Hexagonal QAM-Based Two-Way Generalized Code Index Modulation Over Nakagami-m Fading Channels

We propose a two-way generalized code index modulation scheme with hexagonal QAM (TW-GCIM-HQAM) over Nakagami-m fading. The design combines GCIM and physical layer network coding with energy-efficient HQAM constellations. Using orthogonal Walsh-Hadamard spreading codes, two users exchange data via a half-duplex relay in two time slots (instead of three in conventional two-way DF). Information is carried by both the HQAM symbols and the indices of the spreading codes on the I/Q branches. We compare the scheme with two-way decode and forward at matched rates and evaluate the average bit error rate via Monte Carlo simulations on Nakagami- m channels for several HQAM constellations. Results show competitive or improved error performance, together with better energy use and time slot efficiency.