Spherical Harmonic Atomic Norm and its Application to DOA Estimation

Abstract

Signal processing in the spherical harmonic (SH) domain has the advantages of analyzing a signal on the sphere with equal resolution in the whole space and of decomposite the frequency- and location-dependent components of the signal. Therefore, it finds recent applications in signal recovery and localization. In this paper, we consider the gridless sparse signal recovery problem in the SH domain with atomic norm minimization (ANM). Due to the absence of Vandermonde structure for spherical harmonics, the Vandermonde decomposition theorem, which is the mathematic foundation of conventional ANM approaches, is not applicable in the SH domain. To address this issue, a low-dimensional semidefinite programming (SDP) method to implement the spherical harmonic atomic norm minimization (SH-ANM) approach is proposed. This method does not rely on the Vandermonde decomposition and can recover the atomic decomposition in the SH domain directly. As an application, we develop the direction-of-arrival estimation approach based on the proposed SH-ANM method, and computer simulations demonstrate that its performance is superior to the state-of-the-art counterparts. Furthermore, we validate the results in real-life acoustics scenes for multiple speakers localization using measured data in LACATA challenge.

Keywords

• Spherical harmonic domain
• atomic norm
• gridless sparse signal recovery
• semidefinite programming
• direction-of-arrive estimation