Analysis of Opportunistic Scheduling Algorithms in OFDMA Systems in the Presence of Generalized Fading Models

Analytical expressions for scheduling gain and spectral efficiency of the proportional fair and maximum rate scheduling algorithms for Orthogonal Frequency Division Multiple Access (OFDMA) based systems are derived for the following cases: a) multipath Rayleigh and multipath Nakagami fading, b) Composite channel models which model the combined effect of both small scale and large scale fading. It is shown using Extreme Value Theory (EVT) that the asymptotic distribution of the maxima of the received signal to noise power (SNR) across all the users converges to a Gumbel distribution for both cases. Therefore, we use the Gumbel distribution to derive expressions for both the spectral efficiency and scheduling gain. The scheduling gains obtained through numerical integration (whenever tractable) and simulations match with the analytical values obtained using the EVT based expressions. We also discuss how the moments and order statistics of the Gumbel distribution can be used to study other metrics of the scheduling algorithms.