Noise and interference suppression method for underwater acoustic communication transmission link

Abstract

The invention discloses a noise and interference suppression method for an underwater acoustic communication transmission link, and relates to the technical field of underwater acoustic communication transmission and receiving. Framing and windowing are carried out on the received underwater acoustic communication signals to obtain an observation underwater acoustic communication signal matrix; on the basis of the characteristics that effective communication components are continuously distributed along with time in a time-frequency domain, energy is concentrated in a limited frequency band, and noise and pulse interference are diffused in a full-frequency mode or distributed in an isolated mode, a self-adaptive group sparse modeling framework with introduced scale parameters is constructed, and self-adaptive adjustment is conducted on the penalty intensity of each time-frequency point. Time direction smooth constraint is introduced on scale parameters, a sparse penalty function with saturation characteristics is designed, a joint estimation problem is solved through alternate optimization and a near-end gradient algorithm, enhanced time-frequency energy distribution is obtained, and noise and interference suppression of underwater acoustic communication signals is completed. Background noise and pseudo structure interference are effectively suppressed in a complex marine environment, key structure features of communication signals are kept, and the reliable receiving capability and stability of underwater acoustic communication transmission are improved.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication transmission and reception technology, and in particular to a noise and interference suppression method for underwater acoustic communication receivers, which aims to suppress noise and interference in underwater acoustic communication links and improve signal transmission quality and link reliability. Background Technology

[0002] In underwater wireless communication link construction, underwater sensor network data backhaul, and information exchange between underwater equipment, the communication signals transmitted by the underwater acoustic communication transmitter (e.g., communication waveforms containing synchronization sequences, pilot sequences, and modulation data) propagate through the ocean acoustic channel to the receiver. The reception quality directly affects key aspects such as synchronization acquisition, channel estimation, equalization, demodulation, and decoding, thus impacting the reliability and stability of the transmission link. However, underwater acoustic communication signals are susceptible to complex noise environments and sudden interference during propagation in the ocean. On the one hand, persistent ocean background noise reduces the signal-to-noise ratio at the receiver; on the other hand, occasional non-stationary sound sources and strong pulse-type interference in the ocean can cause sudden damage to the characteristic structure of the communication signal, weakening the receiver's ability to distinguish effective communication components and thus limiting the link's reliable reception capability. Therefore, to improve the reliable reception capability of underwater acoustic communication transmission links in complex ocean environments, it is crucial to introduce enhancement mechanisms for noise and interference suppression at the receiver. These mechanisms should suppress background noise and sudden interference while preserving the structural characteristics of the communication waveform as much as possible to support subsequent reception processing.

[0003] Currently, receivers often employ time-frequency domain characterization techniques to depict the energy distribution of the received signal in a joint time-frequency dimension, assisting in key stages such as synchronization acquisition, pilot sequence detection, and channel estimation and equalization. While classic time-frequency transformation 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 noisy environments, 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 noise resistance of time-frequency representations, existing technologies have proposed various improvement schemes. For example, Chinese patent CN114996641B provides a variational mode decomposition method based on the joint factor of time-frequency correlation coefficients. Although it can separate some noise, it has high computational cost, and short-time pulse interference is prone to energy leakage in the frequency domain, leading to excessive component splitting. On the other hand, time-frequency energy redistribution or synchronous compression methods provide new ideas for signal enhancement. For example, Chinese patent CN117130048B uses a synchronous compression extraction transform method, which can concentrate time-frequency energy into the time-frequency ridge region, making the signal components more prominent on the time-frequency graph. However, under low signal-to-noise ratio conditions, time-frequency energy compression or extraction operations often simultaneously enhance noise components and effective signals, failing to effectively suppress the influence of noise. Since most target communication signals have natural sparsity characteristics in the time-frequency domain, sparsity-based time-frequency representation methods have a natural advantage in denoising and energy extraction. Chinese patent CN114036458A provides an exponential approximation point sparsity constraint, which effectively guides the sparse reconstructed signal to focus on the main energy path of the signal, thereby enhancing the expressive power of the signal components. Chinese patent CN113935146B provides a non-convex variable overlap group sparsity method, which can achieve good enhancement effect under Gaussian background noise.

[0004] The publicly disclosed patented methods mentioned above are mostly based on the assumption that the noise in underwater acoustic communication transmission links is approximately stationary Gaussian noise or unstructured interference. They lack specific modeling and suppression mechanisms for impulse-type non-Gaussian noise and sudden strong interference common in marine environments. These methods either focus on improving the clustering of time-frequency representations or are mainly applicable to background noise scenarios with low power and simple structure. Under conditions of strong impulse noise or sudden interference, it is difficult to simultaneously maintain the structural characteristics of the communication signal and effectively suppress interference, thus limiting the reliable reception capability of the link.

[0005] Therefore, in marine transmission channels with significant impulse interference, effectively distinguishing the true structural characteristics of underwater acoustic communication signals from pseudo-structural disturbances caused by impulse interference in the time-frequency domain has become a critical technical problem that needs to be solved to achieve reliable link reception. On the one hand, it is necessary to construct a time-frequency structural model that can adaptively characterize the local correlation of communication signals in both time and frequency dimensions to maintain the key characteristics of the communication signals. On the other hand, it is necessary to design targeted suppression mechanisms for impulse-type non-Gaussian noise to improve the ability to distinguish between effective communication components and interference, thereby improving the reliable reception performance and robustness of underwater acoustic communication links in complex marine environments. Summary of the Invention

[0006] The purpose of this invention is to address the technical problem that underwater acoustic communication signals are affected by non-Gaussian interference such as impulse noise in marine transmission channels. This interference exhibits local clustering in the time-frequency domain and superimposes on the effective communication components, easily masking or obfuscating the key structural features of the communication signal, leading to a decline in reliable reception performance. The invention provides a noise and interference suppression method for underwater acoustic communication transmission links. This method constructs a time-frequency structural constraint model based on smooth adaptive group sparsity at the receiver end to perform noise and interference anti-interference processing on the received signal. By analyzing the local characteristics and changing trends of the time-frequency coefficients, a small-scale smooth block structure is adaptively formed. Adaptive adjustment of the scale parameter and smoothing constraints in the time direction are introduced, allowing the suppression intensity to adaptively adjust with changes in local structure and energy. This suppresses pseudo-structural disturbances caused by impulse interference while preserving the key structural features of the communication signal as much as possible, thereby improving the reliable reception capability and stability of the transmission link in complex marine environments.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

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

[0009] 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.

[0010] 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.

[0011] 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 realize the time-frequency enhancement of underwater acoustic signal and complete the noise and interference suppression of underwater acoustic communication signal.

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

[0013] Frame segmentation and windowing are performed on the one-dimensional time-domain observed underwater acoustic communication signal to obtain the observed underwater acoustic communication signal matrix. ,in, For frame length, For the number of frames, Represents the complex field; adapted for observing underwater acoustic communication signal matrices, construction and frame length Consistent Discrete Fourier Inverse Transform Matrix The first of the matrix Line number The column elements are:

[0014]

[0015] 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;

[0016] 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 Establish the time-frequency observation equation: This is used to characterize the linear mapping relationship between the frequency domain coefficients after inverse transformation and the time domain observations, where the noise matrix... The noise in the noise does not always satisfy the assumption of Gaussian white noise; it may be impulse noise, which has both non-zero mean and non-stationarity.

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

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

[0019] 2.2) Optimize the group sparsity penalty term: Introduce a scale parameter to the group sparsity penalty term of the initial optimization model, transforming it into a joint optimization problem of the target time-frequency signal matrix and the scale parameter; refine the group partition to the single time-frequency point level, so that each time-frequency point corresponds to an independent scale parameter, and transform the penalty term into a pointwise form; add constraints to the scale parameter and introduce a compensation term to construct a saturation characteristic cost function, taking into account both noise suppression and structure preservation;

[0020] 2.3) Apply smoothing constraints along the time direction: Apply smoothing constraints to the scale parameters on the same frequency channel as they change over time, limit the magnitude of the change in scale parameters at adjacent time points, so that time points with similar energy levels receive similar penalty scales, form an adaptive regionalized structure from the time dimension, and suppress impulse noise;

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

[0022] Furthermore:

[0023] 2.1) Based on the time-frequency observation equation constructed in step 1), a group sparsity regularization term is introduced to construct the equation as shown in formula 1). The preliminary optimization model based on group sparsity constraints is expressed from the observation of the underwater acoustic communication signal matrix. Estimate the sparse and structurally continuous target time-frequency signal matrix. :

[0024]

[0025] 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 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;

[0026] Given the significant non-stationarity of the structural characteristics of the target underwater acoustic communication signal and the distribution of background noise, and the large variations in energy scale and sparsity level in different regions, when using fixed group partitioning or fixed-size group structures, a mismatch between the group size and signal characteristics can easily occur, thereby weakening the expressive power of sparsity constraints and even affecting the noise suppression effect. Therefore, it is necessary to enable the sparsity regularization term to have adaptive adjustment capabilities, so as to dynamically adjust with changes in time-frequency structure, rather than relying on a preset fixed block method.

[0027] 2.2) Regarding the group sparsity penalty term in equation (2), in order to achieve adaptive adjustment of the penalty strength with the energy within the group, a scale parameter is introduced for each group. For any number For each group, the following inequality holds:

[0028]

[0029] 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;

[0030] Therefore, the formula It can be equivalently represented as a time-frequency signal matrix about the target. With scale parameters Joint optimization problem:

[0031]

[0032] 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 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 exhibits the following characteristics in different energy ranges: In the weak energy region, Approximately linear growth, maintaining sufficient noise suppression capability; in the high-energy region, the compensation term... The penalty term can be offset by the target time-frequency signal element. Corresponding scale parameters The excessive amplification caused by shrinking the size avoids over-penalizing high-energy targets;

[0044] 2.3) Smoothing constraints on the scale sequence along the time direction are used to suppress drastic changes in the scale parameter along the time dimension, keeping the scale values ​​between adjacent time points relatively smooth, thereby avoiding excessive local scale contraction caused by isolated points; the expression for the smoothing constraint along the time direction is:

[0045]

[0046] 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 by this constraint. By limiting the variation of scale parameters at adjacent time points, the scale parameters maintain a continuous and gradually changing trend on the time axis. As a result, multiple time points with similar energy levels within the same frequency channel can obtain similar penalty scales, forming an adaptive regional structure in the time dimension. This effectively suppresses impulse noise and various sudden strong interferences, enhances the smoothness and stability of the overall time-frequency structure, and maintains the continuity of the communication signal's time-frequency structure.

[0047] 2.4) Based on the above preliminary optimization model, penalty function, and smoothing constraint along the time direction, this invention further constructs a joint optimization model for the target time-frequency signal matrix and scale parameters:

[0048] (9)

[0049] 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 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 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;

[0061] The target time-frequency signal matrix obtained by fixing the outer layer in the (t+1)th iteration is fixed. Update the corresponding target time-frequency signal elements scale parameters The total variation constraint is applied through the smoothing parameter. Transformed into a penalty term, resulting in a scale parameter. The relevant sub-problems are:

[0062]

[0063] 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;

[0064] Since equation (13) shows the relationship with the scale parameter The subproblems are separable across different frequency channels, therefore the first subproblem can be solved. Frequency channels The time-direction scale parameter sequence of this channel Furthermore, each channel can be executed in parallel, for any fixed number of channels. Each frequency channel, with 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 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;

[0072] Scale parameter sequence Perform gradient updates:

[0073]

[0074] 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, To preset the step size, the non-smooth terms of the objective function are then processed. Perform near-end mapping:

[0075]

[0076] in, This is the scale parameter sequence after 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:

[0077]

[0078] 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.

[0079] After terminating the inner iteration, the scale parameter sequence is obtained. and as the first In the next outer iteration Scale parameters of each frequency channel For all frequency indices Repeat the above process to obtain the first... The outermost iteration corresponds to the target time-frequency signal element. scale parameters ;

[0080] Complete one target time-frequency signal matrix After the update, determine whether the outer iteration has converged; the preferred outer iteration stopping condition is:

[0081]

[0082] 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 stopping threshold for the outer iteration is met... Or reach the maximum number of outer iterations (i.e., the number of outer iterations) When this happens, the final output is the enhanced target time-frequency signal matrix. and its corresponding scale parameters This completes the suppression of noise and interference in underwater acoustic signals.

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

[0084] 1. This invention fully utilizes the structural difference that the target communication signal is continuously distributed over time and its energy is concentrated in a limited frequency band in the time-frequency domain, while interference and background noise are mostly isolated and scattered or spread across the entire frequency. By introducing scale parameters into the sparse modeling process, the penalty intensity at each time-frequency point can be adaptively adjusted according to the local energy and structural signal. By applying smooth constraints along the time direction to the scale parameters of each frequency channel, the abrupt change of scale parameters between adjacent time moments is limited, which can specifically suppress the 'time-instantaneous-frequency dense' characteristics of pulse interference, while maintaining the continuity of the time-frequency structure of the communication signal. Compared with point sparse methods that only apply sparse constraints at the point level and traditional group sparse methods that rely on preset fixed groups, this invention can better maintain the continuity and integrity of the time-frequency structure of the target communication signal in complex marine noise environments, and significantly improve the clarity and stability of the enhancement results.

[0085] 2. The penalty function proposed in this invention exhibits strong sparsity in small-scale, low-energy regions, which is beneficial for suppressing isolated noise and weak interference. In large-scale, high-energy regions, the compensation term offsets the amplification effect of the penalty as the scale decreases, making the penalty intensity gradually level off and avoiding excessive compression of high-energy target components, thereby effectively protecting the main energy of the target communication signal. This penalty function is more conducive to preserving target structural information while suppressing noise, and it is easy to combine with gradient-type and near-end operator optimization methods for efficient solution. Attached Figure Description

[0086] Figure 1A 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, Describes the field of complex numbers, whose first... Line number 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 constrains 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 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 framing 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. Representation of 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 for underwater acoustic communication transmission links, characterized in that, The method comprises the following steps: 1) constructing a time-frequency observation equation: preprocessing the received time-domain observation underwater acoustic communication signal, including frame segmentation and windowing processing, obtaining an observation underwater acoustic communication signal matrix, synchronously constructing an inverse discrete Fourier transform matrix suitable for the observation 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; 2) constructing a joint optimization model: based on the linear mapping relationship obtained in step 1), first establishing a preliminary optimization model containing group sparse constraints, then introducing an auxiliary scale parameter and converting it into a joint optimization problem; refining the group to a single time-frequency point, configuring an independent scale parameter for each time-frequency point and imposing a constraint, introducing a compensation term to construct a saturation type penalty function, imposing a smoothing constraint along the time direction on the scale parameter sequence of each frequency channel, and constructing a joint optimization model of the target time-frequency signal matrix and the scale parameter; 3) obtaining an enhanced signal by alternately solving: using an inner iteration and an outer iteration alternation method, combining a proximal gradient algorithm to solve the joint optimization model constructed in step 2), alternately updating the target time-frequency signal matrix and the scale parameter sequence, until the outer iteration meets the convergence condition or reaches the maximum iteration number, outputting the enhanced target time-frequency signal matrix and the corresponding scale parameter sequence, and completing the noise and interference suppression of the underwater acoustic communication signal.

2. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 1) the observed underwater acoustic communication signal matrix wherein is the frame length, is the number of frames, denotes the complex domain; is an inverse discrete Fourier transform matrix adapted to the observed underwater acoustic communication signal matrix, constructed in accordance with the frame length The element in the i-th row and j-th column of this matrix is: ​​​ wherein is the natural constant, is the imaginary unit, is the constant of the circle, is the row index, , is the complex exponential basis function corresponding to a discrete frequency of the basis vector; 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 inverse discrete Fourier transform matrix , a time-frequency observation equation is established to represent the linear mapping relationship between the inverse-transformed frequency-domain coefficients and the time-domain observation: wherein, is a matrix of observed underwater acoustic communication signals, is an inverse discrete Fourier transform matrix, is a matrix of target time-frequency signals, is a noise matrix.

3. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 2), the preliminary optimization model is: wherein, is the observed underwater acoustic communication signal matrix is the target time-frequency signal matrix is the reconstructed matrix obtained by inverse transformation is the square of the Frobenius norm of, which measures the overall reconstruction error as a data fidelity term; k is the index of quantity, is the total number of groups, is the regularization weight parameter, is the time-frequency point index set corresponding to the th group, is the target time-frequency signal matrix is the group coefficient subset on the set , represents the number of elements contained in the th group, is the group norm.

4. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 2), to achieve the self-adaptive adjustment of the penalty intensity with the group energy, a scale parameter is introduced for each group The group penalty term always satisfies the inequality: wherein, is a target time-frequency signal matrix is a group coefficient subset on a set , denotes the number of elements contained in the th group, is a group norm; is a scale parameter; The preliminary optimization model is converted into a joint optimization problem with respect to the target time-frequency signal matrix and the scale parameter ​ wherein, is the observed underwater acoustic communication signal matrix is the target time-frequency signal matrix is the reconstructed matrix obtained by inverse transformation is the Frobenius norm square of the reconstructed matrix, which is used as a data fidelity term to measure the overall reconstruction error; is the regularization weight parameter, is the total number of groups, is the time-frequency point index set corresponding to the th group, is the target time-frequency signal matrix is the group coefficient subset on the index set , represents the number of elements contained in the th group, is the group norm; is the scale parameter; during the optimization process, the scale parameter is automatically updated according to the change of the group norm , and the optimal value of the parameter is automatically obtained according to the size of the group energy, so as to realize adaptive adjustment of the punishment amplitude of different groups.

5. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 2), the independent scale parameter configured for each time-frequency point and the constraint are scale parameter constraint terms: wherein, is a preset threshold adjustment parameter; the scale parameter constraint term is used to limit the value range of the scale parameter, so as to avoid excessive punishment or insufficient noise suppression caused by abnormal scale parameter.

6. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 2), the compensation term is introduced to construct a saturation type penalty function: wherein, is a target time-frequency signal matrix is a target time-frequency signal element at time index i and frequency index is a scale parameter of the corresponding target time-frequency signal element is an energy value of the target time-frequency signal element is a preset threshold adjustment parameter, is a range constraint of the scale parameter; the saturation type penalty function is approximately linearly increased in a weak energy area, maintaining noise suppression ability; in a strong energy area, the compensation term offsets the excessive amplification of the penalty term as the scale parameter becomes smaller, to avoid excessive punishment of strong energy targets.​​​ 7. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 2), the expression of the smoothing constraint along the time direction is: wherein, is a first-order difference operator matrix along time dimension for calculating the difference value of adjacent time points, denotes the real field, and L is the frame length; denotes the scale parameter sequence of the th frequency channel along the time direction, that is, , is a smoothing parameter, denotes the L1 norm; the time smoothing constraint makes the scale parameter maintain a continuous and slowly varying trend on the time axis by limiting the variation amplitude of the scale parameters of adjacent time points; multiple time points with similar energy levels in the same frequency channel obtain similar penalty scales, forming an adaptive regionalization structure from the time dimension, effectively suppressing impulse noise and burst strong interference.

8. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 2), the joint optimization model of the target time-frequency signal matrix and the scale parameter is: where, denote the optimal solution of the optimization problem, respectively the enhanced target time-frequency signal matrix and its corresponding scale parameters, represent the target time-frequency signal matrix and scale parameters are minimized; is the observed underwater acoustic communication signal matrix and the reconstructed matrix obtained by inverse transforming the target time-frequency signal matrix is the Frobenius norm square of the difference between the observed and reconstructed matrices, which is used as the data fidelity term to measure the overall reconstruction error; is the regularization weight parameter, L and M are the frame length and the number of frames respectively, is the target time-frequency signal matrix the target time-frequency signal element at time index and frequency index denotes the energy value of the target time-frequency signal element is the scale parameter corresponding to the target time-frequency signal element is the threshold adjustment parameter; denotes the constraint condition, is the first-order difference operator matrix in time dimension, is the scale parameter sequence of the jth frequency channel along the time direction, denotes the L1 norm is the smoothing parameter, is the scale parameter range constraint.​​​ 9. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 3), the inner layer iteration is specified as follows: In the first outer layer iteration, the target time-frequency signal matrix is fixed , a sub-problem is constructed with respect to the scale parameter , which is separable over different frequency channels, for any fixed th frequency channel, , the scale parameter sequence of the frequency channel along the time direction, , the scale parameter corresponding to the th time index, , the time index, , , the frequency index, , the sub-problem is formulated as: wherein, is a smooth term of the objective function, used to characterize the association between the scale parameter and the target time-frequency signal; is a non-smooth term of the objective function, containing a smooth constraint and a box constraint, and the subproblem is solved by gradient update and proximal mapping: calculating the gradient of the objective function smooth term F(x) the formula of the 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 of the proximal mapping is: wherein, is the sequence of scale parameters after the k+1 iteration; is the proximal mapping of the non-smooth term of the objective function ; and is the intermediate variable after gradient descent in the k+1 iteration. The stop condition of the inner iteration is: wherein, is the two-norm of the difference between two adjacent inner iteration scale parameter sequences, to measure the iteration variation amplitude; is the normalization processing to avoid too small denominator; is the stop threshold of the inner iteration; is the maximum number of the inner iteration, when the iteration variation satisfies the inner iteration stop condition, the iteration stops, and for all frequency channels repeat the above process to obtain the scale parameter of the target time-frequency signal element corresponding to the th outer iteration.

10. The method for noise and interference suppression for underwater acoustic communication transmission link as claimed in claim 1 wherein, In step 3), the outer iteration is specifically: for the i-th outer iteration, fixing the scale parameter of the i-th outer iteration corresponding target time-frequency signal element , updating the target time-frequency signal matrix G by using an element-wise updating 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 stop condition of the outer iteration is: 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 outer stop threshold or the maximum number of outer iterations is reached , the outer iteration is stopped, the enhanced target time-frequency signal matrix is output, and the noise and interference suppression of the underwater acoustic communication signal is completed.

Images