On the performance of signal-subspace processing--Part II: Coherent wide-band systems

This is the second part of a study which deals with the performance of multiple-source direction finding via signal-subspace processing [1]. An analytical evaluation of detection (determination of the number of sources) and direction estimation performance is presented for the coherent wide-band signal-subspace processing algorithm [2], which operates on the received array signals of large relative bandwidth. The probabilities of underestimating and overestimating the number of sources are derived, under asymptotic conditions and in 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 spatially white noise. A scalar measure is used for the evaluation of the quality of the estimated signal subspaces. It is shown that the detection and estimation performances of the practical coherent algorithm are close to those of the perfectly coherent processing, and that they are relatively insensitive with respect to a preliminary estimate of the angles used to effect an approximate coherence.