This research presents a tight and closed technique towards approximating the Gaussian Q-function for evaluating a critical performance metric, the symbol error probability (SEP), across wireless fading environments. The Gauss-Legendre four-point rule is employed to derive the exponential-type approximation, exhibiting a higher degree of agreement compared to other approximation techniques currently used in SEP computation. Considering the entire low-to-high range of input signal-to-noise ratio (SNR), this approximation provides a tighter fit throughout the range. In addition, this approximation technique is employed to achieve an analytical solution for SEP integrals over the q-Weibull fading channel, which introduces the entropic index q originating from Tsallis’ entropy. By adjusting the range of the entropic index q, this single-statistic fading distribution exhibits adaptive behavior and provides a tighter fit over the synthetic signal than the commonly used composite Weibull-Lognormal distribution. In this context, it is valuable to obtain the analytical solution of the SEP over this fading model for different values of the parameter q and the shape parameter. Further, performance measures viz. , Level Crossing Rate (LCR) and Average Fade Duration (AFD) are also obtained over the q-Weibull fading model.
Samal et al. (Tue,) studied this question.