Comparison of phase modulation systems

Comparison of the energy to noise ratio necessary to obtain a given modulation bit error probability has indicated that three-phase modulation is about 0.75 db superior to four-phase. It is shown that this apparent superiority results entirely from the greater bandwidth required by the three-phase system for the same bit transmission rate. Two further comparison criteria are proposed, which are based on the cut-off rate R sub 0 of the discrete channel created by the modulation system. For the criterion which constrains both the bandwidth and transmitted power, it is shown that four-phase modulation is always superior to three-phase modulation. The conclusion is that three-phase modulation offers no practical advantage over four-phase modulation.