Frequency invariant beamforming via jointly optimizing spatial and frequency responses

An approach to designing broadband frequency invariant beamformer based on finite impulse response (FIR) filters via jointly optimizing the spatial and frequency responses is proposed. The beam responses are jointly optimized to satisfy both spatial and frequency domain specifications by designing a bank of FIR filters corresponding to the input channels. It minimizes the maximum error between the designed beam pattern and the desired one in the mainlobe area over the working frequency band, and guarantees the sidelobes in the passband and the beam magnitude responses in the stopband to be below some given threshold values. White noise gain constraint is used to improve the robustness of the beamformer against random errors. The beam patterns are expressed as a linear function of FIR filter impulse responses, and the design problem is formulated as the second-order cone programming (SOCP), which can be solved efficiently via the well-established interior point methods. Results of computer simulation and lake-experiment for a twelve-element semicircular array demonstrate superior performance of this approach in comparison to the existing approaches.