Design of Frequency Invariant Wideband Beamformer with Real and Symmetric FIR Filters

An approach to wideband beamformer with frequency invariant property is proposed by optimising the space-time two-dimensional finite impulse response (FIR) filters. Frequency invariant beam pattern brings some restrictions on frequency bandwith and filter length. Using the Landau-Pollak theorem to estimate the rank of wideband signals, we give the lower bound of filter length respect to array element numbers and the relative bandwidth of wideband signal. With the expression of beam pattern using real and symmetric FIR filters, we develop corresponding optimisation formation considering the robustness of beamformer as well, which can be easily solved by the least mean square (LMS) algorithm. A design example is provided to show the effectiveness of the proposed method.