Low complexity beamspace super‐resolution for direction‐of‐arrival estimation via prior information encoding

Abstract

Abstract Beamspace processing is widely applied in Direction‐of‐Arrival (DOA) estimation thanks to dimensional reduction and super‐resolution characterisations. However, the conventional atomic norm minimisation (ANM) based methods for beamspace DOA estimation are of high computational complexity for large arrays. To deal with this issue, the proposed method focuses on locating the sources in the mainlobe of the beamspace and encodes such prior information into the ANM problem without frequency‐selective constraints. The proposed method approximates the beamspace array manifold in the mainlobe sector with the truncated sector Fourier series. The theoretical analysis shows that such approximation with the properly designed fitting error relaxation on the boundary yields the low dimensional semidefinite programming (SDP) approximate implementation of the proposed ANM method and guarantees the support recovery inside the mainlobe. Furthermore, the low complexity Burer‐Monteiro factorisation based alternating direction method of multipliers method is proposed to solve the SDP problem. The complexity analysis and simulations show that the proposed method results in significant computational complexity reduction and slightly better performance compared with state‐of‐art benchmarks.

Keywords

• array signal processing
• compressed sensing
• direction‐of‐arrival estimation