Timing Errors in a Chain of Regenerative Repeaters, III

Abstract

We present here a general and rigorous theory of the jitter accumulation in a chain of regenerative repeaters. The sources of jitter are assumed to be the signal-dependent sources, as distinguished from purely random sources independent of the signal. Our results show that while the absolute jitter and its dispersion grow without bound with the number of repeaters, the spacing and the alignment jitter remain bounded. In particular, the spacing jitter bounds are quite optimistic for most practical situations, viz., no greater than twice the absolute jitter injected at a single repeater. This result is of importance in that it ensures proper decoding of the binary signal. Its further importance is that it does ensure, in most cases, the validity of the basic model and thus the validity of other results obtained by that model. One such result shows that the alignment jitter is slowly-varying for repeaters farther along the chain. We also include some results which would be of use in computations, together with a simple example.