# Latency of Concatenating Unlicensed LPWAN with Cellular IoT: An Experimental
QoE Study

Alvin Ramoutar, Zohreh Motamedi and Mouhamed Abdulla
School of Electrical Engineering, Faculty of Applied Science and Tech.
Sheridan Institute of Technology, Toronto, Ontario, Canada
Email: {ramoutal, motamedz<EMAIL_ADDRESS>
###### Abstract

Developing low-power wide-area network (LPWAN) solutions that are efficient to
adopt, deploy and maintain are vital for smart cities. The poor quality-of-
service of unlicensed LPWAN, and the high service cost of LTE-M/NB-IoT are key
disadvantages of these technologies. Concatenating unlicensed with licensed
LPWANs can overcome these limitations and harness their benefits. However, a
concatenated LPWAN architecture will inevitably result in excess latency which
may impact users’ quality-of-experience (QoE). To evaluate the real-life
feasibility of this system, we first propose a concatenated LPWAN architecture
and experimentally measure the statistics of end-to-end (E2E) latencies. The
concatenated delay margin is determined by benchmarking the latencies with
different LPWAN architecture schemes, namely with unlicensed IoT (standalone
LoRa), cellular IoT (standalone LTE-M), and concatenated IoT (LoRa interfaced
with LTE-M). Through extensive experimental measurement campaigns of $30,000$
data points of E2E latencies, we show that the excess delay due to LPWAN
interfacing introduces on average less than $300$ milliseconds. The proof-of-
concept results suggest that the latency for concatenating unlicensed LPWAN
with cellular IoT is negligible for smart city use cases where human
perception and decision making is in the loop.

###### Index Terms:

LPWAN, Cellular IoT, Latency, QoE, Smart Cities.

##  I Introduction

IoT applications for enhanced and massive machine type communications
(eMTC/mMTC) is growing at an unprecedented rate, empowering connectivity in
various fields such as healthcare, agriculture, climate and smart city
applications. To support communications for various IoT use cases, low-power
wide-area network (LPWAN) technologies are used where appropriate to transmit
small payloads at long distances with minimal power consumption.

Figure 1: Application of system concatenation for smart cities with
intelligent parking using unlicensed LPWAN backhauled via cellular IoT uplink.

Traditional LPWAN, such as LoRa/LoRaWAN and Sigfox, operate in unlicensed
radio spectrum. While freely available on ISM bands, unlicensed IoT is prone
to RF interference and poor quality-of-service (QoS). On the other hand,
licensed IoT offers a more reliable communication as it depends on cellular
infrastructure deployed with careful network planning. As a consequence, the
industry is complementing the IoT ecosystem with licensed LPWAN for eMTC and
mMTC applications. Today, this is done through the use of LTE-M and NB-IoT
technologies defined by 3GPP rel. 13-14 (4G), and rel. 15-16+ (5G). Granted,
licensed IoT will require regular subscription for each sensor node with a
mobile network operator, and this is a costly solution for large-scale smart
city deployment.

To overcome these limitations, we propose a concatenated network architecture
that harnesses the advantages of both unlicensed and licensed LPWAN. Consider
the smart parking application shown in Fig. 1, where large or massively
deployed unlicensed IoT sensors detect status changes in parking spaces and
backhauls aggregated data via a number of cellular IoT nodes to the cloud for
user access. Although this concatenated LPWAN architecture combines
affordability and reliability together, the main drawback is the added latency
due to interfacing and data hopping of information packets.

In literature, various contributions have studied the throughput, range, and
power of unlicensed (e.g., [1, 2, 3]) and licensed IoT (e.g., [4, 5, 6]).
Furthermore, a monitoring system was tested by combining NB-IoT and LoRa [7],
and a hybrid 3G-LoRa-Sigfox for power grid monitoring was verified with legacy
technologies [8]. While these works provide valuable insights, a proof-of-
concept (PoC) and quality of experience (QoE) assessment with end-to-end (E2E)
latency measurement for concatenated LPWAN architecture is yet to be explored.

In this paper, we propose a concatenated network architecture and protocols
with unlicensed LPWAN and cellular IoT over a private core infrastructure. Due
to the availability of 3GPP LTE Cat M1 service by local mobile operators, we
implement the architecture with LoRa and LTE-M networks. Through E2E latency
measurement campaigns, $30,000$ data points are experimentally collected and
statistically analyzed for standalone and concatenated LPWAN architectures
[9]. Data-driven discussions and remarks on the feasibility of a concatenated
LPWAN architecture to achieve a target QoE for smart city applications with
users in the loop is also provided.

##  II Network Architecture

The E2E architecture from in-field sensing to remote detection is based on
three major steps: (i) uplink communications, (ii) cloud and core
infrastructure, and (iii) mobile end-user application. Our proposed
concatenated LPWAN architecture with different possible IoT technology choices
is shown in Fig. 2. As seen first, information packets from large or massive
amount of sensor nodes are aggregated by fewer IoT gateways. Then, the
aggregated data from gateways is relayed to cellular IoT nodes for uplink
communication to a mobile carrier network. The data from packets is then
processed, stored, and made available to mobile clients from the core
infrastructure residing in either a public or private cloud. An explanation of
the various sub-components of this concatenated architecture is provided
below.

###  II-A Uplink Communications

Starting with IoT sensor nodes, this subsection covers communications up to
the public cloud.

####  1 Data aggregation of IoT sensors

Payload construction by a sensor IoT node begins after new sensing data is
detected and produced. The payload is then split into byte segments and
transmitted over radio on unlicensed spectrum via LoRa systems. Developed by
Semtech, LoRa is a physical (PHY) and data link (MAC) layers protocol
utilizing chirp spread spectrum modulation to transmit between $0.3$ and $50$
kbps over large distances with minimal power consumption. In North America,
LoRa operates on the unlicensed $902$ to $928$ MHz ISM frequency band. Often
paired with a LoRa system is LoRaWAN, a network layer protocol used to route
data from LoRa nodes to a gateway and then to the internet. From end-user
device to network server and at the application level, LoRaWAN uses two layers
of 128 bits AES encryption [10].

####  2 Gateway to cellular IoT communication

Once the transmitted sensor payloads are received by an unlicensed gateway,
they are first extracted from the LoRa protocol and then sent via a serial
protocol to a licensed cellular IoT radio within the same device package. At
this same point, the payload is wrapped in a lightweight messaging protocol
such as MQTT in preparation for IP routing.

####  3 Transmission from cellular IoT to mobile carrier

This communication serves as the backhaul, forwarding payload via licensed
cellular IoT. LTE Cat M1 or NB-IoT devices will then uplink to nearby eNB or
gNB cell towers to connect to the rest of the mobile carrier network. The
concatenated architecture of Fig. 2 is compatible and it can be adapted with
both LTE-M and NB-IoT. In reality, the regional availability of cellular IoT
by mobile operators will dictate which of these licensed LPWAN options is
accessible by users. In general, NB-IoT service is widely available in Asia
and Europe. Currently in North America, LTE-M service is more common, and NB-
IoT is still in its early stages. Developed by 3GPP rel. 13+ for IoT
applications, LTE-M operates on closed network servers and on several licensed
frequencies (e.g., bands 2, 4, 5, 12 and 13 in Canada). This technology uses
time division duplex and a peak data rate of 1 Mbps for uplink and downlink
with $1.4$ MHz bandwidth. Since each cellular IoT device requires a SIM card
and service contract, large-scale implementation of LTE-M is expensive. The
proposed concatenated architecture alleviates the need for a costly deployment
of large or massive volume of cellular IoT nodes through system interfacing
with unlicensed LPWAN sensors.

####  4 Communication from evolved packet core to cloud

The IP uplink is made possible by the service provider which routes data from
the mobile carrier network through wireline comprising of hybrid coaxial
fiber. Eventually, data packets reaching the evolved packet core are forwarded
to the cloud for computation and transmission.

Figure 2: Proposed E2E concatenated LPWAN network architecture with unlicensed
IoT (LoRa), cellular IoT (LTE-M or NB-IoT) and a private core infrastructure.

###  II-B Cloud and Core Infrastructure

IoT sensor payloads are transferred through the internet to the core
infrastructure for processing.

####  5 TCP/IP routing to core infrastructure

The communication involves routing from the carrier network through IP
communication to a broker hosted by a cloud infrastructure. This architecture
identifies IoT sensor nodes and gateway technology as part of the private
cloud receiving MQTT payloads from concentrated LoRa traffic. A private core
infrastructure could be substituted by a public cloud (e.g., Azure or AWS
IoT). Rather than involved elaborate setups, public cloud solutions facilitate
insights into the analytics of sensor payloads. For instance, Azure Monitor
and AWS Cloud Watch both enable resource metric and telemetry collection while
visualizations are generated by Microsoft Power BI and AWS Quicksight.
Although developers may invest effort into implementing these services for
robust security, cloud native IoT platforms deliver them automatically as pay-
per-use subscriptions which often scale quickly [11]. The cost and offering
implications make public clouds viable for corporate IoT roll-out with private
clouds more suitable and secure for testing and research.

####  6 Delivering data from message broker to core service

To address high traffic from large-scale IoT sensors, MQTT messages are
ingress by a broker such as Eclipse Mosquitto. Similar to publisher/subscriber
paradigms, the broker delivers sensor payload to the core service via a
subscribed channel/topic. The core service is an application that serves three
main objectives: business logic processing, data access layer (DAL), and
application programming interface (API). They all can be decoupled for a
service-oriented architecture.

####  7 Storing sensor information in core service database

The nature of IoT oftentimes results in unstructured data, which is best
suited for NoSQL data stores that can leverage a variety of data models from
tables to documents. The key benefit of going with document-based database
models would be alignment with common and modern web formats and DALs. One
such technology that achieves this is MongoDB, where documents are stored in a
superset of JSON known as BSON.

###  II-C Mobile Application and Core Service

The consumption of IoT sensor data by clients is identified in this final
subsection of the architecture.

####  8 Mobile client request

In this concatenated LPWAN network architecture, the user equipment (UE)
performs an action requesting data over Hypertext Transfer Protocol (HTTP).
This request is sent through the UE’s connected network, eventually reaching
the internet. Once it reaches the core services, the request is routed to the
core service API.

####  9 Core service response

The core service follows the representational state transfer (REST)
architecture for web service communications. RESTful APIs are ideal over
simple object access protocol (SOAP) and others since it not only provides
clear separation between data producers and consumers, but it is also data
format agnostic. This enables developers to create highly compatible APIs to
consume and deliver a variety of IoT sensor data with minimal coupling to UE’s
application. While REST is modern, it is unsuitable and often unnecessary for
certain applications. For instance, when a core service must constantly stream
data to a client or vice-versa, a persistent bi-directional communication
channel should be established. WebSocket is one protocol that serves this
purpose, creating a TCP duplex connection that enables message pooling without
the need to wait for a response like HTTP [12].

##  III Experimental Setup and Methodology

Figure 3: Trace of E2E latency measurement of data from sensing to UE’s
application passing across the different OSI layers of the network
architecture.

As a critical key performance indicator (KPI) for QoE assessment, we
experimentally evaluate a precise E2E latency for the concatenated LPWAN
architecture with LoRa and LTE-M networks. Using the architecture detailed in
Sec. II, we divide the E2E latency $T_{{\rm E2E}}$ into several components
based on where we have measurable insight with data entry and exit of
architecture subsystems to capture timing information. These components are
defined as follows:

  * •

$T_{{\rm UL}}$: uplink communication latency of IoT sensor payload to the core
infrastructure (Fig. 2, links 1 to 7).

  * •

$T_{{\rm Q}}$: queuing delay in the core service database before client
request (Fig. 2, core infrastructure).

  * •

$T_{{\rm DL}}$: mobile client request and resulting core service downlink
response latency (Fig. 2, links 8 and 9).

  * •

$T_{{\rm REND}}$: internal latency for graphical user interface (GUI)
rendering at the UE (Fig. 2, client’s application).

For further clarification, the time measures are also shown in Fig. 3 as the
sensing packets pass across different OSI layers and network components of the
architecture. The resultant E2E latency is represented as the sum of the time
measures; namely

$\displaystyle T_{{\rm E2E}}=T_{{\rm UL}}+T_{{\rm Q}}+T_{{\rm DL}}+T_{{\rm
REND}}\text{ .}$ (1)

The experimental setup that implements the proposed concatenated LPWAN
architecture is detailed in Fig. 4, where the key specifications for the
communication system and network equipment considered for the data collection
campaign are listed in Table I. The PoC experiment was conducted in an outdoor
parking lot in the suburbs of the Greater Toronto Area using the smart parking
LPWAN sensor node shown in Fig. 5. This particular sensor is intended for
efficient deployment and use at the center of a 2-by-2 parking lot
configuration. Contained within this integrated unit is a TTGO LoRa32
microcontroller that processes data from four MB1232 ultrasonic sensors. We
designed the sensor with openings on the top-side of the casing where the
angles of the port holes was determined based on North American parking lot
dimensions with each ultrasonic sensor pointing towards the center of a
parking spot.

During initialization, the LPWAN sensor node with TTGO ESP32 LoRa development
board establishes a $2.4$ GHz radio link connectivity once over IEEE 802.11n.
Time is synchronized via network time protocol (NTP) server before
disconnecting. LoRa packets of $28$ bytes are then built with a $2$ bytes
label, 10 bytes Unix timestamp, 15 bytes static padding for sensor data
fields, including device identification and token-based authentication (auth
token), and finally with a null terminator byte to indicate the end of the
packet. Timing for $T_{{\rm UL}}$ begins immediately once a new data packet is
transmitted by a LoRa sensor node. To gather a large sample size of latency
measurements, the process is repeated every 500 ms, with data flowing at a
rate of $28\times 8/500\text{ ms}=0.448\text{ kps}$.

Another TTGO ESP32 development board is used as a LoRa gateway that scans for
a payload of 28 bytes and validates its integrity against a 2 bytes label.
Once validated, the payload is sent serially to the MKR 1500 which assembles
an MQTT UDP packet. The MKR transmits the packet via LTE-M through Bell
Canada’s network to its final destination at the core infrastructure host that
runs the Eclipse Mosquitto broker. Subscribed to this channel/topic is a
custom lightweight service agent MQTT2HTTP forwarding to the core service API.
Measurement of $T_{{\rm UL}}$ concludes when the payload is received at the
core service, its timestamp difference calculated, and a persistent entry
written to MongoDB database.

Figure 4: Experimental setup for data collection of E2E latency for the
concatenated LPWAN network architecture.  TABLE I: Specifications of
communication system and network components used for empirical measurements

hardware equipment | CPU/MPU | storage | radio access
---|---|---|---
TTGO LoRa32 | ESP32 |  $520$ kB |  $915$ MHz, $150$ Mbps
(LoRa/LoRaWAN) | DOWDQ6 | SRAM |  $20$ dBm (Tx), $-148$ dBm (Rx)
MKR NB 1500 | SAMD21 |  $256$ kB | Bands 4, 5, 12, $375$ kbps (UL)
(LTE Cat M1) | Cortex | SRAM |  $23$ dBm (Tx), $-105$ dBm (Rx)
HPE ProLiant DL380 G5 | Intel Xeon |  $40$ GB disk | Broadcom NC373i
(core infrastructure) | E5440 |  $4$ GB RAM | Gigabit server adapter
Samsung Galaxy S7 | Exynos 8890 |  $32$ GB flash | GSM/HSPA/LTE
(mobile client) | Octa SoC |  $4$ GB RAM | IEEE 802.11n, 2.4/5 GHz

Meanwhile, the core infrastructure host is a Windows Server virtual machine
(VM). This VM runs on as ESXi 5.5 hypervisor installed bare-metal onto an HP
Proliant DL380 G5 rack-mount server. Key software running on this VM are
MongoDB (v4.2.3), Internet Information Services (v10.0), Eclipse Mosquitto
(v1.6.11), and MQTT2HTTP (v0.1). The UE is a Samsung Galaxy S7 G930W8 running
the latest supported build of Android 8.0 Oreo with TouchWiz GUI.

Continuing to $T_{{\rm DL}}$, a GET method is written for the core service API
which responds with a 28 bytes JSON payload. This method is invoked via
barebones flutter application running on the client timing request until core
service response. Finally, the measurement of $T_{{\rm REND}}$ is obtained as
time taken to render a data-driven GUI component on the mobile application. We
designed the mobile app to display the availability of parking spaces (see
Fig. 1) in a specific lot of Sheridan’s Davis campus that features 183 spots.
The application redraws equiangular polygons in Flutter Maps onto a MapBox
PolygonLayer on the client UE’s GUI to illustrate the parking availability and
information.

Overall, the latency measurements were collected during business hours, i.e.,
9:00 to 17:00 on weekdays, over a period of two weeks. For benchmarking
purposes, the experiment was repeated twice more with similar parameters for
standalone LoRa connected through WLAN to the internet service provider, and
LTE-M through Bell’s cellular network.

Figure 5: Smart parking LPWAN sensor with four MaxBotix ultrasonic narrow beam
sensor module with up to 40 Hz read rate, and a TTGO LoRa32 microcontroller
with a 2 dBi omnidirectional antenna operating at 915 MHz.

(a) Unlicensed IoT: standalone LoRa  (b) Cellular IoT: standalone LTE-M  (c)
Concatenated IoT: LoRa interfaced with LTE-M

Figure 6: Probability density function of E2E latency based on $n_{{\rm
s}}=10,000$ experimental data points for each LPWAN network architecture
scheme.

##  IV Experimental Results and Analysis

In order to yield reliable statistics, in excess of $30,000$ E2E latency
measurements are experimentally collected for the standalone and concatenated
LPWAN architecture schemes. Using the dataset that is openly available in [9],
and examining the order of magnitude of the time measures in (1), we notice
that $T_{{\rm UL}}\negthinspace\gtrapprox\negthinspace T_{{\rm
DL}}\negthinspace\thickapprox\negthinspace T_{{\rm
REND}}\negthinspace\gg\negthinspace T_{{\rm Q}}$. The probability density
function (PDF) of the aggregated E2E latency $T_{{\rm E2E}}$ for unlicensed
IoT (LoRa), cellular IoT (LTE-M), and concatenated LPWAN (LoRA interfaced with
LTE-M) are respectively plotted in Fig. 6. The $\hat{f}\left(T_{{\rm
E2E}}\right)$ histogram plots are obtained with a statistically significant
sample size of $n_{{\rm S}}=10,000$ data points for each LPWAN scheme, and
$n_{{\rm B}}=150$ bins is considered for distribution accuracy (see blue
histogram bars in Fig. 6).

In addition, the empirical distributions of $T_{{\rm E2E}}$ are approximated
analytically using the kernel density estimation (KDE),

$\displaystyle\hat{f}_{{\rm kde}}\left(T_{{\rm E2E}}\right)=\frac{1}{n_{{\rm
S}}\thinspace h}\ \sum_{i=1}^{n_{{\rm S}}}K_{{\rm
g}}\negthinspace\negthinspace\left(\frac{T_{{\rm E2E}}-T_{i}}{h}\right)\ \ \ \
\ h>0$ (2)

where a Gaussian kernel function $K_{{\rm
g}}\left(t\right)=e^{-t^{2}/2}/\sqrt{2\pi}$ is used (see red curves in Fig.
6). The bandwidth (BW) of KDE is determined using Silverman’s rule, i.e.,
$h\simeq\hat{\sigma}_{{\rm T}}^{\prime}\sqrt[5]{4/3n_{{\rm s}}}$, where
$\hat{\sigma}_{{\rm
T}}^{\prime}=med\left(\left\\{\left|T_{i}-med\left(\left\\{T_{i}\right\\}\right)\right|\right\\}\right)/0.6745$
is the median absolute deviation (MAD), with $med\left(T\right)$ representing
the median of the finite set $T=\left\\{T_{i}\right\\}$, $i=1,2,\ldots,n_{{\rm
S}}$ for E2E latency measurements. MAD is a variation metric that provides a
more robust estimation for the standard deviation (SD) through greater
resiliency to outliers and extreme values within the dataset. As evident in
Fig. 6, the KDE closely match the experimental plots for the three LPWAN
architecture schemes, where $\widetilde{\sigma}_{{\rm T}}$ is the SD for the
smooth KDE curves.

The KDE can be used to analytically characterize the randomness of the
underlying E2E experimental latencies, which is paramount in predicting and
measuring end-users’ QoE. A larger sample size of latency measurements from
PoC experiments will certainly yield a more robust analytical predictor that
can be used to randomly generate reliable E2E latencies for performance
evaluation of networks.

The statistics and estimation parameters from the density plots are shown in
Table II, where the sample mean and SD (see vertical lines in Fig. 6) are
accordingly evaluated by

$\displaystyle\hat{\mu}_{{\rm T}}=\frac{1}{n_{{\rm
s}}}{\displaystyle\sum_{i=1}^{n_{{\rm s}}}T_{i}}\text{
;}\thinspace\thinspace\thinspace\thinspace\thinspace\thinspace\thinspace\hat{\sigma}_{{\rm
T}}=\sqrt{\frac{1}{n_{{\rm s}}-1}{\displaystyle\sum_{i=1}^{n_{{\rm
s}}}\left|T_{i}-\hat{\mu}_{{\rm T}}\right|^{2}}}\text{ .}$ (3)

From the results, we observe that the concatenated LPWAN architecture has an
excess latency $\Delta\hat{\mu}_{{\rm T}}$ that is on average $284$ ms more
than the standalone cellular IoT with LTE-M communications. In fact, the
excess delay was expected as a consequence of interfacing unlicensed LPWAN
with cellular IoT, as this introduces more data transmission hops on the path
to the core service. Although the comparison of the concatenated scheme to
cellular IoT is more relevant, it is still worthwhile to notice that the
excess latency with LoRa over WLAN is nearly double the average value with
LTE-M.

TABLE II: Statistics and density estimation of empirical E2E latencies

LPWAN | mean | SD | MAD | KDE BW | SD of KDE
---|---|---|---|---|---
schemes |  $\hat{\mu}_{{\rm T}}$ (s) |  $\hat{\sigma}_{{\rm T}}$ (s) |  $\hat{\sigma}_{{\rm T}}^{\prime}$ (s) | $h$ |  $\widetilde{\sigma}_{{\rm T}}$ (s)
LoRa/LoRaWAN | $2.5789$ | $1.2051$ | $0.4321$ | $0.0725$ | $1.2072$
3GPP LTE Cat M1 | $2.9000$ | $0.5571$ | $0.4221$ | $0.0709$ | $0.5616$
LoRa + LTE-M | $3.1836$ | $0.5079$ | $0.3831$ | $0.0643$ | $0.5119$

Moreover, it is interesting to remark that the spread of LPWAN schemes with
cellular IoT is approximately half that of unlicensed IoT with LoRa
technology. This essentially means that E2E latencies with cellular IoT,
irrespective of being standalone or concatenated, have lower entropy. In other
words, these LPWAN networks that are dependent on mobile operators have
$T_{{\rm E2E}}$ values that are more predictable.

The shape of the E2E latency PDFs in Fig. 6 are also unique from one LPWAN
network to the other. In essence, this gives us a signature for the latency
profile of each LPWAN architecture. In particular, unlicensed IoT exhibits a
long-tailed distribution that is positively skewed with a left-leaning curve.
On the other hand, cellular IoT and concatenated LPWAN have E2E latency
distributions that are more symmetrical, where the former is more dispersed
than the latter.

To assess the feasibility of an LPWAN architecture to meet a certain target
QoE, it is insightful to also look at the cumulative distribution function
(CDF) of the particular KPI under study. As plotted in Fig. 7 for the three
LPWAN schemes, the CDF is determined by $\hat{F}\left(T_{{\rm
E2E}}\right)\negthinspace\negthinspace=\negthinspace\negthinspace\intop_{-\infty}^{T_{{\rm
E2E}}}\hat{f}\left(\tau\right)\thinspace{\rm d\tau}$. The E2E latency
probability $\negthinspace\mathcal{P}_{T}\left(\cdot\right)\negthinspace$ that
LPWAN sensors data is received at the application layer of an edge user from
the cloud can be used to assess the QoE performance. This can be determined
from the CDF, i.e., $\mathcal{P}_{T}\negthinspace\left(\tau_{{\rm
target}}\right)\negthinspace=\negthinspace\Pr\left(T\leq\tau_{{\rm
target}}\right)\negthinspace=\negthinspace\hat{F}\negthinspace\left(\tau_{{\rm
target}}\right)$, where
$T\negthinspace\negthinspace\sim\negthinspace\negthinspace\hat{f}\left(T_{{\rm
E2E}}\right)$ is the random variable for latency and $\tau_{{\rm target}}$ is
the stipulated E2E target delay.

Meanwhile, we notice that the CDF plots of KDE (see square marked plots in
Fig. 7) almost perfectly overlap the curves from experimental measurements.
From the plots, we also identify intersection points that help us in
distinguishing the different regimes of the probability distributions of E2E
latency for the LPWAN architectures. These values are:
$\mathbf{P}_{1}\negthinspace\negthinspace:\negthinspace\hat{F}\left(T_{{\rm
E2E}}=3.391\right)=0.8961$;
$\mathbf{P}_{2}\negthinspace:\negthinspace\hat{F}\left(T_{{\rm
E2E}}\negthinspace=\negthinspace 3.571\right)\negthinspace=\negthinspace
0.9063$; and $\mathbf{P}_{3}\negthinspace:\negthinspace\hat{F}\left(T_{{\rm
E2E}}\negthinspace=\negthinspace 3.998\right)\negthinspace=\negthinspace
0.9855$. This means that if $\tau_{{\rm
target}}\negthinspace\apprle\negthinspace 3.4$ s, unlicensed LPWAN outperforms
cellular IoT. For example, if a $3$ s E2E latency is accepted, LoRa surpasses
with nearly $\negthinspace\mathcal{P}_{T}\negthinspace\left(\tau_{{\rm
target}}\simeq 3\right)\negthinspace\simeq\negthinspace 88\%\negthinspace$
likelihood of meeting the latency target, while standalone LTE-M and
concatenated LPWAN achieve $63\%$ and $36\%$ respectively. On the other hand,
if for certain smart city use cases an extra second is tolerated, then, LTE-M
and concatenated LPWAN outperform standalone LoRa by a factor of $6.4\%$. In
this situation, LTE-M and concatenated LPWAN both achieve the same latency
performance of $99\%$, irrespective of excess latency. However, the minimum
QoE threshold for user satisfaction should generally aim to satisfy a
performance of $\negthinspace\mathcal{P}\left(T_{{\rm E2E}}\right)\geq 0.95$
for real-life applications (see horizontal line in Fig. 7).

Figure 7: Empirical CDF of E2E latency for standalone and concatenated IoT.

##  V Conclusion

In this paper, we proposed a concatenated LPWAN architecture over a private
core infrastructure that interfaces LoRa with cellular IoT in order to
mitigate poor QoS and costly service plans. Through precise QoE assessment,
E2E latency measurements were experimentally recorded for the concatenated
architecture, and the data was compared to standalone licensed and unlicensed
LPWANs. The statistics from the density functions reveal that the proposed
concatenated LPWAN added, on average, an excess latency of $23.5\%$ and
$9.8\%$ when compared to standalone LoRa and LTE-M. Nevertheless, such
milliseconds of E2E excess latency is humanly insignificant for use cases
where perception is needed. More importantly, we also found that concatenated
LPWAN outperforms unlicensed IoT by roughly $1.5$ s at the typical QoE
threshold of $95\%$ for users’ satisfaction. Overall, this experimental study
suggests that a concatenated LPWAN is technically feasible and offers an
affordable alternative for real-world smart city deployment.

## Acknowledgments

This research work is supported, in part, by Sheridan’s Research and Creative
Activities Growth Grant, and by Bell Canada’s IoT Solutions for eMTC (3GPP LTE
Cat M1) network access and services. The authors are also grateful to
ENCQOR-5G program for testbed access. They also would like to acknowledge
Keysight Technologies for research discussions regarding implementation and
measurements.

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  * [6] A. I. Sulyman, T. J. Montano, and J. E. Post, “Experimental data on connecting proprietary IoT systems to cellular networks,” in _Proc. of IEEE Intl. Conference on Communications Workshops (ICC)_ , 2019.
  * [7] X. Zhang, M. Zhang, F. Meng, Y. Qiao, S. Xu, and S. Hour, “A low-power wide-area network information monitoring system by combining NB-IoT and LoRa,” _IEEE Internet of Things Journal_ , vol. 6, no. 1, pp. 590–598, 2019.
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Retrodirective Antenna Array Approach to Achieve Maximum Theoretical Beam Efficiency in Microwave Wireless Power Transfer

Charleston Dale M. Ambatali, Member, IEEE, Shinichi Nakasuka,
Bo Yang, Member, IEEE, and Naoki Shinohara, Senior Member, IEEE

Manuscript received September 22, 2023. This work is supported in part by the Intelligent Space Systems Laboratory (ISSL), Department of Aeronautics and Astronautics, The University of Tokyo, and in part by Hitachi, Ltd., Japan. (Corresponding author: Charleston Dale M. Ambatali.)

C. D. M. Ambatali and S. Nakasuka are with the Department of Aeronautics and Astronautics, The University of Tokyo, Hongo, Bunkyo 113-0033, Japan (e-mail<EMAIL_ADDRESS>nakasuka@space.t.u-tokyo.ac.jp).

B. Yang and N. Shinohara are with the Research Institute for Sustainable Humanosphere, Kyoto University, Uji 611-0011, Japan (e-mail<EMAIL_ADDRESS>shino@rish.kyoto-u.ac.jp).

Journal of  Class Files, Vol. 14, No. 8, August 2021
Shell et al.: A Sample Article Using IEEEtran.cls for IEEE Journals

0000–0000/00$00.00  2023 IEEE

Efficient long range wireless power transfer (WPT) is realized if the distance between the source and receiver is less than the Fraunhoffer distance.
This distance increases proportionally to the square root of the antenna size so to achieve efficient long range WPT, larger antennas are mandatory, but that comes with difficulty in implementing both the feeding network and beamforming control of the antenna.
Several proposed implementations require power-hungry processors rendering implementation impractical.
An alternative to reduce usage of digital processing is in the form of retrodirective antenna arrays.
Its core operation is to track an incoming signal's direction of arrival and resend it to the same direction.
This can be implemented by analog circuits.
Retrodirective capability on both the generator and rectenna arrays creates a feedback loop that produces a high efficiency WPT channel.
In this paper, we characterize the dynamics of this phenomenon using a discrete-time state-space model based on S-parameters and show that the system can naturally achieve maximum theoretical WPT efficiency.
We further confirmed the theoretical analysis through a hardware experiment using a 12-port circuit board with measurable S-parameters mimicking a deterministic wireless channel.
The results of the hardware experiment show agreement with the proposed theoretical framework.

Wireless power transfer, dynamic beam focusing, retrodirective antenna arrays, space-based solar power, radiative near-field

§ INTRODUCTION

Propagation of electromagnetic (EM) waves can be divided into three different regions depending on the distance from the signal source demarcated by the Fresnel limit at distance $d_1$ and Fraunhoffer distance at distance $d_2$.
Let $\lambda$ be the wavelength of operation which is related to the wave frequency, $f$, and the speed of light in free space, $c$, by $c=\lambda f$.
If $D$ is the antenna diameter, then <ref> is used to determine the Fresnel limit and Fraunhoffer distance <cit.>.

\begin{equation}
\label{eq:propagation-demarcation}
\end{equation}

The region $d<d_1$ is also known as the reactive near-field region, where the wireless power transfer (WPT) is dominated by inductive and/or capacitive coupling and can be modelled by lumped elements <cit.>.

The region $d>d_2$ is the far-field region where the behavior of the EM wave is modelled by a plane wave.
WPT in this region is inefficient due to the inverse distance squared power loss.

The region between the two demarcations, $d_1\leq d\leq d_2$, is the radiative near-field region, or the Fresnel zone.
It is in this region where the EM wave is spherical and that it imposes an amplitude and phase distribution from the source to a planar receiver.
Conversely, a proper amplitude and phase distribution on the wave source can focus its beam on a planar receiver with minimal power lost to free space.
Thus, operation in this region is widely considered as the means towards an efficient long distance WPT system <cit.>.

Antenna size needed (m) vs. distance (km) for $5.8\;GHz$ where the blue line is the Fraunhoffer distance and the shaded region is the valid antenna sizes given the distance.

Figure <ref> shows the antenna size required to maintain radiative near-field operation in relation to the distance between the power generator (source) and the rectenna (receiver) for a frequency of operation equal to $5.8\;GHz$.
In the scale of space-based solar power (SBSP) from geostationary orbit ($\thicksim$36,000 $km$ distance), a minimum antenna length of $1\;km$ is needed to be in the radiative near-field <cit.>.
Using a radiation pattern based approach to compute wireless power transfer efficiency (WPTE) <cit.>, we estimate that a $2.5\;km\times2.5\;km$ antenna array in orbit can focus a beam to a $5\;km$ diameter on the ground for a high beam efficiency <cit.>.
For a spacing of half a wavelength between antenna elements, this corresponds to approximately 10 billion antennas.

Beam control to track a target receiver in the SBSP scale is a herculean task.
One approach is to find a phase distribution setting that maximizes the power received by the rectenna <cit.>.
In this, the receiving unit (RU) sends telemetry data to the generating unit (GU) that includes the power it is receiving.
The GU then adjusts its antenna array phase distribution taking into account the data sent back by the RU over time through an optimization algorithm (e.g., gradient-descent algorithm).
Even if the location of the RU is unknown at any given time, the GU can correct itself to find the maximum beam setting towards the RU.
The amount of computational power needed in this method on an SBSP scale is impractical for implementation.
An approach which has reduced dependence on computation power requires the use of position tracking.
Examples of tracking methods include the use of satellite positioning, radio/light detection and ranging, radio signal location, acoustic localization, or optical positioning.
By knowing the location, the appropriate phase on each antenna element can be calculated without the need for optimization algorithms <cit.>.
Sensor fusion can increase the precision of tracking <cit.> but this comes at the need for more processing power.

The use of retrodirective antennas can circumvent the need for powerful processors.
Also called a self-phased array <cit.>, a retrodirective antenna array is connected to a circuit that enables the antenna to automatically resend an incoming signal to its direction of arrival.
This is visualized in figure <ref> where an incoming plane wave with reference phase $\phi_{ref}$ is at a distance $L_i$ from the $i^{th}$ element in an array.

Retrodirective operation is achieved if the return phase $\phi_{ret}=\phi_{ref}$.

Without loss of generality, we set the reference plane to have a phase of $\phi_{ref}=0$.
It follows that $\phi_{out}=-\phi_{in}=-2\pi fL_i/c$, thus indicating that at each antenna element, the received phase must be conjugated to perform retrodirective operation.

[very thick]
(-1,0) node[antenna]
(1,0) node[antenna]
(-3,0) node[antenna]
(3,0) node[antenna]
(-3.5,4.5) – (3.5,5.5)

(-0.75,2.5) node[]$\phi_{in}$
(0.75,2.5) node[]$\phi_{out}$
(-1,4.55) node[]$\phi_{ref}$
(0.375,4.75) node[]$\phi_{ret}$
(-0.425,3.7) node[label=left:$L_i$]
[-latex, thick, dashed] (-0.595,4.915) – (-0.25,2.5);
[latex-, thick, dashed] (-0.105,4.985) – (0.25,2.5);

Operation of a retrodirective antenna array <cit.>.

The downside of retrodirective antennas is the need for a pilot signal sent by the RU for the GU to track it which consumes energy that is supposed to supply the RU.
Despite this, the simplicity of implementation through the use of only analog circuitry makes it an attractive solution in the SBSP scale.
If the wireless channel between GU and RU is known, then high efficiency WPT can be achieved with the correct pilot signal beam design <cit.>.
Dynamic channel conditions predicate the need for estimation techniques similar to what is used by multi-input multi-output communication systems to increase channel capacity <cit.>.
Like previously mentioned approaches, this estimation effort also has increased complexity at large scales.

The need for estimation techniques is removed by implementing the retrodirective operation on both the GU and RU sides <cit.>.
This is called the both-sides retrodirective antenna array (BS-RDAA).

The result of its sustained operation is a high efficiency beam between the antenna arrays.
It has been demonstrated in simulation that the aforementioned system can track changes between GU and RU.
Currently, understanding of the dynamics of the system is limited to infinitely large antenna arrays on both sides.
This may not be the case for a finite array size and this is needed to know the limits of the system and how it behaves when changing conditions comes into play.

Therefore, it is imperative that further theoretical analysis in the general case and experimentation should be undertaken to understand the dynamics of BS-RDAA and its resulting steady-state efficiency.

For the rest of this paper, we characterize the BS-RDAA concept using the S-parameter model of WPT <cit.>, building a discrete-time state space model enabling eigenvector and eigenvalue analysis on the system.
Verification of the accuracy of this model through hardware experimentation is also discussed.
We start with defining the S-parameter model of WPT in <Ref> which is an emerging view of WPT that captures the behavior of EM waves in the Fresnel zone <cit.>.

<Ref> discusses the dynamics of the BS-RDAA concept whose behavior is explained by S-parameters
We also prove that it creates a power beam that can maintain high efficiency power transfer as predicted by the S-parameter model.
The hardware experiment is discussed in <Ref> where the channel model, measurement methodology, and analysis of data are also outlined.
The experiment is done on a circuit board with multiple ports where the S-parameters can be easily measured by a vector network analyzer.
Finally, <Ref> concludes this paper and lays out recommendation for further work to be undertaken to realize the BS-RDAA concept in practice.

§ RADIATIVE NEAR-FIELD WPT EFFICIENCY

§.§ Mathematical Notations

A scalar quantity is written in italic form, a column vector quantity is written in lower case bold font, and a matrix is written in upper case bold font.
For example, $a$ and $A$ are scalars, $\mathbf{a}$ is a column vector, and $\mathbf{A}$ is a matrix.
The notation $\{a_i\}$ indicates a column vector for a positive integer set defined by $i$ and $\{A_{ij}\}$ is a matrix with a column index $i$ and a row index $j$, both positive integers.
Since these are complex quantities, we then define $|a|$ and $\angle a$ as the magnitude and phase of $a$, respectively.

The transpose and Hermitian transpose operations of $\mathbf{a}$ are defined by $\mathbf{a}^T$ and $\mathbf{a}^H$, respectively, and these operations transform a column vector into a row vector and vice versa.
The per-element conjugation operation is defined by $\mathbf{\Bar{a}}$ where each element of $\mathbf{a}$ is conjugated.
The three operations outlined above can also be applied to matrices.
The conjugation operation can also be done on scalars.

Since the dynamics of the BS-RDAA concept is discussed, we introduce the discrete-time index $(k)$.
The value of some quantity $a$, $\mathbf{a}$, or $\mathbf{A}$ at some time $(k)$ is denoted by $a^{(k)}$, $\mathbf{a}^{(k)}$, and $\mathbf{A}^{(k)}$, respectively.
We differentiate this with the exponentiation notation $a^k$ where $a$ is a base and $k$ is an exponent.

We denote $\mathbb{R}$ and $\mathbb{C}$ as the set of all real numbers and complex numbers, respectively.
Lastly, we use $\mathbf{I}$ to represent an identity matrix that matches the size of the matrix that is added to it.

§.§ S-parameter model of efficiency

[american voltages]
(-1,0.75) to[open,v=$v_1$] (-1,-0.75)
(-1,0.75) to[TL, bipoles/tline/width=1,o-] (1,0.75) node[antenna]
(-1,-0.75) to[TL, bipoles/tline/width=1,o-] (1,-0.75) node[ground]

(3.25,2.5) node[waves,xscale=-1]
(1.75,1.5) node[waves]

(4,0.75) node[antenna]
(4,-0.75) node[ground]
(4,0.75) to[TL, bipoles/tline/width=1,-o] (6,0.75)
(4,-0.75) to[TL, bipoles/tline/width=1,-o] (6,-0.75)
(6,0.75) to[open,v^=$v_2$] (6,-0.75)

(2.5,0) node[]$\begin{pmatrix}
S_{11} & S_{12} \\
S_{21} & S_{22}
\end{pmatrix}$
[dashed] (0.25,-1.75) rectangle (4.75,3.25);

Wireless channel between two antennas modelled by S-parameters.

S-parameters are used to characterize how a voltage wave is scattered in a microwave circuit with an arbitrary number of ports.
It is a more accurate representation of all electric circuits and it is widely used to characterize high frequency circuits.
S-parameters have been used to characterize waveguides – devices that uses EM fields to propagate information <cit.>.
The wireless channel can also be imagined as a waveguide without boundaries, thus, the S-parameter definition can be extended to antennas communicating with each other via the wireless channel.
<Ref> shows a simple two-antenna channel which can be related by a $2\times2$ S-parameter matrix.
Both $v_1$ and $v_2$ have a forward (or going into the channel) and backward (or going out of the channel) wave components expressed as $v_1=v_{1f}+v_{1b}$ and $v_2=v_{2f}+v_{2b}$, respectively.
The quantities are related by <ref> where subscript $f$ means forward wave while $b$ means backward wave.

\begin{equation}
\begin{pmatrix}
v_{1b} \\ v_{2b}
\end{pmatrix}=\begin{pmatrix}
S_{11} & S_{12} \\
S_{21} & S_{22}
\end{pmatrix}\begin{pmatrix}
v_{1f} \\ v_{2f}
\end{pmatrix}
\label{eq:two-port-s-parameter}
\end{equation}

[american voltages,scale=0.9]
(-2,-3.75) rectangle (2,3.25)
(-0.75,-2.5) rectangle (3.25,4.5)
(-2,-3.75) – (-0.75,-2.5)
(2,3.25) – (3.25,4.5)
(-2,3.25) – (-0.75,4.5)
(2,-3.75) – (3.25,-2.5)

(-3,2.5) to[short,o-] (-1.5,2.5) node[bareantenna,rotate=-90]
(-3,0.5) to[short,o-] (-1.5,0.5) node[ground]
(-3,2.5) to[open,v=$\mathbf{v_1}$] (-3,0.5)
(-2.75,2.75) to[short,o-] (-1.25,2.75) node[bareantenna,rotate=-90]
(-2.75,0.75) to[short,o-] (-1.25,0.75) node[ground]
(-1.75,3.75) to[short,o-] (-0.25,3.75) node[bareantenna,rotate=-90]
(-1.75,1.75) to[short,o-] (-0.25,1.75) node[ground]

(-3,-1) to[short,o-] (-1.5,-1) node[bareantenna,rotate=-90]
(-3,-3) to[short,o-] (-1.5,-3) node[ground]
(-3,-1) to[R,v=$\mathbf{v_3}$,resistors/scale=0.5] (-3,-3)
(-2.75,-0.75) to[short,o-] (-1.25,-0.75) node[bareantenna,rotate=-90]
(-2.75,-2.75) to[short,o-] (-1.25,-2.75) node[ground]
(-2.75,-0.75) to[R,resistors/scale=0.5] (-2.75,-2.75)

(3,2.5) to[short,o-] (1.5,2.5) node[bareantenna,rotate=90]
(3,0.5) to[short,o-] (1.5,0.5) node[ground]
(4.25,3.75) to[open,v=$\mathbf{v_2}$] (4.25,1.75)
(3.25,2.75) to[short,o-] (1.75,2.75) node[bareantenna,rotate=90]
(3.25,0.75) to[short,o-] (1.75,0.75) node[ground]
(4.25,3.75) to[short,o-] (2.75,3.75) node[bareantenna,rotate=90]
(4.25,1.75) to[short,o-] (2.75,1.75) node[ground]

(3,-1) to[short,o-] (1.5,-1) node[bareantenna,rotate=90]
(3,-3) to[short,o-] (1.5,-3) node[ground]
(3,-1) to[R,resistors/scale=0.5] (3,-3)
(3.25,-0.75) to[short,o-] (1.75,-0.75) node[bareantenna,rotate=90]
(3.25,-2.75) to[short,o-] (1.75,-2.75) node[ground]
(3.25,-0.75) to[R,resistors/scale=0.5] (3.25,-2.75)
(4,0) to[open,v^=$\mathbf{v_4}$] (4,-2)

(-4,0.375) node[rotate=90]Rectenna Side
(5,0.375) node[rotate=-90]Generator Side
in 0,...,2
(-2.5+0.25*,1+0.25*) node[circ]
(3.5+0.25*,1+0.25*) node[circ]
(-2.5+0.25*,3+0.25*) node[circ]
(3.5+0.25*,3+0.25*) node[circ]
(-2.5+0.25*,-0.5+0.25*) node[circ]
(-2.5+0.25*,-2.5+0.25*) node[circ]
(3.5+0.25*,-0.5+0.25*) node[circ]
(3.5+0.25*,-2.5+0.25*) node[circ]

S-parameter model of a WPT system

Adopting the formalism from <cit.>, the concept can be extended to $N$ power generating antennas and $M$ power harvesting antennas.
A complete wireless channel view can be modelled by assuming an infinite number of ports where only the power generators and receivers are active as visualized in <ref>.
Here, $\mathbf{v_i=v_{if}+v_{ib}}$ for $i\in\{1,2,3,4\}$, $\mathbf{v_1}\in\mathbb{C}^{M\times1}$, $\mathbf{v_2}\in\mathbb{C}^{N\times1}$, and $\mathbf{v_3}$ and $\mathbf{v_4}$ are infinitely large column vectors terminated by a matched load representing power absorbed by free space.
<Ref> can be used to model the scattering behavior of the system where $\mathbf{v_{3f}=v_{4f}=0}$.

\begin{equation}
\begin{pmatrix}
\mathbf{v_{1b}} \\ \mathbf{v_{2b}} \\ \mathbf{v_{3b}} \\ \mathbf{v_{4b}}
\end{pmatrix}=\begin{pmatrix}
\mathbf{S_{11}} & \mathbf{S_{12}} & \mathbf{S_{13}} & \mathbf{S_{14}} \\
\mathbf{S_{21}} & \mathbf{S_{22}} & \mathbf{S_{23}} & \mathbf{S_{24}} \\
\mathbf{S_{31}} & \mathbf{S_{32}} & \mathbf{S_{33}} & \mathbf{S_{34}} \\
\mathbf{S_{41}} & \mathbf{S_{42}} & \mathbf{S_{43}} & \mathbf{S_{44}}
\end{pmatrix}\begin{pmatrix}
\mathbf{v_{1f}} \\ \mathbf{v_{2f}} \\ \mathbf{v_{3f}} \\ \mathbf{v_{4f}}
\end{pmatrix}
\label{eq:black-box-wpt}
\end{equation}

Let $\mathbf{S}$ be the large S-parameter matrix from <ref>.
Since the channel is lossless and reciprocal, then $\mathbf{S}=\mathbf{S}^T$ and $\mathbf{S}^H\mathbf{S}=\mathbf{S}\mathbf{S}^H=\mathbf{I}$.
Using this model, the location of each element, radiation properties of the antenna, mutual coupling, reflection losses, and channel conditions are all taken into account.
From the formulation in <ref>, the WPTE can be calculated using <ref>.

\begin{equation}
\eta=\frac{\mathbf{v_{1b}}^H\mathbf{v_{1b}}}{\begin{pmatrix}
\mathbf{v_{1b}} \\ \mathbf{v_{2b}} \\ \mathbf{v_{3b}} \\ \mathbf{v_{4b}}
\end{pmatrix}^H\begin{pmatrix}
\mathbf{v_{1b}} \\ \mathbf{v_{2b}} \\ \mathbf{v_{3b}} \\ \mathbf{v_{4b}}
\end{pmatrix}}
\label{eq:wpte-general}
\end{equation}

Combining <ref>, assuming only $\mathbf{v_{2f}\neq0}$, and using the lossless reciprocal channel assumption ($\mathbf{S}^H\mathbf{S}=\mathbf{I}$), the formula for the efficiency can be expressed in terms of the transmitted power from the generator side as seen in <ref>.

\begin{equation}
\eta = \frac{\mathbf{v_{2f}}^H\left(\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T\right)\mathbf{v_{2f}}}{\mathbf{v_{2f}}^H\mathbf{v_{2f}}}
\label{eq:rayleigh-quotient-formulation}
\end{equation}

This is called the Rayleigh coefficient and similar expressions has been found when maximizing the WPTE of antenna arrays <cit.>.
The efficiency expression is also found in <cit.> but they express it in a pure microwave transmission standpoint, i.e., it does not capture the effect of mismatched antennas and mutual coupling.
Nonetheless, <ref> has been used to optimize WPTE by treating $\mathbf{v_{2f}}$ as the input.

Since <ref> is a Rayleigh quotient, then its maxima is the maximum eigenvalue of $\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T$.
Let $\xi$ be the eigenvalues of the matrix expression.
Since $\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T$ is Hermitian, then $\xi\in\mathbb{R}$ for all eigenvalues.
Moreover, due to the unitarity of $\mathbf{S}$, and $\mathbf{S_{21}}$ being a submatrix of it, then the condition $|\xi|\leq1$ holds true for all its possible values.
As a consequence, the maximum theoretical efficiency is governed by the largest possible $\xi$ as expressed in <ref>.

\begin{equation}
\eta_{max}=\max\left(\mathrm{eig}\left\{\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T\right\}\right)=\xi_{max}
\label{eq:max-efficiency}
\end{equation}

In the traditional view of antenna arrays, $\mathbf{v_{2f}}$ is a vector whose components represent the weights of the corresponding antenna elements.
From the given framework, we can represent an arbitrary vector input to the array using a weighted sum of the set of normalized eigenvectors, $\mathbf{a}_i$, of $\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T$ as expressed in <ref> where $v_{2i}\in\mathbb{C}$ for all $i\in\{1,2,...,M\}$.
This assumes that $\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T$ is a full rank matrix.

\begin{equation}
\mathbf{v_{2f}}=\sum_{i=1}^M v_{2i}\mathbf{a}_i
\label{eq:eigen-expression-s12}
\end{equation}

Now, the efficiency of this arbitrary input can be expressed in terms of the weights and eigenvalues as shown in <ref>.
This also shows that each eigenvalue, $\xi_i$, is the WPTE of the beam mode, $\mathbf{a}_i$, and the efficiency is a weighted average of the individual efficiencies of each beam mode.

\begin{equation}
\eta=\frac{\sum\limits_{i=1}^M\xi_i|v_{2i}|^2}{\sum\limits_{i=1}^M|v_{2i}|^2}
\label{eq:efficiency-weights-eigenvalue}
\end{equation}

Transmission modes of a four-element generator to a four-element receiver arranged from (a) smallest eigenvalue to (d) largest eigenvalue.

A scalar multiple of the eigenvector associated with $\xi_{max}$, $\mathbf{a}_{max}$, is the optimum setting for the input.
In the case that multiple eigenvectors are associated with $\xi_{max}$, then the optimum input can be a linear combination of the eigenvectors.
The power can be controlled by the magnitude of the weights.
Then, to achieve high efficiency WPT, a system must be designed such that the maximum WPTE condition, $\mathbf{v_{2f}}=c\mathbf{a}_{max}$, is maintained as the channel changes over time.

§.§ Eigenvectors and beamforming

Each eigenvector, $\mathbf{a}_i$, corresponds to a radiation pattern mode or beam mode of the generator antenna array that transfers power to the rectenna array, and is orthogonal to the other modes.
The orthogonality indicates that each beam mode does not interfere with each other.
This is analogous to the transmission modes of an antenna array with a significant coupling coefficient between elements <cit.>, but instead of decomposing $\mathbf{S_{11}}$, the transmission S-parameter $\mathbf{S_{21}}$ is decomposed.
An illustration of this notion is shown in figure <ref> where a four-element generator is simulated to transfer power to a four-element receiver.
The power flow from the generator side is displayed on all cases.
Each element is driven by a source corresponding to the magnitude and phase of each eigenvector from the resulting S-parameters of the simulation.

In the least eigenvalue case, figure <ref>, the Poynting vectors are seen to be concentrated on the generator side and a minimal amount is being absorbed by the receiver.
The next is figure <ref> where the power flow is more going to the space outside the line of sight between the two antennas.
Figure <ref> shows more power going towards the receiver but some are leaked at the back of the generator.
Lastly, in figure <ref>, the Poynting vectors are moving towards the receiver side indicating the most efficient WPT mode.

[american voltages, american currents, thick]
(s21) at (0,0);
[-] ($(s21)+(2,0)$) – ++(1,0) coordinate(amp1);

($(s21)-(0,0.5)$) rectangle ($(s21)+(2,0.5)$)
($(s21)+(1,0)$) node[]$\mathbf{S_{21}}$
($(s21)+(-0.375,0.375)$) node[]$\mathbf{v_{1f}}$
($(s21)+(1,-0.5)$) node[label=below:Wireless Channel]

(amp1) to[amp,>,t=$G$] ++(2,0) coordinate(amp2)
(amp1) node[above]$\mathbf{v_{2b}}$

[-latex] (amp2) – ++(1,0) coordinate(conj1);
[-latex] ($(conj1)+(2,0)$) – ++(1,0) – ++(0,-1) coordinate(s12);
[-latex] ($(s12)-(0,2)$) – ++(0,-1) – ++(-4,0) coordinate(cplr);

($(conj1)-(0,0.5)$) rectangle ($(conj1)+(2,0.5)$)
($(conj1)+(1,0)$) node[]Conjugate

($(s12)+(0.5,0)$) rectangle ($(s12)+(-0.5,-2)$)
($(s12)-(0,1)$) node[rotate=-90]$\mathbf{S_{21}}^T$
($(s12)+(0.375,0.375)$) node[]$\mathbf{v_{2f}}$
($(s12)-(-0.75,1)$) node[rotate=-90]Wireless Channel

(cplr) node[coupler,anchor=right down](cplrnode)$L$
(cplrnode.right up) to[R] ++(2,0) node[ground,rotate=90]
($(cplr)-(-0.375,0.375)$) node[]$\mathbf{v_{1b}}$

[-latex] (cplrnode.left down) – ++(-2,0) coordinate(powerout);
[-latex] (cplrnode.left up) – ++(-1,0) coordinate(conj2);
[-latex] ($(conj2)-(2,0)$) – ++(-1,0) coordinate(adder1);

(adder1) node[adder,anchor=e](adder1node);
[latex-] (adder1node.w) – ++(-1,0) node[label=left:$\mathbf{U}$](input);
[-latex] (adder1node.n) – (adder1node.n |- s21) – (s21);
(powerout) node[label=left:RF to DC]

($(conj2)+(0,0.5)$) rectangle ($(conj2)-(2,0.5)$)
($(conj2)-(1,0)$) node[]Conjugate
($(conj2)-(2.375,-0.375)$) node[]$\mathbf{v_{1e}}$

($(input)+(-0.75,-1.25)$) node[label=right:Rectenna Side]
($(amp1)+(-0.5,-1)$) node[label=right:Generator Side]

[dashed,blue] ($(input)+(-0.75,1)$) rectangle ($(cplr) + (3.25,-0.75)$);
[dashed,red] ($(amp1)+(-0.5,0.75)$) rectangle ($(s12) + (-0.75,-0.25)$);

Block diagram of a both-sides retrodirective system with a control input.

§ BOTH-SIDES RETRODIRECTIVE SYSTEM

As mentioned in <Ref>, a retrodirective antenna array sends back a received wave to the direction of its arrival.
It can be implemented with only analog circuits so it has a faster response than digital direction-of-arrival estimation methods <cit.>.
By enabling retrodirectivity on both the rectenna and the generator, a feedback loop is created in which the beam adjusts such that most of it is contained between the two antenna arrays.
This system has been proposed and studied in <cit.>, and that a high efficiency WPT process can be achieved at a state of marginal stability.
However, the marginal stability condition derivation from their analysis assumed that the antenna array is infinitely large concluding that the over-all gain must compensate the over-all loss in the retrodirective feedback loop.
In this section, we discuss the condition to achieve marginal stability in the general finite array case and uncover the true condition for marginal stability.
We also characterize the dynamics of the system using a discrete-time state-space model akin to how a control system can be viewed.

The block diagram of a WPT system using the concept of retrodirective antennas is shown in <ref>, assuming negligible mismatch and mutual coupling between antennas on their respective arrays.
From this, the discretized characteristic equation can be derived as <ref>, where one sampling period is assumed to be the round-trip time of the signal from the rectenna side to the generator side.

\begin{equation}
\begin{split}
\mathbf{v^{\mathnormal{(k)}}_{1f}}=\Bar{L}G\mathbf{S_{21}}^H\mathbf{S_{21}v^{\mathnormal{(k-1)}}_{1f}}+\mathbf{U}^{(k)} \\
\mathbf{v^{\mathnormal{(k)}}_{2f}}=L\Bar{G}\mathbf{\Bar{S}_{21}}\mathbf{S_{21}}^T\mathbf{v^{\mathnormal{(k-1)}}_{2f}}+\Bar{G}\mathbf{\Bar{S}_{21}}\mathbf{\Bar{U}}^{(k)}
\end{split}
\label{eq:characteristic-equation}
\end{equation}

Before proceeding, we first express $\mathbf{S_{21}}$ by its singular value decomposition in <ref>.
By definition, $\mathbf{A}\in\mathbb{C}^{N\times N}$ and $\mathbf{B}\in\mathbb{C}^{M\times M}$ are unitary matrices, and $\mathbf{\Lambda}\in\mathbb{C}^{N\times M}$ is a rectangular diagonal matrix consisting of the singular values of $\mathbf{S_{21}}$.

\begin{equation}
\mathbf{S_{21}}=\mathbf{A\Lambda B}^H
\label{eq:singular-value-expression}
\end{equation}

The column vectors of $\mathbf{\Bar{A}}$ and $\mathbf{B}$ are the normal eigenvectors of $\mathbf{\Bar{S}_{21}S_{21}}^T$ and $\mathbf{S_{21}}^H\mathbf{S_{21}}$, respectively.
Then <ref> reveals that the maximum number of eigenvalues is defined by $\min(M,N)$.
It also shows that the eigenvalues for both cases are the same and that they are real.
Without loss of generality, we assume $M<N$.

\begin{equation}
\begin{split}
\mathbf{S_{21}}^H\mathbf{S_{21}}=\mathbf{B\Lambda}^H\mathbf{\Lambda B}^H \\
\mathbf{\Bar{S}_{21}S_{21}}^T=\mathbf{\Bar{A}\Bar{\Lambda}\Lambda}^T\mathbf{A}^T
\end{split}
\label{eq:eigenvalue-decomposition}
\end{equation}

The zero-input response for an arbitrary initial condition is given by <ref>.
Here, $\mathbf{b}_i$ is an eigenvector of $\mathbf{S_{21}}^H\mathbf{S_{21}}$ and $v_{1i}$ are weights for $\mathbf{v_{1f}}$, while $v_{2i}$ and $\mathbf{a}_i$ holds the same definition as that of <ref>.
The set of eigenvectors, $\mathbf{b}_i$, is parallel to the physical aspect of $\mathbf{a}_i$, but it represents the beam modes from the rectenna to the generator.

\begin{equation}
\begin{split}
\mathbf{v^{\mathnormal{(k)}}_{1f}}=(\Bar{L}G)^k\sum_{i=1}^M\xi_i^kv_{1i}^{(0)}\mathbf{b}_i \\
\mathbf{v^{\mathnormal{(k)}}_{2f}}=(L\Bar{G})^k\sum_{i=1}^M\xi_i^kv_{2i}^{(0)}\mathbf{a}_i
\end{split}
\label{eq:zero-input-response}
\end{equation}

Marginal stability is achieved when the steady state value is finite and non-zero as $k$ approaches infinity.
This is satisfied when the value $|LG|$ is the reciprocal of $\xi_{max}$ as expressed in <ref>.
$|LG|>\xi_{max}^{-1}$ will render the system unstable while $|LG|<\xi_{max}^{-1}$ makes it stable.
The resulting steady state expressions in marginal stability are given by <ref>.

\begin{equation}
\xi_{max}=\eta_{max}=\frac{1}{|LG|}
\label{eq:marginal-stability-linear}
\end{equation}

\begin{equation}
\begin{split}
\lim_{k\xrightarrow{}+\infty}\mathbf{v^{\mathnormal{(k)}}_{1f}}=(\Bar{L}G\xi_{max})^kv_{1,max}^{(0)}\mathbf{b}_{max} \\
\lim_{k\xrightarrow{}+\infty}\mathbf{v^{\mathnormal{(k)}}_{2f}}=(L\Bar{G}\xi_{max})^kv_{2,max}^{(0)}\mathbf{a}_{max}
\end{split}
\label{eq:zero-input-steady-state}
\end{equation}

Since steady state value of $\mathbf{v_{2f}}$ is a scalar multiple of $\mathbf{a}_{max}$, computing the efficiency according to <ref> results to $\eta=\xi_{max}$.
Therefore, achieving marginal stability on a both-sides retrodirective system achieves maximum theoretical efficiency for WPT.
The caveat of this system is that an initial condition is needed to start the system running and that the power that will be transferred is difficult to control as $\mathbf{S_{21}}$ changes over time.
Maintaining the marginal stability condition is also a challenge which requires automatic gain/attenuation control.

§ EXPERIMENTATION

Fabricated 12-port channel model with the port numbers labelled.

In this section, we present a hardware implementation of figure <ref> with two identical implementations of the channel model in figure <ref> as $\mathbf{S_{21}}$ and $\mathbf{S_{21}}^T$.
The experiment setup shown in figure <ref>.
Modularized microwave components such as power splitters, amplifiers, isolators, and mixers were used to assemble it.

§.§ Channel model

Figure <ref> is the channel model fabricated on a Rogers TC600 laminate and it was designed for a center frequency of 2.4 GHz.
It consists of multiple directional couplers that makes ports 1 to 6 isolated from each other and transfers most of their power to ports 7 to 12.
The same behavior is also observed in the reverse direction.
With the correct amplitude and phase fed to ports 1 to 6, the power can be focused on any port from 7 to 12, similar to the dynamic beam focusing concept.
By connecting a matched load on a port, we can model the power lost to the wireless channel as that port will absorb any power it receives.

The conjugating circuit has a higher frequency of $2.99\;GHz$ and a lower frequency of $1.81\;GHz$ ensuring the same center frequency of operation.
We originally used $3\;GHz$ and $1.8\;GHz$ but spurious intermodulation products occupied the $2.4\;GHz$ band interfering with measurements.
Note that $2.4\;GHz$ is a fourth-order intermodulation product of $3\;GHz$ and $1.8\;GHz$.
The total bandwidth of the system ranges from $2.34\;GHz$ to $2.53\;GHz$ as limited by the bandpass filter in the conjugating circuit.

Software defined radios (SDR), specifically six (6) Pluto SDRs, are used to measure the power received on each port in the receiver side.
The active SDRs not only measure the signal power but also retransmit them on their corresponding transmit port connected to the forward channel without making any changes to the amplitude and phase.
This simplifies the implementation while keeping the closed feedback loop.
In addition, the gain can be internally controlled and the spectrum of each radio can be tracked on a user interface programmed in GNU Radio.

Hardware experiment setup with Pluto SDRs as loop gain control and power measurement devices, the superheterodyne conjugator implementation, and the channel boards.

§.§ Measurement methodology

The $12\times12$ S-parameter matrix of the channel board in figure <ref> is measured using a vector network analyzer (VNA).
To see the behavior of the system stability, the gain value is swept from high to low.
Theory predicts that the system moves from the unstable condition to the stable condition from this sweep method.

Marginal stability can be found in this transition region and is noted for all test cases that were used.
In each gain point, the efficiency is logged by the SDR host computer with a sampling rate of 40 samples per second.
The mean and standard deviation of the collection of efficiencies at each gain point is calculated.

Alongside the efficiency value, we note the gain point at marginal stability for further statistical analysis using linear regression.
Thirty (30) combinations of transmit ports (Tx ports 7-12) and receive ports (Rx ports 1-6) are tested.
The influence of the Pluto SDR gain tuning is also factored in after the statistical analysis to obtain a more accurate linear regression result.

Efficiency is calculated using the power measured at the Rx ports 1 to 6 using <ref> where $P_i$ is the power measured at the $i^{th}$ port.
Measurement at the power side is avoided so that the SDRs can be set to receive the same power level avoiding signal saturation as they can only receive up to 100 mW.
In effect, there needs to be some compensation factor to measure the real efficiency and this is estimated from the S-parameter measurements of the board using the VNA.

\begin{equation}
\eta_{meas}=\frac{10^{1.65}\alpha\sum_{i=\mathrm{active}}P_i}{P_1+P_2+P_3+P_4+P_5+P_6}
\label{eq:measured-eta}
\end{equation}

The $10^{1.65}$ factor compensates for the loss experienced by the signal when passing through the conjugating circuit at the rectenna side.
A factor $\alpha$ is multiplied to factor in the power lost due to the inactive Tx ports, radiation losses, and ohmic losses by the circuit board implementation.
It is calculated based on the measured S-parameters as defined by <ref> where $\mathbf{v_{3}}$ in figure <ref> represents the inactive ports measured at the rectenna side of the circuit board in figure <ref>.
The vector $\mathbf{v_{2f}}$ that is used to calculate $\alpha$ comes from the resulting eigenvector of the characteristic equation in <ref>.

§.§ Efficiency measurement results

Experiment results from six test cases (out of 30) with a one standard deviation error bar for each gain point (solid blue lines) with the point of marginal stability highlighted and compared to their respective maximum efficiency predicted by theory (dashed black lines).

Figure <ref> show the result of the measurements for six (6) out of thirty (30) test cases.
Graphically, we can observe a sharp change in efficiency measured as we increase the gain of the active SDRs.
As mentioned previously, this is the region where the marginal stability point occurs.
Also notice that at higher maximum efficiency, the transition points also occur at lower values of the gain.
This confirms the condition $|L\Bar{G}|=1/\xi_{max}$ required to achieve marginal stability as higher eigenvalues require lower gain or attenuation.

In the stable condition, on each test case, we can observe a measurement floor where the efficiency measured is dictated by the noise power at each SDR.
In the unstable condition, as the gain is increased, there is a noticeable decreasing trend as gain increases.
This is due to the effect of other eigenvalues becoming more present which reduces the total efficiency as described by <ref>.

Efficiency and estimated loss present in the loop from 6 out of 30 experimental test cases.

Case    Rx Ports    Tx Ports    Theoretical    Experimental    Error    Meas. Gain    Est. Loss
1     30.111, 2     7, 8    0.8329    0.7972    4.29%    10 dB    8.03 dB

2          8, 9    0.6891    0.7124    3.38%    11 dB    8.05 dB

3          9, 10    0.4563    0.4661    2.15%    14 dB    7.36 dB
4     30.112, 3     7, 8    0.6331    0.6601    4.26%    11 dB    7.39 dB

5          9, 10    0.4340    0.4649    8.34%    15 dB    8.60 dB

6          10, 11    0.4862    0.5005    7.99%    14 dB    8.45 dB

Further comparison is summarized in <ref> where the percent error is less than $7\%$ for all test cases.
The other 24 cases have a maximum percent error of 9%.

The floor value (nearest ones) of the gain at marginal stability is also noted as the point of marginal stability.
This accounts the stepping behavior observed in figure <ref> where the gain tuning is only observed to change at $1\;dB$ steps instead of $0.25\;dB$.
We observe a negative correlation between the measured efficiency and the SDR gain setting which predicted by the condition of marginal stability.
It is also around these gain levels are when the plots in figure <ref> transition from stable to unstable.
The results suggest that the behavior of the BS-RDAA described by the previous theoretical analysis is observed in actual hardware.

§.§ Statistical Analysis

The gain at marginal stability and the efficiency at each test case are noted as they are related by <ref>.
By taking the logarithm of the equation multiplied by twenty (20), we obtain the decibel value of the gain and loss terms and are now related linearly with $y=20\log_{10}(\eta_{max})$ with slope equal to $m=-1$.
In general, a linear relationship can be obtained from the dataset can be expressed with <ref> where $m$ is the slope, $G$ is the gain setting, and $L_0$ is a constant related to the loss $L$.
Theoretical prediction tells us that $m=-1$ and $L_0$ should be the average of the estimated loss in <ref> which is at $7.86\;dB$.

\begin{equation}
\label{eq:marginal-stability-decibel}
\end{equation}

By performing a linear regression on the data, we determine that the constant is $L_0=6.46\;dB$ and the slope is $m=-0.8810$.
At first, $L_0$ looks like a bad estimate as compared to the estimations in <ref> but we should factor in the slope $m$.
To estimate the physical loss from the linear regression, we normalize the the slope to $m=-1$ which results to $L=-L_0/m=7.34\;dB$ which is within 2 dB for all the estimations made from the data gathered.

\begin{equation}
R^2=1-\frac{\sum\limits_{i=1}^{30}\left(y_i-mG_i-L_0\right)^2}{\sum\limits_{i=1}^{30}\left(y_i-\langle y\rangle\right)^2}
\label{eq:r-square-definition}
\end{equation}

Further confirmation of the theory can be done by using the coefficient of determination defined by <ref> where $\langle y\rangle$ denotes the mean of $y$ in the dataset.
We compared the dataset to two curves as shown in figure <ref>, namely, the result of the linear regression curve (red) where $m=-0.8810$ and $L_0=6.46\;dB$, and the theoretical prediction (green) where $m=-1$ and $L_0=7.34\;dB$.
By plugging in the measurement data, we determine that $R^2=0.8236$ for the red curve and $R^2=0.6398$, both of which are greater than $0.5$ and this indicates good agreement between measurement and theory.

Efficiency at marginal stability vs. PlutoSDR Rx Gain setting.

§.§ Pluto SDR gain behavior

A source of measurement error possibly comes from the gain tuning of the Pluto SDR.
Ideally, a $1\;dB$ change in the RX gain setting corresponds to a $1\;dB$ change in measured power.
Figure <ref> shows the gain versus power measured by the device when a loop back test is performed.
The stepping behavior of the gain indicates that the gain control of the device can only be done by steps of $1\;dB$ instead of $0.25\;dB$ so the tuning is not as fine as expected.
So we only considered integer values of the gain in dB when looking at the experiment data.
Using linear regression only on integer values, we determine the slope of the linear relationship to be $m=0.9508$ which is close to the ideal case.
This indicates that $1\;dB$ change in the setting corresponds to $0.9508\;dB$ change in power so figure <ref> should include this in determining the slope.
Therefore, the actual slope of the linear regression is $m=-0.8810/0.9508=-0.9267$.
This is an error of $7.33\%$ from the ideal slope of $m=-1$ predicted by the theory.

Gain tuning profile of the Pluto SDR

Other sources of measurement error include the error in measuring the scaling factor in <ref> where the $16.5\;dB$ loss from the conjugating circuit is compensated in the efficiency measurement calculation.
The theoretical results and also the factor $\alpha$ are highly dependent on the S-parameter measurements using the two-port VNA where systematic errors can build up as more ports are needed to be measured.
Another source can be due to an error on the model itself and further refinement must be done.
Better measurement methods and/or use of better instruments can reduce the errors.
Nonetheless, the hardware experiment affirms the theoretical predictions and that the BS-RDAA system can achieve the maximum theoretical WPTE.

§ CONCLUSIONS AND RECOMMENDATIONS

The S-parameter view of WPT predicts a maximum theoretical efficiency for a given wireless channel condition.
It also predicts an eigenvector input that corresponds to the this maximum efficiency which corresponds to the weights of the power transmitting array.
Using the discrete-time state space characteristic equation of the system, we have shown that the both-sides retrodirective antenna array concept naturally tends to this maximum efficiency setting as long as marginal stability is maintained.
The state space model also predicts the condition of marginal stability in terms of the gain in the generator and the loss in the receiver.

Experimentation of the theoretical is analysis is done using a 12-port circuit board modelling a form of a wireless channel.
Thirty (30) cases were tested and the measured efficiency results were within 9% of the prediction in theory.
Moreover, by performing linear regression in the decibel domain, the gain setting in which marginal stability occurs agrees strongly with the theoretical prediction as measured by the coefficient of determination.
Given all these, we therefore conclude that the theory we outlined accurately describes the behavior of the BS-RDAA concept.

Recommendations for future work on this is to implement the experiment in a wireless setting using multiple antennas.
The S-parameters must be easy to measure and repeatable to verify agreement with the theory outlined.
Better equipment must also be used to reduce the systematic errors present.
Another recommendation is to find a way to control the system such that marginal stability is maintained.
One aspect is to make use of a variable gain or an attenuation control.
It is also imperative to compare the BS-RDAA concept in terms of the beam it produces to other proposed long range WPT systems.
A theoretical framework to determine the beam efficiency of this system must be developed for comparison purposes.

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

booktitle2022 IEEE 23rd International Workshop on Signal
Processing Advances in Wireless Communication (SPAWC)
titleNear-Field Wireless Power Transfer with Dynamic Metasurface

titleWireless Power Transfer—An Overview
journaltitleIEEE Transactions on Industrial Electronics

titleWireless Power Transfer in the Radiative Near Field
journaltitleIEEE Antennas and Wireless Propagation Letters

titleNew directions for space solar power
journaltitleActa Astronautica

John wiley & sons

booktitleWireless Power Transfer via Radiowaves
titleTheory of WPT

booktitle2023 17th European Conference on Antennas and Propagation
titleComparison of Different Solar Cell-Antenna Integration
Designs on a Thin Film Space-Based Solar Power Station

titleDynamic Focusing of Large Arrays for Wireless Power Transfer
and Beyond
journaltitleIEEE Journal of Solid-State Circuits

titleAuto-Tracking Wireless Power Transfer System With
Focused-Beam Phased Array
journaltitleIEEE Transactions on Microwave Theory and Techniques

Sensor fusion, probabilistic models, least squares techniques, fuzzy
logic, neural networks, genetic algorithms
titleSensor fusion
journaltitleAnnual Reviews in Control

titleDigital communications using self-phased arrays
journaltitleIEEE Transactions on Microwave Theory and Techniques

titleRetrodirective arrays for wireless communications
journaltitleIEEE Microwave Magazine

Cambridge University Press

titleStudy of a single-frequency retrodirective system with a beam
pilot signal using dual-mode dielectric resonator antenna elements
journaltitleWireless Power Transfer

booktitle2017 IEEE International Conference on Computational
Electromagnetics (ICCEM)
titleBasic study of beam pilot signal for terrestrial microwave
power transmission

titleChannel Estimation for Extremely Large-Scale Massive MIMO
journaltitleIEEE Wireless Communications Letters

titlePilot Beam Pattern Design for Channel Estimation in Massive
MIMO Systems
journaltitleIEEE Journal of Selected Topics in Signal Processing

The Institute of Electronics, Information
Communication Engineers

titleBasic study of both-sides retrodirective system for
minimizing the leak energy in microwave power transmission
journaltitleIEICE Transactions on Electronics

titleS-Parameters for Calculating the Maximum Efficiency of a
MIMO-WPT System: Applicable to Near/Far Field Coupling, Capacitive/Magnetic
journaltitleIEEE Microwave Magazine

John wiley & sons

booktitleMicrowave engineering
titleMicrowave network analysis

titleMaximum Efficiency Beam Synthesis of Radiating Planar Arrays
for Wireless Power Transmission
journaltitleIEEE Transactions on Antennas and Propagation

titleMode-Based Beamforming Arrays for Miniaturized Platforms
journaltitleIEEE Transactions on Microwave Theory and Techniques

§ BIOGRAPHY SECTION

[]Charleston Dale M. Ambatali
(S'15-M'18) graduated from the University of the Philippines and received his BS and MS degree in 2016 and 2017, and currently a PhD candidate in The University of Tokyo expected to graduate in the spring of 2024, supported by the Japan International Cooperation Agency (JICA). From 2017 to 2018, he worked in the PHL-Microsatellite Project 1: Bus Development in which he helped develop the DIWATA-2, a 50-kg class cube satellite. From 2018, he became and is currently an assistant professor at the Electrical and Electronics Engineering Institute, University of the Philippines specializing in RF Engineering and Wireless Communications. His current PhD dissertation topic is on space-based solar power satellites looking into microwave wireless power transfer mechanisms.

[]Shinichi Nakasuka
graduated from the University of Tokyo and received Ph.D in 1988.  He joined IBM Research during 1988-1990, and then has been working for Department of Aeronautics and Astronautics, University of Tokyo as a lecturer, an associate professor since 1990 and became a full professor in 2004. His major research areas include micro/nano/pico-satellites, autonomy and intelligence for space systems and guidance, navigation and control for spacecraft, and novel space systems including space-based solar power satellites. He developed and launched 15 micro/nano/pico-satellites successfully including the world first CubeSat launched in 2003.

[]Bo Yang
(S’16–M’20) received the BE degree in electronic information engineering from China University of Petroleum, Qingdao, China in 2008, the ME and PhD degrees in electrical engineering from Kyoto University, Japan in 2018 and 2020. From 2019 to 2021, he conducted research on high power wireless power transfer systems, supported by Research Fellowships for Young Scientists sponsored by the Japan Society for the Promotion of Science (JSPS). He is currently researching high power microwave wireless power transmission at the Research Institute for Sustainable Humanosphere, Kyoto University.

[]Naoki Shinohara
(M’06–SM’19) received the B.E. degree in electronic engineering, the M.E. and Ph.D (Eng.) degrees in electrical engineering from Kyoto University, Japan, in 1991, 1993 and 1996, respectively. He was a research associate in the Radio Atmospheric Science Center, Kyoto University from 1996, and there he was an associate professor since 2001. He was an associate professor in Research Institute for Sustainable Humanosphere, Kyoto University by recognizing the Radio Science Center for Space and Atmosphere since 2004. From 2010, he has been a professor in Research Institute for Sustainable Humanosphere, Kyoto University. He has been engaged in research on Solar Power Station/Satellite and Microwave Power Transmission system. He is IEEE Distinguish Microwave lecturer, IEEE MTT-S Technical Committee 26 (Wireless Power Transfer and Conversion) vice chair, IEEE MTT-S Kansai Chapter TPC member, IEEE Wireless Power Transfer Conference advisory committee member, international journal of Wireless Power Transfer (Cambridge Press) executive editor, Radio Science for URSI Japanese committee C member, past technical committee chair on IEICE Wireless Power Transfer, Japan Society of Electromagnetic Wave Energy Applications vice chair, Wireless Power Transfer Consortium for Practical Applications (WiPoT) chair, and Wireless Power Management Consortium (WPMc) chair.