Cramér–Rao bound analysis of nested arrays under impulsive noise with coarrays and FLOSs

Abstract

Nested arrays are extensively employed in array signal processing to augment the degrees of freedom and enhance estimation precision, and the Cramér–Rao Bound (CRB) for nested arrays in a Gaussian noise environment has been established. Nevertheless, in a practical wireless communication environment, noise usually exhibits an impulsive characteristic. The impulsive noise applied in a uniform linear array (ULA) has been extensively studied in the literature, but only closed-form expressions of CRB with Cauchy and Gaussian noise distributions are given. Although nested arrays have garnered significant attention recently, research on the CRB under impulsive noise conditions remains scarce. In this paper, we provide the CRB expression for direction of arrival (DOA) estimation with nested arrays in an impulsive noise environment, which indicates that the CRB is formulated in terms of the fractional low-order statistics (FLOSs) of received data. Moreover, we also calculate the CRB results for different FLOSs as well as various sparse arrays and validate that the derived CRB makes an important contribution to the performance analysis of sparse arrays in impulsive noise.