An algebraic approach to rank-constrained beamforming

This paper presents a new approach to solving the rank constrained beamforming problem. Instead of relaxing the problem to a feasible set of the positive semidefinite matrices, we restrict the problem to a space of polynomials whose dimension is equal to the desired rank. The solution to the resulting optimization is then required to be full rank, allowing a simple matrix decomposition to recover the beamforming matrix exactly. Simulation results show an exact agreement of the solution with the proposed algebraic structure, as well as significant performance benefits in terms of sidelobe suppression compared with previous methods.