We jointly study the routing, scheduling, channel assignment and power control problem in Multi-Power-level Multi-Radio (MPMR) Wireless Sensor Networks (WSNs), which is proven to be NP-Hard. We first formulate the optimal routing problem as an integer linear programming problem. Subsequently, we develop a polynomial time heuristic algorithm which can efficiently decrease the computational complexity. Moreover, we design a distributed routing protocol based on the random walk method which is effective in large-scale WSNs by avoiding solving the linear programming formulations. The simulation results show that the cross-layer routing scheme significantly reduces energy consumption and end-to-end transmission delay.
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