DocumentCode :
834921
Title :
Statistical Performance of MUSIC-Like Algorithms in Resolving Noncircular Sources
Author :
Abeida, Habti ; Delmas, Jean-Pierre
Author_Institution :
Dept. CITI, CNRS, Evry
Volume :
56
Issue :
9
fYear :
2008
Firstpage :
4317
Lastpage :
4329
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 proven to be comfortably lower than 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.
Keywords :
Monte Carlo methods; eigenvalues and eigenfunctions; signal classification; Cox criteria; Durrani criteria; Monte Carlo simulations; Sharman criteria; eigenvectors; explicit closed-form expression; mean null spectrum; noise projector; noncircular MUSIC algorithms; noncircular second-order distributions; phase separation; statistical performance; threshold array signal-to-noise ratios; uncorrelated closely spaced transmitters; Algorithm design and analysis; Antenna arrays; Array signal processing; Astronomy; Closed-form solution; Multiple signal classification; Signal processing algorithms; Signal resolution; Signal to noise ratio; Transmitters; Circular and noncircular signal; MUSIC algorithm; direction of arrival (DOA); threshold of resolution;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2008.924143
Filename :
4599158
Link To Document :
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