The Influence of Cycle Slipping on the Error Probability of a PAM Receiver

In this paper, we evaluate the error probability of a PAM receiver, which derives symbol timing from the received waveform by means of a synchronizer. We point out that the conventional way (using the distribution of the synchronizer's modulo-2π- reduced phase error) of evaluating this error probability does not take into account the effect of the synchronizer's cycle slips. We present a correct expression for the error probability, which uses the distribution of the so-called renewal phase. Also, we derive simple but accurate approximations for both the conventional and the correct error probability, which clearly show the influence of the characteristics of the PAM receiver. These approximate expressions indicate that, for a decreasing additive noise level at the receiver input, the conventional error probability becomes vanishingly small, whereas the correct error probability approaches a nonzero value, which is inversely proportional to the mean time between slips. Hence, cycle slipping imposes a (sometimes rather large) lower limit on the attainable error probability.