Adaptive Mapper Design for Spatial Modulation with Lightweight Feedback Overhead

The bits-to-antenna-index (BAI) and bits-to-modulated-symbol (BMS) mappings play important roles in determining the bit error rate (BER) of spatial modulation (SM). To minimize the BER, a plenty of work has paid much attention on optimizing the noise-free receive signal constellation diagram via adaptive power allocation, phase ration, precoding, etc, but overlooked the impact of the BAI and BMS mappings. To fill in this gap, this paper investigates the adaptive mapper design for SM, and proposes a mapper solution named brute forth mapper (BFM). Through adjusting the binary labels of all the closest symbol-pairs to be of one bit difference in a brute force way, BFM achieves the optimal BER in high signal-to-noise-ratio (SNR) regime. The feasibility of BFM is proved over random fading channels, and the performance improvement brought by BFM in terms of BER enhancement and SNR gain as well as the computational complexity and feedback overhead are quantitatively analyzed. Both analysis and simulations show that the proposed adaptive mapper significantly improves the BER performance with lightweight feedback overhead.