  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.
