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

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.