Electronic Health (eHealth) monitoring systems with wireless body area networks (WBANs) have recently emerged as promising solutions to provide sustainable and high-quality health services. In this paper, we propose an optimization framework to maximize the energy efficiency (EE) of a WBAN assisted by backscatter communication (BackCom) and energy harvesting technologies, subject to quality-of-service and power budget constraints. More specifically, the optimization problem jointly optimizes the transmit power of the aggregator, transmission time, and backscatter time of the WBAN consisting of energy-constrained sensor nodes (SNs) which have the ability to harvest energy from the signals transmitted by the aggregator. A generalized gamma distribution is adopted to characterize the channel propagation characteristics of patients under different arbitrary body movements and their corresponding transmission requirements during daily life activities. It is shown that the formulated EE optimization problem is a quasi-concave nonlinear fractional program, and it is transformed to an equivalent parametric problem by using the Dinkelbach algorithm to obtain the solution. We exploit the structure of the optimization problem and propose a low-complexity iterative-based suboptimal heuristic with performance fairly close to the optimized solution. Simulation results demonstrate the effectiveness of the proposed schemes in maximizing EE of the WBAN, whereas the comparisons with the related work from the literature reaffirm the superiority of the proposed algorithms.
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