A method for noise and interference suppression for underwater acoustic communication transmission links

Abstract

A noise and interference suppression method for underwater acoustic communication transmission links is disclosed, relating to the field of underwater acoustic communication transmission and reception technology. The method involves framing and windowing the received underwater acoustic communication signal to obtain the observed underwater acoustic communication signal matrix. Based on the characteristics that the effective communication components exhibit continuous time-frequency distribution and energy concentration in a finite frequency band, while noise and impulse interference spread across the entire frequency range or are isolated, an adaptive group sparse modeling framework incorporating a scale parameter is constructed to adaptively adjust the penalty intensity at each time-frequency point. A time-direction smoothing constraint is introduced into the scale parameter, and a sparse penalty function with saturation characteristics is designed. Through alternating optimization and a near-end gradient algorithm, a joint estimation problem is solved to obtain the enhanced time-frequency energy distribution, thus completing the noise and interference suppression of the underwater acoustic communication signal. This method effectively suppresses background noise and pseudo-structure interference in complex marine environments, maintains the key structural characteristics of the communication signal, and improves the reliable reception capability and stability of underwater acoustic communication transmission.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater acoustic communication transmission and reception, and particularly relates to a noise and interference suppression method for an underwater acoustic communication receiving end, aiming to suppress noise and interference in an underwater acoustic communication link and improve signal transmission quality and link reliable reception capability. BACKGROUND

[0002] In underwater wireless communication link construction, underwater sensor network data backhaul and underwater equipment information interaction communication transmission scenarios, the communication signal (for example, a communication waveform containing a synchronization sequence, a pilot sequence and modulated data) sent by the underwater acoustic communication transmitting end reaches the receiving end after propagating through the ocean acoustic channel, and its reception quality directly affects key links such as synchronization acquisition, channel estimation, equalization and demodulation decoding, and further affects the reliability and stability of the transmission link. However, the underwater acoustic communication signal is easily affected by complex noise environment and burst interference during ocean propagation: on the one hand, the long-term existence of ocean background noise reduces the signal-to-noise ratio of the receiving end; on the other hand, the occasional non-stationary sound source in the ocean, impulse type strong interference will cause burst damage to the characteristic structure of the communication signal, weaken the distinguishability of the receiving end to the effective communication component, and thus limit the reliable reception capability of the link. Therefore, in order to improve the reliable reception capability of the underwater acoustic communication transmission link in the complex ocean environment, it is necessary to introduce an enhanced mechanism for noise and interference suppression at the receiving end, to suppress the background noise and burst interference while maintaining the structural characteristics of the communication waveform as much as possible, to support subsequent reception processing.

[0003] Currently, the receiving end often uses time-frequency domain representation methods to characterize the energy distribution of the received signal in the time-frequency joint dimension to assist in key links such as synchronization acquisition, pilot sequence detection, and channel estimation and equalization. Although classical time-frequency transform methods such as STFT, Gabor transform, and Wigner-Ville transform can provide a representation of the signal in the time-frequency domain, they are not robust enough in a noisy environment, and due to the limitations of the measurement uncertainty principle, a trade-off must be made between time accuracy and frequency accuracy. To improve the anti-noise performance of time-frequency representation, existing technologies propose various improvement schemes, for example, Chinese patent CN114996641B provides a variational mode decomposition method based on time-frequency correlation coefficient joint factors, which can separate part of the noise, but has high computational cost, and short-time pulse interference is prone to energy leakage in the frequency domain, leading to over-splitting of the components. On the other hand, time-frequency energy redistribution or synchronous compression methods provide new ideas for signal enhancement, such as Chinese patent CN117130048B uses a synchronous compression extraction transform method to concentrate time-frequency energy in the time-frequency ridge region, thereby making the signal components more prominent in the time-frequency graph. However, in the case of low signal-to-noise ratio, time-frequency energy compression or extraction operations often simultaneously strengthen noise components and effective signals, and cannot effectively suppress the influence of noise. Since most target communication signals have natural sparse characteristics in the time-frequency domain, time-frequency representation methods based on sparsity have natural advantages in denoising and energy extraction. Chinese patent CN114036458A provides an exponential approximation point sparse constraint that effectively guides the sparse reconstructed signal to focus on the main energy path of the signal, thereby enhancing the expression ability of the signal components, and Chinese patent CN113935146B provides a non-convex variable overlapping group sparse method that can achieve good enhancement effect under Gaussian background noise.

[0004] The above disclosed patent methods are mostly based on the assumption that the noise in the underwater acoustic communication transmission link is approximately stationary Gaussian noise or non-structured interference, and lack specific modeling and suppression mechanisms for the common pulse non-Gaussian noise and burst strong interference in the marine environment. Such methods either focus on improving the aggregation of time-frequency representation or are mainly suitable for low-power and simple-structured background noise scenarios; under strong pulse noise or burst interference conditions, it is difficult to maintain the structural characteristics of the communication signal and effectively suppress the interference at the same time, thereby limiting the reliable reception capability of the link.

[0005] Therefore, in the ocean transmission channel containing significant pulse interference, how to effectively distinguish the real structural characteristics of the underwater acoustic communication signal and the pseudo-structural disturbance caused by the pulse interference in the time-frequency domain becomes a technical problem to be solved for realizing reliable reception of the link: on the one hand, a time-frequency structure model capable of self-adaptively describing the local correlation of the communication signal in the time and frequency dimensions needs to be constructed to maintain the key characteristics of the communication signal; on the other hand, a targeted suppression mechanism needs to be designed for the pulse-like non-Gaussian noise to improve the discrimination ability of the effective communication components and the interference, thereby improving the reliable reception performance and robustness of the underwater acoustic communication link in the complex marine environment. SUMMARY

[0006] The present application aims to solve the technical problems that, when the underwater acoustic communication signal is affected by the non-Gaussian interference such as pulse noise in the marine transmission channel, the interference is locally aggregated in the time-frequency domain and superimposed with the effective communication components, which easily causes masking or confusion of the key structural characteristics of the communication signal, resulting in a decline in the reliable reception performance, and provides a noise and interference suppression method for an underwater acoustic communication transmission link. The method constructs a time-frequency structure constraint model based on smooth adaptive group sparsity at the receiving end, and performs anti-noise and anti-interference processing on the received signal: by analyzing the local characteristics and change trend of the time-frequency coefficients, a small-scale smooth group block structure is adaptively formed, and a scale parameter is adaptively adjusted and a time direction smooth constraint is introduced, so that the suppression strength is adaptively adjusted according to the local structure and energy, thereby suppressing the pseudo-structural disturbance caused by the pulse interference while maintaining the key structural characteristics of the communication signal as much as possible, and improving the reliable reception ability and stability of the transmission link in the complex marine environment.

[0007] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0008] A noise and interference suppression method for an underwater acoustic communication transmission link, comprising the following three key steps: constructing a time-frequency observation equation, constructing a smooth adaptive group sparse time-frequency structure model, and alternately solving the target time-frequency structure and the scale parameter; the specific steps of the method are as follows:

[0009] 1) Constructing a time-frequency observation equation: preprocessing the received time-domain observed underwater acoustic communication signal, including frame segmentation and windowing processing, to obtain an observed underwater acoustic communication signal matrix, synchronously constructing an inverse discrete Fourier transform matrix adapted to the observed underwater acoustic communication signal matrix, defining a target time-frequency signal matrix to be enhanced, introducing a noise matrix, and constructing a time-frequency observation equation to represent the linear mapping relationship between the time domain and the frequency domain;

[0010] 2) Constructing joint optimization model: based on the linear mapping relationship obtained in step 1), a preliminary optimization model containing group sparse constraints is first established, and then auxiliary scale parameters are introduced and transformed into a joint optimization problem; the group is refined to a single time-frequency point, an independent scale parameter is configured for each time-frequency point and a constraint is applied, a compensation term is introduced to construct a saturation type penalty function, a smoothing constraint along the time direction is applied to the scale parameter sequence of each frequency channel, and a joint optimization model of the target time-frequency signal matrix and the scale parameter is constructed;

[0011] 3) Alternating solution to obtain enhanced signal: the joint optimization model constructed in step 2) is solved by using an alternating method of inner iteration and outer iteration combined with a proximal gradient algorithm, the target time-frequency signal matrix and the scale parameter sequence are alternately updated until the outer iteration meets the convergence condition or reaches the maximum iteration number, the enhanced target time-frequency signal matrix and the corresponding scale parameter sequence are output, the time-frequency enhancement of the underwater acoustic signal is realized, and the noise and interference suppression of the underwater acoustic communication signal is completed.

[0012] In step 1), the specific steps of constructing the time-frequency observation equation can be:

[0013] Frame segmentation and windowing processing are performed on the one-dimensional time domain observed underwater acoustic communication signal to obtain an observed underwater acoustic communication signal matrix , wherein is the frame length, is the number of frames, represents the complex domain; adapted to the observed underwater acoustic communication signal matrix, a discrete inverse Fourier transform matrix consistent with the frame length is constructed , the element in the i-th row and the j-th column of the matrix is:

[0014]

[0015] , wherein is a natural constant, is an imaginary unit, is a constant of pi, is a row index, , is a complex exponential basis function, corresponding to a basis vector of a discrete frequency ;

[0016] The target time-frequency signal matrix to be estimated is defined as , and a noise matrix is introduced; based on the observed underwater acoustic communication signal matrix and the discrete inverse Fourier transform matrix , a time-frequency observation equation is established: ​​, for characterizing the linear mapping relationship between the frequency domain coefficients after inverse transform and the time domain observation, wherein the noise matrix The noise in the noise matrix

[0017] In step 2), the specific steps of constructing the joint optimization model can be:

[0018] 2.1) Constructing a preliminary optimization model: based on the time-frequency observation equation of step 1), a group sparse regularization term is introduced to construct a preliminary optimization model based on group sparse constraint;

[0019] 2.2) Optimizing the group sparse penalty term: introduce a scale parameter for the group sparse penalty term of the preliminary optimization model, and transform it into a joint optimization problem of the target time-frequency signal matrix and the scale parameter; refine the group division to the single time-frequency point level, so that each time-frequency point corresponds to an independent scale parameter, and the penalty term is transformed into a point-by-point form; add a constraint to the scale parameter and introduce a compensation term to construct a saturation characteristic cost function, which takes into account noise suppression and structure preservation;

[0020] 2.3) Applying smoothing constraint along time direction: smoothing constraint is applied to the scale parameter along time direction on the same frequency channel, limiting the variation amplitude of the scale parameter at adjacent time points, so that time points with similar energy levels obtain similar penalty scales, forming an adaptive regionalized structure from time dimension, and suppressing impulse noise;

[0021] 2.4) Integrating to construct a joint model: based on the adaptive group sparse term, the penalty function compensation mechanism and the smoothing constraint along time direction, a joint optimization model of the target time-frequency signal matrix and the scale parameter is constructed;

[0022] Further:

[0023] 2.1) Based on the time-frequency observation equation constructed in step 1), a group sparse regularization term is introduced to construct a preliminary optimization model based on group sparse constraint as expressed in formula to estimate the target time-frequency signal matrix which is sparse and has a structured continuity from the observed underwater acoustic communication signal matrix :

[0024]

[0025] wherein, is the Frobenius norm square of the reconstructed matrix obtained by inverse transform of the target time-frequency signal matrix from the observed underwater acoustic communication signal matrix , as a data fidelity term to measure the overall reconstruction error; is the total amount of groups, is a regularization weight parameter, is the index set of time-frequency points corresponding to the th group, is the target time-frequency signal matrix is the group coefficient subset on the set , and denotes the number of elements contained in the th group, is the group norm;

[0026] In view of the significant non-stationarity of the structural characteristics of the target underwater acoustic communication signal and the distribution of the background noise, and the large variation of the energy scale and sparsity level in different regions, when a fixed group division or a fixed size group structure is used, the group scale and the signal characteristics are likely to be mismatched, thereby weakening the expression ability of the sparse constraint and even affecting the noise suppression effect; therefore, it is necessary to make the sparse regularization term have adaptive adjustment ability, which can dynamically adjust with the time-frequency structure change, rather than relying on the preset fixed blocking mode.

[0027] 2.2) For the group sparse penalty term in equation (2), to realize adaptive adjustment of the penalty strength with the group energy, a scale parameter is introduced for each group. For any th group, there is an inequality:

[0028]

[0029] wherein, is the target time-frequency signal matrix is the group coefficient subset on the set , and denotes the number of elements contained in the th group, is the group norm; is the scale parameter;

[0030] Therefore, equation can be equivalently represented as a joint optimization problem about the target time-frequency signal matrix and the scale parameter :

[0031]

[0032] wherein, is the observed underwater acoustic communication signal matrix and the Frobenius norm square of the reconstruction matrix obtained by inverse transformation of the target time-frequency signal matrix is the Frobenius norm square of the reconstruction matrix is a regularization weight parameter, For the number of groups, For the first The set of time-frequency point indices corresponding to each group The target time-frequency signal matrix In the index set A subset of group coefficients on, Indicates the first The number of elements contained in a group It is a group norm 2; For scale parameters;

[0033] During the optimization process, scale parameters The group's norm 2 The parameter is automatically updated based on the change in energy level within the group, thus achieving adaptive adjustment of the penalty magnitude and automatically adjusting the penalty intensity.

[0034] Furthermore, the group division is refined to the single time-frequency point level, so that each group contains only one time-frequency point, i.e., the first... The number of elements contained in a group At this time, the first The set of time-frequency point indices corresponding to each group Refine to include only time index Frequency index At a single time-frequency point, the target time-frequency signal matrix In the index set subset of group coefficients on The target time-frequency signal element at this point is represented as... and scale parameters Let this be the time-frequency signal element of the target. scale parameters , then the formula The group sparsity penalty term in the equation can be written as a pointwise penalty function. :

[0035]

[0036] in, The target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, For the corresponding target time-frequency signal elements The scale parameter, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element);

[0037] Through It allows for independent adjustment of the penalty intensity at each time-frequency point, enabling the target time-frequency signal elements to... Corresponding scale parameters The model can adaptively update according to changes in local energy during the optimization process. The update method is explained in detail in step 3). The model can automatically distinguish continuous target structures without predefining the group size or position. Real structures with similar intensity and continuous distribution will form block clusters during the iteration process.

[0038] Considering the formula The penalty function exerts equal "pushing back to zero" force on small and large coefficients. Small coefficients are compressed, but large coefficients often correspond to high-energy points or continuous structures in the real target. Continuous linear penalty will also significantly suppress these strong components, resulting in over-penalization. Therefore, this invention focuses on the target time-frequency signal elements. Corresponding scale parameters Add constraints:

[0039]

[0040] in, The preset threshold adjustment parameter; when the energy is low, the target time-frequency signal element Corresponding scale parameters It can be reduced to a smaller value to maintain sufficient penalty strength to suppress noise; when the energy is large, the target time-frequency signal elements Corresponding scale parameters The formula can be kept at a moderate size under the upper bound constraint to avoid the penalty term being amplified indefinitely; based on this, the formula can be further improved. The penalty function expressed is used to construct a smooth cost function by introducing a compensation term:

[0041]

[0042] in, The target time-frequency signal matrix In time index i, frequency index The target time-frequency signal element at the location, For the corresponding target time-frequency signal elements scale parameters, For target time-frequency signal elements The model, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element); For the preset threshold adjustment parameters, This constrains the range of values ​​for the scale parameter;

[0043] The improved penalty function has the following characteristics in different energy ranges: in the weak energy region, approximately linear growth, maintaining sufficient noise suppression capability; in the strong energy region, the compensation term can offset the excessive amplification of the penalty term with the corresponding scale parameter becomes smaller, thereby avoiding excessive punishment of strong energy targets;

[0044] 2.3) Smoothness constraint on the scale sequence along the time direction, used to suppress the sharp change of the scale parameter in the time dimension, so that the scale values of adjacent time points remain relatively flat, thereby avoiding local scale over-shrinkage caused by isolated points; the expression of the smoothness constraint along the time direction is:

[0045]

[0046] wherein, is a first-order difference operator matrix along the time dimension, used to calculate the difference between adjacent time points, denotes the real number field, and L is the frame length; denotes the scale parameter sequence of the th frequency channel along the time direction, i.e. , is a smoothing parameter, denotes the L1 norm; this constraint limits the change amplitude of the scale parameter at adjacent time points, so that the scale parameter remains continuous and slowly varying along the time axis; thus, multiple time points with similar energy levels in the same frequency channel can obtain similar penalty scales, forming an adaptive regionalization structure from the time dimension, effectively suppressing impulse noise and various strong burst interferences, enhancing the smoothness and stability of the overall time-frequency structure, while maintaining the continuity of the time-frequency structure of the communication signal;

[0047] 2.4) Based on the above preliminary optimization model, penalty function and smoothness constraint along the time direction, the present application further constructs a joint optimization model of the target time-frequency signal matrix and the scale parameter:

[0048] (9)

[0049] wherein, denotes the optimal solution of the optimization problem, which is the enhanced target time-frequency signal matrix and its corresponding scale parameter, respectively, represents the minimization of the target time-frequency signal matrix and the scale parameter ; is the observed underwater acoustic communication signal matrix and the reconstructed matrix obtained by inverse transforming the target time-frequency signal matrix ​​ The squared Frobenius norm is used as a data fidelity term to measure the overall reconstruction error; Here, L and M are the regularization weight parameters, respectively, representing the frame length and the number of frames. It is the target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element). For the corresponding target time-frequency signal elements The scale parameter, It is a threshold adjustment parameter; Indicates constraints. It is a first-order difference operator matrix in the time dimension. It is the first A sequence of scaling parameters along the time direction for each frequency channel. Describing the L1 norm, It is a smoothing parameter. It is a constraint on the range of values ​​for the scale parameter;

[0050] By simultaneously updating the target time-frequency signal matrix and scale parameters during the optimization process, without pre-setting fixed structural units, the scale parameters can automatically form a segmented and continuous change trend over time, achieving adaptive sparse representation capability for non-fixed group partitioning. This balances the maintenance of the continuity of the target communication signal with the suppression of impulse interference, further improving the stability and robustness of the overall enhancement results.

[0051] In step 3), the specific steps for obtaining the enhanced signal through alternating solutions can be as follows:

[0052] Initialization parameters, target time-frequency signal matrix With target time-frequency signal elements Corresponding scale parameters This invention employs an inner and outer iterative framework, which allows the scale parameters and the target time-frequency signal matrix to be gradually adjusted together during the iterative process.

[0053] With the first Taking the outermost iteration as an example, first fix the first... The target time-frequency signal element during the next outermost iteration scale parameters In the case of the target time-frequency signal matrix Solving this problem can be defined as a convex optimization problem with a regularization term:

[0054]

[0055] in, Represents the number of outer iterations. It is the first The target time-frequency signal element during the next outermost iteration Scale parameters; Represents the target time-frequency signal matrix Perform a minimization solution. To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The square of the Frobenius norm; Here, L and M are the regularization weight parameters, respectively, representing the frame length and the number of frames. It is the target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element). It is a weighted quadratic regularization with weights of . , This is a threshold adjustment parameter;

[0056] Equation (10) applies to the target time-frequency signal matrix Taking the derivative and setting it to zero, we get:

[0057]

[0058] in, It is the discrete Fourier inverse transform matrix. The conjugate transpose of . It is the target time-frequency signal matrix. For regularization weight parameters, This represents element-wise multiplication. This is the weight matrix. Representing the real number field, L and M are the frame length and number of frames, respectively, and their elements are... ; To observe the underwater acoustic communication signal matrix, due to , If it is the identity matrix, then equation (11) yields an element-wise closed-form solution:

[0059]

[0060] in, In the first The target time-frequency signal matrix updated in the next outer iteration In time index , frequency index target time-frequency signal element at time index is a matrix element at time index ; is a regularization weight parameter, is a threshold adjustment parameter; is the t-th outer iteration, scale parameter of the corresponding target time-frequency signal element is updated by substituting the corresponding element of the target time-frequency signal matrix G into the formula (12) one by one;

[0061] fixing the target time-frequency signal matrix G obtained in the t+1-th outer iteration, updating the scale parameter of the corresponding target time-frequency signal element , and converting the total variation constraint into a penalty term through a smoothing parameter , the sub-problem related to the scale parameter is:

[0062]

[0063] wherein, is a regularization weight parameter, denotes a constraint condition, is a first-order difference operator matrix along the time direction, is the t-th outer iteration, scale parameter sequence of the frequency channel denotes an L1 norm, is a smoothing parameter, is a range constraint of the scale parameter; is the target time-frequency signal matrix G obtained in the t-th outer iteration, target time-frequency signal element at time index , frequency index ; and

[0064] Since the sub-problem shown in formula (13) about the scale parameter is separable on different frequency channels, the t-th frequency channel can be processed as follows: scale parameter sequence of the channel along the time direction , and each channel can be executed in parallel. For any fixed t-th frequency channel, let denote the scale parameter sequence of the frequency channel along the time direction, is the t-th outer iteration, ​​​The scale parameter corresponding to each time index. For time indexing, , For frequency index, The subproblem corresponding to this channel is written as:

[0065]

[0066] in, This is the smoothing term of the objective function, used to characterize the relationship between the scale parameter and the target time-frequency signal; The objective function is a non-smooth term, containing smoothness constraints and box constraints:

[0067]

[0068] in, For regularization weight parameters, The frame length is the number of sampling points in a single frame along the time axis. For the first The scale parameter corresponding to each time index. In the first The target time-frequency signal matrix updated in the next outer iteration In time index Frequency Index The target time-frequency signal element at point, where μ is the smoothing parameter. Let be the first-order difference operator matrix along the time direction. To preset a very small positive number, For threshold adjustment parameters, The indicator function for the box constraint set; Represents the L1 norm;

[0069] Based on this, the scale parameter sequence is updated iteratively using proximal gradients. Taking the k-th inner iteration as an example, the inner iteration method is explained. First, the gradient of the smoothing term F(x) of the objective function is calculated. , its first Each component for:

[0070]

[0071] in, For the first The square of the scale parameter corresponding to each time index; Indicates the first After the outermost iteration, the target time-frequency signal matrix In time index , frequency index the modulus of the target time-frequency signal element at

[0072] scale parameter sequence perform gradient update:

[0073]

[0074] wherein, is the scale parameter sequence after the kth iteration, is an intermediate variable after gradient descent in the k+1th iteration, is the gradient of the smooth term F(x) of the objective function at is a preset step size, and then the non-smooth term of the objective function is proximal mapping:

[0075]

[0076] wherein, is the scale parameter sequence after the k+1th iteration; is the proximal mapping of the non-smooth term of the objective function, which is used to solve the update result close to the current variable and satisfying the TV smoothing and box constraint in each iteration, and the inner iteration stopping condition is:

[0077]

[0078] wherein, is the two-norm of the difference between the scale parameter sequences of two adjacent inner iterations, to measure the iteration change amplitude; is a normalization processing to avoid too small denominator; is the stopping threshold of the inner iteration; is the maximum number of inner iterations, when the iteration change satisfies the inner iteration stopping condition to stop iteration;

[0079] After the inner iteration is terminated, the scale parameter sequence is obtained, and is used as the scale parameter of the mth frequency channel in the k+1th outer iteration; repeat the above process for all frequency indexes to obtain the scale parameter of the target time-frequency signal element corresponding to the k+1th outer iteration;

[0080] After completing the update of the target time-frequency signal matrix , it is judged whether the outer iteration converges; preferably, the outer iteration stopping condition is:​​​

[0081]

[0082] wherein, is the target time-frequency signal matrix obtained in the t+1th outer iteration, is the target time-frequency signal matrix obtained in the tth outer iteration, is the Frobenius norm, is a normalization term to avoid the judgment deviation caused by too small denominator, is the stop threshold of the outer iteration; when the stop threshold of the outer iteration is satisfied or the maximum number of outer iterations is reached (i.e., the number of outer iterations ), the enhanced target time-frequency signal matrix and the scale parameter corresponding thereto are finally output, and the noise and interference suppression of the underwater acoustic signal is completed.

[0083] Compared with the prior art, the advantages and technical effects of the present application are as follows:

[0084] 1. The present application makes full use of the structural difference that the target communication signal is continuously distributed in time and the energy is concentrated in a limited frequency band in the time-frequency domain, while the interference and background noise are mostly isolated and scattered or diffused in the whole frequency band. The scale parameter is introduced into the sparse modeling process, so that the punishment strength of each time-frequency point can be adaptively adjusted according to the local energy and the structure signal. By applying a smoothing constraint along the time direction to the scale parameter of each frequency channel, the sudden change of the scale parameter at adjacent time instants is limited, so that the 'time-moment-frequency-dense' feature of the pulse interference can be targetedly suppressed, while the continuity of the time-frequency structure of the communication signal is maintained. Compared with the point sparse method which only applies sparse constraint at the point level and the traditional group sparse method which relies on pre-set fixed grouping, the present application can better maintain the continuity and integrity of the time-frequency structure of the target communication signal in a complex ocean noise environment, and significantly improve the clarity and stability of the enhancement result.

[0085] 2. The penalty function proposed in the present application presents strong sparsity in the small scale and weak energy area, which is conducive to suppressing isolated noise and weak interference. In the large scale and strong energy area, the compensation term is used to offset the amplification effect caused by the decrease of the scale, so that the punishment strength gradually tends to be gentle, avoiding the excessive compression of the high-energy target components, thereby effectively protecting the main energy of the target communication signal. The penalty function is more conducive to preserving the target structure information while suppressing noise, and is convenient for efficient solution combined with gradient type and near-end operator optimization methods. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 ​A flowchart illustrating a noise and interference suppression method for underwater acoustic communication transmission links provided by the present invention;

[0087] Figure 2 A schematic diagram of the equipment layout for conducting experiments provided by this invention;

[0088] Figure 3 The time-frequency representation diagram is obtained by performing time-frequency analysis on the acquired signal using traditional STFT.

[0089] Figure 4 The time-frequency representation obtained by applying the point sparsity method to the acquired signal;

[0090] Figure 5 The time-frequency representation obtained by applying the fixed-group sparse method to the acquired signal;

[0091] Figure 6 The time-frequency representation diagram obtained by applying the method of this invention to the acquired signal;

[0092] Figure 7 This diagram illustrates a comparison of the reconstruction performance of the method of this invention and conventional methods under different input signal-to-noise ratios. Detailed Implementation

[0093] To make the objectives, technical solutions, and beneficial effects of the present invention clearer, the following embodiments will be described in detail with reference to the accompanying drawings.

[0094] Figure 1 This is a flowchart illustrating a noise and interference suppression method for underwater acoustic communication transmission links provided by an embodiment of the present invention. This embodiment specifically includes the following processes:

[0095] S1.1. Let the acquired raw underwater acoustic communication signal be Y; perform frame processing on signal Y, with each frame having a length of L and the number of overlapping sampling points between adjacent frames being O, resulting in a total of M frames; to suppress spectral leakage, apply a window function to each frame signal for windowing processing, and stack all windowed frames column-wise to form an underwater acoustic communication signal matrix. ,in, Represents the field of complex numbers. For frame length, The number of frames is L; the frame length is L=512 and the number of overlap points is O=256 (overlap rate 50%), which is used to suppress spectral leakage and ensure time-frequency continuity.

[0096] S1.2. Based on the set frame length L, construct the discrete Fourier inverse transform matrix that matches the frame length L. This is used to map time-frequency domain signals to time-domain signals, thus reconstructing the time-domain signal; among which, Denotes the field of complex numbers, whose first... Line 1 Column elements for:

[0097]

[0098] in, It is a natural constant. The imaginary unit, Pi is a constant. For row index, For column indexes.

[0099] S1.3, Define the target time-frequency signal matrix to be estimated as follows: And introduce a noise matrix Based on the observation underwater acoustic communication signal matrix With the discrete Fourier inverse transform matrix A time-frequency observation equation is established to characterize the linear mapping relationship between the frequency domain coefficients after inverse transformation and the time domain observations:

[0100]

[0101] in, To observe the underwater acoustic communication signal matrix, It is the discrete Fourier inverse transform matrix. For the target time-frequency signal matrix, Let be the noise matrix, where the noise does not always satisfy the assumption of Gaussian white noise, and may be impulse noise, with both non-zero mean and non-stationarity.

[0102] S2.1 Based on the above time-frequency observation equations, a sparse and structurally continuous target time-frequency signal matrix is ​​estimated from noisy underwater acoustic communication signals. A preliminary optimization model based on group sparsity constraints is established:

[0103]

[0104] in, To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity term to measure the overall reconstruction error; For regularization weight parameters, For the total number of groups, For the first The set of time-frequency point indices corresponding to each group The target time-frequency signal matrix In the index set A subset of coefficients on Indicates the first The number of elements contained in a group It is a group norm 2.

[0105] S2.2, for any group, the... For each group, an auxiliary scale parameter is introduced. The group penalty term always satisfies the inequality:

[0106]

[0107] in, The target time-frequency signal matrix In the set A subset of group coefficients on, Indicates the first The number of elements contained in a group It is a group norm 2; This is the scale parameter.

[0108] Therefore, the optimization model based on group sparsity constraints can be expressed as a function of the target time-frequency signal matrix. With scale parameters Joint optimization problem:

[0109]

[0110] in, To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity measure to assess the overall reconstruction error; k is the quantity index. For the total number of groups, For regularization weight parameters, For the first The set of time-frequency point indices corresponding to each group The target time-frequency signal matrix In the set A subset of group coefficients on, Indicates the first The number of elements contained in a group It is a group norm 2; This is the scale parameter.

[0111] During the optimization process, scale parameters The group's norm 2 The parameter is automatically updated based on the energy level within the group, thus automatically obtaining the optimal value and adaptively adjusting the penalty magnitude for different groups to achieve the goal of automatically adjusting the penalty intensity.

[0112] Furthermore, the group division is refined to the single time-frequency point level, so that each group contains only one time-frequency point, i.e., the first... The number of elements contained in a group At this time, the first The set of time-frequency point indices corresponding to each group Refine to include only time index Frequency Index At a single time-frequency point, the target time-frequency signal matrix In the index set subset of group coefficients on The target time-frequency signal element at this point is represented as... and scale parameters Let this be the target time-frequency signal element at that time-frequency point. scale parameters The group sparsity penalty term can be written as a pointwise penalty function, denoted as... ,for:

[0113]

[0114] in, The target time-frequency signal matrix In time index i, frequency index The target time-frequency signal element at the location, For the corresponding target time-frequency signal elements The scale parameter, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number); the pointwise penalty function. It allows for independent adjustment of the penalty intensity at each time-frequency point, determined by the target time-frequency signal element. Corresponding scale parameters Independent control is implemented to facilitate point-by-point updates during iterative optimization; simultaneously, to suppress over-penalization, the target time-frequency signal elements are... Corresponding scale parameters Introduce an upper bound constraint to satisfy:

[0115]

[0116] in, Preset threshold adjustment parameters; limiting scale parameters The range of values ​​for is determined to prevent the penalty term from weakening indefinitely for high-energy components, while ensuring sufficient suppression for low-energy components; to ensure the continuity of the penalty... Based on this, a correction term is introduced to construct the saturation cost function. :

[0117]

[0118] in, For the target time-frequency signal matrix at the time index Frequency Index The element at that location, For target time-frequency signal elements The corresponding scale parameters, For target time-frequency signal elements The model, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element), and b is the threshold adjustment parameter. This is a constraint on the range of values ​​for the scale parameter.

[0119] The improved penalty function It exhibits the following characteristics in different energy ranges: when the aggregate energy is small... As the energy increases approximately linearly, it demonstrates the ability to suppress the sparsity of weak components. When the energy gradually increases and exceeds the threshold, the growth of the penalty term is limited and tends to saturate, no longer increasing significantly with the energy, thus effectively avoiding the problem of excessive attenuation of strong signal components.

[0120] S2.3 Considering that impulse interference typically exhibits a "time-instantaneous-frequency dense" characteristic in time-frequency diagrams, meaning it lasts for an extremely short time but simultaneously affects multiple frequency channels; from the perspective of a single frequency channel, this type of interference often manifests as isolated time anomalies; to suppress these isolated anomalies, a smoothing constraint along the time direction is applied to the scale sequence corresponding to each frequency channel:

[0121]

[0122] in, Let be the first-order difference operator matrix along the time dimension. Represents the real number field, where L is the frame length. Indicates the first The scale parameter sequence of each frequency channel along the time direction, i.e. , The constraint is a smoothing parameter; by limiting the variation of the scale parameter at adjacent time points, the scale parameter changes smoothly in segments along the time axis, thereby prompting adjacent time points with similar energy levels within the same frequency channel to share similar penalty scales, forming an adaptive regional structure and effectively suppressing the isolated point effect caused by impulse interference.

[0123] S2.4. Based on the above preliminary optimization model, penalty function, and smoothing constraint along the time direction, the target time-frequency signal matrix is ​​finally constructed. With scale parameters The joint optimization model is as follows:

[0124]

[0125] in, The optimal solution to this optimization problem is represented by the enhanced target time-frequency signal matrix and its corresponding scale parameter. Represents the target time-frequency signal matrix With scale parameters Perform a minimization solution; To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity term to measure the overall reconstruction error; Here, L and M are the regularization weight parameters, respectively, and the frame length and number of frames. It is the target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element). For the corresponding target time-frequency signal elements The scale parameter, It is a threshold adjustment parameter; Indicates constraints. It is a first-order difference operator matrix along the time direction. It is the first A sequence of scaling parameters along the time direction for each frequency channel. It is the difference norm of the sequence. It is a smoothing parameter. It is a constraint on the range of values ​​for the scale parameter.

[0126] By solving the adaptive smooth group sparsity model, without pre-fixing the group partition, the scale parameter automatically forms a piecewise consistent penalty scale on the time axis, thereby taking into account both the preservation of the local structure of the target communication signal and the suppression of impulse interference, and improving the overall robustness of the enhancement.

[0127] S3.1 Initialize outer iteration count Set regularization weight parameters Threshold adjustment parameter Stopping threshold (stopping threshold of outer iteration) Stopping threshold of inner iteration Preset threshold ), smoothing parameter Gradient update step size Dual step size Original step size and the maximum number of iterations , , Simultaneously, the target's time-frequency signal With scale parameters An inner and outer layer iterative framework is adopted so that the scale parameters and the target time-frequency signal matrix are gradually adjusted together during the iterative process.

[0128] S3.2, with the first Taking the second outer iteration as an example, the outer iteration method is explained:

[0129] First, fix the number The target time-frequency signal element during the next outermost iteration scale parameters In the case of the target time-frequency signal matrix Solving this problem can be defined as a convex optimization problem with a regularization term:

[0130]

[0131] in, Represents the number of outer iterations. It is the first The target time-frequency signal element during the next outermost iteration Scale parameters; Represents the target time-frequency signal matrix Perform a minimization solution. To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The square of the Frobenius norm; Here, L and M are the regularization weight parameters, respectively, representing the frame length and the number of frames. It is the target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element). This is the threshold adjustment parameter.

[0132] For the above objective function, with respect to the variables Differentiating and setting it to zero, we get the equation:

[0133]

[0134] in, It is the discrete Fourier inverse transform matrix. The conjugate transpose of . It is the target time-frequency signal matrix. For regularization weight parameters, This represents element-wise multiplication. This is the weight matrix. Representing the real number field, L and M are the frame length and number of frames, respectively, and their elements are... ; To observe the underwater acoustic communication signal matrix, due to , If it is the identity matrix, then an element-wise closed-form solution can be obtained:

[0135]

[0136] in, In the first The target time-frequency signal matrix updated in the outer iteration In time index Frequency Index The target time-frequency signal element at the location, It is a matrix exist( The element at position ); the element in the denominator It combines regularization weight parameters , No. The outermost iteration corresponds to the target time-frequency signal element. scale parameters With threshold adjustment parameters The calculation item.

[0137] S3.3.1, with the first Taking the outermost iteration as an example, the target time-frequency signal matrix obtained in the (t+1)th outermost iteration is fixed. Update the corresponding target time-frequency signal elements scale parameters The total variation constraint is applied through the smoothing parameter. Converted into a penalty term, resulting in the same as The relevant sub-problems are:

[0138]

[0139] in, For regularization weight parameters, Indicates constraints. It is a first-order difference operator matrix along the time direction. It is the first A sequence of scaling parameters along the time direction for each frequency channel. Describing the L1 norm, It is a smoothing parameter. It is a constraint on the range of values ​​for the scale parameter; In the first The target time-frequency signal matrix updated in the next outer iteration In time index Frequency Index The target time-frequency signal element at the location;

[0140] Because the above objective function and constraints apply to different... They are independent of each other, therefore each can be... Independent Update Furthermore, each channel can execute in parallel; for any fixed channel ,remember Then the subproblem corresponding to this channel can be written as:

[0141]

[0142] in, This is the smoothing term of the objective function, used to characterize the relationship between the scale parameter and the target time-frequency signal; The non-smooth term of the objective function includes smoothness constraints and box constraints, specifically represented as follows:

[0143]

[0144] For regularization weight parameters, The frame length is the number of sampling points in a single frame along the time axis. For the first The scale parameter corresponding to each time index. In the first The elements of the target time-frequency signal matrix obtained in the outer iteration are updated. For smoothing parameters, Let be the first-order difference operator matrix along the time direction. b is a preset minimum positive number, and b is a threshold adjustment parameter. The indicator function for the box constraint set; This represents the L1 norm.

[0145] Based on this, the scale parameter sequence is updated iteratively using proximal gradients. Taking the k-th inner iteration as an example, the inner iteration method is explained. First, the gradient of the smoothing term of the objective function is calculated. , its first The components are:

[0146]

[0147] in, For the first The square of the scale parameter corresponding to each time index; Indicates the first After the outermost iteration, the target time-frequency signal matrix In time index Frequency Index The modulus of the target time-frequency signal element.

[0148] Scale parameter sequence Perform gradient updates:

[0149]

[0150] in, To preset the gradient update step size, This is the scale parameter sequence after the k-th iteration. The smoothing term F(x) of the objective function is in gradient at, For the (k+1)th iteration, the intermediate variable is obtained through gradient descent. Then, the non-smooth term of the objective function is... Perform near-end mapping:

[0151]

[0152] in, Let be the intermediate variable that has undergone gradient descent in the (k+1)th iteration. For the non-smooth term of the objective function The near-end mapping is used to solve for the update result that is close to the current variable and satisfies TV smoothing and box constraints in each iteration. The inner iteration stopping condition is:

[0153]

[0154] in, It is the L2 norm of the difference between two consecutive inner-layer iteration scale parameter sequences, used to measure the magnitude of iteration change; This is a normalization process done to avoid the denominator being too small; It is the stopping threshold for the inner iteration; This is the maximum number of inner iterations; after terminating the inner iterations, the output is... As the scale sequence update result for this channel, for all Repeat the above process to obtain the first... The outermost iteration corresponds to the target time-frequency signal element. scale parameters .

[0155] S3.3.2, Obtain intermediate variables in step S3.3.1 Next, it is necessary to calculate the TV near-end mapping with box constraints, i.e.:

[0156]

[0157] in, This is the scale parameter sequence after the (k+1)th iteration. For regularization terms Proximal mapping, To preset a very small positive number, For threshold adjustment parameters, The desired scale parameter sequence corresponds to a fixed frequency channel. of , Represents the real number field. This is the result of the gradient descent from the previous sub-step. For the first-order difference operator along the time direction, To update the step size for gradient, To smooth the parameters, and to efficiently solve the above convex optimization problem, dual variables are introduced. Take dual step size and original step size And satisfy the stability condition:

[0158]

[0159] in, A first-order difference operator matrix The square of the spectral norm is usually given by Therefore, it is acceptable. , For dual step size, This is the original step size.

[0160] Initialize the number of projection iterations When, the initial value of the original variable x for:

[0161]

[0162] in, Indicates element-wise projection onto the interval , The initial value of the dual variable y is given; then it is updated using m as the projection iteration index. The update begins with the dual step. Taking the (m+1)th iteration as an example, the dual variable... for:

[0163]

[0164] in, Let be the dual variable of the m-th iteration. Let be the original variable in the m-th iteration; Projected onto radius of A sphere, equivalent to element-wise truncation, then the dual variable in the (m+1)th iteration... for:

[0165]

[0166] In the formula, To update the step size for gradient, For smoothing parameters, Let be the dual variable of the m-th iteration. For dual step size, Let be the first-order difference operator matrix along the time direction. Let be the original variable in the m-th iteration.

[0167] Then perform the original step update:

[0168]

[0169] in, and Representing variables respectively In the Next and first The value at the next iteration; The dual variable corresponding to the time difference constraint is in the th... The value obtained during the next inner iteration; For element-wise projection onto interval The projection operator, ε is a preset minimum positive number, and b is a threshold adjustment parameter. This represents the first-order difference operator matrix along the time dimension, used to characterize the difference changes between adjacent time points. Representing the difference operator matrix The transpose of the variable is used to pass back the dual variable to the variable. dimensional space; This represents an intermediate estimate provided by the current outer layer. This is the original step size.

[0170] When satisfied Or the number of iterations Stop iteration, where, For the preset threshold, The maximum number of iterations is taken after termination. As The solution results are as follows.

[0171] S3.4, Complete one time and After the update, determine whether the outer layer has converged; the preferred outer layer stopping condition is:

[0172]

[0173] in, Let be the target time-frequency signal matrix obtained in the (t+1)th outer iteration. Let be the target time-frequency signal matrix obtained in the t-th outer iteration. The Frobenius norm is used to measure the overall error of a matrix. This is a normalization term to avoid judgment bias caused by an excessively small denominator. The outer iteration threshold is t; t is the number of outer iterations. The outer iteration stops when the outer stopping condition is met or the maximum number of outer iterations is reached. At that time, the final output is the enhanced target time-frequency signal matrix. and its corresponding scale parameters Otherwise, Then return to step S3.2 and continue execution until termination, completing the noise and interference suppression of the underwater acoustic communication signal.

[0174] The following is an example with specific parameters:

[0175] (1) Data and Preprocessing

[0176] The transmitted signal is 8FSK, with carrier frequencies of {2kHz, 2.5kHz, 3kHz, 3.5kHz, 4kHz, 4.5kHz, 5kHz, 5.5kHz}. The system sampling rate is 40kHz, and each symbol duration is 0.05s. The experiment was conducted in a real sea area, with the transmitter (sender) and receiver (receiver) deployed on two separate vessels, approximately 30 km apart horizontally. Figure 2 As shown, the transmitting end uses two transducers with a working frequency band of 2–6 kHz, vertically suspended at a depth of 30 m. The receiving end uses two vertical suspension cables: the first cable places a spherical transducer at a depth of 18 m and another at a depth of 30 m as the main receiver, with a hydrophone at 30 m as a backup receiver; the second cable places spherical transducers at depths of 24 m and 36 m respectively. In the experiment, the received signal was acquired by the main receiver at a depth of 30 m. Further, a 0.5 s segment of the received signal was selected as the observed underwater acoustic communication signal, and framed and windowed according to a frame length L=512 and an overlap sampling point count O=256 between adjacent frames to obtain the observed underwater acoustic communication signal matrix. Construct the unit Fourier matrix And establish the target time-frequency signal matrix G and scale parameters. Joint optimization model:

[0177]

[0178] in, The optimal solution to this optimization problem is represented by the enhanced target time-frequency signal matrix and its corresponding scale parameter. Represents the target time-frequency signal matrix With scale parameters Perform a minimization solution; To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity term to measure the overall reconstruction error; Here, L and M are the regularization weight parameters, respectively, representing the frame length and the number of frames. It is the target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, Represents the target time-frequency signal element The energy value (i.e., the square of the modulus of the complex number element). For the corresponding target time-frequency signal elements The scale parameter, It is a threshold adjustment parameter; Indicates constraints. It is a first-order difference operator matrix along the time direction. It is the scale parameter sequence of the j-th frequency channel along the time direction. It is the first norm of the sequence after taking the difference. It is a smoothing parameter. It is a constraint on the range of values ​​for the scale parameter.

[0179] (2) Initialize parameters

[0180] Set regularization weight parameters Threshold adjustment parameter Smoothing parameters Stop threshold , , Step length Maximum number of iterations , , Dual step size Original step size Initialize the target time-frequency signal With scale parameters .

[0181] (3) Solution by method

[0182] Perform alternating optimization, in the first In the next iteration, first fix the first... The outermost iteration corresponds to the target time-frequency signal element. scale parameters ,according to The update yielded the first The target time-frequency signal matrix of the next outer iteration Then fix the first The target time-frequency signal matrix of the next outer iteration The proximal gradient iterative update is adopted. The outermost iteration corresponds to the target time-frequency signal element. scale parameters If satisfied If the maximum number of iterations is reached, the process terminates and outputs the enhanced time-frequency plot result. Its corresponding scale parameter ;in, Let be the target time-frequency signal matrix obtained in the t-th outer iteration. It is the Frobenius norm. This is a normalization term to avoid judgment bias caused by an excessively small denominator. This is the stopping threshold for the outer iteration.

[0183] (4) Comparison method settings

[0184] To verify the effectiveness of the method of the present invention, under the same observation data and the same frame-splitting and windowing parameters, the following methods were further selected for comparison:

[0185] The time-frequency diagram obtained by processing the acquired signal using the traditional STFT method is as follows: Figure 3 As shown; the time-frequency diagram obtained by processing the acquired signal using the point sparsity method is shown below. Figure 4 As shown in (Patent CN114036458A); the time-frequency diagram obtained by processing the acquired signal using the fixed-group sparse method is as follows. Figure 5 As shown in (Patent CN113935146B).

[0186] The time-frequency diagram obtained by the method of this invention after processing the acquired signal is as follows: Figure 6 As shown.

[0187] The above comparison method and the present invention both use the same input data and employ the same normalization method and display dynamic range for the output time-frequency graph.

[0188] (5) Comparison of conclusions

[0189] from Figures 3-6It is evident that the method of this invention, while suppressing background noise and impulse interference pseudostructures, can better maintain the structural continuity and energy contrast of the communication signal in the time-frequency domain. Figure 6 Compared to the traditional STFT method, it has a higher noise floor, which can easily cause the target component to be submerged. Figure 3 While the point sparsity method can suppress background noise to some extent, it is insufficient in suppressing isolated pseudostructures caused by impulse noise, and significant residues remain. Figure 4 The sparse grouping method, due to its pre-fixed grouping structure, is prone to local noise residue or insufficient enhancement when the actual structure does not match the grouping. Figure 5 In summary, the time-frequency structure boundary obtained by the method of the present invention is clearer, the energy is more concentrated, and the enhancement result is more stable. It can provide higher quality input for subsequent synchronization and parameter estimation at the receiver, thereby improving the reliable reception capability of the underwater acoustic communication transmission link.

[0190] (6) Quantitative evaluation and statistical results

[0191] To further quantitatively evaluate the reconstruction performance of different algorithms under different noise intensities, this embodiment conducts statistical comparison experiments on simulated signals and uses PSNR (Peak Signal-to-Noise Ratio) as an evaluation index to measure the similarity between the reconstructed result G and the ideal result P, defined as follows:

[0192]

[0193] in, This represents the enhanced target time-frequency signal matrix. Represents the reference time-frequency signal matrix. and Representation matrix With matrix In the line, number Elements at column, Indicates the number of rows in the matrix. This represents the number of columns in the matrix. Represents the reference matrix peak amplitude, Represents a logarithmic function.

[0194] Specifically, under multiple test conditions with input SNR (signal-to-noise ratio) values ​​ranging from -10 dB to 5 dB (in 5 dB steps), to ensure the stability and repeatability of the statistical results, 20 sets of simulation test samples were independently generated for each SNR condition. The corresponding PSNR (peak signal-to-noise ratio) was calculated for the reconstruction results output by each algorithm. Finally, the average of the 20 PSNR values ​​was used as the performance index under that SNR condition, and a performance histogram of PSNR versus SNR was plotted, as shown below. Figure 7 As shown.

[0195] like Figure 7 As can be seen, with the increase of SNR (signal-to-noise ratio), the PSNR (peak signal-to-noise ratio) of each method generally shows an upward trend, indicating that the reconstruction error generally decreases and the reconstruction quality improves as noise weakens. Meanwhile, across the entire SNR range, the PSNR of the method in this invention is generally higher than other comparative methods, especially maintaining a high PSNR under medium-low SNR conditions, demonstrating stronger error suppression capability and more stable reconstruction performance even in strong noise environments. In contrast, the PSNR of conventional time-frequency methods is consistently significantly lower, reflecting their limited ability to preserve the effective communication component structure under noisy conditions. Although the point sparse method and the fully overlapping group sparse method show significant improvements over conventional methods, their performance is not as good as the method proposed in this invention. In summary, the method in this invention achieves better quantitative evaluation indicators under different noise intensities, thus verifying its effectiveness and robustness in preserving effective communication structure characteristics and suppressing noise interference under complex marine transmission channel conditions, thereby contributing to improving the reliable reception performance of underwater acoustic communication transmission links.

[0196] It should be noted that the parameters set in this embodiment are not the only limitations. In practical applications, the values ​​of each parameter can be flexibly adjusted according to the modulation method of the communication signal, the carrier frequency, the symbol rate, and the specific environment of the marine channel (such as deep sea, shallow sea, nearshore, etc.). As long as the parameters are adjusted to still meet the technical features defined by this invention, the same or similar noise and interference suppression effect can be achieved.

[0197] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent variations and improvements made in accordance with the claims of this patent application should be covered within the scope of protection of the present invention.

Claims

1. A method for noise and interference suppression in underwater acoustic communication transmission links, characterized in that, Includes the following steps: 1) Constructing time-frequency observation equations: Preprocess the received time-domain observed underwater acoustic communication signals, including frame segmentation and windowing, to obtain the observed underwater acoustic communication signal matrix. Simultaneously construct a discrete Fourier inverse transform matrix adapted to the observed underwater acoustic communication signal matrix, define the target time-frequency signal matrix to be enhanced, introduce a noise matrix, and construct time-frequency observation equations to characterize the linear mapping relationship between the time domain and the frequency domain. 2) Constructing a joint optimization model: Based on the linear mapping relationship obtained in step 1), a preliminary optimization model with sparse group constraints is first established, and then an auxiliary scale parameter is introduced and transformed into a joint optimization problem. The group is refined to a single time-frequency point, and an independent scale parameter is configured and a constraint is applied to each time-frequency point. A compensation term is introduced to construct a saturated penalty function, and a smoothing constraint along the time direction is applied to the scale parameter sequence of each frequency channel. A joint optimization model of the target time-frequency signal matrix and the scale parameter is constructed. Each time-frequency point is configured with an independent scale parameter and constrained, which is the scale parameter constraint term: in, The threshold adjustment parameter is set in advance; the scale parameter constraint is used to limit the range of scale parameter values ​​to avoid excessive penalty or insufficient noise suppression caused by abnormal scale parameters. Constructing a saturation-type penalty function by introducing a compensation term: in, The target time-frequency signal matrix In time index i, frequency index The target time-frequency signal element at the location, For the corresponding target time-frequency signal elements scale parameters, Represents the target time-frequency signal element Energy value; For the preset threshold adjustment parameters, The scaling parameter's value range is constrained; this saturated penalty function grows approximately linearly in the weak energy region, maintaining noise suppression capability; in the strong energy region, the compensation term... Offset penalty term varies with scale parameter The excessive amplification resulting from shrinking is to avoid over-penalizing high-energy targets; The expression for the smoothing constraint along the time direction is: in, This is a first-order difference operator matrix along the time dimension, used to calculate the difference between adjacent time points. Represents the real number field, where L is the frame length; Indicates the first The scale parameter sequence of each frequency channel along the time direction, i.e. , For smoothing parameters, The L1 norm is represented; the time smoothing constraint limits the variation of scale parameters at adjacent time points, so that the scale parameters maintain a continuous and gradual trend on the time axis; it enables multiple time points with similar energy levels in the same frequency channel to obtain similar penalty scales, forming an adaptive regional structure from the time dimension, which effectively suppresses impulse noise and sudden strong interference. 3) Alternating solution to obtain enhanced signal: The joint optimization model constructed in step 2) is solved by alternating inner and outer iterations and combining the near-end gradient algorithm. The target time-frequency signal matrix and scale parameter sequence are updated alternately until the outer iteration meets the convergence condition or reaches the maximum number of iterations. The enhanced target time-frequency signal matrix and corresponding scale parameter sequence are output to complete the noise and interference suppression of underwater acoustic communication signal.

2. The noise and interference suppression method for underwater acoustic communication transmission links as described in claim 1, characterized in that, In step 1), the observed underwater acoustic communication signal matrix ,in, For frame length, For the number of frames, Representing the complex field; to adapt to the observation of underwater acoustic communication signal matrix, constructing a matrix with a frame length... Consistent Discrete Fourier Inverse Transform Matrix The first of the matrix Line number The column elements are: in, It is a natural constant. The imaginary unit, Pi is a constant. For row index, , It is a complex exponential basis function, corresponding to a discrete frequency. basis vectors; Define the target time-frequency signal matrix to be estimated as follows: And introduce a noise matrix Based on the observation underwater acoustic communication signal matrix With the discrete Fourier inverse transform matrix A time-frequency observation equation is established to characterize the linear mapping relationship between the frequency domain coefficients after inverse transformation and the time domain observations: in, To observe the underwater acoustic communication signal matrix, It is the discrete Fourier inverse transform matrix. For the target time-frequency signal matrix, This is the noise matrix.

3. The noise and interference suppression method for underwater acoustic communication transmission links as described in claim 1, characterized in that, In step 2), the preliminary optimization model is: in, To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity measure to assess the overall reconstruction error; k is the quantity index. For the total number of groups, For regularization weight parameters, For the first The set of time-frequency point indices corresponding to each group The target time-frequency signal matrix In the set A subset of group coefficients on, Indicates the first The number of elements contained in a group It is a group norm 2.

4. The noise and interference suppression method for underwater acoustic communication transmission links as described in claim 1, characterized in that, In step 2), to achieve adaptive adjustment of the penalty intensity with the energy within the group, a scale parameter is introduced for each group. The group penalty term always satisfies the inequality: in, The target time-frequency signal matrix In the set A subset of group coefficients on, Indicates the first The number of elements contained in a group It is a group norm 2; For scale parameters; The initial optimization model is transformed into a matrix of the target time-frequency signal. With scale parameters Joint optimization problem: in, To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity term to measure the overall reconstruction error; For regularization weight parameters, For the total number of groups, For the first The set of time-frequency point indices corresponding to each group The target time-frequency signal matrix In the index set A subset of group coefficients on, Indicates the first The number of elements contained in a group It is a group norm 2; The scale parameter; during the optimization process, the scale parameter Normal group inner norm The parameter is automatically updated based on the changes in energy within the group, and the optimal value of the parameter is automatically obtained to achieve adaptive adjustment of the penalty magnitude for different groups.

5. The noise and interference suppression method for underwater acoustic communication transmission links as described in claim 1, characterized in that, In step 2), the joint optimization model of the target time-frequency signal matrix and the scale parameter is as follows: in, The optimal solution to this optimization problem is represented by the enhanced target time-frequency signal matrix and its corresponding scale parameter. Represents the target time-frequency signal matrix With scale parameters Perform a minimization solution; To observe the underwater acoustic communication signal matrix With the target time-frequency signal matrix The reconstruction matrix obtained by inverse transformation The squared Frobenius norm is used as a data fidelity term to measure the overall reconstruction error; Here, L and M are the regularization weight parameters, respectively, representing the frame length and the number of frames. It is the target time-frequency signal matrix In time index Frequency Index The target time-frequency signal element at the location, Represents the target time-frequency signal element Energy value, For the corresponding target time-frequency signal elements The scale parameter, It is a threshold adjustment parameter; Indicates constraints. It is a first-order difference operator matrix in the time dimension. It is the scale parameter sequence of the j-th frequency channel along the time direction. L1 norm It is a smoothing parameter. It is a constraint on the range of values ​​for the scale parameter.

6. The noise and interference suppression method for underwater acoustic communication transmission links as described in claim 1, characterized in that, In step 3), the inner layer iteration specifically involves: in the first... In the outermost iteration, the target time-frequency signal matrix is ​​fixed. Constructing about scale parameters The subproblem, which is separable across different frequency channels, for any fixed first... One frequency channel, This represents the sequence of scale parameters along the time direction for that frequency channel. For the first The scale parameter corresponding to each time index. For time indexing, , For frequency index, The subproblem is expressed as: in, This is the smoothing term of the objective function, used to characterize the relationship between the scale parameter and the target time-frequency signal; The objective function is a non-smooth term, containing smoothness constraints and box constraints. The subproblem is solved using gradient updates and near-end mapping. Calculate the gradient of the smoothing term F(x) of the objective function. The formula for gradient update is: in, This is the scale parameter sequence after the k-th iteration. Let be the intermediate variable that has undergone gradient descent in the (k+1)th iteration. The smoothing term F(x) of the objective function is in gradient at, Preset step size; The formula for the proximal mapping is: in, This is the sequence of scale parameters after the (k+1)th iteration; For the non-smooth term of the objective function Proximal mapping; This represents the intermediate variable that has undergone gradient descent in the (k+1)th iteration; The stopping condition for the inner iteration is: in, It is the L2 norm of the difference between two consecutive inner-layer iteration scale parameter sequences, used to measure the magnitude of iteration change; This is a normalization process done to avoid the denominator being too small; It is the stopping threshold for the inner iteration; This is the maximum number of inner iterations. Iteration stops when the iteration changes meet the inner iteration stopping condition, for all frequency channels. Repeat the above process to obtain the first The outermost iteration corresponds to the target time-frequency signal element. scale parameters .

7. The noise and interference suppression method for underwater acoustic communication transmission links as described in claim 1, characterized in that, In step 3), the outer iteration specifically refers to: for the first... The outermost iteration, with the fixed number of iterations... The outermost iteration corresponds to the target time-frequency signal element. scale parameters The target time-frequency signal matrix G is updated by calculating an element-wise updated closed-form solution, which is: in, In the first The target time-frequency signal matrix updated in the next outer iteration In time index Frequency Index The target time-frequency signal element at the location; It is a matrix exist( The element at position ); For regularization weight parameters, This is a threshold adjustment parameter; It is the first During the next outer iteration, the corresponding target time-frequency signal element The scale parameter; during the update, for each ( ) in the target time-frequency signal matrix G Substitute the corresponding elements one by one into the formula to calculate; The stopping condition for the outer iteration is: in, Let be the target time-frequency signal matrix obtained in the (t+1)th outer iteration. Let be the target time-frequency signal matrix obtained in the t-th outer iteration. It is the Frobenius norm. This is a normalization term to avoid judgment bias caused by an excessively small denominator. This is the stopping threshold for the outer iteration; when the outer stopping threshold is met... Or reach the maximum number of outer iterations When the outer layer iteration stops, the enhanced target time-frequency signal matrix is ​​output, thus completing the noise and interference suppression of the underwater acoustic communication signal.

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