Broadband constant beamwidth beamforming for arbitrary sensor arrays in time domain via second-order cone programming

A method of broadband constant beamwidth beamforming (BCBB) based on finite impulse response (FIR) filters is presented. Firstly, the working frequency band is decomposed into a number of narrow-band frequency bins, and the beamforming weights for each frequency bin are deduced by array pattern synthesis methods. Then, the BCBB is implemented by a set of FIR filters corresponding to the input channels, which provides the frequency response derived from BCBB weights for each sensor. Finally, the outputs of the digital filters are summed up to yield the time domain broadband beam output. BCBB weights can be designed via array pattern synthesis at each frequency bin in bands of interest by imposing mainlobe pattern constraints. The FIR filters are designed to provide required magnitude and phase response by a constrained optimization method. Both the design of beamformers and that of FIR filters can be converted to a convex optimization form as the so-called Second-Order Cone Programming (SOCP) and solved efficiently via the well-established interior point method. Results of computer simulation and lake-experiments for a twelve-element arc array confirmed the satisfactory performance of the approaches developed in this paper.