Exploiting Channel Memory for Joint Estimation and Scheduling in Downlink Networks

We address the problem of opportunistic multiuser scheduling in downlink networks with Markov-modeled outage channels. We consider the scenario in which the scheduler does not have full knowledge of the channel state information, but instead estimates the channel state information by exploiting the memory inherent in the Markov channels along with ARQ-styled feedback from the scheduled users. Opportunistic scheduling is optimized in two stages: (1) Channel estimation and rate adaptation to maximize the expected immediate rate of the scheduled user; (2) User scheduling, based on the optimized immediate rate, to maximize the overall long term sum-throughput of the downlink. The scheduling problem is a partially observable Markov decision process with the classic ’exploitation vs exploration’ trade-off that is difficult to quantify. We therefore study the problem in the framework of Restless Multi-armed Bandit Processes (RMBP) and perform a Whittle’s indexability analysis. Whittle’s indexability is traditionally known to be hard to establish and the index policy derived based on Whittle’s indexability is known to have optimality properties in various settings. We show that the problem of downlink scheduling under imperfect channel state information is Whittle indexable and derive the Whittle’s index policy in closed form. Via extensive numerical experiments, we show that the index policy has near-optimal performance. Our work reveals that, under incomplete channel state information, exploiting channel memory for opportunistic scheduling can result in significant performance gains and that almost all of these gains can be realized using an easy-to-implement index policy.

💡 Research Summary

The paper tackles opportunistic multi‑user scheduling in a downlink system where each user’s channel evolves as a two‑state Markov chain. Unlike many prior works that assume perfect, cost‑free channel state information (CSI), the authors consider a realistic scenario in which CSI must be estimated at a non‑negligible resource cost, and the estimate is imperfect. Each channel has a “low” state ℓ with a non‑zero achievable rate δ (0 ≤ δ < 1) and a “high” state h that supports the normalized rate 1. Transmitting above the state‑specific rate causes outage.

The scheduler operates in two stages each time slot. First, given the current belief π_i (the probability that user i’s channel is in the high state), it selects an optimal estimator‑rate‑adapter pair u = {ε, η} for each user to maximize the expected immediate successful transmission rate R_i(π_i). This maximization accounts for the cost of estimation and the trade‑off between aggressive (high‑rate) and conservative (low‑rate) transmission. Second, based on the resulting immediate rates, the scheduler chooses a single user to actually estimate and transmit to, respecting a one‑hop interference model (only one user can be served per slot). After transmission, the scheduled user feeds back its exact channel state, allowing the belief vector to be updated via Bayes’ rule; unscheduled users’ beliefs evolve according to the known Markov transition probabilities.

Formally, the problem is a partially observable Markov decision process (POMDP) with discount factor β∈