On the Performance of Signal-Subspace Processing—Part I: Narrow-Band Systems

This paper presents an analytical evaluation of detection (determination of the number of sources) and estimation performances of narrow-band 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 the threshold regions, 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.