A novel approach to analytically evaluate the bit error probability in optically preamplified direct-detection systems is presented, which can take into account the effects of pulse shaping, chirping, filtering at the transmitter and the receiver, both pre-and postdetection, chromatic dispersion,and ASE noise. The method is computationally very fast in that the saddle point integration method for solving the resulting line integral of a particular moment generating function is adopted. A closed-form approximation for the bit error probability is also provided, which is within 0.01 dB from the exact numerical results.
Enrico Forestieri, "Evaluating the Error Probability in Lightwave Systems with Chromatic Dispersion, Arbitrary Pulse Shape and Pre-and Postdetection Filtering," J. Lightwave Technol. 18, 1493- (2000)