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 autocorrelations 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.

翻译：共价阵列能够对增加的源数进行抵达方向(DoA)估计。 为此,接收者通过对物理阵列的自成一体线性阵列(coarrary)进行选择或平均地对物理阵列的自成一体线性阵列估计数进行估计,然后进行空间吸附。选择和平均都是在没有最佳性能标准的情况下设计出来的,并且达到了任意(次优)平均平差(MSE)估计性能。在这项工作中,我们设计了一个新颖的组合阵列接收器,用来估计与最低线性阵列(MMSE)的共振动自动关系(MMSE),以了解源的概率分布。我们广泛的数字评估表明,拟议的MMSE方法使高级自成一体估计结果,而这又使得DoA的估算性能高于标准的对应方。