A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matrix has to be (i) Positive Definite, (ii) Hermitian, (iii) Toeplitz, and (iv) its noise-subspace eigenvalues have to be equal. Existing coarray autocorrelation matrix estimates satisfy a subset of the above conditions. In this work, we propose an optimization framework which offers a novel estimate satisfying all four conditions: we propose to iteratively solve a sequence of distinct structure-optimization problems and show that, upon convergence, we provably obtain a single estimate satisfying (i)-(iv). Numerical studies illustrate that the proposed estimate outperforms standard counterparts, both in autocorrelation matrix estimation error and Direction-of-Arrival estimation.

共质数阵列接收器处理接收到的信号快照的集合，以估计较大（虚拟）均匀线性阵列（称为共阵列）的自相关矩阵。根据接收信号模型，此矩阵必须为（i）正定，（ii）Hermitian，（iii）Toeplitz，并且（iv）其噪声子空间特征值必须相等。现有的共数组自相关矩阵估计满足上述条件的子集。在这项工作中，我们提出了一个优化框架，该框架提供了满足所有四个条件的新颖估计：我们提议迭代地解决一系列不同的结构优化问题，并证明在收敛时，我们可证明获得了满足（i）- （iv）。数值研究表明，建议的估算值优于标准估算值，