Hamming Distance Optimization for 16-QAM Symbol Labeling Using GA and SA Algorithms

Abstract

Symbol labeling optimization in modulation is essential for improving Bit Error Rate (BER) in wireless communication systems, particularly under noise and fading. This study investigates 16-QAM symbol labeling using Genetic Algorithms (GA) and Simulated Annealing (SA), focusing on logical-layer optimization of bit-to-symbol mapping on a fixed constellation, thereby enhancing performance without altering hardware. The optimization objective is to minimize the average Hamming distance (HD) between adjacent symbols to reduce BER in Rayleigh fading channels. Simulation results show that GA achieves an average HD of 1.167, compared to 1.33 for Natural, 1.7 for SA, 2.16 for Random, and 1.00 for Gray mapping achieved. At a BER level of 10-2, Gray reaches this target at approximately 23 dB, GA requires 0.5–1 dB more, SA and Natural require about 2 dB more, and Random is nearly 3 dB worse. These findings confirm that GA and SA provide measurable BER gains over Natural and Random, while closely approaching Gray performance. Overall, this work serves as a proof-of-concept validation of logical-layer mapping optimization as a low-complexity, hardware-compatible enhancement for future 5G/6G systems.

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