Simple bound to the error probability in coherent multiphase phase-shift-keyed systems with intersymbol interference and gaussian noise

An upper bound to the probability of error in coherent multiphase phase-shift-keyed digital systems is derived. The union bounding technique and the Chernoff inequality are used in deriving the bound. The bound is general and its accuracy improves as the number of phases N and the signal/noise ratio increase. The bound is given only in terms of the envelope component of interfering pulses and it is easy to compute. To illustrate the utility and the efficiency of the bound, some specific `typical¿ cases of transmission channels are considered, and the results are reported graphically for N = 4, 8 and 16