Method and system for detecting the number of sources based on non-circular signals

Abstract

The application relates to the technical field of wireless communication, and discloses a signal source number detection method and system based on non-circular signals. The method comprises the following steps: calculating a compensated sample covariance matrix of a received signal, and obtaining a sample canonical correlation coefficient through Takagi decomposition of the compensated sample covariance matrix; constructing a marginal likelihood function of a parent canonical correlation coefficient; taking the sample canonical correlation coefficient as an estimated value of the corresponding parent, and establishing an estimated statistic quantity by using a minimum description length criterion; obtaining the number of the parent canonical correlation coefficients when the estimated statistic quantity is minimized, and taking the number as an estimated value of the actual number of non-circular signals. The application fully utilizes the feature that the compensated covariance of the non-circular signal is not 0, and adopts a marginal likelihood function with the least redundant parameters to construct a statistic quantity, so that high-precision estimation of the number of non-circular signals can be realized, and necessary guarantees are provided for practical application scenarios such as direction of arrival estimation and wave velocity formation.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and specifically to a method and system for detecting the number of signal sources based on non-circular signals. Background Technology

[0002] Source number estimation is a crucial research area in array signal processing for radar, communication, and sonar, serving as a prerequisite for super-resolution spatial spectrum estimation techniques such as multi-signal classification and rotatable subspace invariance methods. Traditional source number estimation methods are based on circular signals, meaning the estimation algorithms only use the standard covariance matrix of the received signal. However, real-world source signals often exhibit non-circular characteristics, with non-zero compensated covariance, limiting the performance of existing algorithms. To address this, researchers have utilized this non-zero compensated covariance characteristic to propose a non-circular signal number estimation method based on minimum description length (NC-MDL). However, the estimation performance of this method still requires further improvement. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides a source number detection method and system based on non-circular signals, aiming to improve the accuracy of non-circular signal quantity estimation, especially in complex scenarios such as low signal-to-noise ratio and few snapshots.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] On one hand, embodiments of the present invention provide a source number detection method based on non-circular signals, the method comprising the following steps:

[0006] Calculate the compensated sample covariance matrix of the received signal, and obtain the sample canonical correlation coefficient through the Takagi decomposition of the compensated sample covariance matrix;

[0007] Construct the marginal likelihood function of the population canonical correlation coefficient;

[0008] The canonical correlation coefficient of the sample is used as the estimate of the corresponding population, and the minimum description length criterion is used to establish the estimation statistic;

[0009] Obtain the number of population canonical correlation coefficients that minimize the estimated statistic, and use it as an estimate of the actual number of non-circular signals.

[0010] Optionally, the received signal specifically includes:

[0011] ;

[0012] in, express A non-circular signal, Represents the channel gain matrix. Represents the noise vector. The number of receiving antennas, For signal length, The number of non-circular signals. Represents the complex field.

[0013] Optionally, the calculated compensated sample covariance matrix of the received signal is:

[0014] ;

[0015] in, For the received signal matrix, To compensate for the sample covariance matrix, the superscript... Indicates the transpose symbol. The number of receiving antennas, This represents the sample length.

[0016] Optionally, the canonical correlation coefficient obtained by the Takagi decomposition of the compensated sample covariance matrix is:

[0017] ;

[0018] ;

[0019] in, To compensate for the sample covariance matrix, It is a complex unitary matrix. This is the canonical correlation coefficient matrix of the sample. For the first Canonical correlation coefficient of each sample Represents a diagonal matrix, with superscript Indicates the transpose symbol. This represents the number of receiving antennas.

[0020] Optionally, the marginal likelihood function for constructing the population canonical correlation coefficient is:

[0021] ;

[0022] ;

[0023] in, Let be the marginal likelihood function of the population canonical correlation coefficient. Assuming the number of non-circular signals, For the first Canonical correlation coefficient of the population For the first Canonical correlation coefficient of each sample It is a multivariate gamma function. For gamma function, The number of receiving antennas, This represents the sample length.

[0024] Optionally, the canonical correlation coefficient of the sample is used as an estimate of the corresponding population, and the minimum description length criterion is used to establish the estimation statistic as follows:

[0025] ;

[0026] in, For the estimation statistic based on the minimum description length criterion, Assuming the number of non-circular signals, For the first Canonical correlation coefficient of each sample For gamma function, The number of receiving antennas, This represents the sample length.

[0027] Optionally, the number of population canonical correlation coefficients that minimize the estimated statistic is used as an estimate of the actual number of non-circular signals.

[0028] ;

[0029] in, For the estimation statistic based on the minimum description length criterion, Assuming the number of non-circular signals, This is an estimate of the actual number of non-circular signals.

[0030] On the other hand, embodiments of the present invention provide a source number detection system based on non-circular signals, comprising:

[0031] At least one processor;

[0032] At least one memory for storing at least one program;

[0033] When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0034] On the other hand, embodiments of the present invention provide a computer-readable storage medium storing a processor-executable program, which, when executed by a processor, is used to perform the above-described method.

[0035] The beneficial effects of this invention are as follows: This invention discloses a source number detection method and system based on non-circular signals. This invention calculates the compensated sample covariance matrix of the received signal and obtains the sample canonical correlation coefficients through Takagi decomposition of the compensated sample covariance matrix; constructs a marginal likelihood function of the population canonical correlation coefficients; uses the sample canonical correlation coefficients as estimates of the corresponding population, and establishes an estimation statistic using the minimum description length criterion; obtains the number of population canonical correlation coefficients when the estimation statistic is minimized, and uses this as an estimate of the actual number of non-circular signals. The technical solution of this invention fully utilizes the characteristic that the compensated covariance of non-circular signals is not zero, and uses a marginal likelihood function with the fewest redundant parameters to design the statistic, resulting in superior estimation performance. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a flowchart of a source number detection method based on non-circular signals according to the present invention;

[0038] Figure 2 This is a comparison chart of the estimation probabilities of the non-circular signal number estimation method and the NC-MDL method in this embodiment of the invention. Detailed Implementation

[0039] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0041] It is understood that the terms “first,” “second,” etc., used in this invention may be used herein to describe various concepts, but unless specifically stated otherwise, these concepts are not limited by these terms. These terms are used only to distinguish one concept from another. For example, first information may also be referred to as second information without departing from the scope of embodiments of the invention, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to determination” as used herein may be interpreted as “when…” or “when…” or “in response to determination.”

[0042] The terms “at least one,” “multiple,” “each,” “any,” etc., used in this invention, “at least one” includes one, two, or more than two; “multiple” includes two or more than two; “each” refers to each of the corresponding multiple; and “any” refers to any one of the multiple.

[0043] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0044] refer to Figure 1 ,like Figure 1 The figure shows a source number detection method based on non-circular signals provided by an embodiment of the present invention. The method includes the following steps:

[0045] S100, calculate the compensated sample covariance matrix of the received signal, and obtain the sample canonical correlation coefficient through the Takagi decomposition of the compensated sample covariance matrix.

[0046] S200, the marginal likelihood function for constructing the canonical correlation coefficient of the population;

[0047] S300 uses the sample canonical correlation coefficient as an estimate of the corresponding population and uses the minimum description length criterion to establish the estimation statistic;

[0048] S400 obtains the number of population canonical correlation coefficients when the estimated statistic is minimized, and uses it as an estimate of the actual number of non-circular signals.

[0049] The embodiments of the present invention fully utilize the characteristic that the covariance of non-circular signal compensation is not zero, and use the marginal likelihood function with the fewest redundant parameters to design the statistics, resulting in better estimation performance.

[0050] This embodiment effectively improves the accuracy and robustness of source number detection in non-circular signal scenarios. Specifically, by performing Takagi decomposition on the covariance matrix of the compensated sample of the received signal, the feature information of the non-circular signal can be more fully extracted. Compared with traditional methods that rely solely on the standard covariance matrix, the extracted sample canonical correlation coefficients can more accurately reflect the intrinsic structure of the non-circular signal. The marginal likelihood function of the population canonical correlation coefficient, constructed based on this, considers the statistical characteristics of the sample canonical correlation coefficients, making the estimation of the population parameters closer to the true distribution. Furthermore, by combining the estimation statistics established using the minimum description length criterion and balancing model complexity and goodness of fit, good source number estimation performance can be maintained under different signal-to-noise ratios, sample lengths, and signal non-circularity conditions. This effectively reduces the estimation bias of the traditional NC-MDL method at low signal-to-noise ratios or small samples, providing a more reliable source number premise for subsequent super-resolution spatial spectrum estimation and other techniques.

[0051] In a preferred embodiment of the present invention, the received signal specifically includes:

[0052] ;

[0053] in, express A non-circular signal, Represents the channel gain matrix. Represents the noise vector. The number of receiving antennas, For signal length, The number of non-circular signals. Represents the complex field.

[0054] This embodiment clearly defines the mathematical model of the received signal, laying the foundation for the subsequent calculation of the compensation sample covariance matrix. This model clearly decomposes the received signal into three parts: non-circular signal components, channel gain effects, and noise interference. The number of non-circular signals, the number of receiving antennas, and the signal length are key parameters that jointly determine the dimension and structure of the received data. Specifically, A non-circular signal passes through the channel gain matrix. After being processed, it is superimposed with the corresponding noise vector to form the final result. The received signal matrix captured by each receiving antenna Its dimensions are OK Each column corresponds to a receiving antenna in each row. Each signal sampling time is sampled. The model accurately reflects the actual scenario of multiple antennas receiving multiple non-circular signals in array signal processing, providing a rigorous mathematical description for source number detection using non-circular characteristics in subsequent steps.

[0055] In a preferred embodiment of the present invention, the calculation of the compensated sample covariance matrix of the received signal is specifically as follows:

[0056] ;

[0057] in, For the received signal matrix, To compensate for the sample covariance matrix, the superscript... Indicates the transpose symbol. The number of receiving antennas, This represents the sample length.

[0058] In this embodiment, the received signal matrix is ​​transposed, multiplied by the original received signal matrix, and then divided by the sample length. The compensated sample covariance matrix is ​​obtained. The dimension of this matrix is... OK Columns, whose elements Reflects the first The receiving antenna and the first The correlation of signals received by each receiving antenna after conjugation processing. Compared to the traditional standard covariance matrix, the compensated sample covariance matrix... It can effectively capture the non-zero compensated covariance characteristic unique to non-circular signals, that is, when the signal is non-circular, No longer a zero matrix, it contains rich non-circular signal feature information. Through this calculation method, the non-circular characteristics in the received signal are quantified and presented in matrix form, providing key input data for subsequent extraction of sample canonical correlation coefficients through Takagi decomposition. This is an important foundational step in this invention to improve the source number detection performance by utilizing non-circular signal features.

[0059] In a preferred embodiment of the present invention, the canonical correlation coefficient of the samples obtained by Takagi decomposition of the compensated sample covariance matrix is ​​as follows:

[0060] ;

[0061] ;

[0062] in, To compensate for the sample covariance matrix, It is a complex unitary matrix. This is the canonical correlation coefficient matrix of the sample. For the first Canonical correlation coefficient of each sample Represents a diagonal matrix, with superscript Indicates the transpose symbol. This represents the number of receiving antennas.

[0063] This embodiment compensates for the sample covariance matrix. Perform Takagi decomposition, complex unitary matrix The column vectors form an orthogonal basis after decomposition; The canonical correlation coefficient matrix of the samples is a diagonal matrix, and its diagonal elements are... These are the canonical correlation coefficients of the samples, usually arranged in descending order. These canonical correlation coefficients, from largest to smallest, reflect the correlation strength of non-circular signals across different feature dimensions. Larger values ​​indicate more significant non-circular signal characteristics in that dimension, providing crucial quantitative basis for subsequent construction of the marginal likelihood function and estimation of the number of sources. Through Takagi decomposition, core parameters characterizing the non-circular signal's properties can be effectively extracted from the compensated sample covariance matrix. This step is a key technical means to fully utilize the non-zero nature of the non-circular signal's compensated covariance.

[0064] In a preferred embodiment of the present invention, the marginal likelihood function for constructing the population canonical correlation coefficient is:

[0065] ;

[0066] ;

[0067] in, Let be the marginal likelihood function of the population canonical correlation coefficient. Assuming the number of non-circular signals, For the first Canonical correlation coefficient of the population For the first Canonical correlation coefficient of each sample It is a multivariate gamma function. For gamma function, The number of receiving antennas, This represents the sample length.

[0068] This embodiment constructs a marginal likelihood function by introducing a multivariate gamma function and a gamma function. The construction of this marginal likelihood function is based on the statistical relationship between the sample canonical correlation coefficient and the population canonical correlation coefficient. By treating the sample canonical correlation coefficient as an observed value of the population canonical correlation coefficient, a probability density function is used to describe the probability of such an observation. Specifically, the marginal likelihood function of the population canonical correlation coefficient reflects the probability density contribution of the sample canonical correlation coefficient given the population canonical correlation coefficient. The combination of the multivariate gamma function and the gamma function is used to normalize and adjust this probability density to adapt to the statistical characteristics of non-circular signal scenarios. Compared with the likelihood function in traditional methods, which may introduce too many redundant parameters, the marginal likelihood function constructed in this embodiment focuses on the core parameter of the population canonical correlation coefficient, minimizing redundant parameters. This allows for a more accurate balance between model complexity and data fit when applying the minimum description length criterion, laying an important foundation for improving the accuracy of source number estimation.

[0069] In a preferred embodiment of the present invention, the canonical correlation coefficient of the sample is used as the estimated value of the corresponding population, and the estimation statistic is established using the minimum description length criterion as follows:

[0070] ;

[0071] in, For the estimation statistic based on the minimum description length criterion, Assuming the number of non-circular signals, For the first Canonical correlation coefficient of each sample For gamma function, The number of receiving antennas, This represents the sample length.

[0072] This embodiment directly substitutes the sample canonical correlation coefficient as an estimate of the population canonical correlation coefficient into the marginal likelihood function, and constructs an estimation statistic by combining it with the minimum description length (MDL) criterion. Specifically, in the expression of the estimation statistic, from left to right, the first term is a measure of data fit. This term, weighted by taking the logarithm of the product of the sample canonical correlation coefficients, reflects the model's explanatory power for the observed data under the current assumptions; a smaller value indicates a better fit. The second term is a penalty term for model complexity, which increases with the number of hypothetical signals to prevent overfitting. By combining these two terms, the estimation statistic comprehensively considers both model complexity and data fit; a smaller value indicates that the number of hypothetical signals is closer to the true value. This construction method fully utilizes the non-circular signal information carried by the sample canonical correlation coefficient and effectively controls model complexity through the MDL criterion, avoiding the overestimation problem that traditional methods easily encounter in high-dimensional data or small sample situations. This provides a reasonable and robust basis for determining the number of information sources by minimization.

[0073] In a preferred embodiment of the present invention, the number of population canonical correlation coefficients that minimize the estimated statistic is obtained, and this number is used as an estimate of the actual number of non-circular signals:

[0074] ;

[0075] in, For the estimation statistic based on the minimum description length criterion, Assuming the number of non-circular signals, This is an estimate of the actual number of non-circular signals.

[0076] This embodiment calculates the number of each hypothetical non-circular signal by iterating through all possible hypothetical non-circular signal counts (whose values ​​are typically integers between 0 and the number of receiving antennas). Corresponding estimated statistic And select the number of non-circular signals that minimize the estimated statistic. As an estimate of the actual number of non-circular signals Specifically, when the number of assumed signals... If the value is too small, the model may not be able to fully capture the non-circular signal components in the received signal, resulting in a large goodness-of-fit term (the first term), thus... The value is too high; while when When the value is too large, the model complexity penalty term (the second term) will increase significantly, which will also lead to... The value increases. Therefore, by searching... The minimum point achieves the optimal balance between model complexity and data fit, corresponding to... This represents the number of most likely sources. This process transforms abstract statistical calculations into a concrete numerical optimization problem, ensuring the global optimum is found through a traversal search, and ultimately outputting... As an estimate of the actual number of non-circular signals, it has clear physical meaning and statistical basis, effectively improving the robustness and accuracy of source number detection in complex scenarios such as low signal-to-noise ratio and small sample size.

[0077] The embodiments of the present invention will be described in detail below through simulation experiments.

[0078] Simulation assumes the number of antennas A uniform linear array, with a large number of non-circular signals. And the variances are all The incident angles are respectively The parental canonical correlation coefficients are respectively ,matrix The Listed as , The noise vector follows a standard complex Gaussian distribution. All simulation results are verified. This was obtained from the Monte Carlo experiment.

[0079] Figure 2 A comparison of the probability estimation performance of the proposed method and the NC-MDL method under different sample lengths is presented. It can be seen that the proposed method outperforms the NC-MDL method under all simulation conditions, demonstrating superior estimation performance.

[0080] This invention also provides a source number detection system based on non-circular signals, comprising:

[0081] At least one processor;

[0082] At least one memory for storing at least one program;

[0083] When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0084] The content of the above method embodiments is applicable to this embodiment. The specific functions implemented in this embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. Therefore, they will not be repeated here.

[0085] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0086] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0087] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0088] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0089] This invention also provides a computer program product, including a computer program or computer instructions, which are stored in a memory. A processor of a computer device reads the computer program or computer instructions from the memory and executes the computer program or computer instructions, causing the computer device to perform the above-described method.

[0090] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented by the embodiments of this program product are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0091] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0092] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically include computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0093] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

Claims

1. A source number detection method based on non-circular signals, characterized in that, The method includes the following steps: Calculate the compensated sample covariance matrix of the received signal, and obtain the sample canonical correlation coefficient through the Takagi decomposition of the compensated sample covariance matrix; Construct the marginal likelihood function of the population canonical correlation coefficient; The canonical correlation coefficient of the sample is used as the estimate of the corresponding population, and the minimum description length criterion is used to establish the estimation statistic; Obtain the number of population canonical correlation coefficients that minimize the estimated statistic, and use it as an estimate of the actual number of non-circular signals; The marginal likelihood function for constructing the canonical correlation coefficient of the parent population is: ； ； in, Let be the marginal likelihood function of the population canonical correlation coefficient. Assuming the number of non-circular signals, For the first Canonical correlation coefficient of the population For the first Canonical correlation coefficient of each sample , ; It is a multivariate gamma function. For gamma function, The number of receiving antennas, The sample length; The sample canonical correlation coefficient is used as the estimate of the corresponding population, and the estimation statistic is established using the minimum description length criterion: ； in, This is an estimated statistic based on the minimum description length criterion; The number of population canonical correlation coefficients that minimizes the estimated statistic is used as an estimate of the actual number of non-circular signals. ； in, This is an estimate of the actual number of non-circular signals.

2. The method according to claim 1, characterized in that, The received signal is specifically: ； in, express A non-circular signal, Represents the channel gain matrix. Represents the noise vector. The number of non-circular signals. Represents the complex field.

3. The method according to claim 1, characterized in that, The compensated sample covariance matrix of the received signal is calculated as follows: ； in, For the received signal matrix, To compensate for the sample covariance matrix, the superscript... This represents the transpose symbol.

4. The method according to claim 1, characterized in that, The canonical correlation coefficient of the samples obtained by the Takagi decomposition of the compensated sample covariance matrix is ​​as follows: ； ； in, To compensate for the sample covariance matrix, It is a complex unitary matrix. This is the canonical correlation coefficient matrix of the sample. Represents a diagonal matrix, with superscript This represents the transpose symbol.

5. A source number detection system based on non-circular signals, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 4.

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