A simple polynomial approximation to the gaussian Q-function and its application

A simple polynomial approximation to the Gaussian Q-function is proposed, based on the observation that a Gaussian random variable can be well approximated by a sum of uniform random variables. The approximation can be used to obtain accurate explicit approximations to problems that otherwise do not have explicit solutions or approximate explicit solutions. As an example, an explicit expression for the average symbol error rate of M-ary pulse amplitude modulation in lognormal channels is derived using the new approximation, and the approximate symbol error rate is shown to be very close to the exact value.