Generalised expression for the symbol error floor of M ‐ary phase shift keying in the presence of phase noise, I/Q imbalance and DC‐offset

Abstract

This study, for the first time, presents an exact expression for the symbol error floor (SEF) of M-ary phase shift keying in the presence of phase noise, in-phase/quadrature (I/Q) gain and phase imbalances, and DC-offsets altogether. Accurate calculation of symbol error probability, and also the SEF, in the presence of transmitter and receiver impairments is usually a cumbersome task. In this study, the symbol decision boundaries are moved from the demodulator output to the demodulator input as a means to simplify the SEF calculation. In other words, the effect of the receiver I/Q imbalance and DC-offset is applied on the symbol decision boundaries. Using the decision boundaries at the demodulator input facilitates the exact SEF calculation. The proposed exact expression consists of single integrals. These integrals can be accurately approximated by Gaussian one-dimensional Q-functions assuming a Gaussian distribution for the phase noise. Computer simulations with Gaussian phase noise validate the exactness of the proposed analysis.