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Rate outage probability is an important performance metric to measure the level of Quality of Service (QoS) in the Generation (4G) broadband access networks. Thus, in this paper, the authors 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 is assumed to follow independent non-identical Nakagami-m distributions. Besides the rate outage probability formulas for single hop and multi-hop networks, they also derive 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).
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