Large antenna arrays can steer narrow beams towards a target area, and thus improve the communications capacity of wireless channels and the fidelity of radio sensing. Hardware that is capable of continuously-variable phase shifts is expensive, presenting scaling challenges. PIN diodes that apply only discrete phase shifts are promising and cost-effective; however, unlike continuous phase shifters, finding the best phase configuration across elements is an NP-hard optimization problem. Thus, the complexity of optimization becomes a new bottleneck for large-antenna arrays. To address this challenge, this paper suggests a procedure for converting the optimization objective function from a ratio of quadratic functions to a sequence of more easily solvable quadratic unconstrained binary optimization (QUBO) sub-problems. This conversion is an exact equivalence, and the resulting QUBO forms are standard input formats for various physics-inspired optimization methods. We demonstrate that a simulated annealing approach is very effective for solving these sub-problems, and we give performance metrics for several large array types optimized by this technique. Through numerical experiments, we report 3D beamforming performance for extra-large arrays with up to 10,000 elements.

翻译：超大规模天线阵列可将窄波束对准目标区域，从而提升无线信道的通信容量与无线电感知的保真度。能够实现连续可调相移的硬件成本高昂，带来了扩展性挑战。仅能施加离散相移的PIN二极管具有前景且成本效益高；然而与连续移相器不同，寻找跨阵元的最优相位配置是一个NP难优化问题。因此，优化复杂度成为超大规模天线阵列的新瓶颈。为应对这一挑战，本文提出一种方法，将优化目标函数从二次型比值形式转化为一系列更易求解的二次无约束二元优化（QUBO）子问题。该转化是精确等价的，所得QUBO形式是多种物理启发优化方法的标准输入格式。我们证明模拟退火方法在求解这些子问题时非常有效，并给出了通过该技术优化的几种大规模阵列类型的性能指标。通过数值实验，我们展示了包含多达10000个阵元的超大规模阵列的三维波束赋形性能。