Evaluation of three- and five-phase PSK

Multiple PSK (phase-shift keying) is considered for M=3 and M=5 as alternative nonbinary signaling schemes for small bit error probability and small bandwidth requirements. The number of bits per symbol for three-phase PSK is 1.585, where as it is 2.322 b per symbol for five-phase PSK with the same required bandwidth as with BPSK (binary PSK) and QPSK (quadrature or four-level PSK). It is shown that three-phase PSK yields smaller bit error probability than QPSK but requires a larger bandwidth per bit. Likewise, five-phase PSK yields a larger bit error probability than QPSK but requires a smaller bandwidth per bit