Limitations and capabilities of frequency domain broadband constrained beamforming schemes

Time domain processing of broadband signals using an array of sensors is normally carried out by a transversal filter, and the filter coefficients are adjusted by solving a constrained beamforming problem that requires manipulation of matrices of dimension LJ×LJ with L denoting the number of sensors in the array and J denoting the filter length. This paper studies a frequency domain method to compute the coefficients of transversal filter, compares its performance, sensitivity to the look direction, and computational efficiency with that of the direct method, and shows how the computational saving increases using the frequency domain method as the number of elements and the filter length are increased. The paper presents a number of techniques that exploit the inherent structure present in the frequency domain method to reduce the computation load and shows that the real-time computational saving of the order of 12520 folds is possible for an array of 100 elements using a tap delay line filter of 100 taps. The paper demonstrates that a beamformer using this method is able to produce more output SNR with less computation time than the one using the normal time domain method