Bit Error Rate Degradation Caused by Random Tracking Errors Introduction For coherent detection of digitally modulated signals, the receiver must be provided with accurate carrier phase and symbol timing estimates; these estimates are derived from the received signal itself by means of a synchronizer. The bit error rate (BER) performance under the assumption of perfect synchronization is well documented for various modulation formats [l-5]. However, in practice the carrier phase and timing estimates exhibit small random fluctuations (jitter) about their optimum values; these fluctuations give rise to a BER degradation as compared to perfect synchronization. It is important to know. | Digital Communication Receivers Synchronization Channel Estimation and Signal Processing Heinrich Meyr Marc Moeneclaey Stefan A. Fechtel Copyright 1998 John Wiley Sons Inc. Print ISBN 0-471-50275-8 Online ISBN 0-471-20057-3 Chapter 7 Bit Error Rate Degradation Caused by Random Tracking Errors Introduction For coherent detection of digitally modulated signals the receiver must be provided with accurate carrier phase and symbol timing estimates these estimates are derived from the received signal itself by means of a synchronizer. The bit error rate BER performance under the assumption of perfect synchronization is well documented for various modulation formats 1-5 . However in practice the carrier phase and timing estimates exhibit small random fluctuations jitter about their optimum values these fluctuations give rise to a BER degradation as compared to perfect synchronization. It is important to know this BER degradation in terms of the accuracy of the estimates provided by the synchronizer so that the synchronizer can be designed to yield a target BER degradation which should not exceed about dB for most applications . For various linear modulation formats M-PSK M-PAM and M2-QAM we evaluate the BER degradation caused by random carrier phase and timing errors. In Section we show that the results also apply for the practically important case of coded transmission. For nonlinear modulation and coded transmission we refer to the bibliographical notes in Section . ML Detection of Data Symbols Figure 7-1 conceptually shows how a maximum-likelihood ML decision about the symbol sequence a is obtained. The matched filter output is sampled at the instant kT eT where e denotes the estimate of the normalized time delay Eo The matched filter output samples are rotated counterclockwise over an angle 0 which is an estimate of the unknown carrier phase 0. The receiver s decision about the transmitted sequence is the data sequence which maximizes the ML .
