Variable Window Size Spatial Smoothing for Coarray DOA Estimation with Sparse Arrays

In this paper, we propose variable window size (VWS) spatial smoothing techniques to improve coarray-based direction of arrival (DOA) estimation for sparse linear arrays (SLAs). The introduced approach exploits adjustable spatial smoothing window sizes, which yield significant gains in estimation accuracy for sparse arrays. Intuitively, the window size governs a fundamental bias-variance trade-off in the coarray domain: reducing it increases the number of averaged over lapping subarrays and strengthens the signal/noise subspace separation, but shortens the effective aperture or number of virtual coarray degrees of freedom. We formalize this trade off, establish an admissible compression range that preserves the signal/noise subspaces, and show that within this range smaller windows enhance the Subspace SNR. Specifically, we develop VWS Coarray Multiple Signal Classification (VWS-CA-MUSIC), VWS Coarray Root Multiple Signal Classification (VWS-CA rMUSIC) DOA estimation algorithms and their corresponding generalized versions. These algorithms are designed for fully and partially calibrated SLA geometries. An analysis of the proposed approach in terms of subspace properties is carried out along with an assessment of the computational complexity of the proposed algorithms. The proposed VWS algorithms offer three key advantages over fixed-window coarray methods: (i) improved root-mean-square error (RMSE) by incorporating extra unperturbed covariance components into the spatial smoothing average; (ii) enhanced Subspace SNR, which strengthens the separation between signal and noise subspaces; and (iii) a tunable compression parameter that allows designers to balance aperture and averaging according to the operating conditions. Numerical results assess the performance of the proposed techniques against competing approaches available in the literature.