Frequency invariant beamforming via optimal array pattern synthesis and FIR filters design

An approach to designing time domain broadband frequency invariant beamformer via optimal array pattern synthesis and optimal FIR filters design is proposed. First, the working frequency band is decomposed into a number of narrow band frequency bins.The array weights at each frequency bin are designed via optimal array pattern synthesis methods to insure that the synthesized pattern approximates the desired one within the mainlobe area. Then, a bank of FIR filters corresponding to the input channels are designed to provide the frequency responses that approximate the array weights in the working frequency band for each sensor. Finally, each sensor feeds a FIR filter and the filter outputs are summed to produce the beam output time series. Both array pattern synthesis and FIR filters design problems are formulated as the second-order cone programming (SOCP), which can be easily solved using well-developed interior-point methods. Results of computer simulations and lake-experiment for a twelve-element semicircular array demonstrate satisfactory performance of the proposed approach.