Chapter 8: RIS with Discrete Phase Shifts

Learning Objectives

• Formulate the discrete-phase RIS optimization as a combinatorial problem
• Derive the nearest-point projection from continuous solutions and quantify its loss
• Implement direct discrete optimization: exhaustive (small $N$), greedy (large $N$), SDR with projection
• Characterize the $B$-bit performance loss: $\text{sinc}^2(\pi / 2^B)$ under matched channels
• Choose between continuous-then-project and direct-discrete approaches for a deployment