Asymptotic Properties of Nonlinear Weighted Least Squares in Radar Array Processing

This paper treats nonlinear weighted least squares parameter estimation of sinusoidal signals impinging on a sensor array. We give a consistency proof for a more general model than what has been previously considered in the analysis of two-dimensional (2-D) sinusoidal fields. Specifically, the array can have an arbitrary shape, and spatially colored noise is allowed. Further, we do not impose the restriction of unique frequencies within each dimension, and the number of samples is assumed large in only the temporal dimension. In addition to consistency, we establish that the parameter estimates are multivariate Gaussian distributed under a large class of noise distributions. The finite sample performance is investigated via computer simulations, which illustrate that a recommended two-step procedure yields asymptotically efficient estimates when the noise is Gaussian. The first step is necessary for estimating the weighting matrix, which has a dramatic influence on the performance in the studied scenarios. The number of samples required to attain the Cramér–Rao lower bound is found to coincide with the point where the signal sources are separated by more than one discrete Fourier transform bin. This remains true even when the signals emanate from the same direction of arrival (DOA).