The Influence of Four Types of Symbol Synchronizers on the Error Probability of a PAM Receiver

In this paper we derive a tight upper bound on the symbol error probability of a PAM receiver, consisting of a matched filter, a sampler which is subject to symbol timing errors resulting from a synchronizer, and a Viterbi detector. Our results pertain to four types of symbol synchronizers which have recently been treated in literature, and whose influence on the error probability has not been examined before. For both cases of NRZ-PAM and a cosine rolloff spectrum, we present graphs of the upper bound versus the receiver signal-to-noise ratio (SNR), with the synchronizer bandwidths as a parameter. From these graphs the design engineer directly reads the synchronizer bandwidth that is needed to achieve the desired error probability at the specific receiver SNR. Finally, we point out when an infinite SNR yields either a zero or a nonzero error probability.