Bit Error Rates in the Presence of Untracked Time Base Fluctuation

Abstract

This paper presents a simple four-step procedure for estimating the error probability of an NRZ PCM Synchronizer and Detector operating on an NRZ Bit Stream in the presence of a fluctuating data frequency source. The four steps are as follows. First, the bit error probability is calculated for Gaussian time base fluctuation as a function of the energy per bit to noise power density ratio. The second step is to model the synchronizer as an ordinary linear servo for small phase errors and a closed loop bandwidth, small compared to the bit rate, so that effect of the randomness of the data is averaged out. With the linear model, the time base error in tracking the input signal is calculated also utilizing this approximation as if there were no additive noise. The third step is to calculate the mean squared time base error due to the additive Gaussian noise alone. The fourth step is to combine the errors found in steps two and three as if they were independent and use the graphs found in Step 1 to determine the error rates. It is assumed that the total untracked time base fluctuation is Gaussian. The calculated error probabilities are compared with measured data. There appears to be good correspondence between the calculated and measured error probability.