Direction Finding with Sparse Arrays Based on Variable Window Size Spatial Smoothing

In this work, we introduce a variable window size (VWS) spatial smoothing framework that enhances coarray-based direction of arrival (DOA) estimation for sparse linear arrays. By compressing the smoothing aperture, the proposed VWS Coarray MUSIC (VWS-CA-MUSIC) and VWS Coarray root-MUSIC (VWS-CA-rMUSIC) algorithms replace part of the perturbed rank-one outer products in the smoothed coarray data with unperturbed low-rank additional terms, increasing the separation between signal and noise subspaces, while preserving the signal subspace span. We also derive the bounds that guarantees identifiability, by limiting the values that can be assumed by the compression parameter. Simulations with sparse geometries reveal significant performance improvements and complexity savings relative to the fixed-window coarray MUSIC method.