On optimal transmission algorithms for slotted ALOHA sensor networks with multi-packet reception

In this paper we utilize decentralized channel state information (CSI) for designing optimal transmission schemes for slotted ALOHA sensor networks that have multi-packet reception capability. We prove that under certain conditions the optimal transmit probability function is deterministic, i.e., it is optimal for sensors to either transmit or not transmit with certainty depending on their channel states. We present a provably convergent stochastic approximation optimization algorithm to estimate the optimal transmit policy. Numerical studies illustrate the performance of the algorithm and the degenerate, non-randomized structure of the optimal transmission policy.