Direction finding algorithms using fourth order statistics: asymptotic performance analysis

High-resolution direction finding algorithms using higher-order cumulants of the array data is addressed. Two fourth-order cumulant-based matrices are considered: the diagonal cumulant slice and the contracted quadricovariance. They are evaluated in the context of direction of arrival (DOA) estimation using subspace techniques. To this purpose, an original methodology is introduced to derive the closed form of asymptotical performance. This analysis is applied to the cumulant-based DOA estimation problem, establishing on a rational basis the domain of applicability of HOS in DOA estimation, which is larger than usually believed. It is also shown that the contracted quadricovariance outperforms the diagonal slice in all respects. Some numerical evaluations illustrate the results