DOA Estimation via Continuous Aperture Arrays: MUSIC and CRLB

Abstract: Direction-of-arrival (DOA) estimation using continuous aperture array (CAPA) is studied. Compared to the conventional spatially discrete array (SPDA), CAPA significantly enhances the spatial degrees-of-freedoms (DoFs) for DOA estimation, but its infinite-dimensional continuous signals render the conventional estimation algorithm non-applicable. To address this challenge, a new multiple signal classification (MUSIC) algorithm is proposed for CAPAs. In particular, an equivalent continuous-discrete transformation is proposed to facilitate the eigendecomposition of continuous operators. Subsequently, the MUSIC spectrum is accurately approximated using the Gauss-Legendre quadrature, effectively reducing the computational complexity. Furthermore, the Cram\'er-Rao lower bounds (CRLBs) for DOA estimation using CAPAs are analyzed for both cases with and without priori knowledge of snapshot signals. It is theoretically proved that CAPAs significantly improve the DOA estimation accuracy compared to traditional SPDAs. Numerical results further validate this insight and demonstrate the effectiveness of the proposed MUSIC algorithm for CAPA. The proposed method achieves near-optimal estimation performance while maintaining a low computational complexity.