SNR- Versus Rate-Based Proportional Fair Scheduling in Rayleigh Fading Channels

The initial definition of the Proportional Fair scheduling was based on a transmission rate criterion. However, a Signal-to-Noise Ratio (SNR) based definition is commonly used by researchers due to its mathematical tractability, based on the assumption that the performance of both definitions is equivalent. In this work, we derive closed-form expressions for the probability density function of the system output SNR (i.e. received SNR based on the selected scheduling algorithm) and the per-user SNR over Rayleigh fading channels when a rate-based criterion is used. Additionally, we analyze the common assumption of equivalence between both criteria by comparing their per-user performance. Our analysis reveals that their performance are only similar when users experience high values of average SNR. However, significant differences in terms of user fairness have been found in the lower SNR regime.