Design of FIR beamformer with frequency invariant patterns via jointly optimizing spatial and frequency responses

An approach to the optimal design of FIR broadband beam-former with frequency invariant patterns via joint optimizing the spatial and frequency responses is proposed. The beam responses are jointly optimized to satisfy some 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 patterns and the desired ones over the working frequencies within the mainlobe area while guaranteeing the sidelobes and the array patterns over the stopband to be below some given threshold values. White noise gain constraint is applied to improve the robustness of the beamformer against random errors. The beam response is expressed as a linear function of the FIR filters tap weights, and the design problem is formulated as the second-order cone programming, which can be solved efficiently via the well-established interior point methods. Results of computer simulation for a twelve-element semicircular array confirm satisfactory performance of the approach proposed in this paper.