A closed-form rate outage probability description based on Nakagami-m channel model

Rate outage probability is an important performance metric to measure the level of quality of service (QoS) in the 4^th Generation (4G) broadband access networks. Thus, in this paper, we calculate a closed form expression of the rate outage probability for a given user in a down-link multi-hop OFDMA-based system encountered as a result of links´ channel variations. The channel random behavior on different subcarriers allocated to a given user are assumed to follow independent non-identical Nakagami-m distributions. Besides the rate outage probability formulas, we also derive a novel closed form formulas for the moment generating function, probability distribution function (pdf), and the cumulative distribution function (cdf) of a product of independent non-identical Gamma distributed random variables (RVs). These RVs are functions of the attainable signal-to-noise power ratio (SNR) on the allocated group of subcarriers.