SER of two-dimensional signalings in Rayleigh fading with channel estimation errors

A general analytical framework for evaluating the performance of practical coherent two-dimensional (2-D) signaling in frequency flat Rayleigh fading with channel estimation is proposed in this paper. A new and simple analytical expression for the symbol error rate (SER) of an arbitrary 2-D constellation in Rayleigh fading in the presence of channel estimation errors is presented. This framework is applicable to many current channel estimation methods such as pilot symbol aided modulation and minimum mean square error estimation where the fading estimate is a complex Gaussian variable correlated with the channel fading. The sensitivity of various 2-D signaling formats to static and dynamic channel amplitude and phase estimation errors in Rayleigh fading can be easily studied using the derived formula. The new exact SER expression makes it possible to optimize constellation parameters and various parameters associated with channel estimation schemes. It also provides insights into choosing an appropriate signaling format for a fading environment with practical channel estimation methods used at the receiver.