Delay-Optimal Multi-User Wireless-Powered Relay Networks With Protection Against the Risk of Distributed Algorithm Manipulation

Abstract

We consider simultaneous-wireless-information-and-power-transfer (SWIPT) in a relay network, where multiple users with stochastic traffic flows are serviced by a common wireless-powered relay. A two-phase forwarding protocol is deployed along with power splitting. In the first phase, the relay splits its received signal from sources into two parts: one for information decoding and the other for energy harvesting. In the second phase, the relay allocates the total harvested energy from the first phase to forward each user’s data. To optimize the system’s long-run delay performance, we formulate the relay’s power control problem as a Markov decision process (MDP) with per-stage (energy) budget constraints. We realize that the Bellman’s equations associated with the formulated MDP have a weakly-coupled structure, and assuming that users act as price-takers, the global optimum can be computed distributively via Lagrangian decomposition. We then abandon this assumption to face the more realistic case where the users are price-anticipating and may manipulate the rules of the distributed algorithm to favor themselves. To protect against the risk of unfaithful implementation, we design a dynamic economic mechanism that builds on the notions of transfer payments and periodic ex-post Nash equilibrium to disarm the users’ self-interest and ensure adherence to the algorithm.