Co-prime sampling jitter analysis

Abstract

Abstract-Co-prime arrays and samplers are popular subNyquist schemes for estimating second order statistics at the Nyquist rate. This paper focuses on the perturbations in the array locations or sampling times, and analyzes its effect on the difference set. Based on this analysis we propose a method to estimate the autocorrelation which makes best use of the sampled data in order to improve the estimation accuracy of the autocorrelation and hence the spectral estimate. Our analysis indicates that such an advantage is limited only to samplers, and does not carry over to the antenna arrays. In addition, we obtain expressions for the computational complexity of the autocorrelation estimation and provide an upper bound on the number of multiplications and additions required for its hardware implementation.

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

“…The weight function for the co-prime samplers with multiple periods under the influence of sampling jitters is given by Proposition II, and is similar to Proposition II in [10] which was derived for the prototype co-prime samplers with perturbations. The work in [10] had described two systems; a blind system and a non-blind system, and is also considered here for the multiple period scenario. The blind system is a system in which the presence of jitter is unknown and hence it follows the procedure used in the ideal scenario for autocorrelation estimation.…”

“…Since m 1 +m 2 < 2rM and n 1 +n 2 < 2rN , there is a possibility of obtaining the co-prime ratio on the right-hand-side of equation (10). Hence, the Proposition 6 fails.…”

“…This paper is dedicated to the study of the difference set of the sub-Nyquist co-prime sampler with multiple periods under the influence of jitter. It may be noted that [10] is a special case of the work described here, i.e. it has only one period.…”

“…It shows that the errors in autocorrelation estimation (under certain assumptions) is bounded. Most of the work considers the study of jitters in the statistical sense, however, the work in [10,11] studies the effect of jitter on the difference set of the sub-Nyquist co-prime array. Here, an increase in the number of contributors for estimation is possible only for the case of temporal sampling and fails for antenna arrays.…”

Co-prime arrays and difference set analysis

“…(For an antenna array, only one antenna would be placed at the common zeroth location.) This detailed analysis of the self and cross differences individually will be useful in the analysis of non-synchronized arrays [11]. A summary of the number of unique differences in each difference set is given in Table I.…”