Performance Breakdown in Parameter Estimation Using Co-Prime Arrays

In this paper, we study threshold effects associated with swapping of signal and noise subspaces in estimating signal parameters from co-prime arrays. A subspace swap occurs when the measured data is better approximated by a subset of components of an orthogonal subspace than by the components of the noise-free signal subspace, and is known to be the main source of performance breakdown in many cases. We consider a canonical data model in which the parameters modulate the mean value function of complex multivariate normal measurements, and derive a lower bound on the probability of a subspace swap. Our lower bound can be used to predict the probability of a subspace swap for the case that we have co-prime measurements in temporal/spatial domain. We compare the onset of breakdown for co-prime and dense arrays. Our numerical results show that for the cases where the co-prime array corresponds to subsampling of a bigger dense array by a factor C, the threshold signal-to-noise ratio is increased about 10 log(10) C dB.