Stochastic Dithered Phase Quantization for Beam-Space Enhancement in Multi-Bit Digital Coding Metasurfaces

Digital coding metasurfaces (DCMs) manipulate electromagnetic waves through discrete phase control, but coarse phase quantization can generate coherent parasitic lobes and degrade beam-space performance. This paper proposes a stochastic dithered phase quantization (SDPQ) framework for 1–4-bit DCMs to improve radiation performance. Controlled random phase perturbations are introduced before quantization to redistribute spatially correlated quantization errors into diffuse scattering. The framework is evaluated through array-factor analysis and full-wave simulations of height-step reflectors, considering field fidelity, power-pattern similarity, parasitic- and quantization-lobe levels, steering accuracy, and beam efficiency. Compared with deterministic quantization, 2-bit SDPQ reduces the worst-case parasitic-lobe level from $-7.4$ to $-10.6$ dB and the maximum steering error from $1.9\%$ to $0.8\%$. At unity dither strength, analytical quantization-lobe level reductions reach approximately 7.9 dB at both steering angles, while power-pattern similarity improves despite reduced complex-field fidelity. Full-wave sidelobe-level reductions reach 3.0–3.4 dB at ${20}^{\circ }$ and 4.3–4.5 dB at ${40}^{\circ }$. The 1-bit DCM remains constrained by its inherent symmetric twin-beam response, whereas higher-bit DCMs offer greater phase accuracy but smaller additional sidelobe benefits. These findings identify four-state 2-bit SDPQ as a favorable low-resolution configuration, with dither strength balancing parasitic-lobe suppression, diffuse scattering, and beam preservation. The proposed framework offers a computationally scalable, hardware-agnostic phase-quantization strategy, subject to achievable phase and amplitude responses, for programmable metasurfaces and wireless beam steering.