Statistically Efficient Algorithm for DOA Estimation with Sparse Arrays
Pranav Kulkarni, Palghat P. Vaidyanathan · IEEE Access · 2026
Sparse arrays can identifyO(N2)directions of arrival (DOAs) withNsensors using the difference coarray domain. Coarray-MUSIC relies on eigendecomposition of a Toeplitz matrix formed via ‘direct augmentation’, where the estimated correlations at consecutive lags from the difference coarray are arranged to form the coarray covariance matrix. This paper highlights the inefficiency of the above matrix construction method and proposes to use an alternative. This alternative approach constructs a Toeplitz covariance matrix by solving an optimization problem based on the asymptotic error distribution of known entries from the sample covariance matrix.We experimentally demonstrate that when the number of sourcesDis less thanN, this greatly improves DOA estimation mean squared error (MSE), and importantly, the MSE with this approach does not saturate at high SNR, unlike that of coarray-MUSIC. For cases whereD>N, this method yields MSE close to the Cramér-Rao Bound (CRB). We identify that the key contributor to the observed improvements is the whitening of the error vector, using its asymptotic error distribution. Although this Toeplitz matrix construction approach acts as an interpolation algorithm for arrays that have holes in their difference coarrays (such as coprime arrays), this approach is also observed to greatly improve the DOA estimation MSE for arrays that do not have holes in their difference coarrays (such as nested arrays). Additionally, we suggest a modification to accommodate mutual coupling and present simulation results for various sparse arrays from the literature, and the recently proposed weight-constrained arrays.