Low-frequency Direction-of-arrival Estimation using Generalized Frequency-sum Beamforming

Estimating the direction-of-arrival (DOA) at low frequencies is challenging owing to the inadequate spatial resolution of conventional delay-and-sum beamforming. This study presents an alternative approach based on generalized frequency-sum (gFS) processing, which constructs higher-order spectral autoproducts up to a selected order Q. By combining frequency components, the method enhances spatial resolution when the acoustic wavelength exceeds the array aperture. The upper limit of Q is governed by the condition that the resulting frequency sum remains below the spatial Nyquist limit; in practice, this bound is further limited by noise. In addition, through a framework based on multinomial expansion, we demonstrate that gFS is inherently unsuitable for resolving multiple DOAs. Numerical simulations and experiments confirm that this technique offers a viable solution for single-source DOA estimation in the low-frequency regime.