Design and performance of optimized relay mappings

We look at the three-node relay channel and the transmission of an information symbol from the source node to the destination node. We let the relay be a memoryless function and formulate necessary conditions for the optimality of the relay mapping and the detector. Based on these, we propose a design algorithm to find relay mappings such that the symbol error rate at the destination is minimized. The optimized relay mappings are illustrated for different scenarios and the dependency between the relay mapping and the link qualities is discussed in detail. Furthermore, the performance is compared to the existing schemes detect-and-forward, amplify-and-forward, and estimate-and-forward. It is shown that there is a significant gain in terms of decreased symbol error rate if the optimized relay mapping is used.