DOA Estimation with Non-Uniform Linear Arrays: A Phase-Difference Projection Approach

Phase wrapping is a major problem in direction-of-arrival (DOA) estimation using phase-difference observations. For a sensor pair with an inter-sensor spacing greater than half of the wavelength ($\lambda/2$) of the signal, phase wrapping occurs at certain DOA angles leading to phase-difference ambiguities. Existing phase unwrapping methods exploit either frequency or spatial diversity. These techniques work by imposing restrictions on the utilized frequencies or the receiver array geometry. In addition to sensitivity to noise and calibration errors, these methods may also have high computational complexity. We propose a grid-less \emph{phase-difference projection} (PDP) DOA algorithm to overcome these issues. The concept of \emph{wrapped phased-difference pattern} (WPDP) is introduced, which allows the proposed algorithm to compute most of the parameters required for DOA estimation in an offline manner, hence resulting in a superior computational speed in realtime. Simulation results demonstrate the excellent performance of the proposed algorithm, both in terms of accuracy and speed.