Wavefield modeling and array processing .II. Algorithms

For pt.I see ibid. vol.42, no.10, p.2549, 1994. We present several novel algorithms for array processing, as well as extensions of existing methods based on this approach. We first consider the problem of localization of wideband sources via coherent processing, and show how wavefield modeling enables us to derive expressions for the frequency transformation (focusing) matrices. This method is extended to three dimensions and to sector processing. We then develop computationally efficient implementations of MUSIC and Root-MUSIC for the narrowband and the coherent and incoherent wideband cases, as well as a natural extension of Root-MUSIC to any 2-D array. In addition, wavefield modeling allows us for the first time to extend Root-MUSIC to 3-D arrays and wavefields. We also present a low complexity variant of Root-MUSIC for direction finding within a limited angular sector. Finally, we derive a low-dimensional sufficient statistic and reduced rank processing schemes for the case of oversampled arrays and/or limited angular sector scenarios