Differential phase shift keying in two-path Rayleigh channel with adjacent channel interference

A formula is derived for the error probability of M-ary differential phase-shift keying with differential phase detection in a two-path Rayleigh fading channel taking into account adjacent channel interference (ACI), cochannel interference (CCI), intersymbol interference (ISI), and Doppler frequency shift. Square-root Nyquist filters are used with roll-off, β, the transmitter and receiver as in the proposed US digital mobile radio system. The presence of the second path has a profound effect on increasing the bit error probability (BEP) because it causes ISI. In the absence of ISI, ACI has a smaller effect on BEP than CCI. In the presence of ISI their effect is essentially the same. For a given bit energy-to-noise ratio, the binary system has the lowest BEP; however, the bit rate is also the lowest for a given bandwidth. When the main interference is ACI or CCI, a quaternary system has a lower BEP than the octal system. When the main interference is ISI, this is reversed