Error Probability in the Presence of Intersymbol Interference and Additive Noise for Multilevel Digital Signals

A new method is presented to compute the average probability of error in the presence of intersymbol interference and additive noise for multilevel pulse-amplitude-modulation (PAM) and partial-response-coded (PRC) signaling schemes. The method is based upon nonclassical Gauss quadrature rules (GQR) and suffers no limitation on noise statistics, so that it applies also for non-Gaussian noise. Moreover it yields some remarkable advantages as compared with other methods, in particular, with the series expansion method that has recently received considerable attention. Expressions for the truncation error are also given and their derivation is reported in the Appendix. Finally, examples of applications are presented and comparisons with other methods are carried out.