On the robustness of co-prime sampling

Coprime sampling has been shown to be an effective deterministic sub-Nyquist sampling scheme for estimating the power spectrum of wide sense stationary signals without any loss of information. In contrast to the existing results in coprime sampling which only assume an ideal setting, this paper considers both additive perturbation on the sampled signal, as well as sampling jitter, and analyzes their effect on the quality of the estimated correlation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbations. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Additional results on identifiability in spatial spectrum estimation are derived using the Fisher Information Matrix, which indicate that with high probability, it is still possible to identify O(M²) sources with M sensors, with a perturbed coprime array.