Design of Constellation Sets for Multistage Systems

Abstract

Abstract-We consider the problem of designing constellation sets for multistage systems for high spectral efficiencies. In particular we will focus on two-stage systems where the cascaded decoding stages are associated to three types of receivers with different complexities and performances. The optimal receiver (S) processes the symbol LLR and delivers the maximum possible throughput, the simpler BICM receiver (B) processes in parallel bit LLR derived from the observation, and finally the simplest hard receiver (H) takes an ML hard decision on the observation and processes the sequence of estimated bits with algebraic-like decoders. Optimal constellation sets achieving the maximum possible mutual information depend on the target receiver structure and thus requires separate optimization. Using a variation of the optimization algorithm based on simulated annealing previously introduced we provide optimal constellation sets with 16 to 256 point for four variants of the two-stage receiver offering different trade-offs between complexity and performance. We will show that BH receivers, where the first stage uses a BICM approach and the second stage the even simpler hard decision receiver can provide performances within 0.2 bits from the theoretical Shannon limit in a proper range of Signal to Noise Ratio (SNR) if optimal constellation sets are used.