Broadband beamforming with power complementary filters

This paper addresses the design of broadband finite impulse response (FIR) beamformers with a power complementarity property. The power complementarity requirement is needed to preserve the whiteness of the channel noise at the beamformer output, which allows the application of optimum trellis-based equalizers to the output signal. The power complementarity property imposes non-negative definite quadratic constraints on the beamforming filters so that the beamformer design is expressed as a constrained quadratic optimization problem. Two approaches are proposed to solve this problem. The first method is a Lagrangian relaxation technique, which exploits the fact that the dual mathematical problem reduces to the unconstrained minimization of a convex function over a convex domain. A second approach employs a cascaded lattice representation of the power complementary filterbank and performs the beamformer design incrementally, one lattice stage at a time.