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This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M × K MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statistics based on the eigenvalues of an estimate of the spectral coherence matrix (SCM), obtained as a renormalization of the frequency-smoothed periodogram of the observed signal. If N denotes the sample size and B the smoothing span, it is proved that in the high-dimensional regime where M,B,N converge to infinity while K remains fixed, the SCM behaves as a certain correlated Wishart matrix. Exploiting well-known results on the behaviour of the eigenvalues of such matrices, it is deduced that the standard tests based on linear spectral statistics of the SCM fail to detect the presence of the useful signal in the high-dimensional regime. A new test based on the SCM, which is proved to be consistent, is also proposed, and its statistical performance is evaluated through numerical simulations. © 1991-2012 IEEE.

In the field of DoA estimation in array processing, we summarize recent results on an improved MUSIC method (referred to as G-MUSIC), developed in the context where the number of samples N of the observed signal is large, and of the same order of magnitude than the number of sensors. Using results from random matrix theory, we provide a statistical performance analysis of the G-MUSIC method, in terms of consistency, mean square error, and asymptotic normality, in the context of unknown deterministic source signals. A comparison with the classical MUSIC method is provided in a first scenario with widespace DoA, and in a second scenario with closely spaced DoA.