Optimal Power Allocation over Multiple Identical Gilbert-Elliott Channels

TL;DR

This paper develops an optimal power allocation strategy for multiple Gilbert-Elliott channels, maximizing data transmission by intelligently allocating power based on channel state beliefs modeled as a POMDP.

Contribution

It introduces a belief-based optimal power allocation policy for multiple channels modeled as a POMDP, including a threshold-based policy for three channels and verification via linear programming.

Findings

Optimal policy maximizes expected transmitted bits over infinite horizon.

Derived a threshold-based policy for three-channel systems.

Verified policy structure through linear programming.

Abstract

We study the fundamental problem of power allocation over multiple Gilbert-Elliott communication channels. In a communication system with time varying channel qualities, it is important to allocate the limited transmission power to channels that will be in good state. However, it is very challenging to do so because channel states are usually unknown when the power allocation decision is made. In this paper, we derive an optimal power allocation policy that can maximize the expected discounted number of bits transmitted over an infinite time span by allocating the transmission power only to those channels that are believed to be good in the coming time slot. We use the concept belief to represent the probability that a channel will be good and derive an optimal power allocation policy that establishes a mapping from the channel belief to an allocation decision. Specifically, we first model this problem as a partially observable Markov decision processes (POMDP), and analytically investigate the structure of the optimal policy. Then a simple threshold-based policy is derived for a three-channel communication system. By formulating and solving a linear programming formulation of this power allocation problem, we further verified the derived structure of the optimal policy.