Abstract

Wireless power transfer (WPT) using microwave irradiation can set human free from the annoying wires. However, WPT has low energy efficiency due to electromagnetic wave diffraction in the case of indoor non-line-of-sight (NLOS) and causes electromagnetic radiation pollution around the room in the case of indoor line-of-sight (LOS). Time reversal (TR) technique is an inverse operation of timedomain signals and makes full use of the multipath effect. TR technique can improve the efficiency and reduce the pollution due to its unique temporal–spatial focusing effect. We will detail the principles of TR with the finite TR arrays. What's more, we propose a sequential convex programming (SCP) algorithm based on diode circuit to obtain the optimal frequency point amplitude to further improve energy efficiency. The simulation result shows that the TR-SCP-WPT system model will get the significant energy gain.

Keywords: wireless power transfer, time reversal, sequential convex programming

### 1. Introduction

With the development of economy and science technology, more and more applications of wireless electronic products have been made. People have higher requirements on power transmission mode, efficiency, security, and so on. The traditional battery supply mode limits the using time of electronic products. However, reducing energy consumption or increasing battery capacity is not the most essential solutions to which. The wired cable power supply method is also not suitable for communication electronic products with strong mobility and wide distribution. Therefore, wireless power transfer (WPT) is a trend.

There are four types of WPT: magnetic induction coupling, magnetic coupling resonance, laser, and microwave. Among them, microwave power transmission has a bright prospect, since it is not limited by distance and it does not require a precise angle [1]. But WPT has low energy efficiency due to electromagnetic wave diffraction in the case of indoor non-line-of-sight (NLOS) and causes electromagnetic radiation pollution around the room in the case of indoor line-of-sight (LOS). The transmission efficiency of microwave power transmission is mainly composed of three parts: microwave and direct current (DC) conversion efficiency, antenna receiving efficiency, and electromagnetic wave spatial transmission efficiency.

Time reversal (TR) technique is an inverse operation of time-domain signals and makes full use of the multipath effect, which can improve the efficiency by the

temporal effect and reduce the pollution by the spatial effect. In [2], it conducted a TR indoor experiment with a nanosecond pulse with a carrier frequency of 2.45 GHz. It is proven that TR can achieve an energy gain of 30 dB, and when continuous wave is used, the TR scheme can avoid indoor fading phenomenon. In [3], it explores the spatial profile of TR-WPT for energy reception at the vertical direction of the focus point in a metal cavity and gives a closed-form expression. In [4], it uses the temporal–spatial focusing effect of TR, combined with coils containing metamaterials, to illuminate centimeter-level LED lamps, thus demonstrating the precise control of near-field electromagnetic waves.

TR can improve the transmission efficiency, and we also consider the microwave and DC conversion efficiency. The conversion efficiency depends on rectenna. It is not only a function of rectenna design but also a function of input waveform, i.e., input power and shape. This results in that the conversion efficiency is not a constant, but a nonlinear function of the input waveform [5]. Therefore, we consider a nonlinear rectenna circuit model in our system model with TR technique. Then we propose a sequential convex programming (SCP) to get the optimal frequency amplitude for the better conversion efficiency.

The potential of TR and SCP to handle efficiency issues for WPT systems is investigated in this chapter. We introduce the background of WPT and TR in section 1. Then we detail the principles of TR in section 2. We describe the TR-SCP-WPT system model in section 3. Finally, the energy efficiency performance of the WPT system is proposed.

detection signal. In the second stage, TR stage, TRC records the signal with the channel impulse response (CIR) and then reverses it. The time reversal signal will

An illustration of TR (a) the channel probing phase and (b) the data transmission and focusing phase [7].

The CIR goes through by the multipaths. To more detail, let us imagine that there are two points A and B in the space of the metal box like in Figure 2. When A transmits radio signals, its radio waves bounce back and forth in the box. Some of them bounce back and forth through B. After a period of time, the energy level decreases and can no longer be observed. Meanwhile, B can record the multipath distribution of arrival wave as time distribution. Then, such multipath distribution is inverted (and conjugated) by B and emitted accordingly, the last one and the last one. Through channel reciprocity, all waves following the original path will arrive at A at the same specific time and add up in a perfect and constructive way. This is

The specific operation of TR is to reverse the time-domain signal on the time axis or to adopt phase conjugation for the complex frequency domain signal. In our

The temporal–spatial focusing effect of TR utilizes the principle of channel reciprocity, which means that in the two stages, the channel information is time invariant. Channel reciprocity requires a high correlation between the CIR of the forward link and the backward link, while channel stability requires that the CIR be stationary for at least one of the detection and TR stages. Experiments in the laboratory area show that the correlation of CIR between forward and backward links is as high as 0.98 in [8]. Therefore, TR can play an important role. The temporal focusing effect of TR refers to that the signal originally arriving last will be transmitted first while the signal originally arriving first will be transmitted last,

We consider a long distance and wireless environment, namely, rich multipath

αlδð Þ t � τ<sup>l</sup> (1)

h tðÞ¼ <sup>X</sup> L�1

l¼0

where L is the whole number of multipath, al is the amplitude of the path, τ<sup>l</sup> is

arrive at the same position of the source through the same CIR.

Long-Distance Wireless Power Transfer Based on Time Reversal Technique

DOI: http://dx.doi.org/10.5772/intechopen.89078

called focusing effect [7] (Figure 2).

Figure 2.

2.1 Temporal focusing effect of TR

channel can be represented as

95

research, we choose the operation in time domain.

and finally the signal of all paths arrive at the same moment.

the delay of the path, and δðÞ is the Dirichlet function.
