Simple Approximation Formula for the Symmetric Capacity

In this paper, a very simple formula is presented to approximate the symmetric capacity of the commonly used constellations under additive white Gaussian noise channel. Based on this simple formula, we have derived the ergodic capacity for general fading channels. The capacity of fading channel is determined by the distribution of the fading through the generator moment function (GMF). The formulas provide here is an efficient way to evaluate the channel capacity. Moreover, with this simple closed form formula, many theoretical analysis problems can be greatly simplified or become analytically tractable.