Hybrid Bit-to-Symbol Mapping for Spatial Modulation

In spatial modulation (SM), the information bit stream is divided into two different sets: the transmit antenna index bits (TA-bits) and the amplitude and phase modulation bits (APM-bits). However, the conventional bit-to-symbol mapping (BTS-MAP) scheme maps the APM-bits and the TA-bits independently. For exploiting their joint benefits, we propose a new BTS-MAP rule based on the traditional 2-D Gray mapping rule, which increases the Hamming distance (HD) between the symbol pairs detected from the same transmit antenna (TA) and simultaneously reduces the average HD between the symbol pairs gleaned from different TAs. Based on the analysis of the distribution of minimum Euclidean distance (MED) of SM constellations, we propose a criterion for the construction of a meritorious BTS-MAP for a specific SM setup, with no need for additional feedback links or extra computational complexity. Finally, Monte Carlo simulations are conducted for confirming the accuracy of our analysis.