Statistical properties of timing jitter in a PAM timing recovery scheme

A new technique is presented for evaluating the performance of a popular type of timing recovery circuit for baseband synchronous pulse amplitude modulation (PAM) data signals. The timing circuit consists of a square-law device followed by a narrowband filter tuned to the pulse repetition frequency along with provision for reshaping the pulses entering the timing path (prefiltering). The output of the timing circuit is a nearly sinusoidal timing wave whose zero crossings indicate the appropriate sampling instants for demodulation of the PAM signal. For a random data sequence, the timing wave exhibits phase fluctuations which are strongly dependent on the pulse shapes entering the timing path and the passband shape of the narrow-band filter. Expressions for rms phase fluctuation in the timing wave as a function of the prefiltering and postfiltering characteristics of the filters preceding and following the square-law device are presented. These expressions have a form which is especially suitable for studying the case where the baseband PAM signal is band-limited to frequencies less than the pulse repetition frequency. A condition on prefiltering and postfiltering which gives error-free timing recovery is presented. Results obtained from some specific examples serve to illustrate several aspects of the timing recovery problem.