Optimal Power Allocation Policy over Two Identical Gilbert-Elliott Channels

TL;DR

This paper addresses the problem of optimally allocating power over two identical Gilbert-Elliott channels to maximize data transmission, formulating it as a POMDP and deriving optimal policies analytically and via simulation.

Contribution

It introduces a novel POMDP framework for power allocation over Gilbert-Elliott channels and analytically derives the structure of the optimal policy.

Findings

Optimal policies are characterized analytically.

Two policy structures are identified and verified.

Construction of optimal policies via thresholding and linear programming.

Abstract

We study the fundamental problem of optimal power allocation over two identical Gilbert-Elliott (Binary Markov) communication channels. Our goal is to maximize the expected discounted number of bits transmitted over an infinite time span by judiciously choosing one of the four actions for each time slot: 1) allocating power equally to both channels, 2) allocating all the power to channel 1, 3) allocating all the power to channel 2, and 4) allocating no power to any of the channels. As the channel state is unknown when power allocation decision is made, we model this problem as a partially observable Markov decision process(POMDP), and derive the optimal policy which gives the optimal action to take under different possible channel states. Two different structures of the optimal policy are derived analytically and verified by linear programming simulation. We also illustrate how to construct the optimal policy by the combination of threshold calculation and linear programming simulation once system parameters are known.