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.

互质数组可以实现增加数量的源的到达方向（DoA）估计。为此，接收器通过将选择或求平均值应用于物理阵列的自相关估计，然后进行空间平滑，来估计更大的虚拟均匀线性阵列（共阵列）的自相关矩阵。选择和平均均已在没有最佳标准的情况下进行了设计，并获得了任意（次优）均方误差（MSE）估计性能。在这项工作中，我们设计了一种新颖的共质数阵列接收器，它可以针对源DoA的任何概率分布，估计与最小MSE（MMSE）的协数自相关。我们的大量数值评估表明，所提出的MMSE方法返回了较高的自相关估计，这反过来，