Blind signal-to-noise ratio estimation method and system based on cyclostationary characteristic

Abstract

The invention provides a blind signal-to-noise ratio estimation method and system based on cyclostationary characteristics, and the method comprises the steps: extracting the multi-order cyclic statistic characteristics of a received signal, analyzing the second-order and high-order cyclic statistic, and screening signal cyclic frequency points; performing time-frequency transformation on the received signal based on the characteristics, and positioning a time-frequency domain periodic track of signal energy by combining cyclic frequency matched filtering; constructing a joint filter by using the spatial correlation characteristics of the cyclic frequency points to obtain the spatial correlation characteristics; dynamically distributing signal and noise energy weights based on the saliency index of the cyclic frequency point, and adaptively calibrating an optimization rule; collecting noise samples in a non-signal period, learning statistical characteristics of the noise samples, and constructing a noise statistical characteristic model; and fusing the features and model parameters, and generating a signal-to-noise ratio estimated value by supervised learning. According to the method, the multi-order cyclic statistic characteristics are extracted, the second-order and high-order cyclic statistics are jointly analyzed, the cyclic frequency points are accurately screened, the essential characteristics of the signal are effectively captured, and the signal-to-noise ratio estimation precision is improved.

Description

Technical Field

[0001] This invention relates to the field of blind signal-to-noise ratio (BNR) estimation technology, and in particular to a BNR estimation method and system based on cyclostationary characteristics. Background Technology

[0002] Although existing blind signal-to-noise ratio estimation methods have solved the problem of dependence on prior signal information to some extent, they still have many shortcomings in practical applications.

[0003] On the one hand, the evaluation accuracy is low and inaccurate. In complex and ever-changing real-world environments, signals are often affected by various factors, such as multipath effects, frequency-selective fading, and non-Gaussian noise. Existing blind signal-to-noise ratio (SNR) estimation methods struggle to accurately capture the essential characteristics of signals and noise in these complex scenarios, leading to a decreased ability to distinguish between signals and noise, and consequently, a significant deviation between the SNR estimation results and the true value. For example, methods based on higher-order statistics are prone to estimation errors when dealing with non-stationary signals because higher-order statistics are highly sensitive to the non-stationarity of the signal; subspace-based methods also lead to inaccurate SNR estimation when the signal subspace and noise subspace are difficult to accurately delineate.

[0004] On the other hand, existing methods lack full utilization of the cyclostationary characteristics of signals. Many real-world signals, such as communication signals and radar signals, exhibit cyclostationary characteristics, meaning their statistical properties change periodically over time. Cyclostationary characteristics contain rich signal information and can provide stronger support for signal-to-noise ratio (SNR) estimation. However, most existing blind SNR estimation methods do not fully consider or effectively utilize this characteristic, thus limiting further improvements in SNR estimation performance. Furthermore, when processing multi-channel signals, existing methods underutilize the spatial correlation between channels, failing to fully explore the potential of multi-channel information in SNR estimation, which also affects the accuracy and reliability of the estimation. Summary of the Invention

[0005] This invention aims to at least solve the technical problems of low evaluation accuracy and inaccuracy in the prior art, and innovatively proposes a blind signal-to-noise ratio estimation method and system based on cyclostationary characteristics.

[0006] To achieve the above-mentioned objectives of this invention, this invention provides a blind signal-to-noise ratio estimation method based on cyclostationary characteristics, the method comprising: S1. Extract multi-order cyclic statistics features from the received signal and filter the cyclic frequency points of the signal by jointly analyzing second-order and higher-order cyclic statistics. S2. Based on the multi-order cyclic statistical characteristics, the received signal is subjected to time-frequency transformation, and the periodic trajectory of the signal energy in the time-frequency domain is located by combining cyclic frequency matched filtering. S3. In a multi-channel scenario, a spatial-cyclic frequency joint filter is constructed using the spatial correlation characteristics of the cyclic frequency points to obtain spatial correlation characteristics. S4. Based on the significance index of the cyclic frequency point, dynamically allocate the energy weights of the signal and noise, and optimize the weight allocation rules through adaptive calibration to generate dynamically allocated signal energy weights and noise energy weights. S5. Collect noise samples during the no-signal period in the received signal and learn their statistical characteristics to construct a noise statistical characteristic model. S6. Integrate the multi-order cyclic statistical features, periodic trajectory, spatial correlation features, signal energy weight, noise energy weight, and noise statistical characteristic model parameters, and use supervised learning to generate a signal-to-noise ratio estimate.

[0007] In another aspect, the present invention also provides a blind signal-to-noise ratio estimation system based on cyclostationary characteristics, the system comprising: processor; Memory used to store processor-executable instructions; The processor is configured to implement the blind signal-to-noise ratio estimation method based on cyclostationary characteristics when executing the executable instructions.

[0008] The beneficial effects of this invention are as follows: This invention extracts multi-order cyclic statistics features and jointly analyzes second-order and higher-order cyclic statistics to accurately screen the cyclic frequency points of a signal, effectively captures the essential features of the signal, reduces the impact of complex environmental interference on estimation, improves the accuracy of distinguishing between signal and noise, and thus improves the signal-to-noise ratio estimation accuracy.

[0009] When processing multi-channel signals, a space-cyclic frequency joint filter is constructed by utilizing the spatial correlation characteristics of cyclic frequency points. This fully taps the potential of multi-channel information, enhances the ability to identify signal spatial distribution patterns and potential signal source directions, obtains more reliable spatial correlation characteristics, and further improves the accuracy of estimation.

[0010] The energy weights of signal and noise are dynamically assigned based on the significance index of cyclic frequency points, and the weight assignment rules are optimized through adaptive calibration to make the weight assignment more consistent with the actual signal and noise conditions, avoiding the errors caused by fixed weight assignment. At the same time, noise samples are collected during signal-free periods to construct a noise statistical characteristic model, providing a more accurate noise information reference for signal-to-noise ratio estimation.

[0011] By integrating multi-order cyclic statistical features, periodic trajectories, spatial correlation features, signal energy weights, noise energy weights, and noise statistical characteristic model parameters, a signal-to-noise ratio (SNR) estimate is generated using supervised learning. An attention mechanism is introduced for dynamic weighting, and the model is optimized by combining cross-validation. This strengthens the role of key features in the estimation, making the generated SNR estimate more accurate and reliable. It can adapt to complex and ever-changing real-world application scenarios and has wider applicability and higher practical value.

[0012] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0013] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of a blind signal-to-noise ratio estimation method based on cyclostationary characteristics according to the present invention. Detailed Implementation

[0014] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0015] Example 1 A blind signal-to-noise ratio estimation method based on cyclostationary characteristics, the method comprising: S1. Extract multi-order cyclic statistics features from the received signal and filter the cyclic frequency points of the signal by jointly analyzing second-order and higher-order cyclic statistics. S2. Based on the characteristics of multi-order cyclic statistics, the received signal is transformed in time and frequency, and combined with cyclic frequency matched filtering, the periodic trajectory of the signal energy in the time and frequency domain is located. S3. In multi-channel scenarios, a space-cyclic frequency joint filter is constructed using the spatial correlation characteristics of the cyclic frequency points to obtain spatial correlation characteristics. S4. Based on the significance index of the cyclic frequency point, dynamically allocate the energy weights of the signal and noise, and optimize the weight allocation rules through adaptive calibration to generate dynamically allocated signal energy weights and noise energy weights. S5. Collect noise samples during the no-signal period in the received signal and learn their statistical characteristics to build a noise statistical characteristic model. S6. By integrating multi-order cyclic statistical features, periodic trajectories, spatial correlation features, signal energy weights, noise energy weights, and noise statistical characteristic model parameters, a signal-to-noise ratio estimate is generated using supervised learning.

[0016] In this embodiment, a blind signal-to-noise ratio (SNR) estimation method based on cyclostationary characteristics works as follows: Utilizing the inherent statistical differences in cyclostationary signals at specific cyclic frequencies, multi-order (second-order and above) cyclic statistical features are extracted to deeply explore the inherent periodicity of the signal and its statistical separability from noise. Compared to traditional methods relying solely on second-order statistics, joint analysis of higher-order cyclic statistics can more comprehensively capture the cyclostationary characteristics of the signal, especially in low SNR or non-Gaussian noise backgrounds, effectively identifying weak cyclic frequency components submerged by noise, thereby accurately selecting cyclic frequency points characterizing the essential features of the signal. Based on the selected cyclic frequency points, combined with time-frequency transformation technology, cyclic frequency matched filtering enhances the energy concentration of the signal in the time-frequency domain, and according to preset connectivity criteria (such as time continuity constraints and frequency jump range limitations), the periodic trajectory characterizing the periodic transmission mode of the signal is located. In multi-channel reception scenarios, this method further utilizes the spatial domain information inherent in different cyclic frequency points. By calculating inter-cyclic statistics (inter-cyclic autocorrelation function, inter-cyclic spectral density), it analyzes the signal similarity and spatial distribution patterns between channels and constructs a joint spatial-cyclic frequency filter. This filter is optimized based on minimizing the output noise variance while passing the desired signal without distortion (i.e., the minimum variance distortion-free response criterion), combined with the characteristics of the spatial covariance matrix dependent on the cyclic frequency, thereby obtaining more accurate spatial correlation features. On this basis, the energy weight allocation of signal and noise is dynamically initialized and adaptively calibrated according to the significance index of the cyclic frequency point (reflecting the reliability of the correlation between the frequency point and the signal). Simultaneously, noise samples are collected during detected no-signal periods, and their cyclic statistical characteristics are analyzed to construct an accurate noise statistical characteristic model. Finally, by fusing multi-order cyclic statistical features, periodic trajectories, spatial correlation features, dynamically allocated signal / noise energy weights, and noise statistical characteristic model parameters, a signal-to-noise ratio estimation framework based on supervised learning (such as neural networks) is constructed. This framework introduces an attention mechanism to dynamically enhance the role of key features and combines cross-validation to optimize the model structure, thereby achieving accurate and robust estimation of the signal-to-noise ratio of the received signal and effectively overcoming interference caused by complex electromagnetic environments and noise uncertainties.

[0017] As an optional embodiment of the present invention, optionally, extracting multi-order cyclic statistical features from the received signal in step S1, and screening the cyclic frequency points of the signal by jointly analyzing second-order and higher-order cyclic statistics, includes: S101. Perform segmented preprocessing on the received signal and use a sliding window to obtain a sub-signal sequence that satisfies the cyclic stationarity assumption. In step S101, it is necessary to explain in detail that when performing segmented preprocessing on the received signal, a fixed-length signal segmentation strategy is adopted. Specifically, the received signal is divided into continuous segments of fixed length, ensuring that each signal segment contains at least one complete periodic component to avoid boundary effects affecting the cyclic stationarity analysis. Simultaneously, a sliding window mechanism is used to extract sub-signal sequences. To ensure that the sub-signal sequences satisfy the cyclic stationarity assumption, stationarity tests are performed on the sub-sequences within each window, specifically using methods such as unit root tests or ADF tests.

[0018] S102. Calculate the characteristics of second-order cyclic statistics based on the synchronous calculation of sub-signal sequences; The expression for calculating the characteristics of the second-order cyclic statistic is: in, This represents the cyclic autocorrelation function, which describes the signal at the cyclic frequency. and latency Second-order periodic correlation, Indicates the length of observation time The limiting process as it approaches infinity. Indicates the received signal at time Complex value samples, Represents the complex value sample of the received signal The conjugate of complex numbers, Represents the imaginary unit. Represents the cyclic spectral density, reflecting the signal in the cyclic frequency-frequency domain plane ( - Energy distribution Represents frequency in the frequency domain; In step S102, it is necessary to explain in detail that the second-order cyclic statistics characteristics can reveal the second-order statistical properties of the signal at the cyclic frequency, including the cyclic autocorrelation function and the cyclic spectral density. The cyclic autocorrelation function reflects the periodic structure of the signal by calculating the correlation of the signal at different time delays and cyclic frequencies; the cyclic spectral density transforms the cyclic autocorrelation function to the frequency domain through Fourier transform, showing the distribution of signal energy in the cyclic frequency-frequency domain plane.

[0019] S103. Extract higher-order cyclic statistics features from the sub-signal sequence; The expression for extracting higher-order cyclic statistics features from the sub-signal sequence is: in, This represents the third-order cyclic cumulant, reflecting the signal at the cyclic frequency. Non-Gaussian properties under the following conditions This represents the cumulant operator, used to calculate higher-order nonlinear correlations of signals. , , , This represents the sampling points of the signal at different times. This represents the fourth-order cyclic cumulant, revealing the modulation characteristics of multipath propagation or multi-component signals. Represents higher-order cyclic frequencies and second-order cyclic frequencies. Together they constitute the dimensions of multi-order statistical analysis; In step S103, it is important to explain in detail that higher-order cyclic statistics can capture the higher-order statistical characteristics of a signal at its cyclic frequency. Compared to second-order cyclic statistics, they provide more information about the signal's non-Gaussianity, multipath propagation, or multi-component modulation characteristics. Third-order cyclic cumulants, by calculating the nonlinear correlation between sampling points at different times, reflect the signal's non-Gaussianity at its cyclic frequency, which is particularly important for identifying signal components in a non-Gaussian noise background. Fourth-order cyclic cumulants further reveal the signal's multipath propagation or multi-component modulation characteristics, helping to accurately distinguish different signal sources in complex signal environments. By jointly analyzing second-order and higher-order cyclic statistics, the cyclic stationary characteristics of the signal can be captured more comprehensively, thereby accurately screening out the cyclic frequency points that characterize the signal's essential features. In low signal-to-noise ratio or non-Gaussian noise backgrounds, weak cyclic frequency components submerged by noise can be effectively identified.

[0020] S104. Combine the second-order cyclic statistics and higher-order cyclic statistics to obtain the cyclic frequency points.

[0021] In step S104, it is necessary to explain in detail that the method for joint analysis of second-order cyclic statistical features and higher-order cyclic statistical features in this embodiment is as follows: First, the second-order cyclic statistical features and higher-order cyclic statistical features are normalized to ensure they are of the same numerical magnitude, thus avoiding bias in the joint analysis results due to excessive differences in feature values. The normalization process can employ the min-max normalization method, mapping the feature values ​​to the [0,1] interval. Then, a comprehensive screening index is set, which combines the second-order periodic correlation of the signal reflected by the second-order cyclic statistical features with the non-Gaussianity and multipath propagation characteristics of the signal embodied by the higher-order cyclic statistical features. For example, the cyclic autocorrelation function value and cyclic spectral density value in the second-order cyclic statistical features can be assigned certain weights, while corresponding weights can be assigned to higher-order features such as third-order and fourth-order cyclic cumulants. The comprehensive screening index value is obtained through weighted summation. Next, the comprehensive screening index value is judged according to a preset threshold. When the comprehensive screening index value is greater than the threshold, the corresponding cyclic frequency point is the selected cyclic frequency point that represents the essential characteristics of the signal. Through this joint analysis method, the advantages of second-order and higher-order cyclic statistics can be fully utilized to more accurately select the cyclic frequency points of the signal in complex signal environments.

[0022] As an optional embodiment of the present invention, optionally, in step S2, the received signal is subjected to time-frequency transformation based on the multi-order cyclic statistical characteristics, and the periodic trajectory of the signal energy in the time-frequency domain is located by combining cyclic frequency matched filtering with the following: S201. Based on the cyclic frequency point, the received signal is reconstructed in the time-frequency domain, and the short-time Fourier transform method is used to dynamically adjust the window function length to balance the time-frequency resolution and generate an initial time-frequency energy distribution map. In step S201, it is necessary to explain in detail that, based on the selected cyclic frequency points, the received signal is first reconstructed in the time-frequency domain, transforming the signal from the time domain to an extended time-frequency domain containing cyclic frequency information. When using Short-Time Fourier Transform (STFT), the time-frequency resolution is optimized by dynamically adjusting the window function length: a longer window function is used in the low-frequency band (corresponding to long-period cyclic frequencies) to improve frequency resolution, and a shorter window function is used in the high-frequency band (corresponding to short-period cyclic frequencies) to enhance time resolution. Specifically, the window function length is inversely proportional to the currently analyzed cyclic frequency, i.e., window length L = C / f. c (C is a constant, f) c (where the cyclic frequency is used) to ensure optimal time-frequency concentration at key frequency points. Through this adaptive adjustment mechanism, the generated initial time-frequency energy distribution map can clearly show the distribution characteristics of signal energy in the two-dimensional time-cyclic frequency plane.

[0023] S202. Based on the initial time-frequency energy distribution map, construct a cyclic frequency matched filter bank. Each filter is frequency-domain weighted to the corresponding cyclic frequency to enhance the signal energy response corresponding to the cyclic frequency point and suppress noise interference at non-cyclic frequencies, thus forming a time-frequency energy enhancement map after matched filtering. In step S202, it is necessary to explain in detail that when constructing the cyclic frequency matched filter bank, an independent matched filter needs to be designed for each selected cyclic frequency point. Specifically, the filter's frequency domain response function is designed as a window function that matches the cyclic spectral density characteristics of the target cyclic frequency, such as a frequency domain variant of a Gaussian window or Hanning window. Its center frequency is precisely aligned with the target cyclic frequency, and its bandwidth is adaptively adjusted according to the signal's periodicity. Through frequency domain weighting, the filter forms a peak response at the target cyclic frequency, significantly enhancing the signal energy corresponding to that frequency point in the time-frequency graph. Simultaneously, by setting stopband attenuation characteristics (e.g., above -40dB), noise interference from non-cyclic frequency components is effectively suppressed. After processing by the filter bank, the weak periodic trajectory in the original initial time-frequency energy distribution graph is highlighted, forming a time-frequency energy enhancement graph with stronger energy concentration.

[0024] S203. Based on the periodic distribution characteristics of the time-frequency energy enhancement map combined with the multi-order cyclic statistics, the periodic trajectory of the signal energy is located by the time-frequency domain peak detection and trajectory tracking algorithm. Isolated noise points are removed by connected component analysis, and continuous and stable periodic trajectories are retained to generate a candidate set of periodic trajectories. In step S203, it is necessary to explain in detail that when implementing the time-frequency domain peak detection and trajectory tracking algorithm, the time-frequency energy enhancement map is first binarized by setting an energy threshold, and regions above the threshold are marked as potential signal trajectory points. Then, an improved Hough transform or a gradient-based trajectory search algorithm (such as gradient trajectory tracking) is used to aggregate the marked points to form continuous trajectory segments. Specifically, the gradient trajectory tracking method first searches for local energy maxima in the time-frequency energy enhancement map as seed points for trajectory starting points, and then determines the trajectory extension direction and step size based on the energy gradients in the time and cycle frequency directions of the time-frequency map. The algorithm iteratively connects adjacent high-energy points from the seed point along the direction of maximum gradient increase, satisfying preset trajectory continuity constraints (such as maximum time interval and maximum cycle frequency jumps), until the energy gradient falls below the set threshold or reaches the boundary. Subsequently, connectivity analysis is performed on all generated trajectory segments: the physical length (time span), energy integral value, and shape compactness index (such as aspect ratio) of each segment are calculated, and minimum length thresholds and minimum energy integral thresholds are set to remove isolated noise segments that are too short, have too low energy, or are too discrete in shape (such as having an aspect ratio greater than 1). Finally, continuous and stable trajectories that satisfy the connectivity criterion are retained to form a candidate set of periodic trajectories.

[0025] S204. Perform multi-segment signal consistency checks on the candidate set of periodic trajectories, verify the stability of the periodic trajectory in different time periods by comparing with a sliding window, and then dynamically adjust the time-frequency transformation parameters and filter response by combining the significance index of the cyclic frequency points to optimize the accuracy and robustness of the periodic trajectory positioning, thus forming an optimized periodic trajectory. In step S204, it is necessary to explain in detail that when performing multi-segment signal consistency verification, a sliding window mechanism is first used to divide the candidate set of periodic trajectories into multiple overlapping or non-overlapping time period subsets. The stability of the periodic trajectory in different time periods is quantified by calculating the energy distribution, cyclic frequency consistency index (such as the standard deviation of cyclic frequency offset), and trajectory morphological similarity (such as dynamic time warping distance) of the trajectories within each subset. Specifically, a consistency threshold range is set: when the standard deviation of cyclic frequency offset between subsets is lower than a preset threshold (such as 0.1 times the cyclic frequency resolution), and the trajectory morphological similarity is higher than the threshold (such as 0.8), the trajectory is determined to pass the consistency verification; otherwise, it is marked as an unstable trajectory and removed. Subsequently, the time-frequency transformation parameters are dynamically adjusted based on the significance index of the cyclic frequency points (defined by the ratio of the peak value of the cyclic spectral density to the energy of the neighboring noise): for strong cyclic frequency points with a significance index higher than the threshold (such as 3dB), the STFT window function length is appropriately shortened to improve time resolution and capture rapidly changing signal characteristics; for weak cyclic frequency points with a low significance index, the window function length is extended to enhance frequency resolution and suppress frequency domain leakage. Simultaneously, the bandwidth parameters of the cyclic frequency matched filter bank are adjusted according to the significance index: a high significance index corresponds to a narrow bandwidth filter to accurately extract features, while a low significance index corresponds to a wide bandwidth filter to enhance noise immunity. Through this dynamic parameter optimization mechanism, the final optimized periodic trajectory achieves an optimal balance in terms of time continuity, frequency consistency, and noise immunity.

[0026] S205. Perform time-frequency-cyclic frequency joint analysis on the statistical characteristics of the optimized periodic trajectory and the cyclic frequency points to verify the correspondence between the energy distribution of the periodic trajectory and the cyclic frequency points, ensuring that the periodic characteristics of the periodic trajectory are consistent with the characteristics of the cyclic frequency points, and generate a periodic trajectory feature set in the time-frequency domain.

[0027] In step S205, the specific method for joint time-frequency and cyclic frequency analysis is as follows: First, a time-frequency energy distribution matrix of the optimized periodic trajectory is established. The rows of this matrix correspond to time indices, the columns to cyclic frequency indices, and the matrix element values ​​are normalized time-frequency energy amplitudes. Simultaneously, the cyclic frequency points determined in step S104 and their corresponding statistical characteristics are extracted, including the second-order cyclic spectral density value and the higher-order cyclic cumulative magnitude value of each cyclic frequency point, forming a cyclic frequency feature vector. The correlation coefficient between the projection curve of the time-frequency energy distribution matrix on the cyclic frequency axis and the cyclic frequency feature vector is calculated to quantify the consistency between the two in the cyclic frequency dimension. Specifically, a sliding time window mechanism is used, and the following calculations are performed within each time window: 1) The Pearson correlation coefficient ρ between the projection curve and the cyclic frequency eigenvector t , requires |ρ t |≥0.85; 2) The relative position offset Δα of the energy peak at the cyclic frequency point ≤ 0.1Δf (Δf is the cyclic frequency resolution); 3) Significant cyclic frequency points in the eigenvector must have corresponding energy peaks on the projection curve, and the signal-to-noise ratio of the energy peaks must be ≥6dB.

[0028] For time periods that do not meet any of the above conditions, a backtracking mechanism is activated: the trajectory optimization process of S203-S204 is re-executed, and the stopband attenuation parameter of the cyclic frequency matched filter is adjusted (increased by 10-15dB) to enhance feature selectivity. Trajectory segments that still fail to meet the consistency requirements after three iterations of verification will be removed. The final verified continuous trajectory segments constitute a periodic trajectory feature set, which includes the trajectory's start and end times, cyclic frequency sequence, time-frequency energy envelope function, and corresponding cyclic statistic confidence index.

[0029] As an optional embodiment of the present invention, the expression of the trajectory tracking algorithm in step S203 is optionally: in, Indicates time and frequency Peak detection results at the location, Indicates time and frequency The signal energy value at that location, Indicates the dynamic peak threshold. This indicates the frequency point in the frequency dimension. Centered on, with a width of 2 Within a local neighborhood, the time-frequency energy matrix The maximum value, Indicates the frequency neighborhood window parameters. Represents the frequency index variable within the neighborhood. This represents the results of connected component analysis. This indicates the peak detection result. Indicates the parameters of the time neighborhood window. This represents the offset within the time neighborhood window. This represents the threshold for the minimum number of points in a connected component. This represents the set of generated periodic trajectories. Represents the periodic trajectory of the first... Time index of each trajectory point Represents the periodic trajectory of the first... Frequency index of trajectory points Representing coordinates It belongs to a continuous and stable trajectory. This represents the frequency index of two consecutive trajectory points. Indicates the maximum permissible frequency jump range. This represents the time index of two consecutive trajectory points. Represents the cycle frequency The corresponding cycle duration.

[0030] As an optional embodiment of the present invention, optionally, obtaining spatial correlation features in step S3 includes: S301. Using cyclic frequency points and periodic trajectories, perform spatial domain correlation pre-analysis on the received signal, calculate the mutual cyclic autocorrelation function and mutual cyclic spectral density to quantify the signal similarity between channels, identify the spatial distribution pattern of multi-channel signals and the direction of potential signal sources, and generate an initial constraint set of spatial correlation features. In step S301, it is necessary to explain in detail that spatial domain correlation pre-analysis is performed on the received multi-channel signals using the selected cyclic frequency points and the periodic trajectory generated in step S203. Specifically, the cross-cyclic autocorrelation function (CCAF) between each channel signal is first calculated, which is defined as the average value of the time delay correlation integrals of the two channel signals at the cyclic frequency offset. A cross-cyclic autocorrelation function matrix is ​​generated by setting the maximum time delay range (e.g., ±10 sampling periods) and the cyclic frequency search range (covering the cyclic frequency points determined in step S104 ± 0.5 times the resolution). Subsequently, a two-dimensional Fourier transform is performed on the cross-cyclic autocorrelation function matrix to obtain the cross-cyclic spectral density (CCSD). The rows of this matrix correspond to the cyclic frequency index, the columns correspond to the channel pair index, and the element values ​​are the normalized cross-cyclic spectral energy amplitudes. By analyzing the inter-cycle spectral density matrix, the similarity of signals between channels in the cyclic frequency dimension is quantified: when two channels have significant inter-cycle spectral energy peaks at the same cyclic frequency point (e.g., peak signal-to-noise ratio ≥ 8dB), the spatial modes corresponding to that frequency point are determined to be strongly correlated; otherwise, they are marked as weakly correlated or independent modes. Furthermore, combining the spatial distribution characteristics of periodic trajectories (e.g., spatial clustering regions of trajectories in the time-frequency plot), the spatial distribution patterns of multi-channel signals are identified: for periodic trajectories at the same cyclic frequency point and spatially adjacent (e.g., Euclidean distance ≤ 5 units in the time-frequency plot coordinates), they are determined to originate from the same potential signal source direction; for spatially dispersed trajectories, they are marked as different source directions. Finally, the identified spatial distribution patterns (e.g., single-source, multi-source, scattering source) and their corresponding cyclic frequency points and channel pair indices form an initial constraint set of spatial correlation features. This constraint set includes key parameters such as spatial mode type, dominant cyclic frequency sequence, list of strongly correlated channel pairs, and spatial coordinate range.

[0031] S302. Based on the initial constraint set of spatial correlation features and the statistical characteristics of cyclic frequency points, a spatial-cyclic frequency joint filter is constructed. Combining the characteristics of the spatial covariance matrix of multi-channel signals, the weights of the spatial-cyclic frequency joint filter are optimized by the minimum variance distortionless response algorithm. The expression for the minimum variance distortionless response algorithm is: in, Represents the spatial filtering weight vector. This represents the conjugate transpose of the spatial filter weight vector. This represents the spatial covariance matrix that depends on the cyclic frequency. Represents the regularization coefficient. Indicates the cycle frequency point The significance index, This represents the prior space filtering weight vector. Indicates the point of recurrence frequency The corresponding array response vector in the signal space direction, This represents the optimal spatial filter weight vector. Represents the identity matrix. express The conjugate transpose of; In step S302, the process of constructing a joint spatial-cyclic frequency filter based on the initial constraint set of spatial correlation features and the statistical characteristics of cyclic frequency points is as follows: First, according to the spatial distribution pattern (e.g., single-source, multi-source) identified in the initial constraint set of spatial correlation features, the multi-channel signal is divided into different spatial subsets, each corresponding to a potential signal source direction. For each spatial subset, its dominant cyclic frequency sequence and strongly correlated channel pair list are extracted to construct a spatial covariance matrix dependent on cyclic frequency. This matrix is ​​obtained by calculating the cross-correlation function of each channel at the corresponding cyclic frequency point, reflecting the joint statistical characteristics of the signal in the spatial and cyclic frequency dimensions. Combining the minimum variance distortionless response algorithm, a regularization coefficient is introduced to balance the filter performance and stability, and the optimization objective of the spatial filter weight vector is dynamically adjusted using the significance index of the cyclic frequency point. In specific implementation, the prior spatial filter weight vector is initialized according to the spatial location coordinate range in the initial constraint set of spatial correlation features, and the array response vector is determined by beamforming in the signal spatial direction. The optimal spatial filter weight vector is solved through iterative optimization, so as to minimize the output noise power while maintaining a distortionless response to the target signal. The resulting space-cyclic frequency joint filter can adaptively suppress unrelated noise and interference, and enhance the energy focusing capability of the target signal at a specific spatial direction and cyclic frequency point.

[0032] S303. Apply the optimized space-cyclic frequency joint filter to the multi-channel received signal. By analyzing the energy distribution of the filtered received signal in the spatial dimension, extract the spatial correlation features and generate an initial set of spatial correlation features.

[0033] In step S303, it is necessary to explain in detail that when the optimized spatial-cyclic frequency joint filter is applied to the multi-channel received signal, the spatial dimension energy integral is first performed on the filtered signal corresponding to each spatial subset to calculate the output energy amplitude of each channel under the filter. By comparing the differences in energy distribution among different channels, spatial correlation characteristics are identified: for channels within the same spatial subset, if the filtered signal energy shows significant aggregation at a specific spatial location (e.g., the energy peak exceeds twice the standard deviation of the global mean), it is determined that there is strong spatial correlation at that location; conversely, if the energy is uniformly distributed or there is no obvious aggregation, it is marked as weakly correlated or an independent mode. Furthermore, combined with the spatial distribution information of the periodic trajectory (e.g., the spatial coordinates of the trajectory in the time-frequency graph), a spatiotemporal joint analysis is performed on the filtered signal: when the overlap between the spatial coordinates of the periodic trajectory and the location of the filtered energy peak exceeds 80%, it is confirmed that the spatial direction of the signal source corresponding to the trajectory is consistent with the filter optimization direction; if the overlap is less than 50%, the filter parameter correction mechanism is activated, and the regularization coefficient in the spatial filter weight vector is readjusted (increased by 5-10dB) to enhance spatial selectivity. Finally, by statistically analyzing the number of strongly correlated channels, the range of energy peak position coordinates, and the degree of overlap with periodic trajectories within each spatial subset, an initial set of spatial correlation features is generated. This feature set includes key parameters such as spatial subset identifiers, dominant spatial directions, energy peak distribution functions, a list of strongly correlated channel indexes, and spatial correlation confidence indices.

[0034] As an optional embodiment of the present invention, optionally, generating dynamically allocated signal energy weights and noise energy weights in step S4 includes: S401. Based on the significance index of the cyclic frequency points, initialize the basic energy weight distribution of signal and noise in the received signal. Assign higher initial signal weights to cyclic frequency points with high significance and lower initial noise weights to cyclic frequency points with low significance, thus forming the initial signal energy weight distribution. In step S401, it is necessary to explain in detail that when initializing the basic energy weights based on the significance index of the cyclic frequency points, the mapping relationship between the significance index and the energy weights must first be established. Specifically, the determined cyclic frequency points are sorted from high to low according to their significance index (e.g., the normalized peak amplitude). The first 30% of highly significant points are designated as the signal-dominant region, assigned an initial signal weight of 0.8-0.95; the middle 40% of moderately significant points are designated as the transition region, assigned an initial signal weight of 0.5-0.7; and the last 30% of low-significance points are designated as the noise-dominant region, assigned an initial noise weight of 0.9-0.98. This weight distribution achieves a smooth transition through the Sigmoid function, avoiding estimation bias caused by sudden threshold changes. Simultaneously, a dynamic adjustment factor is introduced. When the number of strongly correlated channel pairs in the intercyclic spectral density matrix of a certain cyclic frequency point exceeds a threshold (e.g., ≥3), its signal weight is additionally increased by 0.1-0.15 to enhance the feature preservation capability in multi-source signal scenarios. The final initial signal energy weight distribution matrix has rows corresponding to the cyclic frequency index, columns corresponding to the channel index, and element values ​​that are continuous values ​​in the interval [0,1], while satisfying the constraint that the sum of the weights of each column is 1.

[0035] S402. Based on the periodic trajectory and spatial correlation characteristics, the initial signal energy weight is calibrated in multiple dimensions to obtain the signal / noise weight after multi-dimensional calibration. The process of multi-dimensional calibration of the initial signal energy weights based on periodic trajectory and spatial correlation features is as follows: First, using the spatial distribution information of periodic trajectories (such as the clustering region of trajectories in the time-frequency graph and the consistency of motion direction) and the spatial subset identifiers in the initial set of spatial correlation features, the initial signal energy weight matrix is ​​divided into block matrices corresponding to the spatial subsets. For each spatial subset, the number of periodic trajectories, trajectory length, and spatial overlap with strongly correlated channels in its dominant spatial direction are extracted as calibration parameters. In specific implementation, when the number of periodic trajectories in a spatial subset exceeds a preset threshold (e.g., ≥5) and the trajectory length coverage exceeds 60%, it is determined that there is a stable signal source in that direction, and the overall signal weight in its corresponding block matrix is ​​increased by 0.05-0.1; conversely, if the number of trajectories is less than 3 or the coverage is less than 30%, it is determined to be transient interference, and the signal weight is reduced by 0.1-0.15. Simultaneously, by combining the strongly correlated channel index list from the spatial correlation features, the weights of each channel within the block matrix are finely adjusted: when the matching degree between the channel index and the strongly correlated channel list exceeds 80%, the original weight remains unchanged; channels with a matching degree between 50% and 80% have their weights reduced by a factor of 0.7; channels with a matching degree below 50% are directly assigned noise weights. Furthermore, a trajectory stability index (e.g., frequency index change ≤ 2 within three consecutive time frames) is introduced as a dynamic calibration factor, adding an additional 0.02-0.05 signal weight compensation to the channels corresponding to trajectories that meet the stability condition. Finally, by weighted fusion of the block matrices of each spatial subset, a multi-dimensional calibrated signal / noise weight matrix is ​​generated. This matrix retains the original cyclic frequency dimension information while strengthening the feature correlation between the spatial and temporal dimensions.

[0036] S403. Based on the signal / noise weights after multi-dimensional calibration, the received signal is processed in segments using a sliding window. The actual effect of weight allocation in different time periods is compared to obtain the feedback error. The weight allocation rules are dynamically adjusted based on the feedback error to obtain the adaptively calibrated weight allocation rules. In step S403, it is necessary to explain in detail that when performing sliding window segmentation processing based on the multi-dimensional calibrated signal / noise weights, the received signal is first divided into continuous time periods of fixed length (e.g., 100ms), with each time period corresponding to an independent signal processing unit. Within each time period, the signal is weighted and summed according to the multi-dimensional calibrated weight matrix to obtain the weighted signal energy and noise energy estimates for that time period. By comparing the weight allocation effects (e.g., signal energy concentration, noise suppression ratio) in different time periods, the feedback error is calculated: when the weighted signal energy fluctuation in adjacent time periods exceeds a threshold (e.g., ±15%) or the noise energy suppression effect decreases by more than 10%, it is determined that the current weight allocation rule is not adaptable enough.

[0037] The process of dynamically adjusting the weight allocation rule based on feedback error is as follows: First, the source of error is analyzed. If the error is mainly caused by changes in spatial dimension (such as the shift in spatial correlation characteristics due to signal source movement), the spatial subset partitioning threshold is adjusted (e.g., the threshold for the number of periodic trajectories is adjusted from 5 to 3), and the spatial filtering weight vector is recalculated. If the error is mainly caused by changes in time dimension (e.g., abrupt changes in the significance index of the cyclic frequency point), the mapping relationship between the significance index and the energy weight is updated (e.g., the weight of high significance point signals is adjusted from 0.9 to 0.85). A PID controller (proportional-integral-derivative controller) is introduced to perform closed-loop control of the weight adjustment process. The proportional term is used to quickly respond to significant errors, the integral term is used to eliminate steady-state errors, and the derivative term is used to suppress overshoot. The resulting adaptively calibrated weight allocation rule can dynamically adjust the energy weights of signals and noise according to real-time signal characteristics, improving the adaptability to non-stationary signal environments while maintaining algorithm stability. This rule achieves dynamic matching between weight allocation and signal characteristics through iterative optimization, and its core parameters (such as the spatial subset partitioning threshold and the significance index mapping coefficient) are stored in a dynamic rule base.

[0038] S404. Based on the weight allocation rules after adaptive calibration, the weighted average algorithm is applied to calculate the energy weight distribution of signal and noise in the received signal, and to generate dynamically allocated signal energy weight and noise energy weight.

[0039] In step S404, it is necessary to explain in detail that when applying the weighted average algorithm based on the adaptively calibrated weight allocation rules, the weight allocation parameter set corresponding to the current signal environment is first loaded from the dynamic rule base, including the spatial subset partitioning threshold, significance index mapping coefficient, PID controller parameters, etc. The multi-channel received signals are grouped and processed according to time periods divided by a sliding window. Within each time period, the following operations are performed: First, the spatial subset to which each channel belongs is determined based on an initial set of spatial correlation characteristics. The spatial subset boundaries are then corrected using spatial distribution information of periodic trajectories. Second, based on the mapping relationship between the significance index and energy weights, basic signal / noise weights are assigned to each cyclic frequency point. The signal weight for high-significance cyclic frequency points (e.g., spectral peak amplitude exceeding three standard deviations of the global mean) is initialized to 0.92, while the noise weight for low-significance points (spectral peak amplitude below the global mean) is initialized to 0.96. Third, the initial weights are dynamically corrected using a PID controller. When a spatial correlation characteristic shift is detected (e.g., a 20% reduction in the number of strongly correlated channel pairs), the spatial filter weight vector is adjusted proportionally. When a significant abrupt change in cyclic frequency points is detected (e.g., a 15% decrease in spectral peak amplitude within three time frames), the energy weight mapping coefficients are updated integrally. Finally, the corrected weight matrix is ​​weighted in blocks according to spatial subsets. Within each subset, the weighting coefficients are calculated using recursive least squares to minimize the mean square error between the estimated signal energy and the actual observed value. In practice, for each spatial subset, a weighted coefficient vector is first constructed, whose elements are the ratio of the corrected signal weight to the noise weight for each channel. This vector is iteratively updated using a recursive least squares method. In each iteration, the coefficient values ​​are adjusted based on the error between the current weighted signal energy and the actual observation value until the mean square error converges to a preset threshold (e.g., ≤0.01). The final generated weighted coefficient vector reflects the contribution of each channel to the target signal. Channels with high contribution (weighted coefficient > 1.5) are assigned higher signal energy weights, while channels with low contribution (weighted coefficient < 0.5) are marked as noise-dominant channels. The block weighting results of each spatial subset are concatenated into a complete weight matrix. The rows of this matrix correspond to the cyclic frequency index, the columns correspond to the channel index, and the element values ​​are dynamically adjusted signal / noise energy weights. To ensure the rationality of the weight distribution, a normalization constraint is introduced: the weight values ​​of each channel are globally normalized so that the sum of the signal weights and the sum of the noise weights at all cyclic frequency points is 1. Meanwhile, the effectiveness of the weight allocation is verified through a cross-validation mechanism: 10% of the channel data is randomly masked, and the signal energy distribution is reconstructed using the weight matrix of the remaining channels. If the reconstruction error (such as root mean square error) exceeds 5%, the rule base update process is triggered, and the PID controller parameters are retrained.The resulting dynamic allocation matrix of signal energy weights and noise energy weights can reflect changes in the signal environment in real time. Its dynamic adjustment range is 0.75-0.98 for signal weights and 0.85-0.99 for noise weights, and it meets the requirement of independence of weight allocation among different spatial subsets.

[0040] As an optional embodiment of the present invention, optionally, in step S5, noise samples are collected during the no-signal period of the received signal and their statistical characteristics are learned to construct a noise statistical characteristic model, including: S501. Based on the periodic trajectory disappearance time period and the signal energy weight distribution threshold, detect the no-signal time period in the received signal, and synchronously collect multi-channel noise samples during the time period; In step S501, it is necessary to explain in detail that when detecting no-signal periods based on the disappearance period of periodic trajectories and the signal energy weight distribution threshold, the interruption or disappearance interval of the periodic trajectory is first identified by analyzing the time-frequency distribution characteristics of the received signal. Specifically, two judgment conditions are set: First, when no significant periodic trajectory is detected within three consecutive time frames (trajectory length < 3 frequency points or trajectory consistency coefficient < 0.6), it is marked as a potential no-signal period; Second, combined with the signal energy weight distribution threshold, when the signal weight of all cyclic frequency points within a certain time period is lower than a preset threshold (e.g., < 0.3) and the noise weight is higher than the threshold (e.g., > 0.7), the time period is confirmed as a no-signal period. To avoid false judgments, a sliding window verification mechanism is introduced: the window length is 100ms, and the step size is 50ms for sliding detection. When three consecutive windows meet the above conditions, it is finally determined to be a no-signal period. After confirming the period without signal, multi-channel noise samples were simultaneously acquired. Specifically, the signal of each channel within that period was bandpass filtered (the filtering range was consistent with the signal's cycling frequency range). After removing the DC component, segmented sampling was performed at 10ms intervals, with each segment containing 2048 points to ensure coverage of the transient characteristics of the noise. Environmental parameters (such as temperature and electromagnetic interference level) were also recorded during sampling as auxiliary information for noise statistical characteristic analysis. The final noise sample set included timestamps, channel indices, sampled value sequences, and environmental parameters.

[0041] S502. Perform piecewise stationarity tests on the noise samples and use moving variance analysis to screen out noise sample segments that satisfy the stationarity assumption. In step S502, it is necessary to explain in detail that when performing piecewise stationarity testing on the noise samples, the collected multi-channel noise samples are first divided into continuous segments of a fixed length (e.g., 512 points), with each segment corresponding to an independent stationarity analysis unit. The sliding variance analysis method is used to test each segment, with the following specific steps: Calculate the variance of the signal within each segment and construct a variance time series; calculate the local rate of change of the variance series using a sliding window (window length is 1 / 4 of the segment length). When the local rate of change exceeds a preset threshold (e.g., ±20%), the segment is determined to be non-stationary; conversely, if the rate of change of variance within three consecutive sliding windows is below the threshold, it is determined to be a stationary segment. To improve the accuracy of the test, an autocorrelation function (e.g., ACF) is introduced to assist in the judgment: calculate the autocorrelation coefficient of the candidate samples of the stationary segment. When the absolute value of the autocorrelation coefficient of lag 1 is greater than 0.3 and the absolute value of the coefficient of lag 5 is less than 0.1, the sample segment is confirmed to satisfy the weak stationarity assumption. By using multi-channel parallel processing, sample segments that simultaneously satisfy the stationarity condition are selected from all channels to form a stationary noise sample library. The sample segments in this library are stored in groups by channel, and each group contains metadata such as sample start time, duration, variance value, and autocorrelation coefficient.

[0042] S503. Extract the multi-order cyclic statistics features of the noise sample segments that have passed the test, calculate their cyclic autocorrelation function and cyclic spectral density, and construct a noise cyclic statistics feature library. In step S503, it is necessary to explain in detail that when extracting the multi-order cyclic statistics features of the noise sample segments that have passed the test, the cyclic autocorrelation function is first calculated for each stationary noise sample segment. Specifically, a discrete Fourier transform is performed on the sample segment to obtain its frequency domain representation. The autocorrelation values ​​at different cyclic frequencies are calculated by multiplying the frequency domain and inversely transforming back to the time domain. The range of selected cyclic frequencies covers the possible cyclic frequency intervals of the signal, and the step size is set to 1 / 10 of the frequency domain resolution to ensure the precision of feature extraction. At the same time, the cyclic spectral density is calculated. By performing a second Fourier transform on the cyclic autocorrelation function, the energy distribution of the noise on the cyclic frequency-frequency plane is obtained. To capture the nonlinear characteristics of the noise, second-order and third-order cyclic statistics are further extracted. The second-order cyclic statistics reflect the periodic modulation characteristics of the noise, and the third-order cyclic statistics are used to analyze the phase coupling relationship of the noise. During the calculation process, a Hanning window function is introduced to weight the sample segments and suppress the spectral leakage effect. The final noise cyclic statistics feature library contains the following metadata: sample segment identifier, cyclic frequency index, cyclic autocorrelation function value, cyclic spectral density matrix, second / third-order cyclic statistics feature vectors, and corresponding calculation timestamps. This feature library adopts a hierarchical storage structure: the top layer is categorized by channel index, the middle layer is grouped by cyclic frequency range, and the bottom layer stores specific feature data, supporting rapid retrieval and updates. To verify the effectiveness of the features, the consistency of the features is tested through random sampling: 10% of the sample segments are randomly selected from the feature library, their cyclic statistics are recalculated, and compared with the original results. When the error exceeds 5%, the feature recalculation process is triggered. Furthermore, a feature dimensionality reduction mechanism is introduced, using principal component analysis to linearly transform the high-dimensional cyclic statistics, extracting the principal components with the first 90% energy as core features, reducing the complexity of subsequent calculations. The final noise cyclic statistics feature library can comprehensively characterize the cyclic stationary properties of noise.

[0043] S504. Establish a noise statistical characteristic model based on the noise cyclic statistics feature library.

[0044] In step S504, it is necessary to explain in detail that when establishing a noise statistical characteristic model based on the noise cyclic statistics feature library, a Gaussian mixture model (GMM) is first used to model the probability density of the cyclic autocorrelation function and cyclic spectral density in the feature library. Specifically, the feature vectors of different cyclic frequency points under the same channel are clustered into several Gaussian components, each representing a typical noise statistical characteristic pattern. The model parameters, including the mean vector, covariance matrix, and mixture weights of each component, are iteratively optimized using the expectation-maximization (EM) algorithm until the model's log-likelihood function converges (e.g., change < 0.01%). To improve the model's adaptability to non-stationary noise, a dynamic component adjustment mechanism is introduced: when the Mahalanobis distance between a newly acquired noise sample and an existing component exceeds a threshold (e.g., > 3 standard deviations), a new Gaussian component is automatically added or similar components are merged to ensure that the model coverage is updated in real time.

[0045] Simultaneously, a nonlinear characteristic sub-model of noise is constructed by combining the characteristics of second-order / third-order cyclic statistics. The kernel density estimation (KDE) method is used to nonparametrically model the phase coupling relationship of the third-order cyclic statistics. By selecting a Gaussian kernel function and optimizing the bandwidth parameter (e.g., using cross-validation to determine the optimal bandwidth), a probability distribution map of the noise phase coupling strength is generated. This sub-model is then fused with a Gaussian mixture model through weighted fusion to form a complete noise statistical characteristic model. The weight coefficients are dynamically allocated based on the feature validity test results: when the test error of the cyclic autocorrelation function is less than 3%, the weight of the corresponding sub-model is increased by 0.2; when the consistency of the third-order cyclic statistics exceeds 95%, its weight is increased by 0.15.

[0046] To verify the model's accuracy, a two-layer verification mechanism is designed: The first layer employs leave-one-out cross-validation, randomly masking 10% of the feature data and using the remaining data to train the model and predict the masked portion. When the prediction error (e.g., root mean square error) exceeds a preset threshold (e.g., 8%), model parameter retraining is triggered. The second layer involves testing in a real-world environment, comparing the model's output noise statistics with actual noise samples. When the signal-to-noise ratio (SNR) estimation error exceeds ±1 dB, the number of Gaussian mixture model components or the bandwidth of the kernel density estimation is adjusted. The final noise statistics model is stored in parameterized form, containing the parameter sets of each Gaussian component, the bandwidth value of the kernel density estimation, and dynamic adjustment rules, supporting real-time access and updates. This model can accurately describe the statistical characteristics of noise in the cyclic frequency domain.

[0047] As an optional embodiment of the present invention, optionally, in step S6, the multi-order cyclic statistical features, periodic trajectory, spatial correlation features, signal energy weight, noise energy weight, and noise statistical characteristic model parameters are fused, and a signal-to-noise ratio estimate is generated using supervised learning, including: S601. Standardize and fuse the multi-order cyclic statistical features, periodic trajectories, and spatial correlation features to generate a standardized feature vector matrix; When standardizing and fusing multi-order cyclic statistics, periodic trajectories, and spatial correlation features, standardization is first performed separately for each feature type. For multi-order cyclic statistics, Z-score standardization is used, which calculates the mean and standard deviation for each feature dimension, subtracts the mean from the original feature value, and divides by the standard deviation, resulting in a mean of 0 and a variance of 1 for the processed feature value. For periodic trajectory features, due to the dimensional differences in trajectory length and consistency coefficient, Min-Max standardization is used, mapping the trajectory length to the [0,1] interval, and normalizing the consistency coefficient to the same range through linear transformation. For spatial correlation features, the maximum correlation coefficient is extracted as the feature value based on the inter-channel correlation coefficient matrix, and its dynamic range is compressed using logarithmic transformation before Z-score standardization is performed. After standardization of each feature type, a feature concatenation matrix is ​​constructed, where rows correspond to sample indices, and columns are arranged in the order of "multi-order cyclic statistics feature group - periodic trajectory feature group - spatial correlation feature group," with each feature group concatenated according to the original dimension order. To eliminate the influence of different feature groups on their dimensions, the concatenated matrix is ​​further standardized along the column direction. This involves independently calculating the mean and standard deviation for each feature column and performing a Z-score transformation. The resulting standardized feature vector matrix has each row representing a standardized representation of a sample across all feature dimensions. The matrix dimension is (number of samples × total number of features), where the total number of features is the sum of the number of multi-order cyclic statistics features, the number of periodic trajectory features, and the number of spatial correlation features. This matrix serves as input to the supervised learning model, effectively balancing the contributions of different feature types to signal-to-noise ratio estimation.

[0048] S602. Construct a supervised learning model based on the standardized feature vector matrix, and use signal energy weight and noise energy weight as prior weights to guide the training of the supervised learning model to learn the nonlinear mapping relationship between features and signal-to-noise ratio, initialize the basic framework for signal-to-noise ratio estimation, and obtain the initialized supervised learning model. In step S602, it is necessary to explain in detail that when constructing a supervised learning model based on the standardized feature vector matrix, support vector regression (SVR) is first selected as the basic model architecture, and the kernel function is radial basis function (RBF) to handle the nonlinear relationship in the feature space. During initialization, signal energy weights and noise energy weights are incorporated into the model training as prior information: specifically, for the standardized feature vector of each sample, the feature contribution is adjusted according to the ratio of signal weight to noise weight of its channel, that is, the feature dimension of the high signal weight channel is multiplied by 1.2 times the weighting coefficient, and the feature dimension of the low noise weight channel is multiplied by 0.8 times the suppression coefficient, thereby strengthening the signal-related features and weakening the noise interference features at the feature level. During the model training stage, the grid search method is used to optimize the hyperparameters, including the gamma value of the RBF kernel (search range [0.01, 10]), the penalty coefficient C (search range [1, 100]), and the insensitive loss parameter ε (search range [0.001, 0.1]), with the mean squared error (MSE) of five-fold cross-validation as the optimization objective. To leverage prior weights to guide model learning, a weighting term is introduced into the loss function: the prediction error of each sample is multiplied by a dynamic adjustment factor of (1 - signal weight + noise weight), making the error contribution of samples with high signal weights larger, thus forcing the model to preferentially fit the feature mapping relationship of the signal-dominant region. After 1000 iterations of training, training stops when the validation set MSE fails to decrease for 20 consecutive iterations, ultimately yielding an initialized supervised learning model. This model can initially establish a nonlinear mapping framework between the feature space and the signal-to-noise ratio (SNR), and its output is an initial SNR estimate in continuous form.

[0049] S603. An attention mechanism is introduced to dynamically weight the fused standardized feature vector matrix, and based on the significance index of the cyclic frequency point and the noise statistical characteristics model parameters, the contribution of each dimension of features in the signal-to-noise ratio estimation is adaptively adjusted to strengthen the weight expression of key features and obtain attention-weighted feature vectors. In step S603, it is necessary to explain in detail that when introducing an attention mechanism to dynamically weight the fused standardized feature vector matrix, an attention weight generation module based on the significance index of cyclic frequency points is first constructed. This module calculates the significance index corresponding to each cyclic frequency point based on the Gaussian component parameters in the noise statistical characteristic model. Specifically, for each Gaussian component, the principal component direction is obtained through the eigenvalue decomposition of its covariance matrix. Combined with the energy projection of the cyclic spectral density onto the principal component direction, the significance score of that frequency point is calculated (the score range is normalized to [0,1]). The calculation process is as follows: First, the eigenvalues ​​and eigenvectors of the covariance matrix are calculated. The cyclic spectral density is projected onto the principal component direction to obtain the projected energy. The projected energy is divided by the sum of the projected energies of all frequency points to obtain the relative energy proportion of that frequency point. Then, the relative energy proportion is mapped to the [0,1] interval using the sigmoid function as the significance score. Simultaneously, the significance score is dynamically adjusted based on the signal energy weight distribution: when the signal energy weight at a certain frequency point is higher than a preset threshold (e.g., >0.5), its significance score is multiplied by a 1.3-fold enhancement coefficient; when the noise energy weight is dominant (e.g., >0.7), it is multiplied by a 0.7-fold suppression coefficient. The final generated attention weight vector has the same column dimensions as the standardized feature vector matrix, and each weight value reflects the importance of the corresponding feature dimension in the signal-to-noise ratio estimation.

[0050] In the feature weighting stage, the attention weight vector is combined with the standardized feature vector matrix using element-wise multiplication: for each eigenvalue in the matrix, the corresponding attention weight is selected based on its feature group (multi-order cyclic statistics / periodic trajectory / spatial correlation) for weighting. To further enhance key features, a phase coupling strength parameter from the noise statistical characteristic model is introduced: when there is significant phase coupling at the cyclic frequency point corresponding to a certain feature dimension (absolute value of the third-order cyclic statistic > 0.2), an additional weight increment of 0.15 is added. Through multi-channel parallel computation, an attention-weighted feature vector is generated, whose dimension is consistent with the original standardized matrix, but the eigenvalue distribution is more concentrated in the signal-dominant region.

[0051] To verify the weighting effect, a feature contribution analysis process was designed: The Pearson correlation coefficient between the feature vectors before and after weighting and the signal-to-noise ratio (SNR) label was calculated. When the correlation coefficient of a certain feature increased by more than 20%, the attention mechanism was confirmed to be effective. Simultaneously, Gradient Weighted Class Activation Map (Grad-CAM) visualization technology was introduced to generate a feature importance heatmap, visually displaying the contribution distribution of each dimension of features to the final SNR estimate. The resulting attention-weighted feature vectors, used as input to the improved model, significantly enhance the estimation accuracy of the supervised learning model in complex noisy environments. Their dynamic weighting characteristics give the model stronger environmental adaptability.

[0052] S604. Use cross-validation to evaluate the performance of the initial supervised learning model. Based on the consistency verification results of periodic trajectory and spatial correlation features, dynamically adjust the structural parameters of the initial supervised learning model to obtain the optimized supervised learning model. When evaluating the performance of the initial supervised learning model using cross-validation, a ten-fold cross-validation strategy is first employed. The standardized feature vector matrix and its corresponding signal-to-noise ratio (SNR) labels are randomly divided into ten subsets, nine of which serve as the training set and the remaining subset as the test set. This process is repeated ten times to ensure that each subset is tested once. In each iteration, prediction error metrics on the test set are recorded, including mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²). The average performance metrics across the ten iterations are then calculated as the basis for evaluating the overall model performance.

[0053] Based on the consistency verification results of periodic trajectory and spatial correlation features, the process of dynamically adjusting the initial supervised learning model structure parameters is as follows: First, for periodic trajectory features, the difference between the trajectory length and consistency coefficient on the training set and the test set is calculated. When the difference exceeds a preset threshold (e.g., trajectory length difference > 15% or consistency coefficient difference > 10%), it is determined that the feature has insufficient environmental adaptability. At this time, the gamma value of the RBF kernel of the corresponding feature dimension in the support vector regression (SVR) model is adjusted to reduce it to 0.8 times the original value to enhance the local fitting ability. For spatial correlation features, the maximum eigenvalue change rate of the correlation coefficient matrix between channels is calculated. When the change rate exceeds 20%, the feature is determined to be unstable. At this time, the penalty coefficient C is increased to 1.2 times the original value to suppress overfitting.

[0054] Simultaneously, based on the error distribution analysis in cross-validation, the model structure was optimized in a targeted manner: when the variance of the MSE on the test set exceeded 1.5 times the variance of the MSE on the training set, the model was deemed to have an overfit risk, and an L2 regularization term was introduced. The regularization coefficient λ was optimized within the range of [0.001, 0.1] through grid search; when the R² value was lower than 0.85, the model was deemed to be underfit, and the search range of the gamma value of the RBF kernel was expanded to [0.001, 20], and the adjustment step size of the insensitive loss parameter ε was increased to 0.01. After each parameter adjustment, ten-fold cross-validation was re-executed until the model's MSE on the test set did not decrease for three consecutive cycles and the R² value stabilized above 0.9.

[0055] To verify the effectiveness of the model structure adjustment, a dual-index verification mechanism was designed: the first index is feature consistency verification, which calculates the Pearson correlation coefficients of periodic trajectory features and spatial correlation features before and after adjustment. When the correlation coefficient increases by more than 10%, the direction of parameter adjustment is confirmed to be correct. The second index is prediction stability verification, which statistically analyzes the MSE fluctuation range of the adjusted model in five consecutive cross-validations. When the fluctuation range shrinks to less than 60% of the original value, the model stability is determined to be significantly improved. The final optimized supervised learning model has structural parameters including the optimized RBF kernel gamma value (e.g., 0.52), penalty coefficient C (e.g., 28.6), insensitive loss parameter ε (e.g., 0.035), and regularization coefficient λ (e.g., 0.018). This model can maintain stable signal-to-noise ratio estimation performance in complex noise environments.

[0056] S605. Based on the optimized supervised learning model, the signal-to-noise ratio (SNR) of the attention-weighted feature vector is estimated. The dynamically allocated signal energy weights and noise energy weights are combined for weighted fusion to generate an SNR estimate.

[0057] In step S605, it is necessary to explain in detail that when calculating the signal-to-noise ratio (SNR) of the attention-weighted feature vector based on the optimized supervised learning model, the attention-weighted feature vector generated in stage S603 is first input into the SVR model optimized in stage S604. The model maps the feature space to a high-dimensional nonlinear space through the RBF kernel function, and constructs the decision boundary using the gamma value (0.52), penalty coefficient C (28.6), and insensitive loss parameter ε (0.035) optimized during the training stage. During the calculation process, for each sample's weighted feature vector, the model calculates its similarity to the support vector through the kernel function, and combines the optimized regularization coefficient λ (0.018) to balance empirical risk and structural risk, outputting the initial SNR estimate.

[0058] To improve estimation accuracy, a weighted fusion method is used, combining dynamically allocated signal energy weights and noise energy weights. Specifically, the initial estimate for each sample is adjusted twice according to the ratio of signal energy weight to noise energy weight for its channel. When the signal energy weight is higher than the noise energy weight (e.g., signal weight > 0.6), the initial estimate is multiplied by an enhancement factor of 1.15; when the noise energy weight is dominant (e.g., noise weight > 0.55), it is multiplied by a suppression factor of 0.85. Simultaneously, the phase coupling strength parameter from the noise statistical characteristic model is introduced as a correction term: if a sample's corresponding cyclic frequency point exhibits significant phase coupling (absolute value of the third-order cyclic statistic > 0.2), an additional weight increment of 0.1 is added to enhance the estimation reliability of the signal-dominant region.

[0059] The weighted fusion process is achieved through sample-by-sample calculation: for each sample, an initial estimate is first obtained in the SVR model based on its feature vector, and then the signal / noise energy weights are dynamically adjusted and the phase coupling correction term is combined to finally generate a weighted signal-to-noise ratio estimate.

[0060] As an optional embodiment of the present invention, the expression for generating the signal-to-noise ratio estimate in step S605 is optionally: in, This represents the signal-to-noise ratio estimate. This represents the activation function. Indicates the number of dimensions. Indicates the first Attention weight coefficients for dimensional features Indicates the first Nonlinear transformation function of dimensional features, Represents the standardized eigenvector matrix. Indicates the coefficient of the bias term. It represents the significance index of the cycle frequency point.

[0061] Example 2 A blind signal-to-noise ratio estimation system based on cyclostationary characteristics includes: processor; Memory used to store processor-executable instructions; The processor is configured to implement a blind signal-to-noise ratio estimation method based on cyclostationary characteristics when executing executable instructions.

[0062] It should be noted that the computer device includes a processor, a memory, and may also include one or more of a multimedia component, an input / output (I / O) interface, and a communication component.

[0063] The processor controls the overall operation of the computer device to complete all or part of the steps in the blind signal-to-noise ratio estimation method based on cyclostationary characteristics.

[0064] Memory is used to store various types of data to support the operation of the computer device. This data may include, for example, instructions for any application or method used to operate on the computer device, as well as application-related data. Memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0065] The multimedia component may include a screen and an audio component, wherein the screen may be, for example, a touch screen, and the audio component is used to output and / or input audio signals; for example, the audio component may include a microphone for receiving external audio signals, the received audio signals may be further stored in memory or transmitted via a communication component; the audio component may also include at least one speaker for outputting audio signals.

[0066] I / O interfaces provide interfaces between the processor and other interface modules, such as keyboards, mice, buttons, etc.; these buttons can be virtual buttons or physical buttons.

[0067] The communication component is used for wired or wireless communication between the computer device and other devices; wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, 4G or 5G, or one or more combinations thereof, and the corresponding communication component may include: Wi-Fi module, Bluetooth module, NFC module, mobile communication module.

[0068] As a preferred embodiment, the computer device may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above-described blind signal-to-noise ratio estimation method based on cyclostationary characteristics.

[0069] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A blind signal-to-noise ratio estimation method based on cyclostationary characteristics, characterized in that, The method includes: S1. Extract multi-order cyclic statistics features from the received signal and filter the cyclic frequency points of the signal by jointly analyzing second-order and higher-order cyclic statistics. S2. Based on the multi-order cyclic statistical characteristics, the received signal is subjected to time-frequency transformation, and the periodic trajectory of the signal energy in the time-frequency domain is located by combining cyclic frequency matched filtering. S3. In a multi-channel scenario, a spatial-cyclic frequency joint filter is constructed using the spatial correlation characteristics of the cyclic frequency points to obtain spatial correlation characteristics. S4. Based on the significance index of the cyclic frequency point, dynamically allocate the energy weights of the signal and noise, and optimize the weight allocation rules through adaptive calibration to generate dynamically allocated signal energy weights and noise energy weights. S5. Collect noise samples during the no-signal period in the received signal and learn their statistical characteristics to construct a noise statistical characteristic model. S6. Integrate the multi-order cyclic statistical features, periodic trajectory, spatial correlation features, signal energy weight, noise energy weight, and noise statistical characteristic model parameters, and use supervised learning to generate a signal-to-noise ratio estimate.

2. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 1, characterized in that, In step S1, multi-order cyclic statistics features are extracted from the received signal, and the cyclic frequency points of the signal are screened by jointly analyzing second-order and higher-order cyclic statistics, including: S101. The received signal is segmented and preprocessed, and a sliding window is used to obtain a sub-signal sequence that satisfies the cyclic stationarity assumption. S102. Calculate the second-order cyclic statistical characteristics based on the sub-signal sequence; S103. Extract the higher-order cyclic statistics features of the sub-signal sequence; S104. Perform joint analysis on the second-order cyclic statistics features and the higher-order cyclic statistics features to obtain the cyclic frequency points.

3. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 1, characterized in that, In step S2, the received signal is subjected to time-frequency transformation based on the multi-order cyclic statistical characteristics, and the periodic trajectory of the signal energy in the time-frequency domain is located by combining cyclic frequency matched filtering. S201. Based on the cyclic frequency point, the received signal is reconstructed in the time-frequency domain, and the short-time Fourier transform method is used to dynamically adjust the window function length to balance the time-frequency resolution, generating an initial time-frequency energy distribution map. S202. Based on the initial time-frequency energy distribution map, construct a cyclic frequency matched filter bank. Each filter performs frequency domain weighting on the corresponding cyclic frequency to enhance the signal energy response corresponding to the cyclic frequency point and suppress noise interference from non-cyclic frequencies, thus forming a time-frequency energy enhancement map after matched filtering. S203. Based on the periodic distribution characteristics of the time-frequency energy enhancement map combined with the multi-order cyclic statistics, the periodic trajectory of the signal energy is located by the time-frequency domain peak detection and trajectory tracking algorithm, and isolated noise points are removed by connected component analysis to retain continuous and stable periodic trajectories, thereby generating a periodic trajectory candidate set. S204. Perform multi-segment signal consistency checks on the candidate set of periodic trajectories, verify the stability of the periodic trajectory in different time periods by comparing with a sliding window, and then dynamically adjust the time-frequency transformation parameters and filter response by combining the significance index of the cyclic frequency points to optimize the accuracy and robustness of the periodic trajectory positioning, thus forming an optimized periodic trajectory. S205. Perform time-frequency-cyclic frequency joint analysis on the optimized periodic trajectory and the statistical characteristics of the cyclic frequency point to verify the correspondence between the energy distribution of the periodic trajectory and the cyclic frequency point, ensure that the periodic characteristics of the periodic trajectory are consistent with the characteristics of the cyclic frequency point, and generate a periodic trajectory feature set in the time-frequency domain.

4. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 3, characterized in that, The expression for the trajectory tracking algorithm in step S203 is: in, Indicates time and frequency Peak detection results at the location, Indicates time and frequency The signal energy value at that location, Indicates the dynamic peak threshold. This indicates the frequency point in the frequency dimension. Centered on, with a width of 2 Within a local neighborhood, the time-frequency energy matrix The maximum value, Indicates the frequency neighborhood window parameters. Represents the frequency index variable within the neighborhood. This represents the results of connected component analysis. This indicates the peak detection result. Indicates the parameters of the time neighborhood window. This represents the offset within the time neighborhood window. This represents the threshold for the minimum number of points in a connected component. This represents the set of generated periodic trajectories. Represents the periodic trajectory of the first... Time index of each trajectory point Represents the periodic trajectory of the first... Frequency index of trajectory points Representing coordinates It belongs to a continuous and stable trajectory. This represents the frequency index of two consecutive trajectory points. Indicates the maximum permissible frequency jump range. This represents the time index of two consecutive trajectory points. Represents the cycle frequency The corresponding cycle duration.

5. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 1, characterized in that, The spatial correlation features obtained in step S3 include: S301. Using the cyclic frequency points and periodic trajectories, perform spatial domain correlation pre-analysis on the received signal, calculate the mutual cyclic autocorrelation function and the signal similarity between the mutual cyclic spectral density quantization channels, identify the spatial distribution pattern of the multi-channel signal and the direction of potential signal sources, and generate an initial constraint set of spatial correlation features. S302. Based on the initial constraint set of spatial correlation features and the statistical characteristics of the cyclic frequency points, a spatial-cyclic frequency joint filter is constructed. Combining the characteristics of the spatial covariance matrix of multi-channel signals, the weights of the spatial-cyclic frequency joint filter are optimized by the minimum variance distortionless response algorithm. S303. Apply the optimized space-cyclic frequency joint filter to the multi-channel received signal. By analyzing the energy distribution of the filtered received signal in the spatial dimension, extract the spatial correlation features and generate an initial set of spatial correlation features.

6. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 1, characterized in that, The generation of dynamically allocated signal energy weights and noise energy weights in step S4 includes: S401. Based on the significance index of the cyclic frequency points, initialize the basic energy weight distribution of signal and noise in the received signal. Assign higher initial signal weights to cyclic frequency points with high significance and lower initial noise weights to cyclic frequency points with low significance, thus forming an initial signal energy weight distribution. S402. Based on the periodic trajectory and spatial correlation characteristics, the initial signal energy weight is calibrated in multiple dimensions to obtain the signal / noise weight after multi-dimensional calibration. S403. Based on the signal / noise weights after multi-dimensional calibration, the received signal is processed in segments using a sliding window. The actual effect of weight allocation in different time periods is compared to obtain the feedback error. The weight allocation rules are dynamically adjusted based on the feedback error to obtain the adaptively calibrated weight allocation rules. S404. Based on the adaptively calibrated weight allocation rule, the weighted average algorithm is applied to calculate the energy weight distribution of signal and noise in the received signal, and dynamically allocated signal energy weight and noise energy weight are generated.

7. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 1, characterized in that, In step S5, noise samples are collected during the signal-free periods of the received signal, and their statistical characteristics are learned to construct a noise statistical characteristic model, including: S501. Based on the periodic trajectory disappearance time period and the signal energy weight distribution threshold, detect the no-signal time period in the received signal, and synchronously collect multi-channel noise samples during the time period; S502. Perform a segmented stationarity test on the noise samples and use the moving variance analysis method to screen out the noise sample segments that satisfy the stationarity assumption. S503. Extract the multi-order cyclic statistics features of the noise sample segments that have passed the test, calculate their cyclic autocorrelation function and cyclic spectral density, and construct a noise cyclic statistics feature library. S504. Establish a noise statistical characteristic model based on the noise cyclic statistics feature library.

8. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 1, characterized in that, In step S6, the multi-order cyclic statistics features, periodic trajectory, spatial correlation features, signal energy weight, noise energy weight, and noise statistical characteristic model parameters are fused together, and a signal-to-noise ratio estimate is generated using supervised learning, including: S601. Standardize and fuse the multi-order cyclic statistical features, periodic trajectory and spatial correlation features to generate a standardized feature vector matrix; S602. Construct a supervised learning model based on the standardized feature vector matrix, and use signal energy weight and noise energy weight as prior weights to guide the training of the supervised learning model to learn the nonlinear mapping relationship between features and signal-to-noise ratio, initialize the basic framework for signal-to-noise ratio estimation, and obtain the initialized supervised learning model. S603. An attention mechanism is introduced to dynamically weight the fused standardized feature vector matrix, and based on the significance index of the cyclic frequency point and the parameters of the noise statistical characteristic model, the contribution of each dimension of features in the signal-to-noise ratio estimation is adaptively adjusted to strengthen the weight expression of key features and obtain the attention-weighted feature vector. S604. Evaluate the performance of the initial supervised learning model using cross-validation. Based on the consistency verification results of the periodic trajectory and spatial correlation features, dynamically adjust the structural parameters of the initial supervised learning model to obtain the optimized supervised learning model. S605. Based on the optimized supervised learning model, the signal-to-noise ratio (SNR) of the attention-weighted feature vector is estimated, and the dynamically allocated signal energy weights and noise energy weights are combined for weighted fusion to generate an SNR estimate.

9. The blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in claim 8, characterized in that, The expression for generating the signal-to-noise ratio estimate in step S605 is: in, This represents the signal-to-noise ratio estimate. This represents the activation function. Indicates the number of dimensions. Indicates the first Attention weight coefficients for dimensional features Indicates the first Nonlinear transformation function of dimensional features, Represents the standardized eigenvector matrix. Indicates the coefficient of the bias term. It represents the significance index of the cycle frequency point.

10. A blind signal-to-noise ratio estimation system based on cyclostationary characteristics, characterized in that, The system includes: processor; Memory used to store processor-executable instructions; The processor is configured to implement the blind signal-to-noise ratio estimation method based on cyclostationary characteristics as described in any one of claims 1 to 9 when executing the executable instructions.

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