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 polynomial rooting algorithm is Root-MUSIC (RM) wherein, for an N-element array, the estimation of the directions of arrivals (DOA) requires the computation of the roots of a 2N−2-order polynomial for a second order (SO) statistics- and a 4N−4-order polynomial for a fourth order (FO) statistics-based approach, wherein the DOA are estimated from L pairs of roots closest to the unit circle, when L signals are incident on the array. We derive SO- and FO statistics reduced polynomial rooting (RPR) algorithms capable to estimate L DOA from L roots only. We demonstrate numerically that the RPR algorithms are at least as accurate as the RM algorithms. Simplified algebraic structure of RPR algorithms leads to better performance than afforded by RM algorithms in saturated array environment, especially in the case of FO methods when number of incident signals exceeds number of elements and under low SNR and/or small sample size conditions.