Multi-H phase-coded modulations with asymmetric modulation indexes

Multi4 phase-coded modulation (MHPM) is a bandwidth efficient modulation scheme which offers substantial coding gain over conventional digital modulations. In this paper, a new concept of MHPM with asymmetric modulation indices corresponding to the bipolar data + 1 and 1 is considered, and numerical results of the minimum Euclidean distances for such asymmetric binary multi-h schemes are provided. It is shown that performance improvements on the error probability are gained over conventional MHPM with essentially the same bandwidth and a very slight modification in implementation. The upper bounds of error probabilities as functions of observation intervals and received E b / N o are also investigated in detail.