Constrained Optimal Energy Allocation in Wireless Sensor Networks Under Stochastic Channel Conditions

Abstract

Wireless sensor networks (WSNs) are networks that often have very limited energy resources and operate with random wireless channel conditions. Thus, allocation of energy needs to be done so as to balance the transmission utility, the individual energy limitations, and the reliability of the communication. The current research on energy allocation has focused on maximizing the lifetime or fairness, coordinating sensing and transmission, adapting the channel, and leveraging energy harvesting; however, many energy-allocation formulations have assumed known or nominal channel distributions, or reliability requirements do not account for distributional uncertainty. To that end, this paper proposes a constrained stochastic energy-allocation setting where (unknown) channel statistics are modelled with a Wasserstein ambiguity set around an empirical channel distribution, and reliability is ensured via a distributionally robust tail-risk constraint. That Wasserstein distributionally robust optimization and conditional value-at-risk are not viewable as two independent corner results is not a concern, since the proposed analysis is used to extract the structural facts of the optimal allocation policy, which are standard results in Wasserstein distributionally robust optimization and conditional value-at-risk studies. An ambitious MV operator is added that can measure the worst-case MV of more energy, under distributional ambiguity. The monotonicity results in the scalar characterisation of the optimal allocation. The reliability requirement further creates a minimum energy threshold for every sensor, which is endogenously determined. This helps to arrive at an operating regime characterized by three different types of allocation policy, namely deactivation, marginal allocation and reliability-dominating allocation. The analysis proves the existence and uniqueness of the optimal allocation, monotonicity with respect to the total energy budget, sensitivity to distributional ambiguity and global convergence of a scalar bisection solution procedure. The numerical evaluation is structured by different channel and reliability conditions and illustrates the resulting allocation structure and how it differs from equal allocation, nominal optimization, and conventional water filling approaches. The protocol offers a mathematically tractable solution towards achieving robust energy management for WSNs that are designed to have simultaneous stochastic-channel uncertainty as well as reliability requirements.