A source number estimation method based on linear scaling factor two-step difference

Abstract

The application relates to a source number estimation method based on linear scaling factor two-step difference, which comprises the following steps: S1: calculating a sample sampling covariance matrix and its eigenvalue based on array antenna output data; S2: constructing a linear scaling factor by using the eigenvalue and completing initial source number estimation based on the maximum difference between the linear scaling factors; and S3: constructing a weight around the initial source number estimation and completing improved source number estimation based on a weighted difference technique. The method has wide applicability to various condition scenes under large-scale arrays and is very efficient in calculation, can provide higher estimation precision compared with current mainstream source number methods, and has good ability for large source number estimation.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a source number estimation method based on two-step difference with linear scaling coefficients. Background Technology

[0002] Source number estimation is an important area of ​​array signal processing, with wide applications in radar, sonar, and wireless communication. It is typically the first step in parameter estimation, and its performance is a crucial factor affecting the overall system performance. In recent years, with the increasing demands for cluster target detection in radar and sonar and positioning in large-scale B5G / 6G wireless communication systems, research into methods suitable for large source number estimation has become urgent. Currently, a wealth of source number estimation methods have emerged, the most representative being those based on information theory criteria, including the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Minimum Description Length (MDL). However, these methods are all based on classical asymptotic theory, and their applicability hinges on a fixed array antenna number and an infinite sample size. However, in practice, with the widespread application of large-scale arrays and the increasing demand for high reliability and low latency, the data received by actual arrays has become high-dimensional finite sample / small sample data. Under these circumstances, existing methods based on information theory criteria will experience a certain degree of degradation and become less effective.

[0003] To improve source number estimation for high-dimensional finite / small sample data, several source number estimation methods based on general asymptotic systems have been proposed in recent years, including the RMT-TT method based on random matrix theory and threshold detection, the LS-MDL method based on linear shrinkage coefficients, and the SCD method based on linear shrinkage systems and threshold detection (or heuristic schemes). thre (or SCD) heur Methods such as [list of methods]. However, analysis revealed that these methods all exhibited significant performance degradation in scenarios with large numbers of data sources, and were largely only applicable to [specific scenarios]. m>n or m≤n The scene here m Indicates the number of array antennas. n This indicates the output data of the array antenna. n Therefore, it is necessary and essential to develop a universal source number estimation method applicable to a wider range of scenarios and large source numbers. Summary of the Invention

[0004] To overcome the shortcomings of existing methods, this invention provides a source number estimation method based on two-step difference with linear scaling coefficients in a general asymptotic system. This method addresses the lack of universality in existing technologies and achieves high-accuracy probability estimation of the source number in scenarios with large-scale arrays, small samples, and large source numbers.

[0005] The technical solution adopted in this invention is a source number estimation method based on two-step difference of linear scaling coefficients, which includes the following steps:

[0006] S1, Settings d A far-field source from angle Incident to m On an array antenna composed of several antennas, the array antenna is used to obtain the data. t Output data at time ,in, express m × d dimensional array guiding matrix, and They represent d ×1 dimension m ×1-dimensional independent and identically distributed Gaussian signal and noise vectors; for the output data Perform n samplings and collect data. n Given a sample, calculate the covariance matrix S and its eigenvalues ​​for each sample. ,in, m Represents the number of array antennas;

[0007] S2, using eigenvalues The process involves constructing linear scaling coefficients and estimating the initial number of information sources based on the maximum difference between these coefficients.

[0008] S2.1 Utilizing eigenvalues Constructing linear scaling coefficients ,in, k This represents the assumed source value. , m and n These represent the number of array antennas and the number of sampled samples, respectively.

[0009] S2.2 Calculate the difference between adjacent linear scaling factors. And find the value corresponding to the maximum difference. k This completes the estimation of the initial number of information sources, and yields the estimated value of the initial number of information sources. ,Right now: ,in, , This indicates an adjustment parameter less than 1;

[0010] S3, in the initial source number estimate A weight is constructed around the source, and the number of sources is further estimated based on the weighted difference technique. The specific process is as follows:

[0011] S3.1, Initial source number estimate From the nearby values, select several values ​​as the hypothetical source values. For each Value, its preceding The difference between the linear scaling coefficients is compared with 0, and the maximum value is output. , ;calculate The mean, expressed as: ;

[0012] S3.2, Utilization Construct the second step of weighted difference, and find the value corresponding to the largest difference. Complete the improved source number estimation, namely: Among them, weighted parameters ≤Number of sources d , represent Several hypothetical source values ​​selected around .

[0013] The beneficial effects of this invention are: compared with the prior art, the method of this invention has better universality, and is applicable to both... m > n This scenario is also applicable m ≤ n This invention is applicable to scenarios with a large number of information sources, and it can provide a higher probability of successful detection. Moreover, the method of this invention only performs simple scaling coefficient difference operations, which is very efficient in computation.

[0014] As a preferred option, parameters The range of values ​​is .

[0015] As a preferred option, weighted parameters The range of values ​​is . Attached Figure Description

[0016] Figure 1 This is a flowchart of a source number estimation method based on two-step difference with linear scaling coefficients according to the present invention;

[0017] Figure 2AThis is a comparison chart showing the variation of the probability of correct detection of the number of sources with the signal-to-noise ratio (SNR) obtained by the source number estimation method used in scenario 1 of the simulation experiment described in this invention.

[0018] Figure 2B This is a comparison chart showing the variation of the probability of correct detection of the number of sources with the signal-to-noise ratio (SNR) obtained by the source number estimation method used in scenario 2 in simulation experiment 1 described in this invention.

[0019] Figure 3A This is a comparison chart showing the change in the accurate detection probability of the number of sources as a function of the number of samples, obtained by the source number estimation method used in scenario 1 in simulation experiment 2 described in this invention.

[0020] Figure 3B This is a comparison chart showing the change in the accurate detection probability of the number of sources as a function of the number of samples, obtained by the source number estimation method used in scenario 2 of the simulation experiment described in this invention.

[0021] Figure 4A This is a comparison chart showing the change in the accurate detection probability of the number of sources as a function of the number of sources, obtained by the source number estimation method used in scenario 1 in simulation experiment 3 described in this invention.

[0022] Figure 4B This is a comparison chart showing the change in the accurate detection probability of the number of sources as a function of the number of sources, obtained by the source number estimation method used in scenario 2 of simulation experiment 3 described in this invention. Detailed Implementation

[0023] The invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can implement it based on the description. The scope of protection of the invention is not limited to these specific embodiments.

[0024] This invention relates to a source number estimation method based on two-step difference with linear scaling coefficients, such as... Figure 1 As shown, the method includes the following steps:

[0025] S1, Settings d A far-field source from angle Incident to m On an array antenna composed of several antennas, the array antenna is used to obtain the data. t Output data at time ,in, express m × d dimensional array guiding matrix, and They represent d ×1 dimension m ×1-dimensional independent and identically distributed Gaussian signal and noise vectors; for the output data Perform n samplings and collect data. n Given a sample, calculate the covariance matrix S and its eigenvalues ​​for each sample. ,in, m Represents the number of array antennas; covariance matrix , where superscript H This represents the conjugate transpose operation, which performs eigenvalue decomposition on S to obtain eigenvalues ​​arranged in descending order. ;

[0026] S2, using eigenvalues The process involves constructing linear scaling coefficients and estimating the initial number of information sources based on the maximum difference between these coefficients (performing the first step of differencing).

[0027] S2.1 Utilizing eigenvalues Constructing linear scaling coefficients ,in, k This represents the assumed source value. , m and n These represent the number of array antennas and the number of sampled samples, respectively.

[0028] S2.2 Calculate the difference between adjacent linear scaling factors. And find the value corresponding to the maximum difference. k This completes the estimation of the initial number of information sources, and yields the estimated value of the initial number of information sources. ,Right now:

[0029] ,in, , This indicates an adjustment parameter less than 1;

[0030] S3, in the initial source number estimate A weight is constructed around the source, and the number of sources is further estimated based on the weighted difference technique. The specific process is as follows:

[0031] S3.1, Initial source number estimate From the nearby values, select several values ​​as the hypothetical source values. For each Value, its preceding The difference between the linear scaling coefficients is compared with 0, and the maximum value is output. , ;calculate The mean, expressed as: ;

[0032] S3.2, Utilization Construct the second step of weighted difference, and find the value corresponding to the largest difference. Complete the improved source number estimation, namely: Among them, weighted parameters ≤Number of sources d , represent Several hypothetical source values ​​selected around .

[0033] Compared with existing technologies, the method of this invention has better universality, applicable to both... m > n This scenario is also applicable m ≤ n This invention is applicable to scenarios with a large number of information sources, and it can provide a higher probability of successful detection. Moreover, the method of this invention only performs simple scaling coefficient difference operations, which is very efficient in computation.

[0034] In step S2.2, the parameters A range of values ​​that balances stability and estimation performance is: .

[0035] In step S3.2, the weighting parameters A range of values ​​that balances stability and estimation performance is: .

[0036] The performance of the source number estimation method based on two-step difference with linear scaling coefficient provided in this invention is analyzed through simulation experiments. The simulation process is carried out using MATLAB software.

[0037] Simulation Experiment 1: Accurate Detection Probability as a Percentage of Signal-to-Noise Ratio (SNR)

[0038] Ten signal sources, evenly distributed at angles in the range [-18°, 18°], are incident on a uniform linear array. The spacing between the array antennas is half the wavelength of the incident signal carrier. Consider the following two different array sample scenarios: Scenario 1: m =50, n =65 (i.e.) m < n The SNR changed from -14 dB to -2 dB; Scenario 2: m =50, n =30 (i.e.) m >n The SNR changed from -10 dB to 2 dB. The source number accurate detection probability change curves for scenarios 1 and 2 are shown below. Figure 2A and Figure 2B As shown, the proposed method is the most stable approach, improving estimation / detection performance in both scenarios. Specifically, the SNR required for accurate source number detection is lower than that for SCD in scenario 1. thre The algorithm is 3 dB lower, and in scenario 2 it is better than LS-MDL and SCD. heur The algorithm is 3 decibels lower, which fully demonstrates the superiority of the method of this invention.

[0039] Simulation Experiment 2: The Probability of Accurate Detection Varies with Number of Samples

[0040] Ten signal sources, evenly distributed at angles in the range [-18°, 18°], are incident on a uniform linear array. The spacing between the array antennas is half the wavelength of the incident signal carrier. Consider the following two different array sample scenarios: Scenario 1: m =60, SNR=-10 dB, n The value changes from 30 to 100; Scenario 2: m =60, SNR=-6 dB, n The number of sources changes from 15 to 50. The curves showing the change in the probability of accurate detection of the number of sources in scenarios 1 and 2 are as follows: Figure 3A and Figure 3B As shown in the figure. It can be seen that the accurate detection probability of the method of the present invention is related to... n The results are directly proportional, and the method of this invention outperforms the comparative method throughout the entire observation interval. In particular, under conditions of low SNR and small sample size (…),… n Even with only a dozen to several dozen sources, the method of this invention still achieves relatively excellent source number estimation performance, further demonstrating the superiority of the method of this invention.

[0041] Simulation Experiment 3: The Probability of Accurate Detection as a Percentage of Sources Changes

[0042] d The signal sources are evenly distributed in the interval [(-3)] at 3° intervals. d +3)°, (3 d -3)°], d As the frequency changes from 1 to 45, the SNR becomes -8 dB, and the antenna spacing is half the wavelength of the incident signal carrier. Two scenarios are also considered: Scenario 1: m =60, n =70 (i.e.) m < n ); Scene 2: m=70, n =60 (i.e.) m > n The curves showing the change in the probability of accurate detection of the number of information sources for scenarios 1 and 2 are as follows: Figure 4A and Figure 4B As shown in the figure. Simulation results demonstrate that the method of this invention can estimate a greater number of information sources with a higher success rate. Figure 4B For example, the method of this invention can detect up to 45 sources with a certain probability, and accurately estimate 20 sources with a probability of over 90%. In contrast, other methods can detect a maximum of less than 20 sources, which fully demonstrates that the method of this invention has a good ability to estimate a large number of sources.

Claims

1. A source number estimation method based on two-step difference with linear scaling coefficients, characterized in that: The method includes the following steps: S1, Settings d A far-field source from angle Incident to m On an array antenna composed of several antennas, the array antenna is used to obtain the data. t Output data at time ,in, express m × d dimensional array guiding matrix, and They represent d ×1 dimension m ×1-dimensional independent and identically distributed Gaussian signal and noise vectors; for the output data Perform n samplings and collect data. n Given a sample, calculate the covariance matrix S and its eigenvalues ​​for each sample. ,in, m Represents the number of array antennas; S2, using eigenvalues The process involves constructing linear scaling coefficients and estimating the initial number of information sources based on the maximum difference between these coefficients. S2.1 Utilizing eigenvalues Constructing linear scaling coefficients ,in, k This represents the assumed source value. , m and n These represent the number of array antennas and the number of sampled samples, respectively. S2.2 Calculate the difference between adjacent linear scaling factors. And find the value corresponding to the maximum difference. k This completes the estimation of the initial number of information sources, and yields the estimated value of the initial number of information sources. ,Right now: ,in, , This indicates an adjustment parameter less than 1; S3, in the initial source number estimate A weight is constructed around the source, and the number of sources is further estimated based on the weighted difference technique. The specific process is as follows: S3.1, Initial source number estimate From the nearby values, select several values ​​as the hypothetical source values. For each Value, its preceding The difference between the linear scaling coefficients is compared with 0, and the maximum value is output. , ;calculate The mean, expressed as: ; S3.2, Utilization Construct the second step of weighted difference, and find the value corresponding to the largest difference. Complete the improved source number estimation, namely: Among them, weighted parameters ≤Number of sources d , represent Several hypothetical source values ​​selected around the perimeter .

2. The source number estimation method based on two-step difference with linear scaling coefficients according to claim 1, characterized in that: parameter The range of values ​​is .

3. The source number estimation method based on two-step difference with linear scaling coefficients according to claim 1, characterized in that: Weighted parameters The range of values ​​is .

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