Ei-transform: A useful and general framework for channel capacity analysis over fading channels

In this paper, we propose a novel unified analytical framework for the analysis of channel capacity over fading channels, which exploits the flexibility and generality of the well-known moment generating function (MGF-) based approach, instead of the usual probability density function (PDF-) based one. In particular, we will introduce a novel transform operator called E_i-transform, and show that channel capacity with side information at the receiver and side information at the transmitter and receiver can be readily expressed as the E_i-transform of the first derivative of the MGF of the received signal-to-noise ratio (SNR) in the former case, and the E_i-transform of a linear combination of MGF and truncated MGF (along with their derivatives) of the received SNR in the latter case. The proposed framework turns out to be a useful technique to the analysis and computation of channel capacity in all those application scenarios in which estimating the MGF of the received SNR is much simpler than estimating the PDF. Finally, a simple numerical method, which is based on the Gauss-Chebyshev quadrature (GCQ) rule, for computing E_i-transform integrals will be described, and numerical results will be shown to validate the accuracy of the proposed MGF-based approach.