Signal source number estimation method based on linear expansion coefficient correction differential operation

Abstract

The invention relates to an information source number estimation method based on linear expansion and contraction coefficient correction differential operation. The method comprises the following steps: firstly, calculating a linear expansion and contraction coefficient and a first-order differential value of the linear expansion and contraction coefficient by utilizing a characteristic value of an array sample covariance matrix; secondly, the estimation value of the initial information source number is completed by searching the maximum first-order difference value under the assumed information source number k; thirdly, constructing a second-order difference value of a linear expansion coefficient based on the new assumed information source number k around the initial information source number estimation value, and constructing a correction factor based on the second-order difference value; and finally, searching a k value which enables the sum value of the first-order difference value and the correction factor to be maximum to complete final signal source number estimation. The method has universality for various scenes under large-scale array configuration, and compared with an existing mainstream signal source number estimation method, the method can provide higher estimation precision and has the good capability of estimating the large signal source number.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and in particular to a method for estimating the number of signal sources based on linear expansion coefficient corrected differential operation. Background Art

[0002] Estimation of the number of signal sources under large-scale array and small sample conditions is one of the key issues in the new generation of wireless communications and phased array radars, and is an important guarantee for achieving high-reliability system performance. Under large-scale array and small sample conditions, due to the problem of inconsistent estimation of the sample covariance matrix, traditional signal source estimation methods based on information theory criteria, such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Minimum Description Length (MDL), cannot provide reliable technical support for high-performance scenarios. It is urgent and necessary to develop a dedicated robust signal source estimation method that fits large-scale array and small sample scenarios.

[0003] In recent years, with the significant advantages of large-dimensional random matrix theory in the application of large-scale array scenarios, such as unbiasedness and noise robustness, several improved source number estimation algorithms based on large-dimensional random matrix theory under large-scale array and small sample conditions have been proposed. Representative algorithms include the LS-MDL method based on linear shrinkage coefficient, the RMT-TT method based on random matrix theory and threshold detection, the SCD method based on linear shrinkage coefficient threshold detection (including SCD thre and SCD heu ) and the second-order difference operation based on linear shrinkage coefficient (LS-SOD) method. Compared with the LS-MDL and SCD methods, the recently proposed LS-SOD method based on linear shrinkage coefficient has shown competitive detection estimation results under various array configuration conditions and has become one of the most representative methods. However, analysis found that this method does not fully utilize the differential information between the first-order and second-order linear shrinkage coefficients, and its performance still has room for further improvement. Therefore, after further mining the differential information of each order, it is of great significance and application value to develop a source number estimation method with better performance and greater universal applicability. Summary of the invention

[0004] The present invention provides a method for estimating the number of signal sources based on a linear shrinkage coefficient corrected differential operation. The method is used to solve the problem that the prior art lacks robustness and universality in signal source number estimation under large-scale array and small sample conditions, and the signal source number estimation performance of the method is better than the signal source number estimation performance of the existing method based on a linear shrinkage coefficient second-order differential operation.

[0005] The technical solution adopted by the present invention is a method for estimating the number of information sources based on linear expansion coefficient corrected differential operation, the method comprising the following steps:

[0006] S1. Set the output data of the array antenna at time t to x t =As t +w t , where A represents the m×d-dimensional array steering matrix, s t and w t Represent d×1-dimensional and m×1-dimensional independent and identically distributed Gaussian signal and noise vectors respectively; for the output data x t After n samplings, the sample covariance matrix R is obtained. Perform eigenvalue decomposition on R to obtain its descending eigenvalues: λ1≥λ2≥…≥λ m , where m represents the number of array antennas, d represents the number of signal sources, and the superscript H represents the conjugate transpose operation;

[0007] S2. Let k be the set source value, and the value range of k is: k∈[0,c]. Within the value range, calculate the linear expansion coefficient α corresponding to each value of k in turn. (k) , in, represents a tuning parameter less than 1;

[0008] S3, obtaining the difference Δ between adjacent first-order linear expansion coefficients (k) , Δ (k) =α (k+1) -α (k) ;

[0009] S4, according to the difference obtained in step S3, find the maximum value from all the difference values, and the value of k corresponding to the maximum value is the estimated initial source value d1;

[0010] S5. Obtain the difference of c second-order linear expansion coefficients

[0011] S6, taking several values ​​near the initial information source value d1 as the new set information source value For each Before obtaining The second-order difference and the The correction factor is obtained by taking the difference of the second-order differences Right now

[0012] S7. Obtaining a corrected differential value based on a linear expansion coefficient Find the maximum value from all the corrected differential values, the maximum value of the corrected differential value corresponds to is the estimated final source value d2, that is

[0013] The beneficial effects of the present invention are as follows: compared with the prior art, the present invention makes full use of the first-order and second-order differential information of the linear expansion coefficient, and is better applicable to large-scale arrays and small sample scenarios. Compared with the prior art solution, the method of the present invention can provide a higher probability of successful detection by increasing the correction factor, and the calculation efficiency is very high.

[0014] Preferably, in step S2, The value range is [0.5-0.8].

[0015] Preferably, in step S4, The selection range is: and BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The present invention provides a method for estimating the number of signal sources based on linear expansion coefficient modified differential operation;

[0017] Figure 2A A comparison diagram of the probability of correct detection of the number of signal sources (Probability of Correct Detection) obtained by the signal source number estimation method adopted in scenario 1 in the simulation experiment 1 described in the present invention as a function of the signal-to-noise ratio (SNR);

[0018] Figure 2B A comparison diagram of the probability of correct detection of the number of signal sources (Probability of Correct Detection) obtained by the signal source number estimation method adopted in scenario 2 in the simulation experiment 1 described in the present invention as a function of the signal-to-noise ratio (SNR);

[0019] Figure 3A A comparison chart showing the variation of the probability of accurate detection of the number of sources obtained by the method for estimating the number of sources in the simulation experiment 2 described in the present invention under scenario 1 with the number of samples (Number of Samples);

[0020] Figure 3B A comparison chart showing the variation of the probability of accurate detection of the number of sources obtained by the method for estimating the number of sources in scenario 2 in the simulation experiment 2 described in the present invention with the number of samples (Number of Samples);

[0021] Figure 4AA comparison chart showing the variation of the probability of accurate detection of the number of sources with the number of sources (Number of Sources) obtained by the method for estimating the number of sources used in scenario 1 in simulation experiment 3 described in the present invention;

[0022] Figure 4B This is a comparison chart of the accurate detection probability of the number of sources obtained by the method for estimating the number of sources used in scenario 2 in simulation experiment 3 described in the present invention as the number of sources (Number of Sources) changes. DETAILED DESCRIPTION

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

[0024] The present invention relates to a method for estimating the number of information sources based on a linear expansion coefficient modified differential operation proposed in a large-dimensional random matrix theory system, such as Figure 1 As shown, the method comprises the following steps:

[0025] S1. Set the output data x of the array antenna at time t t =As t +w t , where A represents the m×d-dimensional array steering matrix, s t and w t Represent d×1-dimensional and m×1-dimensional independent and identically distributed Gaussian signal and noise vectors respectively; for the output data x t After n samplings, the sample covariance matrix is ​​calculated as Perform eigenvalue decomposition on R to obtain its descending eigenvalues ​​λ1≥λ2≥…≥λ m , where m represents the number of array antennas, d represents the number of signal sources, and the superscript H represents the conjugate transpose operation;

[0026] S2. Let k be the set source value, and the value range of k is: k∈[0,c]. Within the value range, calculate the linear scaling coefficient corresponding to each value of k in turn. in, represents a tuning parameter less than 1; where The value range of is [0.5-0.8];

[0027] S3, obtaining the difference Δ between adjacent first-order linear expansion coefficients (k) , Δ (k) =α (k+1) -α (k) ;

[0028] S4. Find the maximum value from all the differences according to the difference obtained in step S3, and the value of k corresponding to the maximum value is the estimated initial source value d1.

[0029] S5. Obtain the differences of c second-order linear stretching coefficients

[0030] S6. Take several values near the initial source value d1 as the newly set source values For each Obtain the difference between the first second-order differences and the last second-order differences to obtain the correction factor

[0031] S7. Obtain the corrected difference values based on the linear stretching coefficients Find the maximum value from all the corrected difference values, and the corresponding to the maximum value of the corrected difference values is the estimated final source value d2, that is

[0032] In step S4, the selection range of is:

[0033] Next, the performance of a source number estimation method based on corrected difference operation of linear stretching coefficients provided by the present invention is analyzed through simulation experiments, and the simulation process is all carried out by MATLAB software.

[0034] Simulation experiment 1: The accurate detection probability varies with the signal-to-noise ratio (SNR)

[0035] Ten source signals with angles uniformly distributed in [-18°, 18°] are incident on a uniform linear array, and the array antenna spacing is 1 / 2 of the carrier wavelength of the incident signal. Consider the following two different array sample scenarios: Scenario 1: m = 50, n = 65 (i.e., m < n), SNR varies from -15 dB to 5 dB; Scenario 2: m = 50, n = 30 (i.e., m > n), SNR varies from -10 dB to 2 dB. The curves of the accurate detection probability of the source number in Scenario 1 and Scenario 2 are shown in Figures 2(A) and 2(B) respectively. It can be seen that the method of the present invention (Proposed) is the most stable method, and can improve the improved estimation / detection performance in both scenarios. In particular, the SNR required for the method of the present aspect to accurately detect the source number is 1 dB lower than that of the algorithm without the correction factor in Scenario 2, which fully proves the superiority of the method of the present invention.

[0036] Simulation Experiment 2: Variation of Accurate Detection Probability with Sampling Samples (Number of Samples)

[0037] Ten source signals with angles uniformly distributed in [-18°, 18°] are incident on a uniform linear array, and the array antenna spacing is 1 / 2 of the carrier wavelength of the incident signal. Consider the following two different array sample scenarios: Scenario 1: m = 60, SNR = -10 dB, n varies from 30 to 100; Scenario 2: m = 60, SNR = -6 dB, n varies from 15 to 50. The variation curves of the accurate detection probability of the number of sources in Scenario 1 and Scenario 2 are shown in Figures 3(A) and 3(B) respectively. It can be seen that the accurate detection probability of the method of the present invention is proportional to n, and in the entire observation interval, the method of the present invention is superior to the method without a correction factor. In particular, in the case of different SNRs, the estimation accuracy in the entire observation interval increases by 5% - 20%, which once again proves the superiority of the method of the present invention.

[0038] Simulation Experiment 3: Variation of Accurate Detection Probability with the Number of Sources (Number of Sources)

[0039] d source signals are uniformly distributed in the interval [(-3d + 3)°, (3d - 3)°] at intervals of 3°, d varies from 1 to 45, SNR = -9 dB, and the array antenna spacing is 1 / 2 of the carrier wavelength of the incident signal. Similarly, consider two scenarios: Scenario 1: m = 60, n = 65 (i.e., m < n); Scenario 2: m = 65, n = 60 (i.e., m > n). The variation curves of the accurate detection probability of the number of sources in Scenario 1 and Scenario 2 are shown in Figures 4(A) and 4(B) respectively. From the simulation results, it can be seen that the method of the present invention can estimate more source numbers with a higher success probability. Especially in the observation interval where the number of sources is greater than 20, the success estimation probability increases significantly. For example, in Figure 4(A), the correct estimation probability of the part with the number of sources being 25 is more than 15% higher than that of the method without a correction factor, which fully shows that the method of the present invention has good ability to estimate a large number of sources.

Claims

1. A method for estimating the number of information sources based on linear scaling coefficient modified differential operation, characterized in that: The method comprises the following steps: S1. Set the output data of the array antenna at time t to x t =As t +w t , where A represents the m×d-dimensional array steering matrix, s t and w t Represent d×1-dimensional and m×1-dimensional independent and identically distributed Gaussian signal and noise vectors respectively; for the output data x t After n samplings, the sample covariance matrix R is obtained. Perform eigenvalue decomposition on R to obtain its descending eigenvalues: λ1≥λ2≥…≥λ m , where m represents the number of array antennas, d represents the number of signal sources, and the superscript H represents the conjugate transpose operation; S2. Let k be the set source value, and the value range of k is: k∈[0, c]. Within the value range, calculate the linear expansion coefficient α corresponding to each value of k in turn. (k) , in, Indicates a tuning parameter less than 1; S3, obtaining the difference Δ between adjacent first-order linear expansion coefficients (k) , Δ (k) =α (k+1) -α (k) ; S4, according to the difference obtained in step S3, find the maximum value from all the difference values, and the value of k corresponding to the maximum value is the estimated initial source value d1; S5. Obtain the difference of c second-order linear expansion coefficients S6, taking several values ​​near the initial information source value d1 as the new set information source value For each Before obtaining The second-order difference and the The correction factor is obtained by taking the difference of the second-order differences Right now S7. Obtaining a corrected differential value based on a linear expansion coefficient Find the maximum value from all the corrected differential values, the maximum value of the corrected differential value corresponds to is the estimated final source value d2, that is 2. The method for estimating the number of information sources based on linear scaling coefficient corrected differential operation according to claim 1, characterized in that: In step S2, The value range is [0.5-0.8].

3. The method for estimating the number of information sources based on linear scaling coefficient corrected differential operation according to claim 2, characterized in that: In step S4, The selection range is: and

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