Design of Signal Constellation Rearrangement (CoRe) for Multiple Relay Links

This paper considers a design of signal constellations for trans-modulation (constellation rearrangement: CoRe) in a relay system with the multiple links in which the same signal is decoded-and-forwarded to the destination over N time slots, each assigned to the different relay node. Demonstrating that the minimal accumulated squared Euclidean distance (MASED) is not an ultimate design metric to minimize the bit error rate (BER), we choose the BER for the joint log-likelihood ratio (LLR) combining scheme as a design metric, so as to find bit-to-symbol mapping for the multiple relay links. To handle the prohibitive amount of computational complexity associated with an exhaustive search over enumeration of all possible mappings, which grows exponentially with the number of relay links, genetic algorithm is employed for searching for the sub-optimal bitto-symbol mappings in the multiple relay links. We show that a new type of CoRe design without the gray-mapping constraint is critical for warranting the LLR-combining gain over the multiple relay links, e.g., approximately 4 dB gain for 4 relay links at high SNR as compared to the CoRe design for hybrid ARQ.