Efficiency of subspace-based DOA estimators

Habti Abeida , Jean-Pierre Delmas (1)

1 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications

The purpose of this paper is to determine the domain of validity of spatial covariance-based narrowband DOA algorithms when processing non-narrowband data. By focusing on the case of one source and two equipowered uncorrelated sources of the same bandwidth, we examine order detection and asymptotic bias and covariance w.r.t. the bandwidth and the number of snapshots given by any narrowband algorithm. An order detector scheme, based on numerical analysis arguments introduced in channel order detection, is proposed. Closed-form expressions are given for the asymptotic bias and covariance of the DOA's estimated by the MUSIC algorithm, for which we show the key role that bandwidth plays w.r.t. the demodulation frequency. Furthermore, a common closed-form expression of the Cramer-Rao bound is given for the DOA parameter of a narrowband or wideband source, whose spectrum is symmetric w.r.t. the demodulation frequency, in the case of an arbitrary array. This allows us to prove that the MUSIC algorithm retains its efficiency over a large bandwidth range under these conditions.

Mots clés: direction of arrival estimation; narrowband source location algorithm; wideband source location algorithm; nonzero bandwidth; offset frequency; direction of arrival estimation; Cramer-Rao bound; efficiency; subspace-based DOA estimation; noncircular signals

Domaines: Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]; Théorie [stat.TH]

Habti Abeida, Jean-Pierre Delmas. Efficiency of subspace-based DOA estimators. Signal Processing, 2007, 87 (9), pp.2075-2084. ⟨10.1016/j.sigpro.2006.12.020⟩. ⟨hal-03399871⟩