WAVEFORMS AND RECEIVERS FOR PULSE AMPLITUDE MODULATION

摘要

Intersymbol interference, additive noise and inexact synchronisation, or timing jitter, are three common sources of distortion in data trans¬mission systems. For pulse amplitude modulation communication links, the combination of transmitter waveform and linear receiver which mini¬mizes the over-all mean square error arising from these sources is determined.nFormulas are derived which permit one to explore the dependence of system performance on the data rate, the correlation properties of the data the noise spectrum, the impulse response of the transmission medium and the probability distribution of the timing jitter,nMean square error vs. signal-to-noise ratio performance character- istics of the optimal systems are determined explicitly for several examples . These characteristics are compared both with those of certain suboptimal systems and with the optimal performance theoretically attainable (OPTA) derived from Shannon's theory of rate distortion functions.nThe optimal PAM systems, which can be interpreted as ideal com¬binations of infinite memory convolution encoders and decoders, are seen to perform very close to the OPTA for low signal-to-noise ratios. For high signal-to-noise ratios, however, the mean square error of an optimal PAM system decreases as the reciprocal of the signal-to-noise ratios, whereas the OPTA generally decreases exponentially. Accordingly, there exists a potential for realizing significant improvement at high signal-to-noise ratios by resorting to complex, nonlinear coding techniques.