Sampling Time Jitter

Abstract

Electrical systems which use voltage transitions to represent timing information suffer from a degrading phenomenon called timing jitter. Sampling time jitter is the deviation of sampling clock from its ideal position. As transmission rates raise above couple of GHz, deviations become significant comparing to signalling interval, jitter becomes a fundamental performance bottleneck. Especially in band-limited communication systems that imperfect sampling times result in Inter-Symbol Interference (ISI) jitter is a very limiting factor to decode correct transmitted data. In this case, jitter timing error translates into amplitude error.

At first, the effect of sampling time jitter at the received signal is modelled as an additive noise .This additive noise signal which we call it jitter noise is a coloured noise that also depends on input signal. Expressions for jitter noise correlation factors, its cross- correlation with input signal are derived. These correlations depend on input spectral density, timing jitter characteristic function (Fourier transform of jitter probability density function) and whether timing jitter is white or coloured. In case of first order Gauss-Markov process for sampling time jitter it is observed that in high memory regime (highly correlated timing jitter) the spectral density of additive jitter noise is concentrated around higher frequencies. Exploiting this quality, a spectral shaping scheme is used to improve the performance in terms of Bit Error Rate (BER) for an AWGN channel with discrete input corrupted by sampling time jitter. Simulation results comparing the proposed scheme performance with a minimum distance decoder are provided.

As another approach the well-known Viterbi Algorithm is used for decoding same AWGN channel suffering from ISI terms due to sampling jitter. The Viterbi algorithm, which basically is a dynamic programming algorithm, finds the most likely input data and jitter times based on observed output sequence. A quantized version of jitter times is used to be able to work with a finite state trellis and to find likelihoods along the paths of the diagram. Then Bit Error Rate curves for different jitter quantization levels and different impulse response lengths of channel are presented.