Blind non-parametric statistics for multichannel detection based on statistical covariances

We consider the problem of detecting the presence of a spatially correlated multichannel signal corrupted by additive Gaussian noise (i.i.d across sensors). No prior knowledge is assumed about the system parameters such as the noise variance, number of sources and correlation among signals. The non-parametric detection statistics were formed based on the statistical covariances obtained through Bartlett decomposition of sample covariance matrix. They are designed such that the detection performance is immune to the uncertainty in the knowledge of noise variance. The analysis presented verifies the invariability of threshold value and identifies a few specific scenarios where the proposed statistics have better performance compared to generalised likelihood ratio test (GLRT) statistics. The sensitivity of the statistic to correlation among streams, number of sources and sample size at low signal to noise ratio are discussed.

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