A two-dimensional version of the matrix pencil method to solve the DOA problem

A method is presented to estimate the 2-dimensional directions of arrival of (coherent) narrow-band plane waves radiated by sources located in the far-field of a receiving array. The approach is an extension of the matrix pencil based ESPRIT algorithm to the multi-dimensional parameter space. The basic strategy that is followed is to decouple the problem into two independent 1-dimensional subproblems, resulting in two 1-D solution sets. Then the correct combination of angles from the two sets, forming a tuple associated with one specific signal, is obtained without doing an extensive search over the 1-D sets. For the coherent situation the concept of spatial smoothing is discussed in combination with a TLS approximation technique that is applicable in both the one- and multi-dimensional cases. Simulation results of the 2-D TLS pencil method for the coherent and non-coherent situation are given