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This paper considers a cross-layer adaptive modulation system that is modeledas a Markov decision process (MDP). We study how to utilize the monotonicity ofthe optimal transmission policy to relieve the computational complexity ofdynamic programming (DP). In this system, a scheduler controls the bit rate ofthe m-quadrature amplitude modulation (m-QAM) in order to minimize thelong-term losses incurred by the queue overflow in the data link layer and thetransmission power consumption in the physical layer. The work is done in twosteps. Firstly, we observe the L-natural-convexity and submodularity of DP toprove that the optimal policy is always nondecreasing in queue occupancy/stateand derive the sufficient condition for it to be nondecreasing in both queueand channel states. We also show that, due to the L-natural-convexity of DP,the variation of the optimal policy in queue state is restricted by a boundedmarginal effect: The increment of the optimal policy between adjacent queuestates is no greater than one. Secondly, we use the monotonicity results topresent two low complexity algorithms: monotonic policy iteration (MPI) basedon L-natural-convexity and discrete simultaneous perturbation stochasticapproximation (DSPSA). We run experiments to show that the time complexity ofMPI based on L-natural-convexity is much lower than that of DP and theconventional MPI that is based on submodularity and DSPSA is able to adaptivelytrack the optimal policy when the system parameters change.

On Monotonicity of the Optimal Transmission Policy in Cross-layer Adaptive m-QAM Modulation