A method for non-circular source number detection under colored noise

Abstract

The application provides a non-circular source number detection method under colored noise, comprising: constructing a compensated sample covariance matrix based on observation samples; Takagi decomposition is performed on the compensated sample covariance matrix to obtain sample canonical correlation coefficients; an estimated value of parent canonical correlation coefficients is constructed based on the sample canonical correlation coefficients; a log-likelihood function is constructed based on the sample canonical correlation coefficients and the estimated value; a minimum description length statistic is constructed based on the log-likelihood function; and the number of parent canonical correlation coefficients when the minimum description length statistic is minimized is taken as an estimated value of the non-circular source number. The application fully describes the statistical characteristics of non-circular observation samples by constructing a log-likelihood function fusing sample canonical correlation coefficients and estimated parent canonical correlation coefficients, and designs a statistic based on the minimum description length criterion, so that the non-circular source number can be accurately estimated under a colored noise environment, and necessary guarantees are provided for practical application scenarios such as direction of arrival estimation and wave velocity formation.

Description

A method for detecting the number of non-circular sources under colored noise Technical Field

[0001] This invention relates to the field of wireless communication technology, and more particularly to a method for detecting the number of non-circular signal sources under colored noise. Background Technology

[0002] In the field of array signal processing, source number estimation is a key technology that directly affects the performance of super-resolution spectral estimation methods such as Multi-Signal Classification (MUSIC) and Rotation Subspace Invariant (ESPRIT). Traditional source number estimation algorithms are usually based on the circular signal assumption, that is, they only use the standard covariance matrix of the received signal for estimation. However, source signals in real-world applications often exhibit non-circular characteristics, and their compensated covariance matrix is ​​non-zero, which limits the estimation performance of traditional algorithms. To overcome this problem, researchers have proposed the Minimum Description Length (NC-MDL) method and the Principal Component Analysis (NC-PCA) method for non-circular signals, which improve estimation accuracy by utilizing the non-zero compensated covariance matrix.

[0003] While NC-MDL and NC-PCA methods perform well in ideal white noise environments, their estimation performance degrades significantly in real-world colored noise scenarios. The statistical properties of colored noise disrupt the structure of the covariance matrix of non-circular signals, making it difficult for existing methods to accurately distinguish between the signal and noise subspaces, leading to incorrect source number estimation. Furthermore, existing algorithms typically assume that the noise covariance matrix is ​​known or can be precisely estimated, while the statistical properties of noise in real-world systems are often unknown or time-varying, further exacerbating performance degradation. Therefore, a non-circular source number detection method that can operate stably in colored noise environments is urgently needed to meet practical application requirements. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for detecting the number of non-circular sources under colored noise. This invention constructs a log-likelihood function that fuses the canonical correlation coefficients of the samples and estimates the canonical correlation coefficients of the population, thus fully describing the statistical characteristics of non-circular observation samples. Furthermore, it designs statistics based on the minimum descriptive criterion, resulting in superior estimation performance under colored noise conditions.

[0005] The technical means employed in this invention are as follows:

[0006] A method for detecting the number of non-circular sources under colored noise includes:

[0007] Based on the observed samples, construct the compensated sample covariance matrix;

[0008] The Takagi decomposition of the covariance matrix of the compensated samples is performed to obtain the canonical correlation coefficients of the samples;

[0009] Based on the sample canonical correlation coefficient, an estimate of the parent canonical correlation coefficient is constructed;

[0010] Based on the estimated values ​​of the sample canonical correlation coefficient and the population canonical correlation coefficient, a log-likelihood function is constructed;

[0011] Based on the log-likelihood function, a minimum description length statistic is constructed;

[0012] The number of population canonical correlation coefficients when the minimum description length statistic is minimized is used as an estimate of the number of non-circular sources.

[0013] Furthermore, based on the observed samples, a compensated sample covariance matrix is ​​constructed as follows:

[0014]

[0015] in, Represents the observed sample matrix, Represents the compensated sample covariance matrix, with superscript indicating the superscript. Indicates the transpose symbol. Indicates the number of receiving antennas. Indicates the sample length.

[0016] Furthermore, the Takagi decomposition is performed on the covariance matrix of the compensated samples to obtain the canonical correlation coefficients of the samples, as follows:

[0017]

[0018]

[0019] in, Represents the compensated sample covariance matrix. Represents a complex unitary matrix. Represents the sample canonical correlation coefficient matrix. Indicates the first Canonical correlation coefficient of each sample Represents a diagonal matrix, with superscript Indicates the transpose symbol. This indicates the number of receiving antennas.

[0020] Furthermore, based on the sample canonical correlation coefficient, the estimated value of the population canonical correlation coefficient is constructed as follows:

[0021]

[0022] , ,

[0023] ,

[0024] in, Indicates the first The value of the next iteration. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the relaxation factor, and its value must satisfy... The condition is that the modulus is smaller than the previous iteration value; otherwise, it should be halved and the iteration value should be recalculated. , Represents the hyperbolic tangent function. Represents the inverse hyperbolic tangent function. This represents the number of hypothetical non-circular signals. Indicates the number of iterations. Indicates the number of receiving antennas. Indicates the sample length.

[0025] Furthermore, based on the estimated values ​​of the sample canonical correlation coefficient and the population canonical correlation coefficient, a log-likelihood function is constructed as follows:

[0026]

[0027] in, The log-likelihood function represents the population canonical correlation coefficient. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the number of hypothetical non-circular signals. Indicates the first Canonical correlation coefficient of each sample Represents the gamma function. Indicates the number of receiving antennas. Indicates the sample length.

[0028] Furthermore, based on the log-likelihood function, a minimum description length statistic is constructed as follows:

[0029]

[0030] in, This represents the minimum description length statistic. The log-likelihood function represents the population canonical correlation coefficient. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the number of hypothetical non-circular signals. Indicates the sample length.

[0031] Furthermore, the number of population canonical correlation coefficients that minimize the minimum description length statistic is used as an estimate of the number of non-circular sources, as follows:

[0032]

[0033] in, This represents the minimum description length statistic. This represents the number of hypothetical non-circular signals. This represents an estimate of the actual number of non-circular signals. This indicates the number of receiving antennas.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] 1. Traditional source number estimation methods only use the standard covariance matrix of the received signal, ignoring the compensated covariance information unique to non-circular signals. This invention constructs a compensated sample covariance matrix, incorporating the elliptic covariance information of non-circular signals into the processing framework, thus enabling a comprehensive characterization of the statistical features of the observed samples.

[0036] 2. This invention performs Takagi decomposition on the covariance matrix of the compensation sample. As a special decomposition method for complex symmetric matrices, Takagi decomposition can effectively extract the canonical correlation structure in the covariance matrix of the compensation sample, transforming the originally complex matrix feature analysis problem into a simple canonical correlation coefficient solution problem. This not only reduces computational complexity, but more importantly, it obtains the sample canonical correlation coefficient that can reflect the essential difference between signal and noise, providing a key intermediate quantity for subsequent parameter estimation.

[0037] 3. This invention employs an iterative optimization method to solve for the population canonical correlation coefficient. By introducing a relaxation factor to adaptively adjust the iteration step size, the convergence stability of the estimation process is ensured. This estimation method fully considers the estimation bias caused by the limited sample length and compensates for the bias through asymptotic mathematical analysis. This allows it to obtain a population canonical correlation coefficient estimate that approximates the theoretical optimum even in practical applications with limited sample length, significantly improving the accuracy of parameter estimation.

[0038] 4. The log-likelihood function constructed in this invention integrates sample observation information and population parameter estimation, comprehensively characterizing the probability distribution of non-circular signals in colored noise environments. This log-likelihood function not only considers the energy distribution of the signal subspace but also fully considers the statistical characteristics of the noise subspace and the phase information unique to non-circular signals. This makes the detection criterion based on this likelihood function statistically optimal and able to maintain robust detection performance in complex electromagnetic environments.

[0039] 5. The minimum description length criterion is essentially an information theory criterion that avoids overfitting by penalizing overly complex models. This invention applies this criterion to the detection of non-circular sources, ensuring that the estimation results adequately explain the signal components in the observed data without introducing excessive spurious sources that could distort the model. This automatic model selection mechanism eliminates the need for manually setting detection thresholds and features strong adaptability and wide applicability.

[0040] This invention effectively suppresses the interference of colored noise on signal feature extraction by constructing a compensated sample covariance matrix and using Takagi decomposition; it enhances the noise resistance of the detection statistics through accurate estimation of the population canonical correlation coefficient and construction of an optimized likelihood function; and it ensures the robustness of the detection results by applying the minimum description length criterion. Combining these techniques, this invention achieves accurate detection of non-circular signal sources in colored noise environments, with a detection probability significantly superior to existing methods, providing reliable technical support for practical applications in array signal processing fields such as radar, communication, and sonar. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 is a flowchart of the method of the present invention.

[0043] Figure 2 is a comparison of the detection probabilities of the non-circular signal number detection method provided in the embodiments of the present invention with those of the NC-MDL method and the NC-PCA method. Detailed Implementation

[0044] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0045] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0046] As shown in Figure 1, this invention provides a method for detecting the number of non-circular sources under colored noise, including:

[0047] S1. Construct the compensated sample covariance matrix based on the observed samples;

[0048] S2. Perform Takagi decomposition on the covariance matrix of the compensated samples to obtain the sample canonical correlation coefficients;

[0049] S3. Based on the sample canonical correlation coefficient, construct an estimate of the population canonical correlation coefficient;

[0050] S4. Based on the estimated values ​​of the sample canonical correlation coefficient and the population canonical correlation coefficient, construct the log-likelihood function;

[0051] S5. Based on the log-likelihood function, construct a minimum description length statistic;

[0052] S6. The number of population canonical correlation coefficients when the minimum description length statistic is minimized is used as an estimate of the number of non-circular sources.

[0053] In a specific implementation, as a preferred embodiment of the present invention, in step S1, a compensation sample covariance matrix is ​​constructed based on the observed samples, as follows:

[0054]

[0055] in, Represents the observed sample matrix, Represents the compensated sample covariance matrix, with superscript indicating the superscript. Indicates the transpose symbol. Indicates the number of receiving antennas. Indicates the sample length.

[0056] In this embodiment, the observation sample specifically refers to:

[0057]

[0058] in, Indicates the observed sample. express A non-circular signal source, Represents the channel gain matrix. Indicates the angle of signal incidence. Represents a colored noise vector. Indicates the number of receiving antennas. Indicates the signal length.

[0059] In a specific implementation, as a preferred embodiment of the present invention, in step S2, the covariance matrix of the compensated sample is decomposed using Takagi decomposition to obtain the sample canonical correlation coefficients, as follows:

[0060]

[0061]

[0062] in, Represents the compensated sample covariance matrix. Represents a complex unitary matrix. Represents the sample canonical correlation coefficient matrix. Indicates the first Canonical correlation coefficient of each sample Represents a diagonal matrix, with superscript Indicates the transpose symbol. This indicates the number of receiving antennas.

[0063] In a specific implementation, as a preferred embodiment of the present invention, in step S3, based on the sample canonical correlation coefficient, an estimated value of the population canonical correlation coefficient is constructed as follows:

[0064]

[0065] , ,

[0066] ,

[0067] in, Indicates the first The value of the next iteration. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the relaxation factor, and its value must satisfy... The condition is that the modulus is smaller than the previous iteration value; otherwise, it should be halved and the iteration value should be recalculated. , Represents the hyperbolic tangent function. Represents the inverse hyperbolic tangent function. This represents the number of hypothetical non-circular signals. Indicates the number of iterations. Indicates the number of receiving antennas. Indicates the sample length.

[0068] In a specific implementation, as a preferred embodiment of the present invention, in step S4, a log-likelihood function is constructed based on the estimated values ​​of the sample canonical correlation coefficient and the population canonical correlation coefficient, as follows:

[0069]

[0070] in, The log-likelihood function represents the population canonical correlation coefficient. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the number of hypothetical non-circular signals. Indicates the first Canonical correlation coefficient of each sample Represents the gamma function. Indicates the number of receiving antennas. Indicates the sample length.

[0071] In a specific implementation, as a preferred embodiment of the present invention, in step S5, a minimum description length statistic is constructed based on the log-likelihood function, as follows:

[0072]

[0073] in, This represents the minimum description length statistic. The log-likelihood function represents the population canonical correlation coefficient. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the number of hypothetical non-circular signals. Indicates the sample length.

[0074] In a specific implementation, as a preferred embodiment of the present invention, in step S6, the number of population canonical correlation coefficients when the minimum description length statistic is minimized is used as an estimate of the number of non-circular sources, as follows:

[0075]

[0076] in, This represents the minimum description length statistic. This represents the number of hypothetical non-circular signals. This represents an estimate of the actual number of non-circular signals. This indicates the number of receiving antennas.

[0077] Example

[0078] The embodiments of the present invention will be described in detail below through simulation experiments.

[0079] Simulation assumes the number of antennas A uniform linear array, with a large number of non-circular signal sources. And the variances are all The incident angle of the signal source is The corresponding maternal canonical correlation coefficient is ,matrix The Listed as , The colored noise vector is obtained by filtering a standard complex Gaussian distribution sample using a first-order autoregressive model, with regression coefficients of... The relaxation factor is initialized to The number of iterations is set to All simulation results were passed. This was obtained from the Monte Carlo experiment.

[0080] Figure 2 shows a comparison of the detection probabilities of the method of this invention with the NC-MDL and NC-PCA methods under different sample lengths. It can be seen that the method of this invention outperforms the other comparative methods in colored noise environments, exhibiting superior detection performance.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for detecting the number of non-circular signal sources under colored noise, characterized in that, include: Based on the observed samples, construct the compensated sample covariance matrix; The Takagi decomposition of the covariance matrix of the compensated samples is performed to obtain the canonical correlation coefficients of the samples; Based on the sample canonical correlation coefficient, an estimate of the parent canonical correlation coefficient is constructed; Based on the estimated values ​​of the sample canonical correlation coefficient and the population canonical correlation coefficient, a log-likelihood function is constructed as follows: in, The log-likelihood function represents the population canonical correlation coefficient. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the number of hypothetical non-circular signals. Indicates the first Canonical correlation coefficient of each sample Represents the gamma function. Indicates the number of receiving antennas. The sample length is represented; based on the log-likelihood function, a minimum description length statistic is constructed; the number of population canonical correlation coefficients when the minimum description length statistic is minimized is used as an estimate of the number of non-circular sources.

2. The method for detecting the number of non-circular signal sources under colored noise according to claim 1, characterized in that, The compensated sample covariance matrix is ​​constructed based on the observed samples as follows: in, Represents the observed sample matrix, Represents the compensated sample covariance matrix, with superscript... Indicates the transpose symbol. Indicates the number of receiving antennas. Indicates the sample length.

3. The method for detecting the number of non-circular signal sources under colored noise according to claim 1, characterized in that, The Takagi decomposition of the covariance matrix of the compensated samples is performed to obtain the canonical correlation coefficients of the samples, as follows: in, Represents the compensated sample covariance matrix. Represents a complex unitary matrix. Represents the sample canonical correlation coefficient matrix. Indicates the first Canonical correlation coefficient of each sample Represents a diagonal matrix, with superscript Indicates the transpose symbol. This indicates the number of receiving antennas.

4. The method for detecting the number of non-circular signal sources under colored noise according to claim 1, characterized in that, The estimated value of the population canonical correlation coefficient is constructed based on the sample canonical correlation coefficient as follows: ， ， ， in, Indicates the first The value of the next iteration. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. Denotes the relaxation factor, satisfying The condition is that the modulus is smaller than the previous iteration value; otherwise, it is halved and the iteration value is recalculated. ， Represents the hyperbolic tangent function. Represents the inverse hyperbolic tangent function. This represents the number of hypothetical non-circular signals. Indicates the number of iterations. Indicates the number of receiving antennas. Indicates the sample length.

5. The method for detecting the number of non-circular signal sources under colored noise according to claim 1, characterized in that, The minimum descriptive length statistic is constructed based on the log-likelihood function as follows: in, This represents the minimum description length statistic. The log-likelihood function represents the population canonical correlation coefficient. Indicates the first Estimates of the canonical correlation coefficients of non-zero populations. This represents the number of hypothetical non-circular signals. Indicates the sample length.

6. The method for detecting the number of non-circular signal sources under colored noise according to claim 1, characterized in that, The number of population canonical correlation coefficients that minimize the minimum description length statistic is used as an estimate of the number of non-circular sources, as follows: in, This represents the minimum description length statistic. This represents the number of hypothetical non-circular signals. This represents an estimate of the actual number of non-circular signals. This indicates the number of receiving antennas.

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