Second and fourth order statistics-based reduced polynomial rooting direction finding algorithms

Polynomial rooting direction finding (DF) algorithms are a computationally efficient alternative to search based DF algorithms and are particularly suitable for uniform linear arrays (ULA) of physically identical elements provided mutual interaction among the array elements can be either neglected or compensated for. A popular algorithm in such situations is Root MUSIC (RM) wherein the estimation of the Directions Of Arrivals (DOA) requires the computation of the roots of a 2N-2order polynomial for second order (SO) statistics based approach, where N represents number of array elements, or 4N-4order polynomial for fourth order (FO) statistics based approach. Directions Of Arrivals (DOA) are estimated from the L pairs of roots closest to the unit circle where L represents number of emitters. When number of array elements is large that leads to large computational load and eventually can introduce numerical errors in the estimated DOA. In this paper we derive a SO and FO statistics based Modified Root Polynomial (MRP) algorithms requiring the calculation of only L roots in order to estimate the L DOA. We evaluate the performance of the MRP algorithms numerically and show that they are at least as accurate as the RM algorithms but with a significantly simpler algebraic structure.