New Tight Bounds for the Gaussian Q-Function and Applications

The Gaussian Q-function (GQF) and its integer powers are quite versatile in various fields of science. In most applications, it is involved in intractable integrals for which closed-form expressions cannot be evaluated. In this paper, six new bounds for the GQF are presented and their tightness and simplicity are discussed compared to existing ones. As an application, these bounds can be efficiently used to evaluate in closed-form upper bounds for the average symbol error rate for various modulation schemes, in the presence of a generalized fading channel whose probability density function can be written as a summation of a particular Bivariate Fox's H-functions. α - μ, κ - μ shadowed, and Málaga distribution models have been considered as particular cases of such distribution. To gain more insight into the system reliability, asymptotic closed-form expressions for the system's ASER over the above fading models are further derived and interesting discussions on the key fading parameters' impact are made. Numerical results and simulations reveal the tightness of the proposed bounds compared to previous ones, while they keep almost the same complexity.