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Rate outage probability is an important performance metric to measure thelevel of quality of service (QoS) in the 4th Generation (4G) broadband accessnetworks. Thus, in this paper, we calculate a closed form expression of therate outage probability for a given user in a down-link multi-hop OFDMA-basedsystem encountered as a result of links channel variations. The channel randombehavior on different subcarriers allocated to a given user is assumed tofollow independent non-identical Nakagami-m distributions. Besides the rateoutage probability formulas for single hop and multi-hop networks, we alsoderive a novel closed form formulas for the moment generating function,probability distribution function (pdf), and the cumulative distributionfunction (cdf) of a product of independent non-identical Gamma distributedrandom variables (RVs). These RVs are functions of the attainablesignal-to-noise power ratio (SNR) on the allocated group of subcarriers. Forsingle-hop scenario, inspired by the rate outage probability closed formula, weformulate an optimization problem in which we allocate subcarriers to userssuch that the total transmission rate is maximized while catering for fairnessfor all users. In the proposed formulation, fairness is considered byguaranteeing a minimum rate outage probability for each admitted user

Closed-Form Rate Outage Probability for OFDMA Multi-Hop Broadband Wireless Networks under Nakagami-m Channels