The evaluation of error probabilities for low-frequency attenuation channels

Channels having large low-frequency attenuation are of much interest. Low-frequency removal may result from transformer or capacitor coupling. Examples include ISDN loop transmission (transformer coupling) and wireless systems (capacitor coupled amplifiers). Despite this interest, few works have explicitly examined the problem of calculating the average probability of error for these systems, in which the intersymbol interference from a single pulse may extend over hundreds or even thousands of symbols. Efficient series techniques for evaluation of the error probabilities of multilevel pulse amplitude modulations and multilevel duobinary signaling are derived. The method is applicable to any additive noise possessing an even probability density function. The Gaussian noise case is examined in detail. Examples of Nyquist I signaling and suboptimal detection of nonreturn-to-zero pulse codes are considered. The results are compared to previous published results. It is seen that an often cited upper bound, though within a factor of about ten in error probability for small to medium intersymbol interference conditions, may significantly overestimate the system degradation due to low-frequency attenuation when the intersymbol interference is large