Optimum parameter combinations for multi-h phase codes

It has been believed that the superiority of multi-h phase codes over constant-h continuous-phase frequency shift keying (CPFSK) schemes is based entirely on the longer temporal separation of any two signal paths. This assumption forces the number of states in the receiver to be lower bounded and requires a fast processor in the receiver. Counterexamples to this common belief are presented as well as results of a systematic search for good multi-h codes for a given bandwidth and complexity constraints. It is shown that quaternary multi-h codes exist for which the first merge of the phase paths in the phase tree is not delayed as compared to the CPFSK scheme, yet which still offer a significant coding gain over the corresponding CPFSK signals. Some quaternary and octal multi-h codes are found with large minimum distance values and a smaller number of receiver states than those known previously