Source Enumeration Method Combining Gerschgorin Circle Transform and Generalized Bayesian Information Criterion in Large-scale Antenna Array
关键词:
Colored noise, corrected Rao’s score test, general asymptotic regime, Gerschgorin circle transform, source enumeration摘要
A new source enumeration method based on gerschgorin circle transform and generalized Bayesian information criterion is devised, for the case that the antenna array observed signals are overlapped with spatial colored noise, and the number of antennas compared with that of snapshots meet the requirement of general asymptotic regime. Firstly, the sample covariance matrix of the observed signals is calculated, and then gerschgorin circle transformation is carried out on the sample covariance matrix. With the help of the more obvious distinction between the transformed signal gerschgorin circle radius and the noise gerschgorin circle radius, the observation statistic used to establish the likelihood function of the information theoretic criterion is constructed, by using the estimated values of the transformed sample covariance matrix’s eigenvalues, and according to the idea of corrected Rao’s score test, the observed statistics used to establish the likelihood function of the ITC are constructed. Based on the statistics, the source number is estimated by employing the generalized Bayesian information criterion (GBIC). The effectiveness of the proposed method is validated by experiments. Compared with the information theoretic criterion (ITC) methods and gerschgorin circle method (GDE), in Gaussian white noise, at the time M/N ≥ 1, that is the relationship between the number of antennas and that of snapshots meets the requirement of the general asymptotic regime, the proposed method can accurately estimate the source number with 100% probability, the other methods failed. Compared with the ITC methods based on eigenvalue diagonal loading and GDE, in colored noise, at the time M/N ≥ 1, the proposed method can accurately estimate the source number with 100% probability, the other methods failed. Compared with the methods based on random matrix theory, in colored noise, the proposed method can estimate the source number with 100% probability, but the estimation of other methods failed. The proposed method has wide applicability, in terms of the relationship between the numbers of antennas and snapshots, it is suitable for both general asymptotic regime and classical asymptotic system, and in terms of noise characteristics, it is suitable for both Gaussian white noise environment and colored noise environment.
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