Super-Nyquist Co-Prime Sensing

Abstract

The theory of co-prime arrays has been studied in the past. Nyquist rate estimation of second order statistics using the combined difference set was demonstrated with low latency. This paper proposes a novel method to reconstruct the second order statistics at a rate that is twice the Nyquist rate using the same sub-Nyquist co-prime samplers. We analyse the difference set, and derive the closed-form expressions for the weight function and the bias of the correlogram estimate. The main lobe width of the bias window is approximately half of the width obtained using the prototype co-prime sampler. Since the proposed scheme employs the same rate prototype co-prime samplers; the number of samples acquired in one co-prime period and hardware cost are unaffected. Super-Nyquist estimation with multiple co-prime periods is also described. Furthermore, n-tuple or multi-level co-prime structure is presented from a super-Nyquist perspective. Here, estimation at a rate q times higher than Nyquist is possible, where q is the number of sub-samplers.