018] Calculate and record the mean square error MSD i =|wh| 2 / |h| 2 .

[0019] The number of iterations above is equal to N.

[0020] Beneficial effects:

[0021] The present invention proposes an underwater acoustic channel estimation method with adaptive sparse domain inverse power normalization to improve the convergence speed and computational efficiency of the filtering algorithm. The beneficial effects are embodied in: the present invention utilizes a discrete cosine transform (DCT) mechanism in combination with an adaptive normalized step size LMS method to dynamically update the power estimation of the input signal to achieve adaptive step size adjustment, thereby effectively improving the convergence speed and stability of the algorithm, and being able to maintain a low computational complexity under the condition of large changes in the input signal power, thereby improving the adaptability and robustness of the filter, and being able to perform adaptive adjustments more quickly and accurately in different underwater acoustic channel environments, thereby enhancing the real-time tracking capability and precise estimation of the underwater acoustic channel. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a graph comparing the learning curves of the method of the present invention (new Discrete Cosine Transform Least Mean Squares, nDCTLMS) with traditional minimum mean square error methods, regularized least-mean-squares algorithm (Normalized least-mean-squares, NLMS) and data-reuse recursive least squares algorithm (Data-Reuse Recursive Least-Squares Algorithms, DR-RLS).

[0023] Figure 2 It is a comparison chart of the calculation time results of the traditional LMS, NLMS, DR-RLS methods and the method of the present invention (nDCTLMS). DETAILED DESCRIPTION

[0024] The present invention will now be further described with reference to the accompanying drawings. Figure 1 ,The parameters during the experiment are set as follows:

[0025]

[0026]

[0027] The results are as follows Figure 1 As shown, Figure 1 The mean square error (MSD) learning curve performance of each adaptive filtering algorithm under different signal-to-noise ratio (SNR) conditions is shown. The left figure corresponds to the case of SNR of 15dB, and the right figure corresponds to the case of SNR of 30dB. The horizontal axis represents the number of iterations, and the vertical axis is the mean square error (expressed in logarithmic coordinates).

[0028] It can be observed that the nDCTLMS algorithm exhibits fast convergence characteristics under both SNR conditions, especially under lower SNR (15dB) conditions. Compared with the traditional LMS and NLMS algorithms, the error of nDCTLMS decreases rapidly and tends to be stable, showing a higher noise resistance. When the SNR is 30dB, nDCTLMS still maintains a good convergence speed and stability. In contrast, the LMS algorithm has the slowest convergence speed and a larger mean square error under lower SNR conditions. The convergence speed of the NLMS algorithm has improved, but it is still not as good as the performance of the nDCTLMS algorithm. Although the nDCTLMS is not as fast as the DR-RLS algorithm in terms of convergence speed, it has a lower steady-state error and a smaller operation time.

[0029] In order to further investigate the computational complexity of different algorithms, Figure 2 The running time comparison of different adaptive filtering algorithms is shown, with the algorithm names (LMS, NLMS, DR-RLS, nDCTLMS) on the horizontal axis and the running time (seconds) on the vertical axis. The running time of each algorithm is represented by a box plot, where the blue box represents the quartile range and the red "+" sign represents the outlier. As can be seen from the figure, the running time of the LMS and NLMS algorithms is the shortest and most stable, and their boxes are low, indicating that the two algorithms have high computational efficiency. In contrast, the running time of the DR-RLS algorithm is significantly longer, and there are more outliers, indicating that its computational complexity is high and the running time fluctuates greatly. The running time of the nDCTLMS algorithm is slightly higher than that of LMS and NLMS, but much lower than that of DR-RLS, and its box is small, showing high computational efficiency and stability.

[0030] In general, the nDCTLMS algorithm has a moderate running time while maintaining high convergence performance, showing good overall performance, and is suitable for use in scenarios that require a balance between convergence speed and computational efficiency.

Claims

1. An adaptive sparse domain inverse power normalization underwater acoustic channel estimation method, characterized by: The method includes the following: S1: Set the parameter μ0 as the initial value of the learning rate, set λ as the forgetting factor, initialize the weight vector w to an all-zero vector, and initialize the mean square error vector MSD to an all-zero vector; S2: Given the input signal x, the expected signal d and the initial weight h, repeat the following i-th iteration until the number of iterations reaches the signal length N: S3: Update the input vector x v , where xv = [x i ,x i-1 ,...,x i-L+1 ]; S4: Calculate the transformed input Where D is the discrete cosine transform matrix (DCT matrix); S5: Update power estimate p, where p = λp + (1-λ) |u| 2 ,|u| 2 represents the square modulus of each element in u; S6: Calculate the inverse diagonal matrix H inv =diag(1 / p); S7: Calculate output y i =u T w and calculate the error e = d i -y i ; S8: Calculate the normalized step size factor μ = μ0 / (u T H inv u+10 -6 ); S9: Update weight vector w=w+μH inv ue * ; S10: Calculate and record the mean square error MSD i =|wh| 2 / |h| 2 .

2. The method for underwater acoustic channel estimation based on adaptive sparse domain inverse power normalization according to claim 1 is characterized in that: The number of iterations above is equal to N.

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