  In this paper, we investigate fundamental performance limits of cumulative
distribution function (CDF)-based scheduling (CS) in downlink cellular
networks. CS is known as an efficient scheduling method that can assign
different time fractions for users or, equivalently, satisfy different channel
access ratio (CAR) requirements of users while exploiting multi-user diversity.
We first mathematically analyze the throughput characteristics of CS in
arbitrary fading statistics and data rate functions. It is shown that the
throughput gain of CS increases as the CAR of a user decreases or the number of
users in a cell increases. For Nakagami-m fading channels, we obtain the
average throughput in closed-form and investigate the effects of the average
signal-to-noise ratio, the shape parameter m, and the CAR on the throughput
performance. In addition, we propose a threshold-based opportunistic feedback
technique in order to reduce feedback overhead while satisfying the CAR
requirements of users. We prove that the average feedback overhead of the
proposed technique is upper bounded by -ln(p), where p is the probability that
no user satisfies the threshold condition in a cell. Finally, we adopt a novel
fairness criterion, called qualitative fairness, which considers not only the
quantity of the allocated resources to users but also the quality of the
resources. It is observed that CS provides a better qualitative fairness than
other scheduling algorithms designed for controlling CARs of users.
