Asymptotic performance analysis of esprit-type algorithms for circular and strictly non-circular sources with spatial smoothing

Abstract

Spatial smoothing is a widely used preprocessing scheme to improve the performance of high-resolution parameter estimation algorithms in case of coherent signals or a small number of available snapshots. In this paper, we present a first-order performance analysis of Standard and Unitary ESPRIT as well as NC Standard and NC Unitary ESPRIT for strictly second-order (SO) non-circular (NC) sources when spatial smoothing is applied. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximations become exact for either high SNRs or a large sample size. Moreover, they are explicit in the noise realizations, i.e., only a zero-mean and finite SO moments of the noise are required. We show that both NC ESPRIT-type algorithms with spatial smoothing perform asymptotically identical in the high effective SNR. Also, for the special case of a single source, we analytically derive the optimal number of subarrays for spatial smoothing and show that no gain from strictly non-circular sources is achieved in this case.