Optimal Networking in Wirelessly Powered Sensor Networks

Abstract: Wireless sensor networks (WSNs) are nowadays widely used for the long-term monitoring of small or large regions, such as lakes, forests, cities, and industrial areas. The performance of a WSN typically consists of two aspects: i) the monitoring performance, e.g., the accuracy and the timeliness of the measurements or estimations produced by the sensor nodes of the WSN; and ii) the lifetime, i.e., how long the WSN can sustain such a performance. Naturally, we would like to have the monitoring performance as good as possible, and the lifetime as long as possible. However, in traditional WSNs, the sensor nodes generally have limited resources, especially in terms of battery capacity. If the nodes make measurements and report them frequently for a good monitoring performance, they drain their batteries and  this leads to a severely shortened network lifetime. Conversely, the sensors can have a longer lifetime by sacrificing the monitoring performance. It shows the inherent trade-off between the monitoring performance and the lifetime in WSNs.We can overcome the limitations of the trade-off described above by wireless energy transfer (WET), where we can provide the sensor nodes with additional energy remotely. The WSNs with WET are called wirelessly powered sensor networks (WPSNs). In a WPSN, dedicated energy sources, e.g., static base stations or mobile chargers, transmit energy via radio frequency (RF) waves to the sensor nodes. The nodes can store the energy in their rechargeable batteries and use it later when it is needed. In so doing, they can use more energy to perform the sensing tasks. Thus, WET is a solution to improve the monitoring performance and lifetime at the same time.  As long as the nodes receive more energy than they consume, it is possible that the WSN be immortal, which is impossible in traditional WSNs. Although WPSNs can potentially break the trade-off between monitoring performance and lifetime, they also bring many fundamental design and performance analysis challenges. Due to the safety issues, the power that the dedicated energy sources can use is limited. The propagation of the RF waves suffers high path losses. Therefore, the energy received by the sensor nodes is much less than the energy transmitted from the sources. As a result, to have a good WSN performance, we should optimize the energy transmission on the energy source side and the energy consumption on the nodes side. Compared to the traditional WSN scenarios where we can only optimize the sensing and data communication strategies, in WPSNs, we have an additional degree of freedom, i.e., the optimization of the energy transmission strategies. This aspect brings new technical challenges and problems that have not been studied in the traditional WSNs. Several novel research questions arise, such as when and how to transmit the energy, and which energy source should transmit. Such questions are not trivial especially when we jointly consider the energy consumption part.This thesis contributes to answer the questions above. It consists of three contributions as follows.In the first contribution, we consider a WPSN with single energy base stations (eBS) and multiple sensor nodes to monitor several separated areas of interest. The eBS has multiple antennas, and it uses energy beamforming to transmit energy to the nodes. Notice that, if we deploy multiple sensor nodes at the same area, these nodes may receive the energy from the eBS at the same time and they can reduce the energy consumption by applying sleep/awake mechanism. Therefore, we jointly study the deployment of the nodes, the energy transmission of the eBS, and the node activation. The problem is an integer optimization, and we decouple the problem into a node deployment problem and a scheduling problem. We provide a greedy-based algorithm to solve the problem, and show its performance in terms of optimality.The second contribution of the thesis starts by noticing that wireless channel state information (CSI) is important for energy beamforming. The more energy that an eBS spends in channel acquisition, the more accurate CSI it will have, thus improving the energy beamforming performance. However, if the eBS spends too much energy on channel acquisition, it will have less energy for WET, which might reduce the energy that is received by the sensor nodes. We thus investigate how much energy the eBS should spend in channel acquisition, i.e., we study the power allocation problem in channel acquisition and energy beamforming for WPSNs. We consider the general optimal channel acquisition and show that the problem is non-convex. Based on the idea of bisection search, we provide an algorithm to find the optimal solution for the single eBS cases, and a closed-form solution for the case where the eBS uses orthogonal pilot transmission, least-square channel estimation, and maximum ratio transmission for WET. The simulations show that the algorithm converges fast, and the performance is close to the theoretical upper bound.In the third contribution, we consider a joint energy beamforming and data routing problem for WPSNs. More specifically, we investigate the WPSNs consisting of multiple eBSs, multiple sensor nodes, and a sink node. Based on the received energy, the sensor nodes need to decide how to route their data. The problem aims at maximizing the minimum sensing rate of the sensor nodes while guaranteeing that the received energy of each node is no less than that is consumed. Such a problem is non-convex, and we provide a centralized solution algorithm based on a semi-definite programming transformation. We extend this approach with a distributed algorithm using alternating direction method of multipliers (ADMM). We prove that the centralized algorithm achieves the optimal energy beamforming and routing, and we show by simulation that the distributed one converges to the optimal solution. Additionally, for the cases where the energy beamforming options are pre-determined, we study the problem of finding the energy that should be spent on each vector. We observe that, if the pre-determined beamforming options are chosen wisely, their performance is close to the optimal.The results of the thesis show that WET can prolong the lifetime of WSNs, and even make them work sufficiently long for general monitoring applications. More importantly, we should optimize the WPSN by considering both the energy provision and the energy consumption part. The studies of the thesis have the potential to be used in many Internet of Things (IoT) systems in smart cities, such as water distribution lines and building monitoring.