Fourth-order cumulant based source localization with spatial matrix prefilter

As an implementation of spatial filtering, spatial matrix filter (SMF), with element-space data output, is able to offer visible performance improvements of direction-of-arrival (DOA) estimation of multiple signals through attenuating the noise and interference in spatial stopband. Our formulation leads to an optimization problem to design SMF, which is solved efficiently in a second-order cone programming (SOCP) framework by an interior point implementation. Based on fourth-order cumulant (FOC) of the data snapshots filtered by the SMF, we proposed a source localization approach. It eliminates the effects caused by the white Gauss noise (WGN) being transformed into color Gauss noise (CGN) after SMF prefiltering. Results of simulation show that our approach has a number of advantages over other source localization techniques, including improved robustness to noise, reduced DOA estimation bias as well as increased precision and resolution. Moreover, the approach attenuates the spatial interferences effectively so that it is possible to estimate DOAs for more than N narrow-band sources using an N-element array. An example is given to illustrate this capability.