RIS Codebook Index Assignment under Imperfect Control Links Using TSP-Inspired Optimization

Abstract: Reconfigurable Intelligent Surfaces (RIS) promise transformative gains in wireless communications by enabling programmable control of the propagation environment through discrete phase configurations. In practical deployments, the control of RIS phase states is typically managed using finite codebooks, with configuration indices transmitted over low latency, yet imperfect, wireless feedback channels. Even rare feedback bit errors can lead to significant mismatches between intended and applied RIS states, degrading system performance. This paper addresses the challenge of robust RIS codebook index assignment by formulating it as a combinatorial optimization problem, equivalent to the Traveling Salesman Problem (TSP), where codewords are "cities" and edge weights reflect SNR degradation under codeword confusion. A novel three-phase heuristic algorithm is proposed to solve this, consisting of a provision phase, a shotgun phase, and a fuzzy concatenation phase. Simulation results show that the method outperforms conventional indexing strategies and achieves near-optimal robustness to index errors, while also being scalable and hardwareagnostic for real time deployment. Future work includes multiple bits error correction and online adaptive mapping for time varying channels.