Log-likelihood Ratio Based Optimum Mappings Selection for Symbol Mapping Diversity with -QAM

Abstract— In this paper, a packet combining method known as symbol mapping diversity (SMD) is investigated. In an SMD scheme, the bit-to-symbol mapping in -ary modulation is varied among multiple transmissions of the same packet (e.g., ARQ). It has been shown that multiple transmissions of the same packet using SMD provide better bit error performance than a scheme where the same bit-to-symbol mapping is used for all transmissions of the same packet. A new contribution in this paper is that we propose a new method to obtain optimum bit-to-symbol mappings for SMD schemes with -QAM. In the proposed method, the optimum mappings are so chosen to maximize a bit loglikelihood ratio (LLR) based metric. We also derive analytical expressions for the bit error rate (BER) of the SMD scheme using LLR based bit decision for 8-QAM. Analytical results are shown to agree very well with the simulation results. Our performance results show that the optimum mappings selected based on our proposed LLR method performs better (in terms of BER) than the mappings selected through other methods proposed in the literature (e.g., the method proposed by Samra et al which minimized an upper bound on the BER to obtain optimum mappings).