MIMO Transmission Control in Fading Channels #x2014;A Constrained Markov Decision Process Formulation With Monotone Randomized Policies

TitleMIMO Transmission Control in Fading Channels #x2014;A Constrained Markov Decision Process Formulation With Monotone Randomized Policies
Publication TypeJournal Article
Year of Publication2007
AuthorsDjonin, D. V., and V. Krishnamurthy
JournalSignal Processing, IEEE Transactions on
Volume55
Pagination5069 -5083
Date Publishedoct.
ISSN1053-587X
KeywordsCMDP, delay constraints, fading channels, Lagrangian formulation, Markov decision process formulation, Markov processes, MIMO communication, MIMO transmission control, monotone randomized policies, multiple input multiple output wireless systems, optimal power, rate allocation control
Abstract

This paper addresses the optimal power and rate allocation control in multiple-input multiple-output (MIMO) wireless systems over Markovian fading channels. The problem is posed as an infinite horizon average-cost constrained Markov decision process (CMDP) with the goal of minimizing the average transmission power subject to delay constraints. By using a Lagrangian formulation of the CMDP, we use the concepts of stochastic dominance, submodularity, and multimodularity to prove that the optimal randomized policies are monotone. Three important structural results on the nature of the optimal randomized policies are derived. First, we show that the action space can be exponentially reduced by decomposing the rate allocation problem into bit-loading problem across individual antennas and the total rate allocation based on the current buffer occupancy and channel state. Second, we show that the optimal rate allocation policy is a randomized mixture of two pure policies that are monotonically increasing in the buffer occupancy. Finally, we show that the optimal power allocation is piecewise linear in the delay constraint. These three structural results can be exploited to devise efficient online reinforcement learning algorithms for optimal rate allocation.

URLhttp://dx.doi.org/10.1109/TSP.2007.897859
DOI10.1109/TSP.2007.897859

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