恒虚警检测信源数的方法

doi:10.12305/j.issn.1001-506X.2022.01.01

Abstract

Abstract:

A new method with a given constant false alarm rate for detecting signal source numbers is proposed. A five-dimension vector with the statistics of the eigenvalue differences of an observation covariance matrix is first defined. Then, the K-means clustering algorithm is used to divide these vectors into two classes. which are respectively regarded as the signal and noises subspaces of the eigenvalues corresponding to the five-dimension vectors. When the eigenvalues of noise are expressed as a probability distribution with a Gaussian mixture one known to be able to describe any probability distribution, the expectation maximization (EM) algorithm can be utilized to estimate the distribution. By means of the estimated distribution, the Neyman-Pearson (NP) hypothesis test is exploited to do source number detection with a given constant false alarm rate. Moreover, an approximated NP hypothesis, where the noise eigenvalue distribution is assumed Gaussian one regardless of the actual one, is given in order to reduce the computation complexity of the proposed method. Numerical simulation results verify the effectiveness of the proposed method while its superiority over the methods reported in literature is shown.

Key words: signal source number detection, constant false alarm rate, expectation-maximization (EM) algorithm, K-means, clustering

CLC Number:

TP957

Yidi ZHANG, Yuebin WANG, Peizhi WANG, Qin YANG, Qiyong LU, Jianqiu ZHANG, Dan LI. A method for detecting the number of signal sources with constant false alarm[J]. Systems Engineering and Electronics, 2022, 44(1): 1-9.

Figures/Tables 8

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Table 1

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高斯混合分布	虚警率
高斯混合分布	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.99
c=2	0.007	0.058	0.111	0.211	0.311	0.407	0.493	0.572	0.654	0.752	0.899	1.000
c=3	0.006	0.056	0.108	0.209	0.306	0.406	0.507	0.584	0.665	0.757	0.891	1.000
c=5	0.005	0.056	0.108	0.208	0.306	0.406	0.502	0.592	0.674	0.763	0.886	1.000
c=10	0.005	0.055	0.108	0.206	0.305	0.404	0.503	0.595	0.681	0.768	0.884	1.000

SNR/dB	虚警率
SNR/dB	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.99
0	0.005	0.055	0.108	0.208	0.307	0.406	0.503	0.591	0.675	0.763	0.886	1.000
10	0.012	0.050	0.098	0.203	0.308	0.409	0.505	0.592	0.673	0.763	0.888	1.000
30	0.031	0.050	0.102	0.211	0.316	0.412	0.496	0.576	0.657	0.755	0.901	1.000

SNR/dB	虚警率
SNR/dB	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.99
0	0.019	0.076	0.128	0.213	0.289	0.364	0.442	0.526	0.624	0.754	0.950	1.000
10	0.032	0.070	0.112	0.189	0.264	0.342	0.424	0.516	0.626	0.776	0.974	1.000
30	0.033	0.033	0.037	0.066	0.067	0.099	0.206	0.516	0.992	1.000	1.000	1.000

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A method for detecting the number of signal sources with constant false alarm

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