Estimation of Constrained Capacity and Outage Probability in Lognormal Channels

The driving force behind this work is the desire to obtain one method for estimating the ergodic capacity of lognormal (LN) channels for both Shannon capacity and constrained capacity. In recent years, researchers have determined methods for calculating the ergodic Shannon capacity for LN channels. However, in practical communication systems, the input signal is constrained to a discrete signaling set such as finite-size quadrature amplitude modulation constellations. At a high SNR, the Shannon capacity greatly overestimates the capacity of these practical systems, particularly for low-order constellations. For this reason, a method is needed to evaluate the capacity and outage probability for LN channels when the signal set is constrained to a finite alphabet. The main contribution of this paper is the introduction of a simple but accurate method for calculating both the ergodic Shannon capacity and the ergodic constrained capacity of practical signals for LN channels. This method also facilitates straightforward computation of outage probability and outage capacity. Prior to this work, the ergodic constrained capacity, outage probability, and outage capacity of practical signals for LN channels had not been dealt with in the literature.