Sparse Spatial Spectrum Estimation for Underwater Multi-rank Signals

Assume a narrowband signal propagate through the ocean waveguide. Due to the waveguide fluctuation, rough boundary effect or random scattering, etc., the signal wavefront would vary from snapshot to snapshot with the signal energy disperse within a small angular bandwidth, resulting in a multi-rank signal covariance. Mathematically, this kind of signals received on the array are named as multi-rank signals, whose spatial signatures lie in a known subspace, but the orientation in that space is unknown and random. Conventional direction-of-arrival (DOA) estimation methods, such as delay and sum (DAS) beamforming and minimum variance distortionless response (MVDR) beamforming, show poor ability to resolve this kind of signals. In this paper, we propose a multi-rank sparse spectrum fitting (MR-SpSF) method to estimate the DOAs of multi-rank signals, which is an extended sparse spectrum fitting (MR-SpSF) method. Performance of MR-SpSF is compared with DAS, MVDR, SpSF and eigenvalue beamforming (EB) by simulation experiments. Simulation results suggest that both EB and MR-SpSF can provide high resolution in resolving multi-rank signals, but MR-SpSF outperforms EB with more accurate signal power estimation without compensation and more reliable DOA estimation results in snapshots limited and signal subspace mismatch scenarios.