Improved closed-form DOA/frequency estimation via ESPRIT using DFT and derivative DFT beamforming

This paper introduces a new algorithm, derivative DFT beamspace ESPRIT, that provides closed-form estimates of the directions-of-arrival (DOAs) of signals impinging on a uniform linear array (ULA). Existing closed-form DOA estimation algorithms for ULAs include TLS-ESPRIT and root-MUSIC. Derivative DFT beamspace ESPRIT outperforms TLS-ESPRIT in terms of both estimation accuracy (provides higher quality estimates in low information-to-noise scenarios) and computational complexity (requires less than 40% of the MATLAB flops of TLS-ESPRIT). Root-MUSIC provides better estimates than the other two algorithms mentioned, but requires orders of magnitude more computation than them. Derivative DFT beamspace ESPRIT improves upon the DFT beamspace ESPRIT algorithm [Zoltowski et al., 1996] by exploiting additional invariances that arise from derivative DFT beamforming. Incorporation of these additional invariances enables derivative DFT beamspace ESPRIT to outperform TLS-ESPRIT