Simple and Accurate Approximations for the Two Dimensional Gaussian Q-Function

The aim of this work is the derivation of two approximated expressions for the two dimensional Gaussian Q-function, Q(x, y, ρ). These expressions are highly accurate and are expressed in closed-form. Furthermore, their algebraic representation is relatively simple and therefore, convenient to handle both analytically and numerically. This feature is particularly useful for two reasons: firstly because it renders the derived expressions useful mathematical tools that can be utilized in numerous analytic performance evaluation studies in digital communications under fading; secondly because the two dimensional Gaussian Q-function is neither tabulated nor a built-in function in popular mathematical software packages such as Maple, Mathematica and Matlab.