Difference-frequency MUSIC for beamforming

A beamforming method is derived to estimate direction-of-arrivals (DOAs) for high-frequency sources. The algorithm uses multiple frequencies and their difference frequencies (DFs). Due to the DFs below the aliasing frequency, the method mitigates spatial aliasing. DF-processing has been applied previously to the conventional beamforming [Abadi et al., J.Acoust. Soc. Am., 132(5):3018–3029, 2012]. The proposed method uses a classical beamformer, MUSIC, which is a subspace method. The MUSIC shows sharp peaks in the beamforming spectrum and high-resolution. The DF-MUSIC integrates data samples into a sample covariance matrix and estimates DOAs. We propose three ways to treat multiple time and DF samples. The time-DF-MUSIC obtains MUSIC spectra at each DF and averages the spectra over time to get final DOAs. The frequency-DF-MUSIC obtains MUSIC spectra at each time snapshot and averages the spectra over frequency to get final DOAs. The time-frequency-DF-MUSIC considers all time and frequency jointly and improves the DOA estimation.