An accurate approximation to channel capacity of wireless communications systems

The ergodic capacity of a wireless channel is usually obtained by averaging its conditional capacity over the probability density function (PDF) of the instantaneous SNR. In this paper, based on its integral representation and relevant Gauss quadrature rule, the conditional channel capacity is accurately approximated by a weighted sum of exponential functions of the instantaneous SNR. As such, the ergodic capacity of various wireless channels can be easily calculated and expressed in closed-form expressions. Several examples are provided to show the usefulness of the proposed approximation.