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Large antenna arrays can steer narrow beams towards a target area, and thusimprove the communications capacity of wireless channels and the fidelity ofradio sensing. Hardware that is capable of continuously-variable phase shiftsis expensive, presenting scaling challenges. PIN diodes that apply onlydiscrete phase shifts are promising and cost-effective; however, unlikecontinuous phase shifters, finding the best phase configuration across elementsis an NP-hard optimization problem. Thus, the complexity of optimizationbecomes a new bottleneck for large-antenna arrays. To address this challenge,this paper suggests a procedure for converting the optimization objectivefunction from a ratio of quadratic functions to a sequence of more easilysolvable quadratic unconstrained binary optimization (QUBO) sub-problems. Thisconversion is an exact equivalence, and the resulting QUBO forms are standardinput formats for various physics-inspired optimization methods. We demonstratethat a simulated annealing approach is very effective for solving thesesub-problems, and we give performance metrics for several large array typesoptimized by this technique. Through numerical experiments, we report 3Dbeamforming performance for extra-large arrays with up to 10,000 elements.

Physics-Inspired Discrete-Phase Optimization for 3D Beamforming with PIN-Diode Extra-Large Antenna Arrays