Fairness-Aware Resource Allocation in Multi-Source WPCN in the Finite Blocklength Regime

In this work, we investigate a wireless powered communication network (WPCN) where multiple sources are jointly utilized for wireless power transfer (WPT). By consuming the energy harvested from the these WPT sources, a set of sensors are expected to accomplish reliable transmissions carried by finite blocklength (FBL) codes. This work proposes a fairness-aware resource allocation design with low-complexity in such a multi-source WPCN, where the practical nonlinear energy harvesting process is considered (including the effects of components nonlinearity in rectifier circuits and mutual interference between multiple radio frequency signals). In particular, a joint power and blocklength optimization problem minimizing the maximum reliability of all short packet transmissions is considered. To cope with the formulated extremely intractable nonconvex problem, we decompose it into two subproblems, i.e., a power allocation problem and a blocklength allocation problem, nevertheless, both of which are still nonconvex. To address the power allocation subproblem, auxiliary variables are introduced. Subsequently variable substitutions are performed to convert the problem into one being analytically tractable, and an efficient iterative approach is provided via applying the successive convex approximation technique. For the blocklength allocation problem, we for the first time verify the convexity of error probability with respect to blocklength under a harvested energy constraint, which is of great theoretical value and can be extended to numerous applications with energy limitations. Finally, by alternatingly addressing the two subproblems, an efficient sub-optimal solution to the original problem is achieved. We provide numerical results to validate and evaluate the proposed design, and a set of guidelines are provided for practical system designs.