Probability of error in CPSK systems with intersymbol interference and additive noise

A simple lower bound, an upper bound and a simple approximation to the upper bound on the probability of error for coherent phase-shift-keyed (CPSK) systems operating in the presence of intersymbol interference and additive noise are obtained. The additive noises in the in-phase channel and the quadrature channel are assumed to be independent, and are independent of the signal, but not restricted to be Gaussian. The approximation to the upper bound is four times the lower bound, hence the tightness of these bounds is uniform for all cases. This fact and the simplicity of the bounds make these bounds a useful system design tool. Numerical examples for quaternary and octonary systems are presented and compared to known results.