Effect of imperfect phase and timing synchronization on the error rate performance of PSK modulations

A great deal of attention has been devoted in the recent literature to the study of the symbol error rate (SER) and bit error rate (BER) performance of phase shift keyed (PSK) constellations due to their high spectral efficiency and constant envelope nature. It is well known that an error in phase or timing synchronization affects the probability of correct decisions at the receiver. This problem becomes much more significant as data rates increase and the corresponding symbol durations decrease. We look into this problem and analyze the exact SER and BER performance of uniform and hierarchical PSK constellations under imperfect phase or timing synchronization over additive white Gaussian noise (AWGN) channels. These expressions are in the form of a weighted sum of Pawula functions and are solely dependent on the constellation size, M, the carrier-to-noise ratio (CNR), the phase/timing error, and, for the case of hierarchical constellations, a priority vector which controls the relative message importance. Because of their purely exponential dependence on the CNR, these expressions can easily be generalized to fading conditions with and without diversity reception. In addition, due to their generic nature, these new expressions readily allow numerical evaluation for various cases of practical interest.