Dynamic channelized spectrum detection method based on eigenvalue fusion

Abstract

This invention relates to the field of radar signal processing, specifically to a dynamic channelized spectrum detection method based on eigenvalue fusion. The method includes: obtaining a 3D observation matrix from the 1st subband signal output by multi-channel conversion of a single-channel signal; constructing a sampling covariance matrix; performing eigenvalue decomposition on the sampling covariance matrix; constructing a test statistic using the maximum eigenvalue, average eigenvalue, and minimum average eigenvalue across subbands through fusion parameters; deriving a detection threshold based on the false alarm probability, fusion parameters, and sampling parameters to achieve blind detection independent of noise power; and further proposing an improved algorithm that doubles the number of effective samples by performing IQ orthogonal decomposition on the subband signal, improving the eigenvalue estimation accuracy under small sample conditions. Compared to existing technologies, this method achieves higher detection performance under low signal-to-noise ratio and small sample conditions, better meeting the engineering application requirements of complex electromagnetic environments.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing, specifically to a dynamic channelized spectrum detection method based on eigenvalue fusion that can be used for subband spectrum detection in dynamic digital channelized receivers. Background Technology

[0002] With the increasing complexity of the electromagnetic environment in modern electronic warfare, dynamic digital channelized receivers can dynamically adapt to signals with large instantaneous bandwidths, enabling the extraction and separation of multiple signals within a broadband signal. Accurately determining the presence of signals in sub-channels is a crucial step in subsequent signal processing within dynamic digital channelized receivers.

[0003] Current classic spectrum detection methods mainly include energy detection, matched filtering, and cyclostationary feature detection. Energy detection is simple to implement, but in low signal-to-noise ratio environments, the signal energy and noise energy are not much different, resulting in a significant decrease in detection performance. It is difficult to provide a reliable basis for subsequent signal reconstruction, and it requires threshold setting based on noise variance, making it highly susceptible to noise uncertainty.

[0004] In recent years, eigenvalue detection methods based on random matrix theory have attracted widespread attention because they do not require any prior information about the signal and noise. Algorithms such as Maximum-Minimum Eigenvalue (MME), Average-Maximum Eigenvalue (AME), Different Between the Maximum and Minimum Eigenvalue (DMM), and Minimum-Average Maximum Eigenvalue (MAME) have emerged. However, existing algorithms often limit themselves to extracting only local information such as the maximum, minimum, or average eigenvalues ​​when constructing test statistics, failing to effectively utilize the complementary advantages of eigenvalues ​​of different dimensions in distinguishing signals from noise. In practical scenarios with limited observation time, the number of samples is often small, and the actual empirical eigenvalue distribution deviates from the theoretical limiting distribution, leading to threshold setting failure and decreased detection performance. Summary of the Invention

[0005] This invention addresses the shortcomings and deficiencies of existing technologies by providing a dynamic channelized spectrum detection method based on feature value fusion that achieves higher detection performance under low signal-to-noise ratio and small sample conditions, realizes detection without relying on noise prior information, and better meets the engineering application requirements in complex electromagnetic environments.

[0006] The objective of this invention is achieved as follows: A dynamic channelized spectrum detection method based on feature value fusion, characterized by comprising the following steps: Step 1: Channelization Decomposition: The broadband received signal is channelized using an analysis filter bank to obtain... Parallel narrowband subband output signal Each sub-band output signal is composed of the useful signal and a signal with a mean of 0 and a variance of . Composed of superimposed Gaussian noise; Step 2: Data Matrix Construction: For the first... Path with output signal Dimension transformation is performed using the interval sampling method. Single-channel observation vector transformed into Multi-channel sampling data matrix ; The first in the matrix Line channel signal Each channel contains One sampling point, and The selection must meet the following requirements. The asymptotic conditions are used to ensure the applicability of subsequent random matrix theory; Step 3: Calculation of the sampling covariance matrix: Calculate the first sampled covariance matrix based on the multi-channel sampling data matrix. Sampling covariance matrix of the route: (1), when When established, the received signal contains only noise. (2), at this time The Wishart random matrix has its largest eigenvalue following a first-order Tracy-Widom distribution after centering and scaling. ; Step 4: Eigenvalue extraction and test statistic construction: Sampling covariance matrix for each sub-band Perform eigenvalue decomposition to obtain Given 1 set of eigenvalues, calculate the maximum eigenvalue of the current sub-band. Average eigenvalues and across all Minimum value of the mean of the eigenvalues ​​of each sub-band Introducing fusion parameters Construct the test statistic: (3); Step 5: Detection threshold calculation: In Assuming, The Wishart random matrix has a centralized scaling statistic for its largest eigenvalue that follows a first-order Tracy-Widom distribution. Based on the set false alarm probability fusion parameters and matrix parameters , The derivation yields -Analytical expression for the detection threshold of the MAMAE algorithm: (4), In the formula , , Let Tracy-Widom be the cumulative distribution function. This indicates the number of channels after the sub-band output signal is converted. This represents the number of sampling points per channel, and the detection threshold depends only on the false alarm probability. fusion parameters and sampling parameters , It is independent of the received signal power and noise power; Step Six: Spectral Decision: Apply the test statistic With detection threshold Comparison: When When, determine if a signal exists in the sub-band; when When this happens, it is determined that there is no signal in the sub-band.

[0007] In step four of this invention, the fusion parameters The optimal selection criterion is: fusion parameters The smaller the value of , the higher the detection probability under low signal-to-noise ratio; theoretical derivation proves that the ratio of the test statistic to the decision threshold It is about A monotonically decreasing function. The detection performance is optimal.

[0008] In step three of this invention, IQ- is further proposed. -MAMAE improved algorithm, Decompose into I components and Q components, and stack the I components and Q components into a real matrix: (5), (6), In the formula, It is the carrier frequency. It is the sampling frequency. The I and Q components of each sub-band are stacked sequentially to form... 3D matrix : (7); IQ- -The test statistic form of MAMAE is similar to -MAMAE is the same, but the number of matrix rows is different. Expand to The corresponding detection threshold is updated to the threshold expression above. Replace with The form of IQ decomposition doubles the number of effective samples, improving the accuracy of feature value estimation and detection performance under small sample conditions.

[0009] The beneficial effects of this invention are as follows: 1. This invention introduces fusion parameters and fuses data in a power-law manner. The maximum eigenvalue and the average eigenvalue can simultaneously perceive the concentration of signal energy in the direction of the strongest feature and the overall shift of all eigenvalues, fully mining the overall structural information of the covariance matrix and overcoming the inherent limitations of a single feature; 2. This invention uses the minimum average eigenvalue across subbands as a benchmark, and the detection threshold expression is only related to the false alarm probability. fusion parameters and sampling parameters , 1. It is independent of the received signal power and noise power, enabling blind detection unaffected by noise; 2. The IQ-MAMAE invention doubles the effective sample number by orthogonally decomposing the sub-band signal, significantly improving the eigenvalue estimation accuracy under small sample conditions, and showing outstanding advantages in scenarios with limited sampling resources; 3. Theoretical analysis shows that the fusion parameters are independent of the received signal power and noise power, enabling blind detection unaffected by noise; 4. Theoretical analysis shows that the fusion parameters are independent of the received signal power and noise power, enabling blind detection unaffected by noise; 5. The invention is related to the received signal power and noise power, enabling blind detection unaffected by noise; 6. The invention is related to the received signal power and noise power, enabling blind detection unaffected by noise; 7. The invention is related to the received signal power and noise power, enabling blind detection unaffected by noise; 8. The invention is related to the received signal power and noise power, enabling blind detection unaffected by noise; 9 A smaller threshold indicates better detection performance. Simulation results validated the performance of the proposed algorithm across four dimensions: detection threshold effectiveness, different signal-to-noise ratios, different numbers of sampling points, and different numbers of matrix rows. -MAMAE's advantages are most prominent in low signal-to-noise ratio and small sample scenarios, which fully demonstrates its engineering applicability. Attached Figure Description

[0010] Figure 1 This is a flowchart of the present invention.

[0011] Figure 2 For different The curve showing the relationship between detection probability and signal-to-noise ratio under various values.

[0012] Figure 3 A comparison chart showing the relationship between detection probability and signal-to-noise ratio for different algorithms.

[0013] Figure 4 Detection probability and number of sampling points for different algorithms A comparison diagram of the relationships.

[0014] Figure 5 Detection probabilities and matrix row numbers for different algorithms A comparison diagram of the relationships. Detailed Implementation

[0015] To make the objectives, features, and advantages of the present invention more apparent and understandable, the present invention will be further described below in conjunction with the accompanying drawings and embodiments: The specific implementation method of the dynamic channelized spectrum detection method based on feature value fusion in this example is described as follows: Assume the number of channels in the dynamic digital channelization receiver system is . Input signal After analyzing the filter bank, we can obtain... Sub-band output signal of the path ; It consists of two parts: signal and noise. (8), of which Indicates the first Path channel in the first The signal obtained by sampling at each time point This represents the Gaussian noise in the i-th sub-channel, with a mean of 0 and a variance of . ; Spectral detection of each subband in dynamic channelization can be represented as a binary hypothesis testing problem: Assuming the channel contains only noise, Assume the channel contains useful signals and noise.

[0016] In dynamic digital channelization architectures, the received data processed by each sub-band is typically in single-channel format. To obtain the sampling covariance matrix of the received signal in each sub-band, it is necessary to convert the single-channel received signal into a multi-channel received format, that is,... The observed data vector is converted into The data matrix format; This example uses interval sampling to process the output data of each sub-channel. The output signal of each sub-band By using the interval sampling method, the following observation data matrix can be obtained: (9), In the formula Indicates a single-channel signal After performing multi-channel conversion on a single-channel signal, each channel's signal contains... One sampling point.

[0017] Construct the sampling covariance matrix, the first... The sampling covariance matrix of the sub-band output signal is: (2), when Under the condition that it holds true, if only noise exists in the received signal, then the sampling covariance matrix can be expressed as: (10).

[0018] When the received signal contains only noise, according to the theory of random matrices, the sampling covariance matrix is ​​a Wishart random matrix, and its eigenvalues ​​satisfy the following theorem: Theorem 1: Assume the noise is a real signal. make (11), (12) (13) Assumption , , Represents a random matrix The largest eigenvalue, then Follows a first-order Tracy-Widom distribution .

[0019] Theorem 2: Assume the noise is a complex signal. make (14) (15) (16) Assumption , , Represents a random matrix The largest eigenvalue, then Follows a 2nd-order Tracy-Widom distribution .

[0020] , hour, (17) (18) The expression for the Tracy-Widom distribution function is quite complex, and its first-order cumulative distribution function... The inverse function can be obtained by looking up a table for the discrete values ​​of the first-order Tracy-Widom distribution. The value of .

[0021] Previous algorithms often used only some eigenvalues ​​as detection statistics, neglecting other eigenvalues ​​in the covariance matrix, making their detection performance sensitive to the number of sampling points and signal-to-noise ratio. This invention introduces a fusion parameter. By using multiple eigenvalues ​​to achieve the ratio combination of eigenvalues, the test statistic is: (3), In the formula For fusion parameters, This represents the largest eigenvalue of the subband sampling covariance matrix. This represents the minimum value of the average of the eigenvalues ​​of all sub-bands. This represents the average characteristic value.

[0022] By introducing adjustable fusion parameters This allows the test statistics to simultaneously perceive two types of complementary information: the maximum eigenvalue reflects the concentration of signal energy in the direction of strongest feature, making it more sensitive to single strong signal scenarios; the mean eigenvalue reflects the overall shift of all eigenvalues, making it more robust to signals with multiple components of similar power. All test statistics are cross-subband estimators. As a benchmark, the influence of unknown noise power is eliminated.

[0023] As a test threshold, when the statistic Exceeding the preset threshold If an authorized user exists, the system determines that the spectrum is available; otherwise, it determines that the spectrum is idle. The decision rule can be expressed as follows: (19) The detection threshold is based on the false alarm probability. To derive, Substituting the values ​​and using the approximate expression for the average eigenvalue, we can obtain: By Theorem 1, for the largest eigenvalue... Use parameters , Standardization yields -MAMAE algorithm detection threshold analytical expression: (20) in, This indicates the number of channels after the sub-band output signal is converted. This represents the number of sampling points per channel. Substituting into Theorem 1: (twenty one), (twenty two), right By inverting the function, we can obtain the detection threshold: (twenty three), It is the inverse function of the Tracy-Widom cumulative distribution function; the detection threshold depends only on the false alarm probability. fusion parameters and sampling parameters , It is independent of the received signal power and noise power, thus enabling blind signal detection; Signal decomposition can obtain more correlation information and increase the number of logical signals: make For the first Sub-channels Matrix, Decomposed into I components and Q components: (5), (6), In the formula For carrier frequency, This is the sampling frequency. (Through recombination) Such a signal vector can be used to construct a new one. 3D matrix: (7), IQ- -The test statistic form of MAMAE is similar to - Same as MAMAE. The number of rows in the new sample covariance matrix is ​​from... Expand to , number of columns The corresponding detection threshold remains unchanged; it is updated to the value in the formula. Replace with Format: (twenty four), IQ decomposition doubles the number of effective samples, improving the accuracy of eigenvalue estimation under small sample conditions.

[0024] The value of the fusion parameter directly determines the preference of the test statistic for extracting signal features, thus affecting the detection probability under low signal-to-noise ratio. .

[0025] To determine The optimal value of the test statistic will be determined by... With detection threshold Divide and rearrange. make (25), (26) The ratio can then be expressed in the form of a standard exponential function: (27) when When the assumption holds, let the unique non-zero eigenvalue of the signal covariance matrix be... The noise variance is Define subband signal-to-noise ratio (28) The basis can be derived as follows: (29) Under low signal-to-noise ratio conditions, the preceding term Slightly greater than 1, while the centralization parameter Strictly greater than after expansion This results in the latter term always being less than 1, and the product of the two terms ensures that the basis strictly satisfies... .

[0026] right about Taking the partial derivative, we get .because Must have The partial derivatives are always less than 0, that is It is about It is a monotonically decreasing function.

[0027] The larger the threshold, the easier it is for a weak signal to exceed the detection limit and be successfully detected. The lower the signal-to-noise ratio, the higher the detection probability. This is verified by both theoretical derivation and simulation. Time-based detection offers the best performance and is recommended for engineering implementation. .

[0028] -MAMAE and IQ- The MAMAE algorithm differs only in the calculation of the covariance matrix; the specific steps are as follows: 1) Channelize the input signal to obtain the sub-channel output signal; 2) The sub-band output signal is transformed into a multi-dimensional multi-channel sampling data matrix by using the interval sampling method; 3) Calculate the eigenvalue matrix of the sampling covariance matrix; 4) Calculate the detection statistic using the maximum, minimum, and average eigenvalues. ; 5) Utilize false alarm probability and fusion parameters and the sampled data matrix and Calculate the detection threshold ; 6) Compare the detection statistic with the detection threshold: If If so, it indicates that a signal exists; if If the signal is zero, it indicates that no signal exists.

[0029] The effects of this invention can be further illustrated by the following simulations: Simulation Experiment 1: Fusion parameters The impact on detection performance was compared under different signal-to-noise ratio conditions through 10,000 Monte Carlo simulations. -MAMAE and IQ- -MAMAE in different The detection probability for values ​​[0.1, 0.3, 0.5, 0.7, 0.9]. like Figure 2 The results shown indicate that the detection probability increases with... The decrease leads to an increase. The system achieved optimal detection performance, consistent with theoretical analysis.

[0030] Simulation Experiment 2: Performance comparison of different detection algorithms, fixed Matrix parameters , False alarm probability The signal-to-noise ratio ranges from -25 to 10 dB, compared to MME, AME, MAME, DMME, -MAMAE and IQ- - The MAMAE algorithm performs 10,000 Monte Carlo simulations under each set of conditions; like Figure 3 The results show that IQ- - The MAMAE algorithm has the most outstanding performance advantage across the entire signal-to-noise ratio range, and its detection probability is significantly higher than other algorithms in regions with a signal-to-noise ratio below -15 dB. -MAMAE followed closely behind, and together they constituted the top tier of performance.

[0031] The signal-to-noise ratio was further fixed at -13 dB. , , Number of sampling points 10,000 Monte Carlo simulations were performed with a step size of 50 between 300 and 3,000 to analyze the detection performance of each algorithm as the number of sampling points changes.

[0032] like Figure 4 The results show that IQ- -MAMAE algorithm in The detection probability is significantly higher than other comparative algorithms. It can achieve a high detection probability without relying on a large amount of sampling resources, making it more suitable for practical application scenarios where sampling resources are limited in digital channelized receivers.

[0033] In fixed , , Number of rows in the sampling matrix 10,000 Monte Carlo simulations were performed, increasing by a step size of 2 between 2 and 14, to analyze the detection performance of each algorithm with the number of sampled rows.

[0034] from Figure 5 It can be seen from IQ- The MAMAE algorithm is most efficient at utilizing low-dimensional sampled data and can achieve high-performance detection even when the number of rows in the subband sampling matrix is ​​small.

[0035] In summary, the simulation results fully verify the effectiveness of the proposed invention from four dimensions: detection threshold validity, different signal-to-noise ratios, different numbers of sampling points, and different numbers of matrix rows. -MAMAE and IQ- The performance advantages of the MAMAE algorithm demonstrate its engineering applicability in scenarios with limited sampling resources.

Claims

1. A dynamic channelized spectrum detection method based on eigenvalue fusion, characterized in that, include: Step 1: Channelization decomposition. The broadband received signal is processed by an analysis filter bank to obtain... Parallel narrowband subband output signal ; Step 2: Data matrix construction, for the first... Path with output signal Dimension transformation is performed using the interval sampling method. Transformation of a single-channel observation vector into Multi-channel sampling data matrix; Step 3: Calculate the sampling covariance matrix. Calculate the first covariance matrix based on the multi-channel sampling data matrix. Sampling covariance matrix of the route ; Step 4: Eigenvalue extraction and test statistic calculation, based on the sampling covariance matrix of each sub-band signal. Perform feature decomposition to obtain One eigenvalue; Calculate the largest eigenvalue Average eigenvalues And across all Minimum value of the mean of the eigenvalues ​​of each sub-band Construct the test statistic When the received signal contains only noise, according to the theory of random matrices, the sampling covariance matrix is ​​a Wishart random matrix. Step 5: Calculate the detection threshold based on the set false alarm probability. fusion parameters Matrix parameters and The detection threshold is derived using the Tracy-Widom distribution. The parsing expression; Step Six: Spectral Decision. The test statistic is compared with the detection threshold to determine whether the signal exists, i.e., when... If the signal is present, determine if a signal exists; otherwise, determine if a signal does not exist.

2. The dynamic channelized spectrum detection method based on feature value fusion according to claim 1, characterized in that: The multi-channel conversion process of the single-channel signal in step two is as follows: Assume the system is divided into channels of number . Then the input signal After analytical filtering by the analytical filter bank, its output can obtain... The path has an output, which will be the first The output signal of the circuit is represented as The spectrum detection process can be viewed as a binary hypothesis problem: （30）， In the formula, the first... Path channel in the first The signal obtained by sampling at each time point Representing the The Gaussian noise in the path channel has a mean of 0 and a variance of . , The state indicates that the channel contains only noise. The state indicates that there are useful signals present in the channel in addition to noise; No. Each child has an output signal After interval sampling processing, the result is obtained 3D observation matrix This yields the observation matrix shown below: ， In the formula Indicates a single-channel signal After performing multi-channel conversion on a single-channel signal, each channel's signal contains... One sampling point.

3. The dynamic channelized spectrum detection method based on feature value fusion according to claim 2, characterized in that, The process of constructing the sampling covariance matrix in step three is as follows: No. The sampling covariance matrix of the sub-band output signal is: （2）， when When established, the received signal contains only noise, and the sampling covariance matrix is: （10）， at this time It is a Wishart random matrix.

4. The dynamic channelized spectrum detection method based on feature value fusion according to claim 3, characterized in that, The construction of the test statistic in step four is as follows: （3）， In the formula For fusion parameters, The largest eigenvalue of the current sub-band sampling covariance matrix. This represents the average eigenvalue of the current sub-band. For all The minimum value of the mean of the eigenvalues ​​of each sub-band; Estimation across subbands As a benchmark, the influence of unknown noise power is eliminated.

5. The dynamic channelized spectrum detection method based on feature value fusion according to claim 1, characterized in that, Fusion parameters The smaller the value of , the higher the detection probability under low signal-to-noise ratio, and the ratio of the test statistic to the decision threshold. It is about A monotonically decreasing function. The detection performance is optimal.

6. The dynamic channelized spectrum detection method based on feature value fusion according to claim 1, characterized in that, The analytical expression for the detection threshold in step three is: （4）， In the formula , , Let be the cumulative distribution function of the Tracy-Widom distribution. This indicates the number of channels after the sub-band output signal is converted. This represents the number of sampling points per channel. The detection threshold depends only on the false alarm probability and the fusion parameters. and sampling parameters , It is independent of the received signal power and noise power.

7. The dynamic channelized spectrum detection method based on feature value fusion according to claim 1, characterized in that: Step three also includes IQ- -The improved MAMAE algorithm is as follows: Will Decompose it into I components and Q components, and stack the I components and Q components into a real matrix, as shown in the following expression: （5）， （6）， In the formula, It is the carrier frequency. It is the sampling frequency, which stacks the I and Q components to construct a new... 3D matrix: （7）， IQ- -The test statistic form of MAMAE is similar to -MAMAE is the same, but the number of matrix rows is different. Expand to The corresponding detection threshold is updated to the threshold expression above. Replace with In the form of.

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