Towards Immortal Wireless Sensor Networks by Optimal Energy Beamforming and Data Routing

The lifetime of a wireless sensor network (WSN) determines how long the network can be used to monitor the area of interest. Hence, it is one of the most important performance metrics for WSN. The approaches used to prolong the lifetime can be briefly divided into two categories: reducing the energy consumption, such as designing an efficient routing, and providing extra energy, such as using wireless energy transfer (WET) to charge the nodes. Contrary to the previous line of work where only one of those two aspects is considered, we investigate these two together. In particular, we consider a scenario where dedicated wireless chargers transfer energy wirelessly to sensors. The overall goal is to maximize the minimum sampling rate of the nodes while keeping the energy consumption of each node smaller than the energy it receives. This is done by properly designing the routing of the sensors and the WET strategy of the chargers. Although such a joint routing and energy beamforming problem is non-convex, we show that it can be transformed into a semi-definite optimization problem (SDP). We then prove that the strong duality of the SDP problem holds, and hence, the optimal solution of the SDP problem is attained. Accordingly, the optimal solution for the original problem is achieved by a simple transformation. We also propose a low-complexity approach based on pre-determined beamforming directions. Moreover, based on the alternating direction method of multipliers, the distributed implementations of the proposed approaches are studied. The simulation results illustrate the significant performance improvement achieved by the proposed methods. In particular, the proposed energy beamforming scheme significantly outperforms the schemes where one does not use energy beamforming, or one does not use optimized routing. A thorough investigation of the effect of system parameters, including the number of antennas, the number of nodes, and the number of chargers, on the system performance is provided. The promising convergence behavior of the proposed distributed approaches is illustrated.