Estimation of Constrained Capacity and Outage Probability in Rayleigh Channels

Ergodic capacity and outage probability are two important performance measures of communication systems in fading channels. The goal of this work is to develop a simple method for tightly estimating the ergodic capacity and outage probability of a Rayleigh channel with and without antenna combining for constellation constrained capacity. Researchers have determined methods for calculating the ergodic Shannon capacity for Rayleigh channels for single and multiple receive antenna systems. However, in practical communications systems, the input signal is constrained to a discrete signalling set such as finite-size quadrature amplitude modulation constellations. Under these conditions the ergodic constellation constrained capacity is a more accurate measure. Relatively loose bounds for the ergodic constellation constrained capacity of a Rayleigh channel have been exposited in the literature for a single antenna system. This paper details a method that provides a uniform expression for accurately estimating the ergodic capacity, both Shannon and constellation constrained, of Rayleigh channels with and without antenna combining. Expressions are derived using this method for both the noise limited and interference limited cases. These expressions facilitate straightforward computation of outage probability as well. To date, no other method for calculating the ergodic constellation constrained capacity of an interference limited Rayleigh channel or estimating the outage probabilities for the constellation constrained capacity of a noise limited or interference limited Rayleigh channel has been published.