Quantization-constrained harmonic disentanglement for space-time-coding reconfigurable intelligent surfaces

Abstract

Space-time-coding reconfigurable intelligent surfaces enable harmonic beamforming through periodic modulation of element-wise reflection coefficients. However, harmonic coupling induced by a shared low-bit coding sequence poses a nonconvex discrete synthesis problem. This letter proposes a twostage solver for quantization-constrained harmonic disentanglement. A projected-gradient stage first computes a continuous unit-modulus solution, which is subsequently refined via the alternating direction method of multipliers to enforce discrete phase constraints and suppress out-of-band leakage. Numerical results demonstrate accurate multi-harmonic synthesis for prescribed harmonic coefficients under low-resolution phase control, outperforming direct quantization and characterizing tradeoffs among phase resolution, synthesis accuracy, and spectral concentration.