Combined Effects of Intersymbol, Interchannel, and Co-Channel Interferences in M-ary CPSK Systems

An expression for the error probability of multilevel coherent phase-shift-keyed (CPSK) systems in the presence of intersymbol, interchannel, and co-channel interferences and additive Gaussian noise is derived. An exact expression is given for the binary CPSK system, whereas upper and lower bounds are presented for the multilevel systems. The approach proposed in this paper overcomes the difficulties of the exhaustive methods and allows accurate and fast evaluation of the character error probability. Only the impulse responses of the overall channels are needed, and the computational labor is reduced to the numerical evaluation of one particular type of integral, whose computation is based upon nonclassical Gaussian quadrature rules. The model of the system is general enough to allow the choice of a rectangular or otherwise-shaped modulating pulse and a constant or shaped envelope of the modulating carrier. Phase incoherence between adjacent carriers is also assumed, and a random misalignment among the modulating bit streams can be taken into account, if necessary. Extensive numerical results are presented for 2- and 4-level systems. The presentation of the results stresses a possible utilization of them in system design problems.