A Branch-and-Bound Algorithm for Discrete Receive Beamforming with Improved Bounds

We discuss the SINR-maximization problem for analog receive beamforming with finite resolution phase shifters and amplifiers. This discrete optimization problem can be globally solved by means of branch-and-bound. The performance of the algorithm depends on the quality of bounds for the subproblems which are determined within the branch-and-bound procedure. These subproblems can be generated by a successive fixing of beamforming components but turn out to be difficult nonconvex optimization problems. It is known that the introduction of an additional variable yields easier convex problems such that bounds can be determined efficiently. We use the concept of fractional programming to improve these bounds and show that this may provide a significant reduction of iterations and computational expense.