Partially Relaxed Fourier Domain Direction of Arrival Estimation

In this paper, the recently introduced concept of Partial Relaxation in Direction-of-Arrival (DoA) estimation [1], [2] is extended to a new class of Partially Relaxed Fourier Domain DoA estimation methods. The periodic cost function of the Partially Relaxed Deterministic Maximum Likelihood and the Partially Relaxed Weighted Subspace Fitting DoA estimation method are approximated by means of a truncated Fourier series expansion. The truncated Fourier series is expressed as a polynomial and the source DoAs are estimated from its roots, similar to root-MUSIC. Simulation results show that the proposed Partially Relaxed Fourier Domain DoA estimation techniques provide improved estimation accuracy over their conventional counterparts especially in difficult scenarios with limited sample size and low Signal-to-Noise Ratio.