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Citation Author(s):
Alexis Rosuel, Pascal Vallet, Philippe Loubaton, Xavier Mestre
Submitted by:
Alexis Rosuel
Last updated:
14 May 2020 - 8:44am
Document Type:
Presentation Slides
Document Year:
Presenters Name:
Alexis Rosuel
Paper Code:



We address the problem of detection, in the frequency domain, of a M-dimensional time series modeled as the output of a M × K MIMO filter driven by a K-dimensional Gaussian white noise, and disturbed by an additive M-dimensional Gaussian col- ored noise. We consider the study of test statistics based of the Spectral Coherence Matrix (SCM) obtained as renormalization of the smoothed periodogram matrix of the observed time series over N samples, and with smoothing span B. To that purpose, we con- sider the asymptotic regime in which M, B, N all converge to infin- ity at certain specific rates, while K remains fixed. We prove that the SCM may be approximated in operator norm by a correlated Wishart matrix, for which Random Matrix Theory (RMT) provides a precise description of the asymptotic behaviour of the eigenvalues. These results are then exploited to study the consistency of a test based on the largest eigenvalue of the SCM, and provide some numerical illustrations to evaluate the statistical performance of such a test.

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