Title: On the Performance of RIS-assisted Networks with HQAM

Abstract: In this paper, we investigate the application of hexagonal quadrature amplitude modulation (HQAM) in reconfigurable intelligent surface (RIS)-assisted networks, specifically focusing on its efficiency in reducing the number of required reflecting elements. Specifically, we present analytical expressions for the average symbol error probability (ASEP) and propose a new metric for conditioned energy efficiency, which assesses the network energy consumption while ensuring the ASEP remains below a certain threshold. Additionally, we introduce an innovative detection algorithm for HQAM constellations that implements sphere decoding in O(1) complexity. Finally, our study reveals that HQAM significantly enhances both the ASEP and energy efficiency compared to traditional quadrature amplitude modulation (QAM) schemes.