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Statistical performance of MUSIC-like algorithms in resolving noncircular sources

Abstract : This paper addresses the resolution of the conventional and noncircular MUSIC algorithms for arbitrary circular and noncircular second-order distributions of two uncorrelated closely spaced transmitters observed by an arbitrary array. An explicit closed-form expression of the mean null spectrum of the conventional and noncircular MUSIC algorithms is derived using an analysis based on perturbations of the noise projector instead of those of the eigenvectors. Based on these results, theoretical and approximate interpretable closed-form expressions of the threshold array signal to noise ratios (ASNR) at which these two algorithms are able to resolve two closely spaced transmitters along the Cox and the Sharman and Durrani criteria are given. It is proved that the threshold ASNRs given by the conventional MUSIC algorithm do not depend on the distribution of the sources including their noncircularity, in contrast to the noncircular MUSIC algorithm for which they are very sensitive to the noncircularity phase separation of the sources. This threshold ASNR given by the noncircular MUSIC algorithm is proved to be comfortably lower that that given by the conventional MUSIC algorithm except for weak phase separations of the sources for which the resolving powers of these two algorithms are very close. Finally, these results are analyzed through several illustrations and Monte Carlo simulations.
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https://hal.archives-ouvertes.fr/hal-01372028
Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Monday, September 26, 2016 - 5:12:36 PM
Last modification on : Wednesday, June 24, 2020 - 4:19:30 PM

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Habti Abeida, Jean-Pierre Delmas. Statistical performance of MUSIC-like algorithms in resolving noncircular sources. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2008, 56 (9), pp.4317 - 4329. ⟨10.1109/TSP.2008.924143⟩. ⟨hal-01372028⟩

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