Performance of narrowband signal-subspace processing

This paper presents an analytical evaluation of detection (determination of the number of sources) and estimation performances of narrowband signal-subspace processing for multiple-source direction finding. The probabilities of underestimating and overestimating the number of sources are derived, under asymptotic conditions and around threshold region, in terms of the choice of a penalty function and signal, noise and array parameters for the cases of at most two closely-spaced sources in the spatially white noise. A scalar measure is introduced for the evaluation of the quality of the estimated signal-subspace. Based on the statistics of this measure performance thresholds are demonstrated for the signal-to-noise ratio, angle separation and correlation between two equipowered sources.