Efficient Approximated Q-Function Form for Error Probability over Rayleigh Fading Channels

Abstract

Error rate probability is considered as important metric to evaluate the behavior of communication system. Gaussian Q-function is gaining more intention from researchers due to its direct relation in computing the error probability in terms of symbol error rate (SER) or bit error rate. In literature, several approximated functions have been proposed to evaluate and analyze the error rate in fading channel. In this paper, a novel, simple and accurate closed form for Gaussian Q-function is derived. In contrast to previous related approximated functions; it is noticeable that the designed formula improves the accuracy for large range of positive argument. Furthermore, an efficient SER formula is derived for additive white Gaussian noise and for Rayleigh fading channel. Numerical analysis and simulation were conducted to verify and validate the designed approximated functions. The results show that the proposed form can achieve high accuracy compared to that of previous work; and also simplify the evaluation analysis of SER in fading channels.