Extremely Accurate, Generic and Tractable Exponential Bounds for the Gaussian Q Function With Applications in Communication Systems

In this letter, we apply the Fejer’s Rule of interpolatory integration in a modified manner to obtain a very generic, tractable and extremely accurate approximation for the Gaussian
$Q$
function. We further show the utility of the proposed approximation by simplifying the error performance metrics like average symbol error probability (ASEP) of popular digital modulation techniques over a very useful
$\kappa -\mu $
shadowed fading channel. This eliminates the need of mathematical softwares which require very high processing power (a constraint at the receiver side) yielding simplified and cost effective receiver’s design. In addition, an insight on the asymptotic ASEP (and diversity order thereof) is also highlighted in this letter.