Recently, utilizing renewable energy for wireless system has attracted extensive attention. However, due to the instable energy supply and the limited battery capacity, renewable energy cannot guarantee to provide the perpetual operation for wireless sensor networks (WSN). The coexistence of renewable energy and electricity grid is expected as a promising energy supply manner to remain function for a potentially infinite lifetime. In this paper, we propose a new system model suitable for WSN, taking into account multiple energy consumptions due to sensing, transmission and reception, heterogeneous energy supplies from renewable energy, electricity grid and mixed energy, and multidimension stochastic natures due to energy harvesting profile, electricity price and channel condition. A discrete-time stochastic cross-layer optimization problem is formulated to achieve the optimal trade-off between the time-average rate utility and electricity cost subject to the data and energy queuing stability constraints. The Lyapunov drift-plus-penalty with perturbation technique and block coordinate descent method is applied to obtain a fully distributed and low-complexity cross-layer algorithm only requiring knowledge of the instantaneous system state. The explicit trade-off between the optimization objective and queue backlog is theoretically proven. Finally, the extensive simulations verify the theoretic claims.
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