Rui Wang

- Email Address：ilovescinece720@gmail.com
- Mailing Address: Atwater Kent Building, Office 311, 100 Institute Road, Worcester, MA 01609-2280

Since the invention of Tesla Coil in 1893, there has beenmore than a century of research on methods for wirelessly transferring power using radio waves. In recent years, the development of efficient radio frequency (RF) radiation wireless power transfer (WPT) systems has become an active research area, motivated in part by the widespread use of low-power devices that can be charged wirelessly.

Besides RF radiation, there are typically two other types of WPT techniques: inductive coupling (IC) in low-frequency bands andmagnetic resonant coupling (MRC) in high-frequency bands. In inductive coupling, the transmitter and receiver coils together form a transformer and power is transferred between the coils by a magnetic field. Inductive coupling is the most mature wireless power technology and is essentially the only technology so far which is used in commercial products such as charging of mobile phones, electric vehicles, and biomedical prosthetic devices implanted in the human body. MRC is a form of inductive coupling in which power is transferred by magnetic fields between two resonant circuits, one in the transmitter and one in the receiver. Recently, MRC-based WPT (MRC-WPT) with multiple transmitters and/or multiple receivers has been studied in the literature. The WiTricity system is an example of a standardized commercial MRC-WPT system.

Compared to other two types of WPT techniques, i.e., IC-WPT and MRC-WPT, an significant advantage of RF radiation is that it has much a longer power transmission range. Both of IC and MRC are near-field wireless transmission featured with high power density and conversion efficiency. As such, RF-WPT can be be more efficient than IC-WPT and MRC-WPT over longer range links and can be suitable for powering a larger number of devices distributed in a wide area. Second, RF-WPT does not require a large coil like IC-WPT and MRC-WPT. In fact, RF-WPT can use antennas already present in a device for wireless communications. Such antennas can also be used for power transfer or simultaneous wireless information and power transfer (SWIPT). These characteristics can make RF-WPT appealing in low-cost communication devices.

Besides RF radiation, there are typically two other types of WPT techniques: inductive coupling (IC) in low-frequency bands andmagnetic resonant coupling (MRC) in high-frequency bands. In inductive coupling, the transmitter and receiver coils together form a transformer and power is transferred between the coils by a magnetic field. Inductive coupling is the most mature wireless power technology and is essentially the only technology so far which is used in commercial products such as charging of mobile phones, electric vehicles, and biomedical prosthetic devices implanted in the human body. MRC is a form of inductive coupling in which power is transferred by magnetic fields between two resonant circuits, one in the transmitter and one in the receiver. Recently, MRC-based WPT (MRC-WPT) with multiple transmitters and/or multiple receivers has been studied in the literature. The WiTricity system is an example of a standardized commercial MRC-WPT system.

Compared to other two types of WPT techniques, i.e., IC-WPT and MRC-WPT, an significant advantage of RF radiation is that it has much a longer power transmission range. Both of IC and MRC are near-field wireless transmission featured with high power density and conversion efficiency. As such, RF-WPT can be be more efficient than IC-WPT and MRC-WPT over longer range links and can be suitable for powering a larger number of devices distributed in a wide area. Second, RF-WPT does not require a large coil like IC-WPT and MRC-WPT. In fact, RF-WPT can use antennas already present in a device for wireless communications. Such antennas can also be used for power transfer or simultaneous wireless information and power transfer (SWIPT). These characteristics can make RF-WPT appealing in low-cost communication devices.

Recently, researchers have considered the use of distributed transmit beamforming (DTB) in wireless communication systems where two or more individual transmit nodes pool their antenna resources to emulate a virtual antenna array. In principle, the distributed array works in the same way as the conventional (centralized) array: the individual transmit nodes use the CSIT obtained either by feedback (“feedbackbased” DTB) or through channel reciprocity (“reciprocity-based” DTB) to form a beam by controlling the phase of their passband transmissions so that the signals constructively combine at an intended receive node. Unlike conventional transceivers, however, a distributed transmit beamformer naturally allows for low-cost deployment of robust large-aperture arrays suitable for efficient wireless communications and WPT.

The follwoing figure shows an example wireless charging application of DTB for WPT. The goal in this setting is for the receive nodes (the Nr = 4 cellphones shown on the table in Figure 1) to charge wirelessly by receiving power from the transmit nodes (the Nt = 5 white boxes mounted on the walls of the room). Note that the transmit nodes are autonomous and are not connected to a central controller. To facilitate efficientWPT, the receive nodes periodically estimate the forward link channels and provide channel state feedback to the transmit nodes. The transmit nodes use the CSIT to form beams toward the receive nodes and the receive nodes use energy harvesting devices to collect the wireless energy and charge their batteries.

The follwoing figure shows an example wireless charging application of DTB for WPT. The goal in this setting is for the receive nodes (the Nr = 4 cellphones shown on the table in Figure 1) to charge wirelessly by receiving power from the transmit nodes (the Nt = 5 white boxes mounted on the walls of the room). Note that the transmit nodes are autonomous and are not connected to a central controller. To facilitate efficientWPT, the receive nodes periodically estimate the forward link channels and provide channel state feedback to the transmit nodes. The transmit nodes use the CSIT to form beams toward the receive nodes and the receive nodes use energy harvesting devices to collect the wireless energy and charge their batteries.

This research studies the fundamental tradeoff between the feedback period and the efficiency of the WPT system as shown notionally in the following figure. We show that there exists optimal feedback period such that the receivers canmaximize their netmean energy harvesting rate after the cost of feedback and accounting for losses due to errors in the channel state information. This research is focused on the question of how to find a globally optimal feedback period to maximize the mean energy harvesting rate at the receivers.

The main contributions of this research are summarized as follows:

(1) We develop a new model for WPT with DTB, explicitly accounting for losses caused by imperfect channel state information and independent oscillator dynamics and also accounting for the cost of feedback energy from the receive nodes.

(2) We formulate a "Normalized Weighted Mean Energy Harvesting Rate" (NWMEHR) maximization problem to select the feedback period to maximize the weighted averaged amount of net energy harvested by the receive nodes per unit of time as a function of the oscillator parameters. By maximizing the NWMEHR, the receive nodes maximize the net weighted harvested energy after feedback.

(3) Since the NWMEHR objective function is non-convex and implicit (involving the solution of a discrete-time algebraic Riccati equation), we develop an explicit method to numerically calculate the globally optimal feedback period. Our method solves the problem in two steps: (i) bounding the search region into a closed interval and (ii) applying the DIRECT algorithm on the bounded search region to find the globally optimal solution.

(1) We develop a new model for WPT with DTB, explicitly accounting for losses caused by imperfect channel state information and independent oscillator dynamics and also accounting for the cost of feedback energy from the receive nodes.

(2) We formulate a "Normalized Weighted Mean Energy Harvesting Rate" (NWMEHR) maximization problem to select the feedback period to maximize the weighted averaged amount of net energy harvested by the receive nodes per unit of time as a function of the oscillator parameters. By maximizing the NWMEHR, the receive nodes maximize the net weighted harvested energy after feedback.

(3) Since the NWMEHR objective function is non-convex and implicit (involving the solution of a discrete-time algebraic Riccati equation), we develop an explicit method to numerically calculate the globally optimal feedback period. Our method solves the problem in two steps: (i) bounding the search region into a closed interval and (ii) applying the DIRECT algorithm on the bounded search region to find the globally optimal solution.

In this research, we consider WPT system called a "wireless powered communication network" (WPCN). A WPCN is a network in which wireless devices are powered only by WPT. The WPCN model is shown in the following figure, where one hybrid access point (H-AP) with an effectively unlimited power supply coordinates the wireless energy/information transmissions to/from a set of distributed users. Each user is equipped with an energy storage device and thus can harvest and store the wireless energy broadcasted by the H-AP in the downlink. The users transmit their independent information using their individually harvested energy to the H-AP in the uplink.

We consider the problem of maximizing the sum throughput over a finite horizon with energy saving. The analysis assumes an "oracle" provides knowledge of the channel states for all blocks prior to the commencement of the first block. Hence, the results developed in this paper can be considered an upper bound for finite-horizon energy saving schemes with causal channel knowledge. The initial optimization problem is separated into two sub-problems: (i) calculating the optimal time allocation by fixing energy allocation and (ii) calculating the optimal time allocation and energy allocation of downlink WET. The former is a convex optimization problem, which gives us a closed-form relation between the time allocation of donwlink WET and uplink WIT and the latter can be formulated as a standard box-constrained nonlinear programming problem, which can be solved efficiently using the trust-region-reflective algorithm.
An upper bound with low computational complexity is provided by relaxing the energy harvesting causality, which give us a water-filling typed solution.