The distribution of peak factor in QPSK Multi-Carrier modulation

This paper presents the results of a preliminary investigation into the distribution of peak factors in the QPSK message space for different numbers of carriers with the aim of determining those messages which exhibit a low peak factor relative to a given threshold. A group structure is suggested which associates cosets of 16 messages into equivalence classes having the same peak power. Algorithms for finding the members of cosets and equivalence classes are given. These messages are then rank ordered by peak power to show how a suitable code could be derived. It appears that allocating just one or two bits of redundancy to such a code will be sufficient to achieve substantial reductions in peak factor.