Asymptotically optimal downlink scheduling over Markovian fading channels

We consider the scheduling problem in downlink wireless networks with heterogeneous, Markov-modulated, ON/OFF channels. It is well-known that the performance of scheduling over fading channels heavily depends on the accuracy of the available Channel State Information (CSI), which is costly to acquire. Thus, we consider the CSI acquisition via a practical ARQ-based feedback mechanism whereby channel states are revealed at the end of only scheduled users´ transmissions. In the assumed presence of temporally-correlated channel evolutions, the desired scheduler must optimally balance the exploitation-exploration trade-off, whereby it schedules transmissions both to exploit those channels with up-to-date CSI and to explore the current state of those with outdated CSI. In earlier works, Whittle´s Index Policy had been suggested as a low-complexity and high-performance solution to this problem. However, analyzing its performance in the typical scenario of statistically heterogeneous channel state processes has remained elusive and challenging, mainly because of the highly-coupled and complex dynamics it possesses. In this work, we overcome these difficulties to rigorously establish the asymptotic optimality properties of Whittle´s Index Policy in the limiting regime of many users. More specifically: (1) we prove the local optimality of Whittle´s Index Policy, provided that the initial state of the system is within a certain neighborhood of a carefully selected state; (2) we then establish the global optimality of Whittle´s Index Policy under a recurrence assumption that is verified numerically for the problem at hand. These results establish, for the first time to the best of our knowledge, that Whittle´s Index Policy possesses analytically provable optimality characteristics for scheduling over heterogeneous and temporally-correlated channels.