Optimal Power Allocation Over Two Identical Gilbert-Elliott Channels

With the popularity of wireless networks, applications based onwireless network have increasingly penetrated into our life. But the limitedpower resources of wireless devices limits the application business expan-sion based on wireless network, thus there is an urgent need for effectivepower allocation strategy. We study the fundamental problem of optimalpower allocation over two identical Gilbert-Elliott (Binary Markov) communi-cation channels. Our goal is to maximize the expected discounted number ofbits transmitted over an infinite time span by judiciously choosing one of thefour actions for each time slot:1) allocating power equally to both channels,2) allocating all the power to channel1,3) allocating all the power to chann-el2,4) allocating no power to any of the channels. As the channel state is u-nknown when power allocation decision is made, we model this problem asa partially observable Markov decision process (POMDP), and derive theoptimal policy which gives the optimal action to take under different possi-ble channel states. Two different structures of the optimal policy are derivedanalytically and verified by linear programming simulation. We also illustratehow to construct the optimal policy by the combination of threshold calcula-tion and linear programming simulation once system parameters are known.