Delay-optimal distributed power and transmission threshold control for S-ALOHA network with FSMC fading channels

This paper considers the delay-optimal power and transmission threshold control design in S-ALOHA network with FSMC fading channels. The random access system consists of an access point with K competing users, each has access to the local channel state information (CSI) and queue state information (QSI) as well as the common feedback (ACK/NAK/Collision) from the access point. We seek to derive the delay-optimal control policy (composed of threshold and power control) in symmetric network. The optimization problem belongs to the special memoryless policy case of K-agent infinite horizon decentralized Markov decision process (DEC-MDP), and finding the optimal memoryless policy is shown to be computationally challenging. To obtain a feasible and low complexity solution, we recast the optimization problem into two subproblems, namely the power control problem and the threshold control problem. For a given threshold control policy, the power control problem is decomposed into a reduced state MDP for single user so that the overall complexity is O(NJ), where N and J are the buffer size and the cardinality of the CSI states. For the threshold control problem, we exploit some special structure of the collision channel and common feedback information to derive a low complexity solution. The delay performance of the proposed design is shown to have substantial gain relative to conventional throughput optimal approaches for S-ALOHA.