Improved Coefficients for the Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian <i>Q</i>-Function

We revisit the Karagiannidis-Lioumpas (KL) approximation of Q-function by optimizing its coefficients in terms absolute error, relative error and total error. For minimizing maximum absolute/relative we describe targeted uniform functions sets nonlinear equations so that optimized are solutions thereof. The is minimized with numerical search. also introduce an extra coefficient KL to achieve significantly tighter at expense unbounded Furthermore, extend expression lower upper bounds minimize measures same way as for approximations.