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 Eb/No are also investigated in detail.
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