Comparing frequency-difference beamforming and delay-and-sum beamforming as an estimator of direction-of-arrival

Direction-of-arrival estimation (DOA) is an important and long-studied problem in array signal processing. Existing algorithms such as conventional delay-and-sum beamforming are limited in performance and become inadequate for a high-frequency broadband source and when the receiving linear array is sparse. Abadi, Song, and Dowling (2012), however, showed that DOAS estimation is possible in this case with an algorithm they introduced called frequency-difference beamforming. This was demonstrated empirically in their previous work using a real dataset. In addition, the resemblance between frequency-difference beamforming and delay-and-sum beamforming was briefly discussed. The purpose of this study is to analyze this relationship further and determine how well frequency-difference beamforming compares to delay-and-sum beamforming as an estimator of DOA. The approach taken in this study is to explicitly formulate the estimator equation for frequency-difference beamforming and compare it mathematically to the...