  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. Numerical studies illustrate that the proposed estimate
outperforms standard counterparts, both in autocorrelation matrix estimation
error and Direction-of-Arrival estimation.
