Error probability of offset differential phase shift keying with intersymbol and adjacent channel interference

Abstract

We compute the error probability for conventional and for symmetric differential phase shift keying (CDPSK and SDPSK) with differential detection in systems with binary, ternary and quaternary symbols and with two kinds of filters. In the first system the system response is a Butter-worth filter with two, three and four poles, which causes both intersymbol interference (ISI) and noise correlation which depend on the normalised 3 dB filter bandwidth B. In the second system the system response is a Nyquist filter with excess bandwidth β. In this system we consider both ISI caused by errors in sampling time and adjacent channel interference (ACI) caused by a signal in a neighbouring channel with frequency separation fA. We show that for B<1.0 binary and ternary SDPSK is better than CDPSK, while for quaternary symbols the difference is negligible. The difference is also negligible for B≥1.0 for all symbols. For B<1.0 the lowest error probability is achieved in a system with second order filter. For the latter system with binary symbols, B=0.7, and a signal to noise ratio of 12 dB we show that the best phase offset is π/2 (hence SDPSK is the best offset DPSK) and that SDPSK is better than CDPSK with optimal (and unequal) decision regions. In the system with Nyquist filter SDPSK is either better or the same as CDPSK when ISI is taken into account, but the opposite is true when ACI is considered. However, in the latter case the difference is small.