Generalized frequency-sum beamforming for low frequencies

For direction-of-arrival (DOA) estimation in the low-frequency range, we improve spatial resolution using generalized frequency-sum (gFS) beamforming with the Qth order frequency-sum autoproduct. The order Q does not exceed the maximum value, determined by the criteria that the sum of frequencies used to create the autoproduct must be less than the array's spatial Nyquist frequency. Unlike other high-resolution beamformers, gFS maintains stable performance even with a single snapshot and is unaffected by the coherence of steering vectors. Rigorous analysis using the multinomial expansion has shown the inapplicability of gFS to multi-DOA scenarios. Simulation and experimental results support that the method is a practical alternative for low-frequency single-DOA estimation with limited data.