Uniform circular broadband beamformer with selective frequency and spatial invariant region

Most existing frequency-invariant (FI) beamformer algorithms design array beampattern response across the entire frequency bands. In this paper, the design of array gain response is extended to both selective frequency and spatial region. The algorithm consists of an objective function that has a two-dimensional constraint. One dimension constraint is on frequency range; this is to ensure a selective frequency invariant region is formed. The second dimension constraint is on spatial direction; this is to maintain the array response of the beamformer constant for a small amount of angle centered at the desired direction. Having such constant gain response over a selective spatial region makes the array beamformer less sensitive to the exact position of the source. Advanced optimization method such as second order cone programming (SOCP) is used to solve this complex optimization problem with high efficiency and accuracy. Simulation results are compared with other existing algorithms. It demonstrates that the proposed method is able to achieve a constant gain over the specified sector of angle and at the same time having a lower mean square error on the FI performance over the specified frequency region.