Asymptotic Performance Analysis of Direction-Finding Algorithms Based on Fourth-Order Cumulants

In the narrow-band array processing context, the use of higher order statistics has been often advocated because consistent and asymptotically unbiased parameter estimates can be obtained without it being necessary to know, to model, or to estimate the spatial covariance of the noise as long as it is normally distributed. However, experimentation shows that this 'noise insensitivity' is traded for increased variability of the parameter estimates. The main purpose of this contribution is to derive and work out closed-form expressions of the asymptotic covariance of MUSIC-like direction-of-arrival estimates based on two fourth-order cumulant matrices: the diagonal slice and the contracted quadricovariance. This is compared with the standard covariance-based MUSIC estimate establishing on a rational basis the domain of applicability of higher order statistics for DOA estimation. In particular, the actual impact of the noise variance and of the dynamic range of the sources is investigated. This asymptotic performance analysis is achieved within a general framework, which we believe to be of general interest.