# Foundations of Wireless Information and Power Transfer: Theory, Prototypes,
and Experiments

Bruno Clerckx, Fellow, IEEE, Junghoon Kim, Member, IEEE, Kae Won Choi, Senior
Member, IEEE, Dong In Kim, Fellow, IEEE Bruno Clerckx and Junghoon Kim are
with the Department of Electrical and Electronic Engineering, Imperial College
London, London SW7 2AZ, UK (email: {b.clerckx,junghoon.kim15}@imperial.ac.uk).
Kae Won Choi and Dong In Kim are with the Department of Electrical and
Computer Engineering, Sungkyunkwan University, Suwon 16419, South Korea
(e-mail: {kaewonchoi,dongin}@skku.edu). This work has been partially supported
by the EPSRC of UK under grant EP/P003885/1 and EP/R511547/1, and partially
supported by the National Research Foundation of Korea (NRF) Grant funded by
the Korean Government (MSIT) under Grants 2020R1A2C1014693 and
2021R1A2C2007638.

###### Abstract

As wireless has disrupted communications, wireless will also disrupt the
delivery of energy. Future wireless networks will be equipped with (radiative)
wireless power transfer (WPT) capability and exploit radio waves to carry both
energy and information through a unified wireless information and power
transfer (WIPT). Such networks will make the best use of the RF spectrum and
radiation as well as the network infrastructure for the dual purpose of
communicating and energizing. Consequently those networks will enable
trillions of future low-power devices to sense, compute, connect, and energize
anywhere, anytime, and on the move. In this paper, we review the foundations
of such future system. We first give an overview of the fundamental
theoretical building blocks of WPT and WIPT. Then we discuss some state-of-
the-art experimental setups and prototypes of both WPT and WIPT and contrast
theoretical and experimental results. We draw a special attention to how the
integration of RF, signal and system designs in WPT and WIPT leads to new
theoretical and experimental design challenges for both microwave and
communication engineers and highlight some promising solutions. Topics and
experimental testbeds discussed include closed-loop WPT and WIPT architectures
with beamforming, waveform, channel acquisition, and single/multi-antenna
energy harvester, centralized and distributed WPT, reconfigurable metasurfaces
and intelligent surfaces for WPT, transmitter and receiver architecture for
WIPT, modulation, rate-energy trade-off. Moreover, we highlight important
theoretical and experimental research directions to be addressed for WPT and
WIPT to become a foundational technology of future wireless networks.

###### Index Terms:

Wireless power transfer, wireless information and power transfer, rectenna,
harvester, beamforming, reconfigurable intelligent surface, intelligent
reflecting surface, waveform, multi-antenna, prototypes, experiments

##  I Introduction

Wireless information and power transfer (WIPT) is an emerging paradigm in
future Internet of Things (IoT) and wireless sensor networks (WSN).
Radiofrequency (RF) waves have traditionally been used for wireless
information transfer (WIT) or wireless communications. However, radio waves
carry both energy and information. Thanks to the reduction in the power
consumption of electronics and the increasing need to energize a massive
number of low-power autonomous devices, far-field/radiative RF wireless power
transfer (WPT) has attracted attention as a feasible and promising power
supply technology for remotely energizing low-power devices, such as sensors,
radio-frequency identification (RFID) tags, and consumer electronic [1, 2, 3].
WPT has numerous advantages for low-power wireless applications since it
eliminates the hassle of connecting cables, is controllable with on-demand
energy delivery, preserves the environment by avoiding massive battery
disposal, can operate in dangerous (e.g., in hazardous environment) or even
impossible (e.g., for biomedical implants) environments, delivers power over
long distances, and can be implemented in a small form factor at the receiver
compared to other technologies such as inductive coupling or magnetic
resonance [4]. In addition, WPT can be integrated with WIT so as to exploit
radio waves for the dual purpose of communicating and energizing.

For over 100 years, energy and information have been studied separately and
have evolved as two separate fields [5]. WIT was pioneered by Marconi and is
currently in its fifth generation (5G), while WPT was pioneered by Tesla but
is not even in its first generation (1G) [3]. This separation has two main
consequences. First of all, today’s wireless networks blast RF energy in the
air for communication but do not make use of it to charge devices. Second,
delivering ubiquitous wireless power would require the deployment of a
separate network of dedicated power transmitters [6].

Imagine instead future networks that reconcile Tesla and Marconi visions into
a new and unified network paradigm where radio waves are exploited to the full
potential to carry both energy and information. Information and energy would
flow hand in hand via the wireless medium. WIT and WPT would refer to two
extreme strategies targeting communication and power supply, respectively. A
unified WIPT design could smoothly evolve between the two extremes to make the
most of the RF spectrum/radiation and the network infrastructure for
communications and power delivery, thereby surpassing traditional systems that
separate communications and power. Such a capability would be a game changer
for future networks such as sixth generation (6G) and beyond. Future network
operators will be telecommunication and energy providers and offer a true
ubiquitous wireless connectivity such that trillions of future low-power
devices will sense, compute, connect, and energize anywhere, anytime, and on
the move. Such a capability will also address the growing need for high energy
efficiency, green connectivity, and energy-neutral/zero-power IoT. As
illustrated in Fig. 1, numerous applications will emerge in many sectors such
as smart homes (monitoring and detection of fire, carbon monoxide, leak,
moisture, temperature, motion), smart city (management of infrastructure, air
quality, traffic, parking, waste), healthcare (in-body, around the body),
transportation (connected car, vehicle-to-vehicle), automotive and airline
(replacing cables), agriculture (forest/soil/crops monitoring), logistics,
emergency, security, prevention, defence, etc.

Figure 1: Applications of WPT and WIPT.

Such vision comes with numerous engineering requirements and design challenges
[4, 7, 8]: 1) Charging range of 5-100 meters (m) in indoor and outdoor
deployments; 2) End-to-end power transfer efficiency of up to a fraction of a
percent to a few percents; 3) Operate in line of sight (LoS) and non-line of
sight (NLoS) to broaden the applications of WPT-aided networks; 4) Support
mobility at pedestrian speed; 5) Deliver power ubiquitously within the network
coverage area; 6) Ensure WPT is safe; 7) Reduce the energy consumption of
wireless powered devices; 8) Unify communication and power into WIPT; 9)
Integrate WPT with sensing, computing and communication in 6G and beyond
networks.

To address those challenges, integrated efforts across societies must be made,
including circuit, sensors, systems, antenna, propagation, communication,
microwave design, signal processing, information theory, machine learning,
sensing, and computing.

Challenges (1)–(7) are studied in various review papers emphasizing separately
RF, circuit and antenna solutions [12, 13, 14, 15], communications, signal and
system design solutions [4, 8], as well as integrated solutions bridging RF,
signal and system designs to get a better grasp of the basic building blocks
of an efficient WPT architecture [3]. This integration has led to the
noticeable and welcomed trend to depart from naive and oversimplified models
and has triggered the need to design efficient WPT signal strategies
accounting for the various sources of nonlinearity (transmitter and energy
harvester) in the system [8].

Challenge (8) is reviewed in [8, 9, 11, 10, 7] with the objective to lay the
fundamentals of WIPT from energy harvester models to signal and system
designs. This challenge requires the characterization of the trade-off between
the amount of information and the amount of energy that can be delivered in a
wireless network and the design of (single-user and multi-user) signal
strategies to achieve this trade-off. Importantly, [7] demonstrated how
crucially the trade-off, the signaling and resource allocation strategy depend
on the energy harvester model and related nonlinearity.

Challenge (9) is reviewed in [8] where it is shown that WPT, sensing,
computing, edge learning, and communication need to be jointly controlled so
as to optimize the efficiency of a system supporting specific applications. In
particular, there exist trade-offs between transferred energy and energy
consumption of sensing/computing and communication. Quantifying and exploiting
such trade-offs can substantially improve system performance.

Various methodologies have also been used to tackle the above challenges and
optimize the system, including the model-based optimization approach and the
data-driven machine learning approach. The pros and cons of each approach,
especially when accounting for various nonlinearities in wireless-powered
networks, and interesting emerging opportunities for the approaches to
complement each other have been discussed and identified in [8].

This paper complements the existing literature and contributes to the
literature by discussing one key missing and timely piece of the puzzle,
namely real-world prototype and experimentation to validate theory. This paper
gives an overview111This is by no means a comprehensive review of the
literature. on the fundamental theoretical building blocks of WPT and WIPT,
discusses some state-of-the-art experimental setups and prototypes of both WPT
and WIPT, and contrasts theoretical and experimental results. We draw a
special attention to the integration of RF, signal and system designs in
modern WPT and WIPT. We stress how such integration leads to new theoretical
and experimental design challenges for both microwave and communication
engineers and highlight some promising solutions. Topics and experimental
testbeds discussed include closed-loop WPT and WIPT architectures with
beamforming, waveform, channel acquisition, and single/multi-antenna energy
harvester, centralized and distributed WPT, reconfigurable metasurfaces and
intelligent surfaces for WPT, transmitter and receiver architecture for WIPT,
rate-energy trade-off. Moreover, we highlight important theoretical and
experimental research directions to be addressed for WPT and WIPT to become a
foundational technology of future wireless networks.

_Organization:_ Section II discusses WPT architecture, prototypes and
experiments. Section III builds upon the WPT section to design, prototype and
experiment WIPT. Section IV draws some conclusions and discusses promising
future research directions.

_Notation:_ In this paper, $j$ denotes the imaginary unit, i.e., $j^{2}=-1$.
Scalars are denoted by italic letters. Vectors and matrices are denoted by
boldface lower- and upper-case letters, respectively. $\mathbb{E}[\cdot]$
denotes statistical expectation or direct current (DC) averaging and
$\Re\\{\cdot\\}$ represents the real part of a complex number. $|.|$ and
$\left\|.\right\|$ refer to the absolute value of a scalar and the 2-norm of a
vector. The complex conjugate, transpose, Hermitian transpose, and Frobenius
norm of an arbitrary-size matrix $\mathbf{A}$ are denoted as $\mathbf{A}^{*}$,
$\mathbf{A}^{T}$, $\mathbf{A}^{H}$, and $\|\mathbf{A}\|_{F}$, respectively.

##  II Wireless Power Transfer

###  II-A Architecture

Fig. 2 shows a modern WPT system architecture where an RF energy transmitter
(ET) is separated from an energy receiver (ER) by the wireless channel. A
signal generated by a DC power source is upconverted to the RF domain at the
ET, is then broadcasted over the air by one or multiple transmit antennas, and
is finally collected at an ER in the RF domain before being converted to DC.
The ER consists of one or multiple receive antennas combined with one or
multiple rectifiers (the combination of antenna and rectifier being denoted as
rectenna) and a power management unit (PMU). Since the electronics
conventionally require a DC power source, a rectifier is needed to convert RF
to DC.

A low power device is then directly supplied from the recovered DC power. The
recovered DC power can also be stored in a battery or in a super capacitor for
high power low duty-cycle operations or be fed to a DC-to-DC converter before
being stored. Importantly, the ET and ER in the WPT system of Fig. 2 can be
fully optimized/adjusted in a closed-loop and adaptive manner as a function of
the wireless channel. Such adaptation requires a channel acquisition/feedback
module and a signal optimization module. Therefore, WPT offers full control of
the design to maximize as much as possible the end-to-end power transfer
efficiency defined as

$\displaystyle
e=\frac{P_{\mathrm{dc}}^{s}}{P_{\mathrm{dc}}^{t}}=\underbrace{\frac{P_{\mathrm{rf}}^{t}}{P_{\mathrm{dc}}^{t}}}_{e_{1}}\underbrace{\frac{P_{\mathrm{rf}}^{r}}{P_{\mathrm{rf}}^{t}}}_{e_{2}}\underbrace{\frac{P_{\mathrm{dc}}^{r}}{P_{\mathrm{rf}}^{r}}}_{e_{3}}\underbrace{\frac{P_{\mathrm{dc}}^{s}}{P_{\mathrm{dc}}^{r}}}_{e_{4}},$
(1)

where $e_{1}$, $e_{2}$, $e_{3}$, and $e_{4}$ denote the DC-to-RF, RF-to-RF,
RF-to-DC, and DC-to-DC power conversion efficiency, respectively.

Figure 2: A block diagram of a modern closed-loop and adaptive WPT
architecture.

####  II-A1 Energy Transmitter

We consider a multi-antenna ET equipped with $M$ antennas (with a single
antenna being a special case) that transmits an unmodulated multisine waveform
over multiple $N$ frequencies (with a single frequency being a special case)
$f_{n}$, $n=0,...,N-1$. The frequencies $f_{n}=f_{0}+n\Delta_{f}$ are evenly
spaced by an inter-carrier frequency spacing $\Delta_{f}$. The transmit signal
spanning all $M$ transmit antennas can be written in a vector form as

$\mathbf{x}_{\mathrm{rf}}(t)=\sqrt{2}\Re\left\\{\sum_{n=0}^{N-1}\mathbf{x}_{n}e^{j2\pi
f_{n}t}\right\\}$ (2)

where $\mathbf{x}_{n}\triangleq\big{[}x_{1,n},...,x_{M,n}\big{]}^{T}$ denotes
the weight vector across the $M$ antennas at frequency $f_{n}$, with each
complex weight scalar $x_{m,n}=s_{m,n}e^{j\phi_{m,n}}$ used to adjust the
magnitude $s_{m,n}$ and the phase $\phi_{m,n}$ of the sinewave on antenna $m$
and frequency $f_{n}$. Such adjustement is controlled by the signal
optimization module of Fig. 2 so as to benefit from a joint waveform and
active beamforming gain [16]. The total average transmit power is expressed as
$P_{\mathrm{rf}}^{t}=\sum_{m=1}^{M}\sum_{n=0}^{N-1}s_{m,n}^{2}$ and is subject
to the constraint $P_{\mathrm{rf}}^{t}\leq P$. In order to operate at high
conversion efficiency $e_{1}$, efficient high power amplifiers (HPA) have to
be used and the transmit signal (2) may have to be adjusted by the signal
optimization module to satisfy constraints on peak-to-average power ratio
(PAPR).

####  II-A2 Wireless Channel

The transmit WPT signal propagates through a multipath channel, characterized
by $L$ paths, each path $l$ with a delay $\tau_{l}$, an amplitude gain
$\alpha_{l}$, and a phase shift $\zeta_{q,m,n,l}$ between transmit antenna $m$
and receive antenna $q$ at frequency $f_{n}$. The signal at antenna $q$ is
then written as

$y_{\mathrm{rf},q}(t)=\sqrt{2}\Re\left\\{\sum_{n=0}^{N-1}\mathbf{h}_{q,n}\mathbf{x}_{n}e^{j2\pi
f_{n}t}\right\\}+w_{\textnormal{A},q}(t),$ (3)

where the antenna noise is denoted as $w_{\textnormal{A},q}(t)$, the channel
vector from the $M$ transmit antennas to receive antenna $q$ is denoted as
$\mathbf{h}_{q,n}\\!\triangleq\\!\big{[}h_{q,1,n},...,h_{q,M,n}\big{]}$, and
the baseband channel frequency response between transmit antenna $m$ and
receive antenna $q$ at frequency $f_{n}$ is written as
$h_{q,m,n}=\\!\sum_{l=0}^{L-1}\alpha_{l}e^{j(-2\pi
f_{n}\tau_{l}+\zeta_{q,m,n,l})}$.

Conventionally, we have no control over the wireless channel vector
$\mathbf{h}_{q,n}$, i.e., it is dictated by the environment between the
transmitter and the receiver. Nevertheless, with the advances in
reconfigurable intelligent surfaces (RIS) [17, 18] and intelligent reflecting
surfaces (IRS) [19], one can envision that the wireless channel can be
engineered in the future222RIS and IRS refer to the same thing under different
terminologies and can be used interchangeably. For simplicity, we use RIS in
the sequel. RIS is obtained by integrating in the propagation environment a
large number of $R$ reconfigurable passive elements that do not require any RF
chain. By collaboratively adjusting the impedance of all those passive
elements (through the signal optimization module in Fig. 2), the transmitted
and reflected signals add coherently at the desired receiver, therefore
enabling an additional passive beamforming gain and increasing the received RF
signal power [19, 20]. Thanks to the passive structure, RIS is appealing for
its relatively low power consumption, light weight, conformal geometry, low
profile, low cost, and absence of additive thermal noise during the
reflection.

With RIS-aided WPT, the wireless channel vector between the multi-antenna
transmitter and receive antenna $q$ on frequency $f_{n}$ can be written as
$\mathbf{h}_{q,n}=\mathbf{g}_{\mathrm{d},q,n}+\mathbf{g}_{\mathrm{r},q,n}\mathbf{\Theta}\mathbf{G}_{\mathrm{i},n}$
where the direct channel between the ET and antenna $q$ of ER is denoted as
$\mathbf{g}_{\mathrm{d},q,n}$, the $1\times R$ vector channel between the RIS
(equipped with $R$ elements) and antenna $q$ of ER is denoted as
$\mathbf{g}_{\mathrm{r},q,n}$, and the $L\times M$ matrix channel between the
ET and the RIS is denoted as $\mathbf{G}_{\mathrm{i},n}$. Finally, the
scattering matrix of the $R$-port reconfigurable impedance network333Note that
$\mathbf{\Theta}$ is assumed constant across frequencies. More involved
designs could enable frequency-dependent scattering matrices
$\mathbf{\Theta}_{n}$. is denoted as $\mathbf{\Theta}$ and has to satisfy the
constraints $\mathbf{\Theta}=\mathbf{\Theta}^{T}$ and
$\mathbf{\Theta}^{H}\mathbf{\Theta}=\mathbf{I}_{L}$ [21]. The $R$-port
reconfigurable impedance network is constructed with reconfigurable and
passive elements that reflect the incident signal in the direction of interest
and effectively engineer the wireless channel.

####  II-A3 Energy Receiver

ER can be equipped with a single or multiple antennas, therefore enabling a
multiple input-single output (MISO) and multiple input-multiple output (MIMO)
WPT, respectively. In both cases, the essential building block of the ER is
the rectenna [22].

Let us start with the single-antenna case. A rectenna first harvests
electromagnetic energy, then rectifies and finally low-pass-filters it. The
input power level and input waveforms as well as the operating frequencies
influence the design and optimization of the rectenna. Rectifiers are commonly
made of a single and multiple (likely Schottky) diodes [12, 13, 14, 15]. Fig.
3 illustrates two different rectifier topologies. The simplest form of
rectifier, so-called single diode rectifier, is made of a matching network
used to match the antenna impedance to the input impedance of the rectifier, a
single diode and a low-pass filter (LPF). It is the general understanding that
single-diode rectifiers are more suited for low input power and multiple-
diodes rectifiers for higher power.

(a) Single diode rectifier (b) Voltage doubler rectifier

Figure 3: (a) Single series rectifier suited for an average RF input power of
-20dBm (10$\mu$W) at 2.45GHz. $v_{\mathrm{s}}$ is the voltage source of the
antenna. R1 denotes the antenna impedance. C1 and L1 together form the
matching network. SMS-7630 denotes the type of Schottky diode. Cout and Load
together act as the low-pass filter with Load being the output load. (b)
Multiple diode rectifier.

Figure 4: RF-to-DC conversion efficiency $e_{3}$ as a function of the average
RF input power $P_{\mathrm{rf}}^{r}$ with the single-series rectifier of Fig.
3(a) [23].

Fig. 4 illustrates the dependency of the RF-to-DC conversion efficiency
$e_{3}$ to the average RF signal power and shape at the rectifier input, when
a single diode rectifier (as in Fig. 3(a)) is excited by a continuous wave
(CW), i.e., a single sinewave ($N=1$), and a multisine waveform (with uniform
power allocation across $N=8$ equispaced carrier frequencies) [23]. The same
average RF input power $P_{\mathrm{rf}}^{r}$ is assumed for those two types of
waveforms, but their shape is obviously different. We notice that $e_{3}$ is
low at low input power for both types of excitation due to the rectifier
sensitivity to turn on at low input power. Nevertheless, $e_{3}$ is larger
with the multisine waveform than with CW since it conveys bursts of energy
that help turning on the diode and increase the rectifier sensitivity in the
low power regime. Importantly, for both CW or multisine, $e_{3}$ increases
with $P_{\mathrm{rf}}^{r}$ whenever the breakdown region is not reached.
Beyond a few hundreds of $\mu$W input power, irrespectively of the input
waveform, the rectifier enters the diode breakdown region444The diode SMS-7630
becomes reverse biased at $P_{\mathrm{rf}}^{r}\approx 500\mu$W to 1mW for CW..
Consequently the output DC power saturates and $e_{3}$ significantly drops. To
operate beyond such input power and eliminate the saturation problem,
multiple-diode rectifier is recommended [13, 15, 24].

We observe from Fig. 4 that $e_{3}$ is not a constant, but rather depends on
1) the input power level and 2) the shape of the input signal
$y_{\mathrm{rf}}$ [13, 25, 26, 27, 16]. This can be reflected mathematically
by writing the output DC voltage as
$v_{\mathrm{out}}=f_{\mathrm{EH}}\left(y_{\mathrm{rf}}(t)\right)$ with
$f_{\mathrm{EH}}\left(y_{\mathrm{rf}}(t)\right)$, a nonlinear function of
$y_{\mathrm{rf}}(t)$. Since the harvested DC power $P_{\mathrm{dc}}^{r}$ is
related to $v_{\mathrm{out}}$ through the relationship
$P_{\mathrm{dc}}^{r}=\frac{v_{\mathrm{out}}^{2}}{R_{\mathrm{L}}}$ (with
$R_{\mathrm{L}}$ denoting the output load), $P_{\mathrm{dc}}^{r}$ is a
nonlinear function of $y_{\mathrm{rf}}(t)$. We can therefore write
$P_{\mathrm{dc}}^{r}=e_{3}\left(y_{\mathrm{rf}}(t)\right)P_{\mathrm{rf}}^{r}$
to stress that $e_{3}$ is not a constant but a nonlinear function of
$y_{\mathrm{rf}}(t)$. The function $f_{\mathrm{EH}}$ can be further
investigated by looking at the diode I-V characteristics and taking a
polynomial (Taylor) expansion truncated to the fourth order. We then can
approximate the output DC voltage of the rectifier $v_{\mathrm{out}}$ across
the load (denoted as $R_{\mathrm{L}}$) in Fig. 3 as the following nonlinear
function of $y_{\mathrm{rf}}(t)$

$v_{\mathrm{out}}=f_{\mathrm{EH}}\left(y_{\mathrm{rf}}(t)\right)=\beta_{2}\mathbb{E}\left[y_{\mathrm{rf}}(t)^{2}\right]+\beta_{4}\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$
(4)

where
$\beta_{i}=\frac{R_{\mathrm{ant}}^{i/2}}{i!\left(nv_{\mathrm{t}}\right)^{(i-1)}}$
with $R_{\mathrm{ant}}$ the antenna impedance, $v_{\mathrm{t}}$ the thermal
voltage and $n$ the ideality factor [16]. The operator $\mathbb{E}[\cdot]$ in
(4) takes the DC component of the argument.

We note that (4) is a function of the input signal average power
$P_{\mathrm{rf}}^{r}=\mathbb{E}\left[y_{\mathrm{rf}}(t)^{2}\right]$ (i.e., the
second moment of $y_{\mathrm{rf}}(t)$) but also of its higher moments
$\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$. The dependency on the second
and higher moments of $y_{\mathrm{rf}}(t)$ explains the results of Fig. 4 for
input power levels below the diode breakdown region [16]. Indeed, since the
I-V characteristics and the polynomial expansion in (4) are convex, we can
apply Jensen’s inequality and write

$\mathbb{E}\left[y_{\mathrm{rf}}(t)^{i}\right]\geq(\mathbb{E}\left[y_{\mathrm{rf}}(t)^{2}\right])^{\frac{i}{2}}=\left(P_{\mathrm{rf}}^{r}\right)^{\frac{i}{2}}$
(5)

for $i=2,4$, so that

$v_{\mathrm{out}}\geq\beta_{2}P_{\mathrm{rf}}^{r}+\beta_{4}\left(P_{\mathrm{rf}}^{r}\right)^{2}.$
(6)

From (6), we can conclude that $e_{3}$ is an increasing function of
$P_{\mathrm{rf}}^{r}$. If $y_{\mathrm{rf}}(t)$ is chosen as a multisine
waveform with average power $P_{\mathrm{rf}}^{r}$ uniformly distributed across
the $N$ sinewaves, $\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$ can be
shown to scale proportionally to $N\left(P_{\mathrm{rf}}^{r}\right)^{2}$,
therefore demonstrating that
$\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]>\left(P_{\mathrm{rf}}^{r}\right)^{2}$
for sufficiently large $N$. This explains analytically why multisine (and
other types of signals) can outperform CW ($N=1$) [16]. Two interesting
observations can be drawn from (5) and (6), respectively [8].

###### Observation 1

Two input signals may have the same
$\mathbb{E}\left[y_{\mathrm{rf}}(t)^{2}\right]=P_{\mathrm{rf}}^{r}$ but
different $\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$. From (5), input
signals with large $\mathbb{E}\left[y_{\mathrm{rf}}(t)^{i}\right]$ are
preferred to boost $e_{3}$ and $P_{\mathrm{dc}}^{r}$. This explains
mathematically the dependence of $e_{3}$ on the shape of the input signal in
Fig. 4.

###### Observation 2

The lower bound (6) highlights that $e_{3}$ increases with
$P_{\mathrm{rf}}^{r}$. This explains why $e_{3}$ depends on the input power
level in Fig. 4 whenever the rectifier is not in breakdown, and stresses that
the strategy that maximizes $P_{\mathrm{rf}}^{r}$ only maximizes a lower bound
on $P_{\mathrm{dc}}^{r}$ and therefore does not maximize $P_{\mathrm{dc}}^{r}$
itself.

It is important to note that emphasis is here put on conditions where the
rectifier is not in breakdown (i.e., below saturation) since this is the
proper operating regime of a rectifier. Experimental results in Section II-B
also confirm that rectifiers in real wireless deployments are unlikely to
enter breakdown whenever designed for the expected range of power levels.

In multi-antenna ER, two main combining strategies (and combination thereof)
can be used, namely DC combining and RF combining as per Fig. 5 [28, 29, 30,
31]. Such combiners open the door to MIMO WPT equipped with multi-antenna
arrays at both the ET and ER.

Figure 5: Two types of multi-antenna energy receivers (a) DC combining
receiver (b) RF combining receiver.

In DC combining, there is one rectifier per receive antenna and the number of
rectifiers therefore increases with the number of receive antennas $Q$. In
contrast, in RF combining, a single rectifier is used to rectify a single
combined RF signal obtained by the combination in the RF domain of all the RF
signals from all receive antennas. With the DC combiner architecture,
$P_{\mathrm{dc}}^{r}=\sum_{q=1}^{Q}\frac{v_{\mathrm{out},q}^{2}}{R_{\mathrm{L}}}$
with $v_{\mathrm{out},q}=f_{\mathrm{EH}}\left(y_{\mathrm{rf},q}(t)\right)$ the
output DC voltage of the rectifier connected to receive antenna $q$. With the
RF combiner architecture, an analogue (potentially constant modulus)
combiner555Frequency-dependent analogue combiner $\mathbf{w}_{\mathrm{R},n}$
is also possible but has higher complexity. $\mathbf{w}_{\mathrm{R}}$ is
applied to the received signals (3) such that the combined RF signal fed to
the single rectifier is given by

$\tilde{y}(t)=\sqrt{2}\Re\left\\{\sum_{n=0}^{N-1}\mathbf{w}_{\mathrm{R}}^{H}\mathbf{H}_{n}\mathbf{x}_{n}(t)e^{j2\pi
f_{n}t}\right\\}+\tilde{w}_{\textnormal{A}}(t),$ (7)

with the effective combined noise denoted as $\tilde{w}_{\textnormal{A}}$. Due
to the passive nature of the RF combining circuit, the RF combining circuit
output power cannot be larger than its input power. This is reflected
mathematically in the design of the combiner by the constraint
$\left\|\mathbf{w}_{\mathrm{R}}\right\|^{2}\leq 1$. Finally, the output DC
power is given by
$P_{\mathrm{dc}}^{r}=\frac{v_{\mathrm{out}}^{2}}{R_{\mathrm{L}}}$ where
$v_{\mathrm{out}}=f_{\mathrm{EH}}\left(\tilde{y}(t)\right)$.

Notably, since higher RF input power level leads to higher $e_{3}$ (recall
Observation 2 and Fig. 4 for power levels below saturation) and the rectifier
in RF combining operates on a higher RF power input signal compared to DC
combining, RF combining theoretically achieves a higher RF-to-DC conversion
efficiency than DC combining. Expressed differently, $P_{\mathrm{dc}}^{r}$
increases with $Q$, but the increase is more significant with RF combining
than DC combining. Hence, in MIMO WPT, increasing $M$ and $Q$ helps increasing
$P_{\mathrm{rf}}^{r}$ and therefore $e_{2}$, but a proper choice of the
receiver combiner can provide a further boost in $e_{3}$ [31].

Following the rectenna, a DC-to-DC switching converters is used to dynamically
track the rectifier’s optimum load and enhance the DC-to-DC conversion
efficiency $e_{4}$. Indeed, such converter dynamically tracks the maximum
power point condition so as to convert the output DC voltage
$v_{\mathrm{out}}$ of the rectenna to a higher DC voltage level required by
the specific application in use [32, 33]. Due to the variable load on the
rectenna, changes in diode impedance with power level, and the rectifier
nonlinearity, the rectifier input impedance becomes variable, which makes
matching (as well as any joint optimization of the matching and load)
difficult [34]. Nevertheless, multisine signals lead to more efficient DC-to-
DC voltage boost [35] and benefit from configurable DC-to-DC converter to
trace the optimal efficiencies as a function of the input waveform shape and
power level [36].

####  II-A4 Signal Optimization

The above discussion sheds a new technical challenge and opportunity in modern
WPT (and consequently in WIPT) system design. WPT system should not be
designed by maximizing $e_{1}$, $e_{2}$, $e_{3}$, $e_{4}$ independently from
each other as such approach would not maximize $e$. Indeed, since $e_{1}$,
$e_{2}$, $e_{3}$, $e_{4}$ are coupled due to rectenna and HPA nonlinearities,
the transmit signal and the channel state influence the input signal shape and
power to the rectifier and therefore $e_{3}$ but also influence $e_{2}$ and
$e_{1}$. This motivates the design of new and efficient signal optimization
and channel acquisitions modules to adapt as a function of the wireless
channel state, the transmit signals, the RIS and the receive combiner. Such
entire link optimization can maximize $e$ while accounting for the
nonlinearities.

A common formulation of such optimization consists in finding the signaling
strategies that maximize $P_{\mathrm{dc}}^{r}$

$\displaystyle\max_{\mathbf{x}_{0},...,\mathbf{x}_{N-1},\mathbf{w}_{\mathrm{R}},\mathbf{\Theta}}\hskip
8.5359pt$ $\displaystyle
P_{\mathrm{dc}}^{r}(\mathbf{x}_{0},...,\mathbf{x}_{N-1},\mathbf{w}_{\mathrm{R}},\mathbf{\Theta})$
(8) $\displaystyle\mathrm{subject\,\,to}\hskip 8.5359pt$ $\displaystyle
P_{\mathrm{rf}}^{t}\leq P,$ (9)

where maximization is here performed over the transmit vector on all $N$
frequencies $\mathbf{x}_{0},...,\mathbf{x}_{N-1}$, the receive combiner
$\mathbf{w}_{\mathrm{R}}$ (for RF combining in multi-antenna ER), and the
scattering matrix $\mathbf{\Theta}$ (if RIS is present as part of the wireless
channels) under the average transmit power constraint $P_{\mathrm{rf}}^{t}\leq
P$. Additional constraints can also be added to problem (8) to account for
$e_{1}$ and HPA nonlinearity - for instance in the form of peak-to-average
power (PAPR) constraints [16].

The WPT signal optimization of (8) was initiated in [16] for joint waveform
and active beamforming. Due to the complexity of the optimization, suboptimal
low complexity methods, called SMF (scaled matched filter), have also been
used in [37]. SMF designs $\mathbf{x}_{n}$ by performing maximum ratio
transmission (MRT) in the spatial domain and non-uniform power allocation in
the frequency domain as

$\mathbf{x}_{n}=\frac{\mathbf{h}_{n}^{H}}{\left\|\mathbf{h}_{n}\right\|}\left\|\mathbf{h}_{n}\right\|^{\beta}\sqrt{\frac{2P}{\sum_{n=0}^{N-1}\left\|\mathbf{h}_{n}\right\|^{2\beta}}}.$
(10)

We notice the conventional MRT beamforming
$\frac{\mathbf{h}_{n}^{H}}{\left\|\mathbf{h}_{n}\right\|}$ on each frequency
$n$. Using an exponent $\beta>1$ of the channel norm
$\left\|\mathbf{h}_{n}\right\|$, the power is allocated across all
sinewaves/frequencies but more (resp. less) power is allocated to the
frequency components corresponding to large (resp. weak) channel norms, which
replicates the behavior of the optimal strategy of [16]. This is shown in Fig.
6 where the upper graph is the magnitude of the channel frequency response,
and the lower figure displays the solution of problem (8) (“opt”) at $N=16$
uniformly spaced frequencies, as well as the SMF solution (10) with
$\beta=1,3$. By adjusting $\beta>1$, SMF comes closer to the optimal power
allocation. This non-uniform power allocation can be traced back to the
nonlinearity in (4) and originates from a trade-off between maximizing the
first term $\beta_{2}P_{\mathrm{rf}}^{r}$ (and therefore maximize
$P_{\mathrm{rf}}^{r}$) by allocating power to a single sinewave and leveraging
the nonlinearity of the second term
$\beta_{4}\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$ (and therefore
maximize $e_{3}$) by allocating power across multiple sinewaves.

Figure 6: Frequency response of the wireless channel and WPT waveform
magnitudes (N = 16) for 10 MHz bandwidth [37].

In the presence of multi-antenna ER with RF combiner, the waveform, transmit
beamforming and receive combining need to be jointly optimized as in [31, 38],
which offers additional performance enhancements over a transmitter-only
optimization. In the presence of RIS, the signal optimization in [40, 39]
leads to an additional passive beamforming on top of the joint waveform and
active beamforming gain provided by the transmitter.

The above signal optimization leads to an architecture in which the rectifier
is, as much as possible, fixed (for example, with a fixed load) but the
transmit signal (and potentially combiner) is adaptive. Nevertheless, recall
the aforementioned discussions on configurable DC-to-DC converter to track the
optimum load and trace the optimal efficiency as a function of the input
waveform shape and power level. Because the wireless channel changes, it is
envisioned that an entire end-to-end optimization of the system should be
conducted, likely resulting in an architecture in which the transmit signal,
combiner and the rectifier are jointly optimized and adapt themselves
dynamically as a function of the channel state [3]. The challenge is how to
operate and design such an adaptive system keeping in mind the energy
constraint of the devices. Machine learning techniques may be helpful to that
end [8], though this research area remains largely underexplored.

####  II-A5 Channel Acquisition

Optimization of
$\mathbf{x}_{0},...,\mathbf{x}_{N-1},\mathbf{w}_{\mathrm{R}},\mathbf{\Theta}$
in (8) requires knowledge of the wireless channel state information (CSI) at
the transmitter (CSIT), i.e., $\mathbf{h}_{q,n}$ (or
$\mathbf{g}_{\mathrm{d},q,n}$, $\mathbf{g}_{\mathrm{r},q,n}$, and
$\mathbf{G}_{\mathrm{i},n}$ in RIS-aided WPT). In practice, the CSI should be
acquired by the signal optimization module at the ET. Fig. 7 illustrates
several CSI acquisition strategies, including forward-link training with CSI
feedback, reverse-link training via channel reciprocity, power probing with
limited feedback, and channel estimation based on backscatter communications
[4, 41, 42, 60, 44, 45, 46].

(a) Forward-link training (b) Reverse-link training (c) Power probing with
limited feedback (d) Backscatter-based training

Figure 7: Four strategies of channel state information acquisition at ET.

The first two are inspired by strategies used in modern communication systems,
but incur complex processing and/or high energy consumption for low power
nodes. Indeed the first one requires channel estimation at the low power node
and the second one relies on pilot transmission. The third appears more
appealing for WPT because it is implementable with low communication and
signal processing requirements at the ER and simply relies on the measurement
of a DC power level at the output of the harvester and the feedback of some
limited information (no channel estimation or pilot transmission is required).
The fourth one is also encouraging due to the low energy consumption at the
device and relies on the idea that the ET can exploit the backscatter signals
to estimate the backscatter channel (i.e., ET-to-ER-to-ET) state information,
from which the transmit signal needs to be designed.

The framework of [45] revisits optimization problem (8) for the general setup
of multi-antenna multisine WPT of (2) under power probing with limited
feedback. It shows that joint waveform and beamforming benefits can be
exploited with just a few bits of CSI feedback. To this end, it relies on
measuring the output DC power for a selected set of joint waveform and
beamforming weights/precoders and a limited number of feedback bits.
Specifically, over a training period made of multiple time slots, the ET sends
in each time slot with a different (joint waveform and beamforming) precoding
codeword within a codebook, and the ER reports the index of the codeword in
the codebook that offers the largest $P_{\mathrm{dc}}^{r}$.

In the presence of multiple receive antennas, RF combining is more complex to
implement than DC combining as it requires the knowledge of the Channel State
Information at the Receiver (CSIR) for the receive combiner optimization or
alternatively needs a communication link between the ET and ER to tell the ER
what receive combiner to use.

The smart integration of the ET, wireless channel, ER, channel acquisition and
signal optimizations modules ultimately leads to the closed loop, adaptive and
optimized WPT architecture of Fig. 2.

###  II-B Prototypes and Experiments

The previous section highlighted key features such as beamforming, waveform,
multi-antenna ER, RIS, channel acquisition and signal optimization. We now
detail several state-of-the-art WPT prototypes developed at Imperial College
London (ICL) [47, 48, 49, 50] and Sungkyunkwan University (SKKU) [52, 53, 51,
54, 55] and illustrate the real-world performance benefits of some of those
features based on experimental results obtained from over the air measurements
in various indoor and outdoor deployments.

Though we here limit to ICL and SKKU prototypes, readers are also referred to
other WPT experimental works conducted by other groups around the world, in
particular on digital beamforming through baseband precoding using
backscattering for feedback [56], analog beamforming through phased array
[57], time-modulation array [58], adaptive beamforming using receive signal
strength indicator feedback [59, 60], adaptive beamforming using the second
and third harmonics for feedback [61, 62].

####  II-B1 920 MHz Long-Range MISO WPT Prototype

We have built a long-range WPT prototype testbed for demonstrating the real-
time operation of a wireless-powered sensor network (WPSN) [52, 53]. To enable
long-range WPT, a relatively low frequency band (920 MHz) is used, and a
large-scale rectangular phased antenna array of 4$\times$16 antenna elements
is employed to enable active beamforming. The prototype testbed consists of
one ET and one sensor device which relies solely on power supplied by the ET.
This WPT testbed is fully autonomous in that the ET is able to adaptively
focus its power beam on the sensor device, and the sensor device can
dynamically adjust its power consumption according to the stored energy level
for long-term survival.

The ET is equipped with a phased antenna array with 64 antenna elements. We
have fabricated a 16-way phased array board in Fig. 8(a) that outputs 16 RF
signals with controllable phase and magnitude. The phased array board receives
a CW source signal and splits it into 16 RF path by using a power splitter.
Each RF path has a variable attenuator, a phase shifter, and an amplifier. The
variable attenuator and phase shifter are all voltage-controlled by an on-
board digital-to-analog converter (DAC) chip. We use a computer and a field
programmable gate array (FPGA) device to control the phased array board
through the DAC chip. We have combined four 16-way phased array boards to
implement 64 RF paths of the ET. Four microstrip patch antenna arrays, each of
which has 16 antenna elements with 8 dB gain, are fabricated and connected to
the phased array boards via coaxial cables.

The sensor device is comprised of a rectifier board, an energy storage, and a
sensor board, which are all commercial off-the-shelf (COTS) components (Fig.
8(b)). The rectifier board is an evaluation board of a Powercast P1110 chip
with various functions such as rectification, power management, and receive
power measurement. A supercapacitor with the capacitance of 0.1 F is used as
an energy storage, which is connected to the output of the rectifier board.
The sensor board is the Zolertia Z1 mote with TI MSP430 as an MCU and TI
CC2420 as an RF transceiver. The RF transceiver, which implements the 802.15.4
protocol on the 2.4 GHz frequency band, is used for communicating with the ET.
The software platform of the sensor board is the Contiki operating system
(OS).

(a) Phased array board

(b) Sensor device

(c) Outdoor test environment

(d) 50 meter WPT test

Figure 8: 920 MHz WPT prototype testbed.

We have performed beamforming experiments to demonstrate that the ET can focus
a beam on the sensor device. The CSI acquisition is based on the power probing
strategy where the indices of multiple codewords in the codebook (along with
their power levels) are reported and the transmitter adjusts the beamformer
based on the collected feedback. This test is first conducted in an indoor
environment where the ET is deployed on one side of a room. Fig. 9 shows the
heat map of the received RF power inside a room, where the location of the
sensor device is indicated by a black X mark. We can see that the ET
accurately focuses the energy at the sensor device.

The received RF power is measured according to the distance in Figs. 10(a) and
10(b). The indoor test results from 5 to 10 meters are shown in Fig. 10(a).
For this test, the total transmit power from all antenna elements is limited
to 400 mW. We can see that the received RF power is up to 87 mW at 2 meters
distance, at which the power transfer efficiency is 21.8 %. The tests from 15
to 50 meters are also conducted in an outdoor environment (Fig. 8(c)), and the
received RF power is shown in Fig. 10(b). In this test, the total transmit
power can go up to 9.5 W. In this figure, we can see that a few mW can be
transferred to tens of meters, which is enough to operate a low-power sensor
device.

We have placed the sensor device at 50 meters away from the ET (Fig. 8(d)) to
test if the sensor device can be kept alive resorting only to the power
transferred from the ET. Fig. 11(a) shows that the sensor device constantly
receives around 0.72 mW from the ET at 50 meters away. With this power supply,
the stored energy in the sensor device is successfully kept to a certain level
as long as 20 minutes as shown in Fig. 11(b).

Figure 9: Measured beam shape.

(a) 2–5 m (indoor)

(b) 15–50 m (outdoor)

Figure 10: Received RF power over distance.

(a) Received RF power

(b) Stored energy

Figure 11: Survivability test results.

####  II-B2 2.4 GHz MISO WPT Prototype with Adaptive Waveform

Previous experiment demonstrates the key benefit of multi-antenna ET and
active beamforming with CW. We now expand the signal optimization to joint
space and frequency and demonstrate the benefits of joint waveform and active
beamforming. To that end, we have developed in [47, 48, 49] a prototype of
closed-loop WPT system (Fig. 12) with adaptive waveform and beamforming that
relies on the general modern architecture of subsection II-A. The operation of
the prototype follows the frame structure of Fig. 13 consisting of a training
phase and a WPT phase.

Figure 12: Closed-loop WPT prototype system with limited feedback: (a) System
prototype; (b) Transmit antennas and amplifiers for long-range experiment; (c)
ER and feedback system using Zolertia RE-Mote.

Figure 13: Frame structure of the WPT prototype system operation.

The system consists of three important functional blocks: the intelligent ET
equipped with an adaptive waveform and beamforming signal generator module,
the CSI acquisition and feedback module, and the ER. The ET is made up of
multiple Software-Defined Radio (SDR) equipments and antennas to generate and
radiate adaptive waveform and beamforming RF signals chosen according to CSI.
The system operates in the 2.4 GHz band and supports up to eight antennas. All
the antennas are identical universal omnidirectional 2.4GHz antennas with 3
dBi antenna gain and 85% radiation efficiency. The system has external power
amplifiers (Mini-Circuits ZHL-16W-43-S+ with 45dB of gain and 41dBm of P1dB)
to generate high-power RF signals to experiment WPT performance at longer
range of up to 5.5 m. We limited the maximum transmit power of the system
below 30 dBm to comply with the maximum Effective Isotropic Radiated Power
(EIRP) of 36dBm and conduction power of 30dBm specified in FCC Title 47, Part
15 regulations. The SDR equipment, based on National Instrument (NI)
USRP-2942, can generate multi-sine waveforms with different magnitudes and
phases at each tone. We consider up to 8-tone signals so that the generated RF
signal is in the linear region of the power amplifier. The $N$-tone multisine
signal has a uniform frequency gap of $\Delta_{f}=B/N$ where the bandwidth $B$
= 10 MHz.

The ER is implemented using a single diode rectifier (similar to Fig. 3(a))
which consists of a matching network, rectifying Schottky diode, and low pass
filter. The entire circuit is fabricated on a 1.6 mm thick FR-4 substrate and
the mounted lumped element values of the matching network were chosen to fit
the operating frequency of 2.4GHz. We chose Skyworks SMS7630 Schottky diode as
a rectifying diode, which can be operational with low input power because of
its low turn-on voltage.

Figure 14: Cumulative distribution of the output DC power
($P_{\mathrm{dc}}^{r}$) measurement results at different distances (0.6 m -
5.4 m) with the number of transmit antennas $M$=1, 2, 4, 8, and the number of
carriers (tones) $N$=1 and 8 [48].

Figure 15: Measurement results and curve fitting of output DC power
($P_{\mathrm{dc}}^{r}$) versus distance with $N$=1, 8 and $M$=1,2,4,8 [48].

Figure 16: Measurement results of output DC power $P_{\mathrm{dc}}^{r}$ of
joint waveform and beamforming with limited feedback for $M=2,4$, $N=2,8$ and
1 to 6 bits of feedback [49].

In order to complete the closed-loop configuration, both ET and ER are also
equipped with a communication module to enable CSI feedback from the ER to the
ET, respectively. Two CSI acquistion strategies of Fig. 7 are considered,
namely forward-link training with very accurate over-the-air feedback and
power probing with limited feedback. The former is consuming a lot of energy
but is instrumental in providing an upper bound on the performance of this
system since the CSIT is very accurate. The latter is very realistic and
similarly to the prototype of subsection II-B1, it is implemented using
Zolertia RE-mote (Contiki operating system), which is equipped with ARM-based
MCU and IEEE 802.15.4 RF interface. The RE-mote at the ER records the output
DC voltage of the rectifier through the built-in ADC and seeks the highest
value and corresponding codewords (i.e., finds the codeword in the codebook of
joint waveform and beamformers that achieves the highest
$P_{\mathrm{dc}}^{r}$) during the training phase as per Fig. 13. Then, the RE-
mote transmits the codeword index to the RE-mote at the ET side using
IEEE802.15.4 interface. The ET-side RE-mote receives the codeword index and
reports to the ET (USRP) using RS-232C interface. The codeword index fed back
from the ER is the basis for signal generation in the consecutive frame.
Following the training phase, energy is transmitted in the WPT phase using the
optimized signal designed to span space (multi-antenna beamforming) and
frequency (waveform) according to the selected codeword. This operation of
training phase and WPT phase is repeated periodically with the period
depending on the rate of change of the channel (e.g., the velocity of the ER).

Figs. 14 and 15 illustrate the output DC power $P_{\mathrm{dc}}^{r}$ and range
of WPT achieved with MRT beamforming with 1, 2, 4, 8 transmit antennas and CW
($N=1$, 1 tone), as well as joint SMF waveform and beamforming ($N=8$, 8
tones) based on experimental data collected in a typical indoor environment at
2.4GHz under an EIRP of 36dBm [48]. In those figures, CSI acquisition is based
on forward-link training with very accurate over-the-air feedback. Though the
optimal design of joint waveform and beamforming results from the solution of
an optimization problem [16], the simple and low complexity design of the
joint waveform and beamforming based on SMF (10) is shown to significantly
boost the output DC power and the range of WPT. We see that WPT efficiency can
be enhanced by using either the frequency domain, the spatial domain or both
domains together. In addition, a 1-tone (CW) waveform with 8 antennas shows
similar performance as an 8-tone waveform with 4 antennas. Similarly, a 1-tone
waveform with 4 antennas (1-tone with 2 antennas) offers similar performance
as a 8-tone waveform with 2 antennas (8-tone with with 1 antenna). Hence
increasing the number of tones from 1 to 8 has a similar effect as doubling
the number of antennas. Such behavior shows that it is possible to replace the
spatial domain processing (number of antennas) with the frequency domain
processing (number of tones) and vice versa. The gains in terms of output DC
power and range can also be accumulated using a joint beamforming and waveform
strategy.

Results in Figs. 14 and 15 were based on forward-link training with CSI
feedback, which is too high energy consuming and/or too complex for low power
nodes. Next, we illustrate the performance of a more practical joint waveform
and beamforming architecture based on power probing with limited feedback
using off-the-shelf Zolertia nodes. Fig. 16 illustrates the experimental
results obtained with such a strategy for 1 to 6 bits of feedback with $M=2,4$
and $N=2,8$ [49]. As $M$ and $N$ increase, we note the significant increase in
$P_{\mathrm{dc}}^{r}$ but also the need for larger codebook sizes (and
therefore larger feedback overhead) to come closer to the perfect CSIT
performance.

####  II-B3 920 MHz and 2.4 GHz Distributed Antenna WPT Prototypes

The former two prototypes were based on co-located transmit antennas, i.e.,
antennas are separated by about half a wavelength. Another attractive
architecture is to distribute the transmit antennas across the coverage area
and enable some form of cooperation or coordination among those antennas [4].
Such distributed antennas system (DAS) distributes energy more evenly in space
and makes wireless power accessible ubiquitously compared to a co-located
deployment. High energy beams in the direction of users are also avoided,
which is desirable from a safety perspective.

The prototype of Section II-B2 has recently been leveraged to demonstrate
experimentally the benefits of WPT based on DAS at 2.4 GHz in [50]. It has
been shown that WPT DAS relying on a low cost and low complexity dynamic
selection of transmit antenna and frequency can boost $P_{\mathrm{dc}}^{r}$ by
up to 30 dB in a single-user setting and broaden the coverage area.

Another WPT DAS prototype at 920 MHz has been built and tested in [54]. Here
all distributed antennas fully cooperate such that the phases of the received
signal from all transmit antennas are constructively aligned (based on MRT
beamforming) at the receive antenna. Results show that the received RF power
distribution with DAS is more evenly distributed than that of the co-located
antennas. Consequently, it is shown that the coverage probability (e.g.,
achieving the received RF power larger than 0 dBm) is higher with DAS than
with co-located antennas.

####  II-B4 5.8 GHz RIS-aided MIMO WPT Prototype

The prototypes so far relied on active antenna arrays (providing an active
beamforming gain) and on single-antenna ER. RIS in subsection II-A2 was
introduced as a promising technology to engineer the channel and provide an
additional passive beamforming gain. Moreover, subsection II-A3 advertised
that the use of multi-antenna ER leads to MIMO WPT and can further boost the
output DC power.

We have built a medium-range 5.8 GHz RIS-aided MIMO WPT system prototype using
DC combining, jointly providing an active, passive, and combining gains [51].
This WPT system is integrated with an RIS with 256 unit cells to enhance the
power transfer efficiency and extend the range. A conceptual application
scenario is given in Fig. 17, in which an RIS in the ceiling focuses power on
the sensor device on the ground by reflecting an EM wave beam emitted by the
ET (power beacon) equipped with a phased antenna array.

Figure 17: RIS-aided WPT conceptual application scenario.

The ET is very similar to that of the 920 MHz WPT system of subsection II-B1.
It is equipped with a rectangular 8$\times$8 phased antenna array. We have
adopted a sandwich structure stacking four boards, which are power divider,
phase control, amplifier, and antenna boards, by using board-to-board
connectors (Fig. 18(a)). The sensor device is equipped with a 4$\times$4
antenna array (Fig. 18(b)). The rectifier attached to each antenna element is
a one-stage Dickson charge pump. In this system, we use a DC combining
technique which combines the DC outputs of the 16 rectifiers in parallel (see
Fig. 5 (a)). The combined DC power is delivered to a DC-DC converter (TI
BQ25570) for the maximum power point tracking (MPPT), voltage regulation, and
battery management.

We have fabricated a 16$\times$16 RIS with 256 unit cells as shown in Fig.
18(c). Each unit cell is a rectangular patch resonating at 5.8 GHz, equipped
with a single PIN diode for one-bit control. The incident wave on each unit
cell travels to the PIN diode, and is reflected back to be re-radiated to the
air. The unit cell is designed in such a way that the phase of the reflected
wave has a 180 degree difference according to the ON/OFF states of the PIN
diode. The RIS is controlled by an FPGA and a control board for serial-to-
parallel conversion, which consists of shift registers, decoders, and D-type
flip flops.

(a) 5.8 GHz phased array transmitter

(b) Sensor device

(c) RIS board

(d) Experiment set-up

Figure 18: 5.8 GHz RIS-aided MIMO WPT prototype testbed.

We have proposed a power-based scanning algorithm based on the power probing
CSI acquisition strategy specifically designed for RIS, so as to enhance the
beam focusing capability and the received power at the sensor device. For the
scanning algorithm, the RIS is divided into smaller RIS tiles. Based on the
power level feedback from the device, each RIS tile is iteratively optimized
to constructively add up the received power at the sensor device. We have
performed experiments to verify the proposed algorithm. The transmitter and
sensor device are located at 2 meters away from the RIS as shown in Fig.
18(d). The sensor device is moved to assess the performance at different
distances $x$ (see Fig. 18(d)) from 0 meters to 2.5 meters. Fig. 19(c) shows
the received DC power over the test distance with different RIS tile sizes. In
this test, the total transmit power from all antenna elements is 2 W. It can
be observed that around 22 mW is transferred to the sensor when RIS tile size
$2\times 2$ (4 unit cells) is used at the test distance of $x=0.3\text{ m}$,
which is significantly higher than the power level collected at the sensor in
the absence of RIS. The corresponding transmitter and RIS phase control states
are given in Figs. 19(a) and Fig. 19(b), respectively. In these figures, we
can see that the transmitter directs the beam towards the RIS, and the RIS
makes the reflected beam focused onto the receiver by forming a convex lens-
like phase pattern.

(a) Phase of the $8\times 8$ array transmitter

(b) Phase control of the $16\times 16$ RIS

(c) Received DC power over distance

Figure 19: RIS-aided WPT experimental results.

##  III Wireless Information and Power Transfer

Building upon WPT, we can now investigate WIPT. WIPT can be categorized into
three different types.

Simultaneous Wireless Information and Power Transfer (SWIPT): The term was
first coined in [64] and refers to scenarios where information and power are
simultaneously sent from the transmitter(s) to the receiver(s)[5, 63, 64, 65,
66]. The information receiver(s) (IR) and ER can be co-located or separated.
With co-located receivers, a single (typically low-power) device equipped with
an IR and ER is simultaneously wireless powered and receiving data. With
separate receivers, the ER and IR refer to different devices, with ER being a
low-power device being wireless powered and IR being a device receiving data.

Wirelessly Powered Communication Networks (WPCNs): Energy is transmitted in
the downlink from a base station to a device and information is transmitted in
the uplink [68]. The device harvests energy in the downlink and uses the
harvested energy to transmit data in the uplink.

Wirelessly Powered Backscatter Communication (WPBC): the downlink is used to
transmit energy to a device and the uplink is used to transmit information
using backscatter modulation from a tag to a reader by reflecting and
modulating the incoming RF signal [69]. Thanks to backscatter communications,
tags do not require oscillators to generate carrier signals and power
consumption can be decreased by several orders-of-magnitude compared to
conventional wireless communications [70].

Moreover, a network could have a mixture of all of these types of
transmissions with multiple co-located and/or distributed ETs and information
transmitter(s) (IT).

In the sequel, we further detail SWIPT architectures, prototytpes and
experiments.

###  III-A Architecture

We can now build upon Section II to integrate communications and power into a
SWIPT architecture.

####  III-A1 Transmitter

Since both information and power are transmitted simultaneously, the transmit
signal (2) needs to be upgraded with the weight vector $\mathbf{x}_{n}$
replaced by a time-varying $\mathbf{x}_{n}(t)$ (due to modulation) that
contains random complex-valued information and power carrying symbols (drawn
from a certain input distribution), instead of just a deterministic power
carrying symbol.

####  III-A2 Receiver

Several receiver architectures for SWIPT have been proposed in Fig. 20 that
integrate information decoder (ID) and energy harvester (EH).

(a) Ideal Receiver

(b) TS Receiver

(c) PS Receiver

(d) Integrated Receiver

Figure 20: Four single-antenna receiver architectures for SWIPT: (a) Ideal
receiver (using the same signal for both information and energy receivers);
(b) TS receiver (switching the signal to either information or energy
receiver); (c) PS receiver (splitting a portion of the signal to information
receiver and the rest to the energy receiver); and (d) Integrated receiver
(demodulation is performed after rectification).

An Ideal Receiver (Fig. 20(a)) assumes the same signal $y_{\mathrm{rf}}(t)$ is
simultaneously conveyed to the harvester and to the decoder [5, 63]. No
practical circuits can currently realize this operation.

A Time Switching (TS) Receiver (Fig. 20(b)) consists of a co-located decoder
and harvester (following the structure in subsection II-A3) [64, 65, 66]. The
transmission is divided into two orthogonal time slots, one for WPT and the
other for WIT. In each slot, the transmit signal is optimized for either WPT
or WIT and the receiver switches accordingly its operation periodically
between harvesting energy and decoding information.

In a Power Splitting (PS) Receiver (Fig. 20(c)), the harvester and decoder are
the same as those of a TS receiver. The transmit signals are jointly optimized
for information and energy transfer and the received signal is split into two
parts, where one part with PS ratio $0\leq\rho\leq 1$ is conveyed to the
harvester, and the other with power ratio $1-\rho$ is utilized by the decoder.
[64, 65, 67]. Assuming perfect matching, the input voltage signals $\sqrt{\rho
R_{\mathrm{ant}}}y_{\mathrm{rf}}(t)$ and
$\sqrt{(1-\rho)R_{\mathrm{ant}}}y_{\mathrm{rf}}(t)$ are, respectively,
conveyed to the harvester and the decoder.

In the Integrated Receiver (Fig. 20(d)), the received RF signal is first
rectified and then the rectified voltage signal is used as an input signal to
the ID receiver[65]. Hence, in contrast to prior architectures, the received
RF signal is not divided into EH and ID receivers, instead the received RF
signal is fully harvested by EH, so it can maximize RF-to-DC conversion
efficiency. However, in terms of information decoding, the rectified voltage
signal looses some of the characteristics of the original signal during the
rectification process so that the information decoding performance (e.g.,
rate, throughput) are degraded, though a proper signal design can help
improving the performance. Such integrated architecture eliminates the need
for energy-consuming RF components such as local oscillators and mixers needed
for the ideal, TS and PS architectures, therefore making it more suitable for
low power applications not demanding high throughput.

####  III-A3 Signal Optimization

The trade-off between rate and energy in SWIPT is captured by the Rate-Energy
(R-E) region $\mathcal{C}_{\textnormal{R}-\textnormal{E}}$ that contains all
pairs of rate $R$ and energy $E$ that can simultaneously be
achieved/harvested. It is obtained through a collection of input distributions
$p(\mathbf{x}_{0},...,\mathbf{x}_{N-1})$ that satisfies the average RF
transmit power constraint $P_{\mathrm{rf}}^{t}\leq P$ and can be written
mathematically as

$\mathcal{C}_{\textnormal{R}-\textnormal{E}}(P)\\!\triangleq\\!\bigcup_{p}\Bigg{\\{}(R,E):R\leq\sum_{n=0}^{N-1}I_{n},E\leq
P_{\mathrm{dc}}^{r}\Bigg{\\}}$ (11)

where $I_{n}$ refers to the rate (measured in terms of mutual information
between the channel input and the channel output) on subband $n$. Both $I_{n}$
and $P_{\mathrm{dc}}^{r}$ are functions of the input
$\mathbf{x}_{0}(t),...,\mathbf{x}_{N-1}(t)$.

The R-E region can be identified by calculating the capacity (supremization of
the mutual information over all possible input distributions
$p(\mathbf{x}_{0},...,\mathbf{x}_{N-1})$) of a channel subject to an average
RF transmit power constraint $P_{\mathrm{rf}}^{t}\leq P$ and a receiver
delivered power constraint $P_{\mathrm{dc}}^{r}\geq\bar{E}$, for different
values of $\bar{E}\geq 0$. Namely,

$\displaystyle\sup_{p(\mathbf{x}_{0},...,\mathbf{x}_{N-1})}\hskip 8.5359pt$
$\displaystyle\sum_{n=0}^{N-1}I_{n}$ (12)
$\displaystyle\mathrm{subject\,\,to}\hskip 8.5359pt$ $\displaystyle
P_{\mathrm{rf}}^{t}\leq P,$ (13) $\displaystyle
P_{\mathrm{dc}}^{r}\geq\bar{E},$ (14)

where $\bar{E}$ denotes the minimum required or target delivered power. The
above problem can be tackled for the receiver architectures of Fig. 20 along
with the specific parameters of the receiver [7]. For instance, with the TS
receiver, different R-E trade-offs are achieved by varying the length of the
WPT time slot, jointly with the transmit signals; while with the PS receiver,
different R-E trade-offs are obtained by adjusting the value of $\rho$ jointly
with the transmit signals.

There is no communication or information transmission without randomness in
the signal. Hence, designing SWIPT requires the transmit signals to be subject
to some randomness, which has an impact on the amount of harvested DC power.
This raises interesting questions on how modulation and waveform need to be
re-thought for SWIPT.

Starting with the modulation design in single-subband ($N=1$), as a
consequence of (4) and Observation 1, conventional modulation (such as PSK and
QAM) and input distribution (such as circularly symmetric complex Gaussian -
CSCG) used in communications are clearly suboptimal for SWIPT. Indeed, (4) and
Observation 1 call for modulation and input distribution with large higher
moments so as to boost $\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$.
Consequently, to obtain the best trade-off between rate and energy, the
modulation should change according to the target delivered power $\bar{E}$.
Indeed, it is remarkably shown in [71] that the information theoretic optimal
solution to Problem (12)-(14) is obtained by adopting a combination of CSCG
and on-off-keying inputs with CSCG used for low target delivered power
$\bar{E}$ and on-off keying increasingly used as $\bar{E}$ increases. This is
due to the fact that on-off keying can be adjusted such that one constellation
point is at 0 and is drawn with probability $1-\frac{1}{l^{2}}$ and the other
constellation point has an amplitude $l\sqrt{P}$ and is drawn with probability
$\frac{1}{l^{2}}$, for $l\geq 1$. Such a modulation has the same average power
$P$ for all values of $l$ but has a fourth moment that increases with $l$.
Consequently, as $l$ increases, such a modulation exhibits a low probability
of high amplitude that leads to increasing higher moments
$\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$ and therefore
$P_{\mathrm{dc}}^{r}$.

On-off keying has been shown to significantly boost $e_{3}$ conversion
efficiency over various baselines [48, 71]. In Fig. 21, we display measurement
results of various modulations using the rectifier of Fig. 3(a). We note that
on-off keying ($l$=1,2,3,4,5) provides almost two times more output DC power
($P_{\mathrm{dc}}^{r}$) than conventional modulations as BPSK and 16-QAM
though all have the same average RF input power ($P_{\mathrm{rf}}^{r}$).

Figure 21: Measured output DC power ($P_{\mathrm{dc}}^{r}$) of conventional
and WPT-optimized modulations [48]. CG refers to CSCG, and RG to real
Gaussian. $l$=1,2,3,4,5 refer to on-off keying modulations.

Such on-off keying can be used in the ideal, TS and PS receiver. Inspired by
the benefits of on-off keying, another type of modulation particularly suited
for the integrated receiver has been designed in [72]. The so-called $M$-PPM
is a modified version of conventional pulse-position modulation (PPM) suited
for SWIPT integrated receiver architecture ($M$ represents a modulation order)
as illustrated in Fig. 22. The information is encoded on the pulse position
during the symbol period of the time domain signal, and all the transmit
signal power is concentrated on the corresponding pulse, thus increasing the
PAPR of the signal and improving harvested DC power at the receiver (since
high PAPR pulse boosts $\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$ in
(4)). In terms of information transfer, the PPM is a non-coherent modulation
that does not need a power-consuming local-oscillator at the receiver; thus,
it is suitable for low-power integrated SWIPT receiver.

Figure 22: Example of PPM ($M$=4) symbols and baseband signal [72].

In the multi-subband case ($N>1$), waveform and modulation/input distribution
also need to be tailored for SWIPT. Remarkably, as a consequence of
Observation 1, it was shown in [73] that the solution to Problem (12)-(14) is
such that the input distribution/modulation on each subband, i.e., the entries
of $\mathbf{x}_{n}(t)$, are non-zero mean in general. Specifically, for
$\bar{E}=0$, the distribution is zero mean on all subbands and the rate is
maximized, and as $\bar{E}$ increases, the waveform becomes more and more
deterministic, i.e., the variance of the distribution on each subband
decreases, and the rate decreases. Ultimately the waveform reaches the
perfectly deterministic multisine waveform of WPT in (2) in the limit of large
$\bar{E}$ and zero rate. Concretely, what that suggests is that the waveform
for SWIPT can be written as a superposition of two waveforms, one
deterministic/unmodulated waveform for WPT in the form of a multisine
contributing to the non-zero mean (i.e., DC bias), and one modulated waveform
for communication in the form of OFDM with zero mean inputs [73].

The benefit of superposed waveform (or equivalently the superiority of non-
zero mean inputs over zero mean inputs) can be explained by the fact that a
multi-carrier unmodulated waveform, e.g., multisine, is more efficient in
boosting $\mathbb{E}\left[y_{\mathrm{rf}}(t)^{4}\right]$ and therefore
$P_{\mathrm{dc}}^{r}$ compared to a conventional multi-carrier modulated
communication waveform [73].

###  III-B Prototypes and Experiments

The previous section highlighted key SWIPT features. Though SWIPT prototypes
and experiments remain less investigated compared to WPT, we detail and
illustrate the real-world performance benefits of several state-of-the-art
SWIPT prototypes developed at ICL [75, 72] and SKKU [74]. A special emphasis
is put on the effect of modulation, superposed waveform and the role of
receiver design. A particular attention is drawn to the integrated receiver
which is deemed to be more practical for low power applications. Readers are
also referred to [76, 77] for other experiments on SWIPT with integrated
receivers.

####  III-B1 920 MHz SWIPT Prototype with Integrated Receiver

We have built and tested a full-fledged SWIPT system prototype with an
integrated receiver operating at 920 MHz [74]. This prototype is a Single-
Input Single-Output (SISO) testbed with single-antenna transmitter and
receiver. Uniquely, the transmitter of this SWIPT system sends the power via a
high-power CW signal at the carrier frequency while the data is transmitted
via a low-power modulated signal around the carrier frequency. The integrated
receiver first rectifies the received signal, and then the rectified signal is
split into two branches: the power and communication branches. The CW power
signal is routed to the power branch for WPT, while the modulated
communication signal is fed into the communication branch for decoding.

The DC-biased OFDM is a common modulation technique for an intensity channel
without phase information, for example, visible light communications (VLC).
Since we use an integrated receiver, in which the information decoder receives
a rectified signal, the channel has only intensity information and the DC bias
is provided by the CW power signal. Therefore, the DC-biased OFDM is the most
appropriate choice for this experiment. The spectral efficiency is halved
since the phase information is lost in the intensity channel. The
communication in this experiment exploits very wide difference in the power
requirements of WPT and communications. Since the communication signal is
allocated a much lower power than the CW power signal, the communication
signal goes through a linear channel in the rectifier due to the small signal
assumption. Thus, we can avoid the intermodulation distortion, and the OFDM
modulation is possible. At the rectifier, the received signal amplitude is
almost constant since the communication power is very small. Therefore, we do
not exploit the non-linearity of the rectifier in this experiment.

At the transmitter (Fig. 23(a)), an SDR platform generates the communication
and power signals and transmits them through two different output ports. The
power signal is amplified by the high power amplifier (HPA) and combined with
the communication signal by using the RF combiner. The combined signal is
transmitted and received by circularly polarized panel antennas. At the
receiver (Fig. 23(b)), the received signal is rectified and decomposed into
the power and communication signals by means of the receiver board. We have
designed and fabricated the receiver circuit with the one-stage Dickson charge
pump as shown in Fig. 24(a). The received power signal is controlled and
measured by a source meter. On the other hand, the received communication
signal is amplified by a voltage amplifier, digitized by an ADC, and processed
by an FPGA. The transmit and receive codes for the DC-biased OFDM are
implemented in the SDR platform and FPGA, respectively, by using the Labview
FPGA software for fast signal processing.

The sampling rate of the communication signal is 25 MS/s. The FFT size for the
DC-biased OFDM is 2048, and the subcarrier spacing is 12.21 kHz. We use 512
subcarriers among the 2048 available subcarriers, and 96 subcarriers around
the center and 1440 subcarriers around the edge of the bandwidth are unused.
Therefore, the actual bandwidth of the communication signal is about 6.25 MHz.
The transmit power is equally distributed to all active subcarriers. We have
implemented the quadrature phase shift keying (QPSK), 16QAM, 64QAM, and 256QAM
modulation schemes.

(a) Transmitter architecture

(b) Receiver architecture

Figure 23: SWIPT architecture.

(a) Receiver board photo

(b) SWIPT system testbed photo

Figure 24: SWIPT prototype testbed.

We have conducted the experiments of SWIPT with integrated receiver using the
testbed shown in Fig. 24(b). In the experiment, the transmit power of the
power signal (i.e., 1 W) is a thousand times higher than that of the
communication signal (i.e., 1 mW). Despite the comparatively small power of
the communication signal, the constellation diagrams of the QPSK, 16QAM, and
64QAM modulation schemes at the distance of 4 meters are very clear as shown
in Fig. 25.

The bit error rate (BER) of the modulation schemes over the distance is shown
in Fig. 26(a). In this figure, we can see that all modulation schemes are
usable within the given distance range with just 1 mW transmit power for the
communication signal. In Fig. 26(b), we show the received RF and DC power of
the power signal over the distance. The received RF power is measured by the
RF power meter directly connected to the receive antenna, whereas the received
DC power is the DC power measured by the source meter connected to the power
connector of the receiver board. Fig. 26(b) shows that the received DC power
at 4 m distance is higher than 0.5 mW, which is sufficient power for charging
an IoT device. From Figs. 26(a) and 26(b), we can see that the SWIPT system
testbed is capable of simultaneously transmitting information and power.

(a) QPSK

(b) 16QAM

(c) 64QAM

Figure 25: Constellation diagram.

(a) Bit error rate (BER)

(b) Received RF and DC power

Figure 26: SWIPT performance over distance.

####  III-B2 2.4 GHz SWIPT Prototype with TS, PS and Integrated Receivers

Previous experiment relied on the integrated receiver architecture. We may
wonder how such an architecture compare with the TS and PS receivers. To
answer that question, we have built a SISO666Further enhancements can be
obtained by combining with the multi-antenna architectures at both the ET and
ER from Section II. point-to-point SWIPT testbed with three different types of
receiver architectures as TS, PS, and integrated receiver. The SWIPT
transmitter is implemented using SDR equipment (USRP-2942R), which is able to
generate various SWIPT signals from conventional modulations to tailored
signal design for SWIPT. The testbed system operates at 2.4GHz carrier
frequency, which is the same as WiFi in the ISM band. The transmitter includes
features to generate the WPT and communication waveforms and to combine them
into SWIPT transmission signals in a time-sharing or superposition manner for
the TS and PS receivers and also to generate specially designed SWIPT signal
for the integrated receiver. For the TS and PS receivers, a power splitter or
an RF switch is located directly behind the receiving antenna to distribute
the received signals to both ID and EH blocks in PS and TS manner,
respectively. The ID is implemented using additional USRP to demodulate
information from the received RF signal and the EH is a simple single diode
rectifier to convert RF signals to DC voltage. PS and TS ratios can be
adjusted by a control signal for RF switch or by replacing the power
splitter/coupler with different coupling ratios. The integrated receiver is
implemented using the same EH as for TS/PS receivers and an oscilloscope plays
the role of ADC and modem for the ID. We have used Agilent DSO5012A
oscilloscope to read DC voltage signal and it supports up to 2GHz sampling
rate. Digital input signal to the ID is read from the oscilloscope and
processed for demodulation of the information. Meanwhile, the harvested DC
power is also measured from the voltage output of the EH. The operation is
implemented in LabView, and the entire system is controlled by a host PC. Fig.
27 displays the prototype of SWIPT with different types of receiver
architectures.

Figure 27: SWIPT prototype system with (a) PS/TS receiver architecture (b)
Integrated receiver architecture.

The performance of various signal design methods for each SWIPT receiver
architecture was evaluated from both information and power transfer
perspectives using the aforementioned prototype and testbed [75, 72]. Here, we
present a performance comparison between PS receiver and integrated receiver
using various signal designs tailored for each receiver architecture. The PS
receiver used in this experiment is equipped with a 10dB power coupler which
means 90% of input RF power is distributed to the EH and the remaining 10%
goes to the ID. In [75], we showed that such a low portion of 10% of input RF
power is enough for information decoding at a coherent information receiver.

Figure 28: Throughput and harvested DC power performance of different signals
with different receiver architecture in various input RF power levels.

Fig. 28 displays the performance of throughput and harvested DC power of
various signal designs and receiver architectures for several input RF power
ranges. We measured the DC output power at the EH and BER at the ID, and the
throughput is calculated as $(1-BER)\times maxrate$, where $maxrate$ is the
maximum achievable rate of each signal design. The experimented signal’s
$maxrate$ are 5Mbps for 4-PPM, 40Mbps for 64-QAM, and 60Mbps for superposed
OFDM-SMF, with all operating over a 10MHz bandwidth. The experiment ran for
one second for each signal and was repeated 100 times, then the measurement
results were averaged. Superimposed SWIPT signal (denoted as OFDM-SMF) and
conventional 64-QAM modulation signals were used when experimenting the PS
receiver architecture. The superimposed SWIPT signal is a combination of WPT
and WIT signal with a certain power ratio, and we used OFDM (40subcarriers,
64QAM modulations) as a WIT signal and 8-tone SMF (channel-adaptive low
complex multi-tone WPT signal design) as a WPT signal, and the power ratio
between WPT and WIT is 9:1. Both signals show no error in the input RF power
range of -30 to -15 dBm with the PS receiver, so its throughput is the same as
the maximum rate of 40Mbps and 60Mbps, respectively, for both 64-QAM and OFDM-
SMF superimposed signals with 10 MHz bandwidth. For the integrated receiver
architecture, a 4-PPM signal with 10MHz bandwidth for SWIPT is used. Its
maximum rate is 5Mbps and the maximum throughput is achieved at the higher
input RF power of -15dBm. The throughput of QAM and OFDM signals is much
higher than that of PPM and shows much stable performance in the low-input
power region. The ID in the PS receiver (coherent information decoder) for
those signals is equipped with LNA, oscillator, and mixers, so it highly
outperforms the ID in the integrated receiver, but also consumes significantly
more energy. In contrast, the ID in the integrated receiver spends much less
energy but its throughput performance is degraded.

To compare more accurately the performance of PS and integrated receivers, CW
is added for the power transfer experimental results in Fig. 28. As expected,
CW at the integrated receiver shows higher output DC power (with 10 to 20%
gain) over CW at PS receiver. The 4-PPM signal at the integrated receiver
shows the best power transfer performance gain over CW due to its high PAPR
signal design and also does not incur any power loss at ID. The superimposed
OFDM-SMF signal at the PS receiver also shows attractive gains but it cannot
exceed PPM due to the power loss induced by the PS process. Additionally, CSI
is required to generate the OFDM-SMF superimposed signal, so additional power
consumption at the ER is required to feedback CSI to the ET.

Figure 29: Throughput-Energy region with various signal designs and TS, PS,
and integrated receiver architectures, measured at -17dBm RF input power to
the receiving antenna.

Results can also be illustrated using the R-E (or throughput-energy) region of
PS, TS, and integrated receivers in Fig. 29. The throughput-energy region has
been measured by sweeping the TS and PS ratios of TS and PS receivers at the
fixed RF receiving power level of -17dBm. The same transmit signal of 64QAM
modulation has been experimented for both TS and PS receivers. The R-E region
of PS is significantly expanded compared to TS due to the PS receiver’s
capability of information decoding with only a small portion of power to the
ID. Additional R-E region expansion is confirmed using superimposed OFDM-SMF
relying on the use of multi-carrier and CSIT based channel adaptive design to
boost throughput and energy performance, respectively. The PPM signal applied
to an integrated receiver exhibits completely different performance
characteristics with large power transfer performance but lower throughput.
However, it should be noted that the high throughput in TS and PS receivers is
made possible by the large power consumption at the ID. Several hundreds of mW
of power are consumed for decoding those OFDM WiFi-like information signals at
TS and PS receivers [78]. Additional power consumption for acquiring CSIT is
required for the superimposed OFDM-SMF signal. On the other hand, the non-
coherent PPM signal for the integrated receiver demands less than a few mW for
information decoding [79]. Overall, the PS receiver can potentially achieve a
wider R-E region at the cost of large energy consumption. In contrast, the
integrated architecture achieves a smaller region but with less than 1% of the
energy consumption of the PS receiver.

Figure 30: CDF of output DC power ($P_{\mathrm{dc}}^{r}$) measurement results
at different distances from 0.5 to 5.3 m with two different receiver and
various signal designs.

Power transfer performance experiments in many different wireless environments
were also carried out using the PS and integrated SWIPT receivers. We have
measured the output DC power at 70 different locations in our testbed using
various signal design methods such as CW, QAM, OFDM and PPM. The distance
between the transmitter and the receiver varies between 0.5 and 5.3 meters,
and the transmission power is fixed at 27dBm. Cumulative distribution
functions (CDF) of measured DC output power with various modulation signals
and receiver architecture are presented in Fig. 30. We clearly observe that
the CDFs of integrated receiver are shifted to the right compared to the PS
receiver, which means that the integrated receiver enables to harvest more
energy. These observations are consistent with the results in Fig. 28 and 29.

##  IV Conclusions and Future Research

The paper has provided an overview of fundamental building blocks of modern
WPT and WIPT systems and demonstrated their feasibility using prototype and
experiments.

One first conclusion of the paper is that the integration of emerging ideas
from RF, communications and signal processing is instrumental in boosting the
performance of WPT and in enabling a fully closed-loop and channel-controlled
WPT architecture capable to adapt to any wireless environment and to engineer
the wireless channel for maximum WPT (and WIPT) performance. Nevertheless, the
adoption and design of large scale system and WPT-based future networks calls
for a stronger integration of various expertise ranging from RF design,
circuit, antenna, sensing, computing, communications, networking, and signal
processing.

A second conclusion is that the inter-disciplinary design of WPT and WIPT
leads to new theoretical and experimental design challenges for engineers that
are worth considering in future research.

First, various societies have an important role to play in WPT for future
networks, but the techniques need to be developed in light of the physics and
hardware constraints of WPT. Recall for instances that techniques like
waveform, receive combiner, joint waveform and beamforming are deeply rooted
in the harvester nonlinearity and only appeared to light once the nonlinearity
is accounted for in the signal design. This calls communication engineers for
abandoning naive and oversimplified models and accounting for various sources
of nonlinearities and nonidealities in the signal and system optimization
(e.g., [80]) and RF engineers to account for multipath fading and advanced
adaptive and closed-loop WPT architecture inspired by modern wireless
communication systems. A genuine integration of RF, communication and signal
processing is crucial for an end-to-end system optimization and efficiency
maximization. Much work remains also to be done to prototype and experiment
those end-to-end system optimization solutions in larger networks composed of
multiple nodes (and therefore going beyond the single-user or point-to-point
experiments discussed in this paper).

Second, the prototyping and experimental results discussed in this paper are
strongly rooted in a “model and optimize” design approach of WPT and WIPT.
Indeed, the approach relies on RF, optimization and communication theories to
derive efficient and implementable strategies for WPT/WIPT. This has shown
significant benefits as demonstrated by the prototyping and experimental
results. Nevertheless such an approach also has some limitations: 1)
difficulty to analytically account for various sources of nonlinearity and
nonidealities, 2) mathematically extremely challenging and computationally
intensive problems to solve. The lack of tractable mathematical models of the
entire WPT chain (accounting for transmitter-receiver including HPA, RF
impairments, rectenna, DC-to-DC converter, imperfect matching, non-ideal low
pass filter, load, parasitics, etc), as well as algorithms to solve WPT/WIPT
signal/system optimizations in general settings is a bottleneck towards
efficient WPT/WIPT designs. In this regard, machine learning (ML) is
instrumental since they can be used to circumvent these modelling and
algorithmic challenges. This calls for a “learning” approach for WPT and WIPT
advocated in [8, 81]. A learning approach towards WPT and WIPT signal and
system design, and an _integrated_ approach that leverages the complementarity
and synergy of the learning and the model-and-optimize approaches, remain
largely uncharted research territories, both on the theoretical and
experimental sides.

Third, the biggest hurdle in the widespread adoption of WPT remains its low
power transfer efficiency. Although a large-sized transmit antenna arrays
makes a smaller focal spot, it restricts the applicability of the WPT system
and increases the manufacturing cost. The form factor of a sensor device is
restricted by the application demands as well. Therefore, another opportunity
to further increase the efficiency is to use higher frequency with shorter
wavelength. Generally, high frequency circuits pose many design challenges,
and more importantly, the number of antenna elements and RF paths in the power
beacon is proportional to the frequency squared, which potentially leads to
very high manufacturing cost. Thus, the prerequisite for the prevalence of
wireless-powered networks is the development of high frequency (e.g.,
millimeter wave range) WPT systems with a moderate cost. Upcoming
proliferation of millimeter wave communications and massive MIMO technologies
is expected to push down the cost of high frequency WPT systems. Another
direction can be developing a low cost alternative architecture for
synthesizing a focused beam other than the phased antenna array, for example,
a tunable metasurface-based power transmitter.

Fourth, long-term exposure of a human body to a strong radio wave potentially
has a risk of adverse health effect even if it is not proven by concrete
evidences. To prevent such a harmful effect, the regulatory bodies limit
specific absorption rate (SAR), which measures the absorption rate of the
radio wave by a human body. Strong electromagnetic fields at a focal point of
the microwave beam is very likely to give rise to a violation of the SAR
limit. Therefore, WPT and WIPT can then be designed and optimized to account
for such safety constraints, as in [82], and countermeasures could be
prepared. One option is to actively detect the presence of a human body by
using some external sensors such as vision, depth, and passive infrared (PIR)
sensors. Then, the transmitter can suppress a radio wave emission towards the
direction of the detected human body by completely turning off, steering a
beam away, or forming a null.

Fifth, more studies need to be conducted to reduce the power consumption and
device complexity by combining the RF communications and WPT. In the downlink,
the transmitter transfers power and data via the same radio wave by means of
the SWIPT technique. To that end, a modulated source signal is fed into the
phased antenna array to piggyback data on a power RF signal. Then, the sensor
device splits the receive power into the rectifier and the decoding circuits,
or simply detects the envelope of the receive signal for data decoding. In the
uplink, the sensor device can use backscatter communications that reflect the
incident wave to generate an uplink modulated signal. Backscatter
communications consume very small power since a sensor device does not have to
create an RF signal from its own energy. The interplay between closed-loop
WPT/SWIPT and backscatter communication (for both channel acquisition and data
transmission) need further investigation. However, short communication
distance and instability are the shortcomings that need to be overcome.

Sixth, the sensor device has a great impact on the power transfer efficiency
due to the polarization and antenna gain. If linearly-polarized (LP) antennas
are used, the mismatch in the polarization vectors of antennas deteriorates
the polarization loss factor, resulting in low power transfer efficiency. To
overcome this difficulty, circularly-polarized (CP) antennas are used or the
transmit antenna array with the ability of controlling a polarization vector
can be designed.

If a high gain antenna is used in the sensor device, it well receives the
radio wave only from a specific direction. On the other hand, a low gain
antenna such as a dipole antenna has a wide reception angle, but has a small
effective antenna aperture. A high flexibility at the sensor device should be
carefully taken into account to meet the application needs.

Moving to multiple antennas at the sensor, the experimental validation of the
benefits and drawbacks of closed-loop MIMO WPT with RF and DC combining
remains uncharted. Though RF combining appears appealing, loss may decrease
its efficiency.

Seventh, multiple distributed antennas can be deployed to extend the WPT
system coverage area. Sophisticated solutions are nevertheless needed to
establish a means to attain frequency and phase synchronization across
different antennas, and to adaptively control the phases of radio waves for
making sure they constructively interfere at a sensor device. Scaling up the
number of antennas, WPT DAS can leverage advances in joint transmission and
cell-free massive MIMO in communications.

Eighth, a proper channel model for the theoretical WPT studies should be
established based on the physical characteristics of RF WPT (i.e., physics-
based channel model). Typically, the required receive power for WPT is several
orders of magnitude higher than that for communications. This makes NLoS
deployment particularly challenging and maybe less practical for WPT.
Therefore, the random channel model that has been used for describing NLoS and
rich scattering environment may not be as useful in WPT as in communications
since the received power may be too low in such an environment. To achieve a
reasonable power transfer efficiency, LoS is needed to be secured and the
distance should not be too large. For multi-antenna WPT, the angular-domain
channel of the LoS path should be properly modeled so that the microwave beam
can be formed towards the receiver. Moreover, beam focusing is possible if the
transmitter and receiver are within the radiative near field. In the radiative
near-field region, the transmitted microwave beam can be focused onto the
receiver to enhance the power transfer efficiency, which is called beam
focusing. To describe this scenario, a radiative near-field channel model is
required [55]. Recently, the communications in mmWave or sub-THz frequencies
are actively studied. These high frequency channels have very similar
characteristics to the WPT channel, e.g., limited distance, dominance of LoS,
importance of beamforming, and consideration for the radiative near field.
Therefore, it is possible to use the channel model developed for mmWave or
sub-THz, for example, the clustered delay line (CDL) channel model of 3GPP.

It is hoped that the techniques, prototypes, and challenges presented here
will help inspire future research in this promising area and pave the way for
designing and implementing efficient WPT, WIPT, and wireless-powered systems
and networks in the future.

## References

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|  Bruno Clerckx (Fellow, IEEE) is a (Full) Professor, the Head of the
Wireless Communications and Signal Processing Lab, and the Deputy Head of the
Communications and Signal Processing Group, within the Electrical and
Electronic Engineering Department, Imperial College London, London, U.K. He
received the M.S. and Ph.D. degrees in Electrical Engineering from the
Université Catholique de Louvain, Louvain-la-Neuve, Belgium, in 2000 and 2005,
respectively. From 2006 to 2011, he was with Samsung Electronics, Suwon, South
Korea, where he actively contributed to 4G (3GPP LTE/LTE-A and IEEE 802.16m)
and acted as the Rapporteur for the 3GPP Coordinated Multi-Point (CoMP) Study
Item. Since 2011, he has been with Imperial College London, first as a
Lecturer from 2011 to 2015, Senior Lecturer from 2015 to 2017, Reader from
2017 to 2020, and now as a Full Professor. From 2014 to 2016, he also was an
Associate Professor with Korea University, South Korea, and from 2021 to 2022,
he is a visiting Professor at Seoul National University, South Korea. He also
held various long or short-term visiting research appointments at Stanford
University, EURECOM, National University of Singapore, The University of Hong
Kong, Princeton University, The University of Edinburgh, The University of New
South Wales, and Tsinghua University. He has authored two books on “MIMO
Wireless Communications” and “MIMO Wireless Networks”, 250 peer-reviewed
international research papers, and 150 standards contributions, and is the
inventor of 80 issued or pending patents among which 15 have been adopted in
the specifications of 4G standards and are used by billions of devices
worldwide. His research spans the general area of wireless communications and
signal processing for wireless networks. He has been a TPC member, a symposium
chair, or a TPC chair of many symposia on communication theory, signal
processing for communication and wireless communication for several leading
international IEEE conferences. He was an Elected Member of the IEEE Signal
Processing Society “Signal Processing for Communications and Networking”
(SPCOM) Technical Committee. He served as an Editor for the IEEE TRANSACTIONS
ON COMMUNICATIONS, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, and the
IEEE TRANSACTIONS ON SIGNAL PROCESSING. He has also been a (lead) guest editor
for special issues of the EURASIP Journal on Wireless Communications and
Networking, IEEE ACCESS, the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,
the IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, and the PROCEEDINGS
OF THE IEEE. He was an Editor for the 3GPP LTE-Advanced Standard Technical
Report on CoMP. He received the prestigious Blondel Medal 2021 for exceptional
work contributing to the progress of Science and Electrical and Electronic
Industries. He is a Fellow of the IEEE and an IEEE Communications Society
Distinguished Lecturer 2021-2022.
---|---
|  Junghoon Kim (Member, IEEE) received the B.Sc. degree in electronic and
electrical engineering from Hongik University, Seoul, South Korea, in 2008,
and the M.Sc. degree in telecommunications from University College London,
London, U.K., in 2015, and the Ph.D. degree in electrical and electronic
engineering from Imperial College London, London, U.K., in 2020. He is
currently a Postdoctoral Research Associate with Imperial College London. From
2008 to 2014, he was with Mobile Communication Division, Samsung Electronics,
Suwon, South Korea, as an R&D engineer. His current research interests include
RF energy harvesting, wireless information and power transfer, multiple-input
and multiple-output systems, and Internet-of-Things.
---|---
|  Kae Won Choi (Senior Member, IEEE) received the B.S. degree in Civil,
Urban, and Geosystem Engineering in 2001, and the M.S. and Ph.D. degrees in
Electrical Engineering and Computer Science in 2003 and 2007, respectively,
all from Seoul National University, Seoul, Korea. From 2008 to 2009, he was
with Telecommunication Business of Samsung Electronics Co., Ltd., Korea. From
2009 to 2010, he was a postdoctoral researcher in the Department of Electrical
and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada. From
2010 to 2016, he was an assistant professor in the Department of Computer
Science and Engineering, Seoul National University of Science and Technology,
Korea. In 2016, he joined the faculty at Sungkyunkwan University, Korea, where
he is currently an associate professor in the College of Information and
Communication Engineering. His research interests include RF energy transfer,
metasurface communication, visible light communication, cellular
communication, cognitive radio, and radio resource management. He has served
as an editor of IEEE Communications Surveys and Tutorials from 2014, an editor
of IEEE Wireless Communications Letters from 2015, an editor of IEEE
Transactions on Wireless Communications from 2017, and an editor of IEEE
Transactions on Cognitive Communications and Networking from 2019.
---|---
|  Dong In Kim (Fellow, IEEE) received the Ph.D. degree in electrical
engineering from the University of Southern California, Los Angeles, CA, USA,
in 1990. He was a Tenured Professor with the School of Engineering Science,
Simon Fraser University, Burnaby, BC, Canada. Since 2007, he has been an SKKU-
Fellowship Professor with the College of Information and Communication
Engineering, Sungkyunkwan University (SKKU), Suwon, South Korea. He is a
Fellow of the Korean Academy of Science and Technology and a Member of the
National Academy of Engineering of Korea. He has been a first recipient of the
NRF of Korea Engineering Research Center in Wireless Communications for RF
Energy Harvesting since 2014. He has been listed as a 2020 Highly Cited
Researcher by Clarivate Analytics. From 2001 to 2020, he served as an editor
and an editor at large of Wireless Communications I for the IEEE TRANSACTIONS
ON COMMUNICATIONS. From 2002 to 2011, he also served as an editor and a
Founding Area Editor of Cross-Layer Design and Optimization for the IEEE
TRANSACTIONS ON WIRELESS COMMUNICATIONS. From 2008 to 2011, he served as the
Co-Editor-in-Chief for the IEEE/KICS JOURNAL OF COMMUNICATIONS AND NETWORKS.
He served as the Founding Editor-in-Chief for the IEEE WIRELESS COMMUNICATIONS
LETTERS, from 2012 to 2015. He was selected the 2019 recipient of the IEEE
Communications Society Joseph LoCicero Award for Exemplary Service to
Publications. He is the General Chair for IEEE ICC 2022 in Seoul.
---|---