Results useful in the calculation of the exact closed-form expression for the minimum average probability of error

of a binary pulse linear communication system with

intersymbol interferences and additive colored Gaussian noise are given. By first performing statistical averaging and then using the variational method, a compact form of

that depends only on the overall system impulse response taken over

time instants is obtained. These

unknowns are given as the solution of

simultaneous nonlinear equations. Specific examples illustrating this approach are considered.