Asymptotically optimal pilot allocation over Markovian fading channels

TL;DR

This paper addresses the challenge of pilot allocation in wireless networks with Markovian fading channels, proposing an asymptotically optimal heuristic based on Whittle index policy for large user systems.

Contribution

It introduces a low-complexity approximation for pilot allocation, proving asymptotic optimality in large-scale systems using a Lagrangian relaxation approach.

Findings

Whittle index policy performs remarkably well across scenarios.

The proposed heuristic is asymptotically optimal as the number of users grows.

The problem is modeled as a restless bandit, enabling effective approximation.

Abstract

We investigate a pilot allocation problem in wireless networks over Markovian fading channels. In wireless systems, the Channel State Information (CSI) is collected at the Base Station (BS), in particular, this paper considers a pilot-aided channel estimation method (TDD mode). Typically, there are less available pilots than users, hence at each slot the scheduler needs to decide an allocation of pilots to users with the goal of maximizing the long-term average throughput. There is an inherent tradeoff in how the limited pilots are used: assign a pilot to a user with up-to-date CSI and good channel condition for exploitation, or assign a pilot to a user with outdated CSI for exploration. As we show, the arising pilot allocation problem is a restless bandit problem and thus its optimal solution is out of reach. In this paper, we propose an approximation that, through the Lagrangian relaxation approach, provides a low-complexity heuristic, the Whittle index policy. We prove this policy to be asymptotically optimal in the many users regime (when the number of users in the system and the available pilots for channel sensing grow large). We evaluate the performance of Whittle's index policy in various scenarios and illustrate its remarkably good performance.