MGF and high order moment of channel capacity in log-normal fading environment

Abstract

The analytical expression for the MGF (Moment Generating Function) of the channel capacity in log-normal fading environment is derived. Using MGF, the closed form expression for higher order moments of channel capacity are computed as a rapidly convergent infinite series. Explicit expression for error and its upper bound resulting on account of truncation of series are obtained. Numerical results based on truncated infinite series are found to be in excellent agreement with those based on Monte Carlo simulation and Gauss Hermite method. Statistical measures like coefficient of variation, skewness and kurtosis are obtained for different values of shadowing level over a range of practical interest. It is found on the basis of skewness and kurtosis that gaussian approximation for channel capacity in log-normal fading environment is not in general valid over the entire range of dBspread. Keywords-Channel capacity, log-normal fading, diversity method, moment generating function