Power Allocation over Two Identical Gilbert-Elliott Channels

TL;DR

This paper addresses optimal power allocation over two identical Gilbert-Elliott channels to maximize expected data transmission, modeling the problem as a partially observable MDP and deriving threshold-based policies.

Contribution

It introduces a threshold-based optimal policy framework for power allocation over Gilbert-Elliott channels, with numerical methods for policy determination.

Findings

Optimal policies exhibit threshold structures.

Linear programming can numerically determine thresholds.

Strategies depend on channel state observations and system parameters.

Abstract

We study the problem of power allocation over two identical Gilbert-Elliot communication channels. Our goal is to maximize the expected discounted number of bits transmitted over an infinite time horizon. This is achieved by choosing among three possible strategies: (1) betting on channel 1 by allocating all the power to this channel, which results in high data rate if channel 1 happens to be in good state, and zero bits transmitted if channel 1 is in bad state (even if channel 2 is in good state) (2) betting on channel 2 by allocating all the power to the second channel, and (3) a balanced strategy whereby each channel is allocated half the total power, with the effect that each channel can transmit a low data rate if it is in good state. We assume that each channel's state is only revealed upon transmission of data on that channel. We model this problem as a partially observable Markov decision processes (MDP), and derive key threshold properties of the optimal policy. Further, we show that by formulating and solving a relevant linear program the thresholds can be determined numerically when system parameters are known.