The Mean-Squared-Error of autocorrelation sampling in coprime arrays

Standard direction-of-arrival estimation using coprime arrays samples the entries of the estimated physical-array autocorrelation matrix, organizes them in a matrix structure, and conducts multiple-signal classification (MUSIC) with singular vectors of the resulting matrix. A majority of the existing literature samples the physical-array autocorrelations by selection, retaining only one of the samples that correspond to each element of the difference coarray. Other more recent works conduct averaging of all samples that relate to each coarray element. Even though the two methods coincide when applied on the nominal/true physical-array autocorrelations, their performance differs significantly when applied on finite-snapshot estimates. In this paper, we present for the first time in closed form the mean-squared-error of both selection and averaging autocorrelation sampling and clarify/establish the superiority of the latter.