New Approximation Formulas for Tighter Bounds of the Q-Function and its Applications

The approximation problem of Gaussian Q-function plays a key role in estimation of the symbol error probability (SEP) for several digital modulation schemes and has wide applications in signal processing and communication theory. This paper presents a Pade approximation based method for achieving much tighter bounds of Q-function, and also provides the corresponding proof of the bounds. It can be efficiently applied to compute the integrals in SEP expressions of various digital modulation schemes over additive white Gaussian noise (AWGN) as well as fading channels. By using the proposed approximation formula, one can achieve much better approximation effect for approximating the Q-function, and the integral of SEP expressions as well.