Minimum Mean-Squared-Error autocorrelation processing in coprime arrays

•Review of existing autocorrelation combining approaches in coprime array literature.•Novel coprime array autocorrelation combiner designed under the MMSE criterion.•Proposed MMSE autocorrelation combiner accompanied by formal derivation proofs.•Carried out complexity analysis of the proposed MMSE autocorrelation combiner.•Offered derivation proofs for the MSE expressions of selection/averaging combining. Coprime arrays enable Direction-of-Arrival (DoA) estimation of an increased number of sources. To that end, the receiver estimates the autocorrelation matrix of a larger virtual uniform linear array (coarray), by applying selection or averaging to the physical array's autocorrelation estimates, followed by spatial-smoothing. Both selection and averaging have been designed under no optimality criterion and attain arbitrary (suboptimal) Mean-Squared-Error (MSE) estimation performance. In this work, we design a novel coprime array receiver that estimates the coarray autocorrelation with Minimum-MSE (MMSE), for any probability distribution of the source DoAs. Our extensive numerical evaluation illustrates that the proposed MMSE approach returns superior autocorrelation estimates which, in turn, enable higher DoA estimation performance compared to standard counterparts.