Analytical performance assessment of esprit-type algorithms for coexisting circular and strictly non-circular signals

Abstract

Estimating the directions of arrival (DOA) of coexisting circular and strictly second-order (SO) non-circular (NC) signals has recently emerged as an active field of research. In previous work, we have proposed two ESPRIT-type algorithms, i.e., C-NC Standard ESPRIT and C-NC Unitary ESPRIT, for this scenario that improve the estimation accuracy of the conventional schemes and increase the number of resolvable signals. In this paper, we present a first-order performance assessment of these two ESPRIT-type algorithms. Specifically, we derive closed-form mean square error (MSE) expressions that 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. Apart from a zero mean and finite SO moments, no further assumptions on the noise statistics are required. We show that both algorithms perform identical in the high effective SNR regime. Moreover, the analytical results verify the previously observed property that the presence of strictly non-circular sources improves the estimation accuracy of the circular signals.