Co-Prime Sensing with Multiple Periods and Difference Set Analysis in the Presence of Sampling Jitter

Abstract

Co-prime arrays and samplers with multiple periods is a framework in which the co-prime structure is repeated multiple times. In this paper, the effects of perturbations in sampling locations on the difference set of the prototype co-prime structure with multiple periods is analysed. Based on this analysis, a method to estimate the autocorrelation that maximizes the amount of information extracted from the data is proposed. The advantage is limited only to samplers, and is not observed in antenna arrays. The expression for the number of additional contributors available for estimation is derived. The contributors increase with the increase in the number of periods. In addition, the expressions for the computational complexity are derived in the presence of jitter. This provides an upper bound on the number of multiplications and additions for hardware implementation.