On the Efficiency of Coarray-Based Direction of Arrival Estimation

Abstract

Sparse arrays are widely known for their ability to identify 𝒪(N²) directions of arrivals (DOAs) using N sensors through the difference coarray domain. However, coarray-MUSIC, a commonly used method for obtaining the DOA estimates through the coarray domain, has been found to be inefficient for sparse arrays, even under high signal-to-noise ratios (SNR) and a large number of snapshots. This means that the coarray-MUSIC mean squared error (MSE) is larger than the Cramér-Rao bound (CRB) even for a large SNR and a large number of snapshots. In this paper, to understand when and how the coarray-MUSIC loses its efficiency, we consider the simplest case of a uniform linear array (ULA) when the number of sources D is less than the number of sensors N. Standard (element-space) MUSIC already achieves CRB in this case, but we observe that coarray-MUSIC suffers significant performance loss, similar to what has been observed for sparse arrays. We also consider two variations of the coarray-MUSIC algorithm by using tall and fat variations of the coarray covariance matrix. Additionally, we experimentally find that coarray-MUSIC MSE for 2-source cases varies in surprising ways with DOA separation. We also demonstrate that perturbing different array output correlations have an unequal effect on coarray-MUSIC MSE. These observations provide valuable insights into the (in)efficiency of coarray-MUSIC and provide directions for further investigations.

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