Application of Gauss Quadrature Rules to Digital Communication Problems

In multilevel bandpass data transmission there is usually a difference between the phase of the carrier signal and the phase of the receiver oscillator, thereby causing imperfect demodulation. The use of nonclassical Gauss quadrature rules (GQR's) allows: 1) a theoretical study of the joint effects of phase jitter, thermal noise, and intersymbol interference on average error probability; and 2) a maximum-precision sampling technique in the simulation of digital communication systems. On this basis, the mean-square-error and zero-forcing equalizers are considered, and their performances evaluated in terms of the average error probability for multilevel pulse-amplitude-modulation (PAM) and partial-response-coded (PRC) signaling schemes.