# Localization in Power-Constrained Terahertz-Operating Software-Defined
Metamaterials

Filip Lemic  Sergi Abadal  Chong Han  Johann M. Marquez-Barja  Eduard Alarcón
Jeroen Famaey  Internet Technology and Data Science Lab, University of Antwerp
- imec, Belgium  NaNoNetworking Center in Catalunya, Polytechnic University of
Catalunya, Spain  Terahertz Wireless Communications Lab, Shanghai Jiao Tong
University, China

###### Abstract

Software-Defined Metamaterials (SDMs) show a strong potential for advancing
the engineered control of electromagnetic waves. As such, they are envisioned
to enable a variety of exciting applications, among others in the domains of
smart textiles, high-resolution structural monitoring, and sensing in
challenging environments. Many of the applications envisage deformations of
the SDM structures, such as their bending, stretching or rolling, which
implies that the locations of metamaterial elements will be changing relative
to one another. In this paper, we argue that if the metamaterial elements
would be accurately localizable, this location information could potentially
be utilized for enabling novel SDM applications, as well as for optimizing the
control of the elements themselves. To enable their localization, we assume
that these elements are controlled wirelessly through a Terahertz
(THz)-operating nanonetwork. We consider the elements to be power-constrained,
with their sole powering option being to harvest energy from different
environmental sources. By means of simulation, we demonstrate sub-millimeter
accuracy of the two-way Time of Flight (ToF)-based localization, as well as
high availability of the service (i.e., consistently more than 80% of the
time), which is a result of the low energy consumed in the localization
process. Finally, we qualitatively characterize the latency of the proposed
localization service, as well as outline several challenges and future
research directions.

###### keywords:

Software-defined metamaterials/metasurfaces , localization , two-way ToF
trilateration , terahertz nanonetworks , energy harvesting

##  1 Introduction

Metamaterials are manufactured structures with engineered properties not found
in natural materials. As such, metamaterials (and metasurfaces, their
2-Dimensional (2D) counterparts) can support controlled manipulation of
electromagnetic waves (e.g., reflection, absorption, scattering) [1, 2]. This
unprecedented level of control is achieved by carefully designing a periodic
array of sub-wavelength metamaterial elements, also known as unit cells [2].
Until recently, these unit cells have been designed for supporting a single
application and/or operational condition, and, therefore, have not been
reusable across applications nor operations. To enable a substantially higher
level of controllability of metamaterial elements in real-time, Liaskos _et
al._ [3] proposed Software-Defined Metamaterials. The SDM paradigm envisions
embedding a communication nanonetwork of controllers within the metamaterial
or metasurface, with the roles of controllers being i) actuation of the
metamaterial elements and/or ii) collection of sensed readings from the
elements through a two-way exchange of the sensing/actuation commands and
responses between the metamaterial elements and the outside world [4].

There are several technological candidates for enabling a nanocommunication
network to support the above-mentioned controllability features, including
both wired (primarily Field Programmable Gate Arrays [2]) and wireless
solutions (mainly graphene-based Terahertz (THz) nanonetworks [5]).
Intuitively, both candidates come with strengths and weaknesses, with the
primary concern being the wiring and form-factor vs. communication reliability
trade-off between wired and wireless solutions [6, 2, 5]. The question of
which candidate to utilize for enabling the foreseen nanonetwork is currently
not fully answered and a subject of ongoing research [7, 8].

SDMs are envisioned to enable a variety of novel applications in a number of
domains [1]. They will have to be flexible to fully achieve the promise of
some of the envisioned applications (more details in Section 2). Hence, one of
the aims of metamaterial-focused research is to develop SDMs that have the
possibility of bending, stretching, and rolling. [9]. In such setups, the
locations of the metamaterial elements will be dynamically changing relative
to one another. Intuitively, for such SDM-based applications the location of a
given metamaterial element will play a role in the control of that element.
However, to the best of our knowledge, the question if it is at all possible,
as well as how to localize the metamaterial elements relative to one another
did not receive any attention in the research community to date.

###  1.1 Contributions

To address the above issues, we start by considering different approaches for
traditional localization (i.e., the ones originating from e.g., Wireless
Sensor Network (WSN) and the Internet of Things (IoT) contexts) utilizing
Radio Frequency (RF) signals. Based on these insights, we argue that the two-
way Time of Flight (ToF)-based trilateration is the most suitable candidate
for enabling localization in THz-operating SDMs. Consequently, we demonstrate
the feasibility of localizing SDM elements by utilizing RF signals in THz
frequencies (i.e., 300 GHz to 10 THz). We do that for power-constrained SDMs,
where harvesting energy from nearby environmental sources is the sole powering
option for the SDM elements. This is done as it is expected that such power-
constrained SDMs will be utilized in the future, primarily to reduce their
form-factors by removing the need for excessive wiring [1]. In particular, we
demonstrate that the two-way ToF-based trilateration for Time-Spread ON-OFF
Keying (TS-OOK), a relatively novel modulation and coding scheme specifically
designed for nanocommunication, can achieve a sub-millimeter-level average
errors in localization, even for highly constrained SDMs powered solely
through harvesting energy from surrounding air-vibrations by exploiting
piezoelectric effect of ZnO nanowire-based harvesters. In addition, we
demonstrate consistently high availability of the localization service,
resulting from the low energy consumed in the process, showing the
applicability of the proposed localization scheme for highly power-constrained
SDMs. Further, we characterize the influence of a large number of relevant
system parameters along the values expected to be utilized in real-life
deployments (e.g., operational bandwidth, energy harvesting rate, SDM spacing,
number of localization anchors, etc.) on the localization accuracy and
availability. Finally, we provide a rule-of-thumb characterization of the
latency of performing such localization as a function of different system
parameters, and outline several open challenges and future research
directions.

###  1.2 Structure

This paper is structured as follows. In Section 2, we discuss the related
works and efforts pertaining to traditional RF-based localization, followed by
outlining several potential benefits of the localization feature in SDMs. In
Section 3, we discuss the envisioned system for two-way ToF-based localization
in THz-operating and power-constrained SDMs. In Section 4, we outline the
evaluation methodology, while in Sections 5 and 6 we deliver the results of
our evaluation and discusses several open challenges and potential future
research directions, respectively. The paper is concluded in Section 7.

##  2 Related Works

###  2.1 Localization in Software-Defined Metamaterials: Opportunities

SDMs are envisioned to serve as an enabler of a variety of applications in
different domains [1, 2]. Among others, SDMs are expected to be embedded in
smart textiles for supporting features such as wireless touch [10]. SDMs are
also expected to be used in vehicular communication for enhancing ranging
capabilities [11] or noise cancellation [12]. Moreover, some SDM applications
envision metamaterial-based sensing on rough mobile surfaces (e.g.,
temperature [13] and strain sensing [14]), or sensing in fluids [15]). To
enable such applications, one of the aims of metamaterial-focused research is
to develop flexible SDMs with the possibility of bending, stretching, rolling,
etc. [9], providing a strong indication that SDMs will eventually be utilized
in scenarios with mobility, hence the locations of the metamaterial elements
will be dynamically alterable relative to one another.

As mentioned, localization in SDMs is a topic that did not receive any
attention from the community to date. That is with an exception of our
previous work [16] (n.b., a conference paper), where we outlined the concept
of two-way ToF-based trilateration for enabling localization in THz-operating
power-constrained SDMs. In this work, we extend our initial findings by, among
others, evaluating the proposed approach with a substantially higher level of
realism (e.g., by considering an SDM-specific and frequency-dependent channel
model) and along a more exhaustive set of system parameters (e.g., by
considering the effects of the number and constellation of localization
anchors and mobility patterns of the nanonodes), as well as by utilizing a
more comprehensive set of performance metrics (i.e., localization accuracy and
availability, and latency of reporting location estimates).

Given the novelty of the topic at hand, to the best of our knowledge there are
no obvious related works along which we could position and benchmark our work
against. Therefore, in the following we take a “what if” perspective and aim
at providing a high-level outline of some potential benefits of the
localization feature in SDMs. We categorize these opportunities based on the
application and network optimization standpoints. Note that our intention is
to present a few motivating examples, in contrast to providing an exhaustive
overview of all the potential opportunities.

####  2.1.1 Application Perspective

Taking the application perspective, the possibility of estimating the
locations of mobile wireless communication-enabled devices is an enabler of a
variety of novel services, traditionally known as location-based services [17,
18]. In the context of SDMs, arguably the most intuitive example of the
benefits of localization of metamaterial elements comes from the
aforementioned fact that some SDMs are envisioned to be used for sensing
applications in challenging environments, usually with mobility [19, 13, 14,
15]. It is well-known from traditional WSNs that the location where a reading
is obtained is an important piece of metadata [20] about the reading itself.
Hence, it is reasonable to assume that in the domain of SDM-based sensing
localizable readings would be of a certain value (e.g., wireless touch should
be a localizable stimulus). SDMs also find their applications in intelligent
wireless environments [21, 22]. Although initially SDMs are in this context
expected to be static entities (often attached to walls and ceiling of a
deployment environment) [23], with the progress in their development they
could become entities integrated in e.g., person’s clothes, thus the person
could become an active participant in the intelligent wireless environments.
Introducing a person as an active element could for example benefit the mmWave
communication or macro-scale localization capabilities. This is because a
mobile obstacle that the human body represents usually has a negative effect
on the performance of these and similar systems [24, 25]. Given that
eventually humans could become the active elements by means of e.g., smart
textiles, it becomes clear that the locations of the SDM elements embedded in
such textiles could be used for a more optimized control of the impinging
electromagnetic signals based on the locations of the elements themselves,
which in turn could be used for fine-grained optimizations of the macro-scale
communication and localization capabilities in the intelligent wireless
environments.

####  2.1.2 Network Optimization Perspective

From the network optimization standpoint, it is first worth emphasizing that
location-based optimizations represent a promising research domain for
optimizing the performance of more traditional wireless networks across their
entire protocol stacks [26]. In the context of SDMs, the aim of location-based
optimizations would be to improve the performance of the wireless nanonetworks
for controlling the metamaterial elements (more details in Section 3.1).
Generally speaking, the reactivity of any SDM to electromagnetic waves of a
given frequency changes as the spacings between its metamaterial elements
change [27, 2]. By quantifying the level of these changes (i.e., the locations
of the metamaterial elements), one could potentially design more advanced
approaches for controlling the radiation pattern characteristics of the SDMs.
Similarly, one could develop a mechanism for excluding certain elements from
the operation of an SDM for a fraction of time, as they have been e.g., overly
stretched (i.e., roughly speaking extended beyond the wavelength of the
controlled waves) [2]. Finally, given that SDMs are envisioned to consist of a
relatively large number of elements (from hundreds to multiple thousands) [1],
it is an open question on how to individually address each element in a
constrained time-frame. In this regard, directing wireless signals from the
gateways/controllers toward the metamaterial elements is a promising option
[28], as it would reduce the interference with other elements compared to
omnidirectional communication, thus also reducing the time needed for the
control of the elements. However, under mobility of the SDM, fast directional
communication (i.e., without a time-consuming beam-search [24]) between the
controllers and the elements could be feasible if the locations of the
elements would be known with a high level of accuracy. In other words, if the
locations are known, the beams could be steered in the Line of Sight (LoS)
direction of the elements. Such a location-based optimization has been shown
to mitigate interference [29] and significantly reduce the beam-search latency
[30] in macro-scale mmWave systems, which could serve as an additional
argument about its utility in the SDM context.

###  2.2 Traditional RF-based Localization

Traditional RF localization approaches (i.e., algorithms) can be roughly
categorized into fingerprinting, proximity, and geometric-based [31, 32].
Fingerprinting approaches rely on correlating various signal features from an
unknown location with a set of respective signal features at pre-surveyed
locations [33]. Due to the fact that it is practically impossible to pre-
survey signal features at nanoscale, we believe fingerprinting is infeasible
for localization in SDMs. Proximity-based approaches rely on the proximity
between a device to be localized and a set of anchors with known locations.
These approaches are designed to provide coarse-grained localization [34] and
are, therefore, not suitable for the desired nanoscale localization with high
accuracy. Geometrical approaches utilize different signal features (mostly
Received Signal Strength (RSS), Angle of Arrival (AoA), and ToF) for
estimating distances (or angles) between devices, which then serve as a basis
for estimating the unknown locations [35].

Table 1: Popular physical layers used in localization [36]. Physical layer |  Bandwidth |  Raw resolution
---|---|---
IEEE 802.11a/g |  20 MHz |  15 m
IEEE 802.11n |  40 MHz |  7.5 m
IEEE 802.11ac |  $<$160 MHz |  $>$1.9 m
Ultra WideBand (UWB) |  $>$500 MHz |  $<$0.6 m
IEEE 802.11ad |  $>$2 GHz |  $<$15 cm
Terahertz - macroscale |  $\bm{>}$10 GHz |  $\bm{<}$3 cm
Terahertz - nanoscale |  $\bm{>}$1 THz |  $\bm{<}$0.3 mm

AoAs cannot be estimated without antenna arrays or complex signal processing,
both being infeasible for the considered nanonodes with highly constrained
capabilities [37]. RSS is a highly fluctuating signal feature with logarithmic
dependence to the distance between devices, hence it is known to be highly
inaccurate [35, 38]. Estimation of the ToF requires tight synchronization
between the communicating devices, which is hardly achievable for the
considered resource-constrained nanonodes.

Luckily, a two-way ToF-based approach removes the synchronization requirement
and we, therefore, reason that two-way ToF-based localization can potentially
enable localization in SDMs. For estimating two-way ToF, a signal is
transmitted by one device and the time measuring is started. After a
predefined period upon the reception of the original signal, the other device
retransmits the signal. Upon the following reception, the first device can
estimate the two-way ToF by subtracting the predefined time that passed
between the reception of the original signal and the transmission of the new
one from the total time passed since the original transmission. The accuracy
of this method will depend on the sampling constraints resulting from the
Nyquist theorem. Extending the classification proposed by Xiong  _et al._
[36], in Table 1 we summarize the raw resolution of different physical layers
prominently used for localization, with the raw resolution defined as the
speed of light divided by the available bandwidth. In the THz frequencies,
different spectrum windows of at least 10 GHz are unlicensed and ubiquitously
available [39] for macroscale communication. Moreover, at the nanoscale (i.e.,
with the communication ranges of less than 50 cm) the available bandwidth is
in the range of several THz [40]. The discrepancy between the available
bandwidths at macro and nanoscale is primarily due to increase in the
molecular absorption with communication distance, as shown in [40]. This
yields the theoretically achievable raw resolutions of less than 3 cm and less
than 0.3 mm at the macro and nanoscale, respectively, which demonstrates a
potential for high accuracy in THz-based localization.

##  3 Localization in SDMs

###  3.1 Software-Defined Metamaterials: Context

Figure 1 depicts the envisioned SDM architecture, where each controller can
interact with its associated metamaterial elements. The interaction is
supported through power-constrained nanonodes, whose main purpose is two-way
wireless communication with the controllers for the functionalities of
adjusting the properties of the metamaterial elements and delivering their
readings. We consider THz-based wireless nanocommunication between the
controllers and the power-constrained nanonodes, which allows (compared to a
wired solution) for a reduced form factor, however at the cost of highly
constrained amount of available energy (i.e., with harvesting energy from
environmental sources being the only powering option) [41]. THz-based
nanoscale wireless communication between the controllers and the nanonodes can
be supported by emerging materials, primarily graphene, and its feasibility
has been demonstrated by various works in the literature, e.g., [41, 40].
Moreover, transceivers for THz-based communication at more than 10 GHz
bandwidth, featuring low energy consumption approaching 1 pJ per bit, have
been demonstrated within small areas expected in the SDM context (e.g., [42]),
paving the way toward the envisioned SDM localization.

We use TS-OOK as the modulation and coding scheme as it is a de-facto standard
for THz nanocommunication [43]. TS-OOK is based on the exchange of short
pulses (usually 100 fs long [43]) spread in time, where the pulse carries one
bit of information, i.e., a logical ”1”, while a logical “0” is represented by
silence. The time between the transmission/reception of two consecutive bits
of a packet is characterized by the ratio $\beta$ between the duration of a
TS-OOK pulse and the time between the transmissions/receptions of two
consecutive bits of information. $\beta$ is usually fixed and much longer
(typically two to three orders of magnitude) than the duration of a TS-OOK
pulse. The benefits of THz-based TS-OOK communication include simplicity of
transceiver architecture [44], extremely low energy consumption in the range
of 1 pJ per transmitted bit of information [43] for omni-directional
communication ranges of up to 1 m [40], making it a suitable candidate for the
realization of the envisioned SDM localization. This is further accentuated by
the fact that THz channel path loss within an SDM should, perhaps
counterintuitively, not necessarily be very high because distances are small
and the environment is enclosed [21].

Figure 1: Envisioned SDM architecture for controlling and localizing
metamaterial elements Figure 2: Lifecycle of an power-constrained nanonode [5]

###  3.2 Power-Constrained Nanonodes: Context

The usual energy lifecycle of an power-constrained nanonode is depicted in
Figure 2. At certain points in time (i.e., the “turn-off threshold”) the
energy of the nanonode will be at a critically low level and the nanonode will
turn off. At a certain later point in time, the nanonode will have harvested
enough energy to turn on (i.e., the “turn-on threshold”) and will become
operational again. Intuitively, the nanonode will continue to harvest energy
if it is turned on until its energy level reaches the maximum storage
capacity, as depicted in the figure. During transmission, reception, or any
other operational periods (e.g., idling, sensing, actuation), the nanonode
will loose energy, while simultaneously gaining some due to harvesting.

We consider nanoscale energy harvesters that exploit piezoelectric effect of
ZnO nanowires [45], where the energy is harvested in nanowires’ compress-and-
release cycles. The harvested energy can be specified with the duration of the
harvesting cycle $t_{cycle}$ and the harvested charge per cycle $\Delta Q$.
Capacitor charging through energy harvesting can be accurately modeled as an
exponential process [46], accounting for the total capacitance $C_{cap}$ of
the nanonode, where $C_{cap}=2E_{max}/V_{g}^{2}$, i.e., $C_{cap}$ depends on
the maximum energy storage capacity $E_{max}$ and the generator voltage
$V_{g}$. In the modeling, it is required to know in which harvesting cycle
$n_{cycle}$ the nanonode is, given its current energy level $E_{n_{cycle}}$,
which can be derived from [46] as follows:

$n_{cycle}=\left\lceil\frac{-V_{g}C_{cap}}{\Delta
Q}ln\left(1-\sqrt{\frac{2E_{n_{cycle}}}{C_{cap}V_{g}^{2}}}\right)\right\rceil.$
(1)

The energy in the next energy cycle $n_{cycle}+1$ is then:

$E_{n_{cycle+1}}=\frac{C_{cap}V_{g}^{2}}{2}\left(1-e^{-\frac{\Delta
Q(n_{cycle}+1)}{V_{g}C_{cap}}}\right)^{2}.$ (2)

###  3.3 Localizing Software-Defined Metamaterials

We envision the localization setup as depicted in Figure 3. Specifically,
there is a number of controllers (four depicted in the figure) serving as
localization anchors. They are not power-constrained and their locations are
known with perfect accuracy. The assumption of the controllers not being
power-constrained (i.e., mains- or battery-powered) has been widely used in
the literature (e.g., [6, 5]). This is mainly because there are substantially
less controllers than the metamaterial elements that they are controlling
(i.e., one controller is envisioned to control hundreds of elements [5]),
hence their wiring requirements are less stringent. The assumption that their
locations are known is reasonable as their locations can be fixed and measured
(e.g., when an SDM is mounted on a rough surface). Adversely, their locations
can be estimated by utilizing some of the traditional approaches, as they are
not size-, resource-, or power-constrained. Localization could also be done in
two-steps, where first the controllers are localized by utilizing two-way ToF-
based trilateration, followed by localizing the nanonodes. This can be done as
the controllers are not power-constrained, thus they can utilize higher
transmit power for localization, which in turn would attribute to the enhanced
range of localization.

Figure 3: Trilateration setup

Under the above assumptions, the localization process includes each controller
transmitting one or multiple TS-OOK pulses, which are upon reception
retransmitted by the nanonode whose location is to be estimated. If the
retransmitted signals are received by the controller, the distances between
the controller and the nanonode can be estimated from the two-way ToF
measurements. The reasons why the retransmitted signals could be missed are
two-fold. First, the nanonode’s energy could be depleted, hence it would not
be able to retransmit the original signal(s). Second, due to mobility (e.g.,
stretching, bending, or rolling of an SDM) a controller could move out of the
communicating range of the nanonode. If the distances between at least four
controllers and the nanonode can be estimated, a standard trilateration
approach can then be utilized for estimating the unknown location of the
nanonode in a 3-Dimensional (3D) space. More details on how to estimate the
distance between each controller and the nanonode, as well as the basics of
trilateration, can be found in e.g., [20].

The operational timeline of the nanonode whose location is to be estimated is
given in Figure 4. Due to potentially continuous mobility, the location of the
nanonode will usually have to be estimated periodically. Hence, we envision
three phases in the operational timeline, i.e., the operational, localization
announcement, and localization phase. During the operational phase the
nanonode performs its envisioned functionalities (e.g., sensing, actuation).
In the localization announcement phase, a distinct set of signals (i.e., a
codeword) is sent by the controller(s) to the nanonodes to announce the
beginning of the localization phase. This is done as the nanonodes internal
clocks are not synchronized with the controllers, hence there is a need to
announce a “switch” in their reactivity to the signals issued by the
controllers, i.e., the end of the operational and the beginning of the
localization phase. Note that this does not imply the need for synchronizing
the nanonodes with the controllers, only the need for coarse-grained
announcement of the switch between operations. In the localization phase, the
locations of the nanonodes are envisioned to be estimated. The frequency of
location estimation in this scenario is application-specific and depends on
the location updating period, as shown in the figure.

Figure 4: Operational timeline of a nanonode

##  4 Evaluation Methodology

The main goal of the evaluation is to establish the accuracy and availability
of the THz-based two-way ToF approach for localization in SDMs. These
performance metrics are to be derived as a function of a large number of
relevant system parameters, i.e., operational bandwidth, energy harvesting
rate, location update period, spacing between metamaterial elements, receiver
sensitivity, number of TS-OOK pulses used for ToF estimation, number and
constellation of localization anchors, errors in the localization of the
anchors, nanonodes’ mobility patterns, nanonodes’ energy consumption and
harvesting patterns, and metamaterial-specific attenuation.

The localization accuracy is characterized by the localization error, which is
defined as the Euclidean distance between the true and estimated locations of
a nanonode [47, 48]. The localization availability for one attempt at
localizing a nanonode is defined as a binary value indicating the success of
localizing the nanonode or the lack thereof. Each instance of the results
depicted in Figures 6 to 17 provides insights summarized over all nanonodes
and iterations of the simulation (cf., Table 2). The localization accuracy in
each instance of the results is depicted in a regular boxplot fashion. In an
individual boxplot of the localization errors, the boxes extend from the lower
to upper quartile of the derived localization errors, with an orange line at
the median. The whiskers extend from the boxes to show the range of the
localization errors, while the flier points represent the outliers in the
localization errors, with the outliers defined as the lowest and highest 5
percentiles of the errors. Moreover, the localization availability has been
depicted as a ratio between the number of successful and the total number of
localization attempts, summarized over all nanonodes and iterations of the
simulation.

In addition, we aim at deriving the first rule-of-thumb insights on the
latency of estimating location information, which is among the most important
parameters for characterizing the performance of localization solutions [49],
however currently lacking in the context of SDM localization. Localization
latency in this context essentially equals the duration of the localization
phase (cf., Figure 4) and consists of the time needed to obtain the ToF
characterization for all controller-nanonode pairs plus the time needed to
estimate the nanonodes’ locations based on the derived ToFs. The summary of
the default simulation parameters is given in Table 2.

Table 2: Simulation parameters Parameter | Value
---|---
Number of nanonodes and controllers | (25x25) 625
Distance between nanonodes [mm] | 9.0
Generator voltage $V_{g}$ [V] | 0.42
Energy consumed in pulse reception $E_{R_{Xpulse}}$ [pJ] | 0.1
Energy consumed in pulse transmission $E_{T_{Xpulse}}$ [pJ] | 1.0
Maximum energy storage capacity [pJ] | 800
Turn OFF/ON thresholds [pJ] | 10/0
Harvesting cycle duration [ms] | 20
Harvested charge per cycle [pC] | 6
Transmit power $P_{T_{X}}$ [dBm] | -20
Data packet size [bits] | 8
Operational bandwidth [THz] | 1
Receiver sensitivity [dBm] | -110
Operational frequency [THz] | 1
Simulation time [# of iterations] | 1000
Localization update period [sec] | 0.1
Environment-specific attenuation [dB] | 0

We have carried out our evaluation by means of simulation, with the primary
reason for not aiming at a full scale experimental evaluation coming from the
fact that there are currently no operational prototypes of THz-operating
power-constrained SDMs available for experimentation. To carry out the
evaluation, we have developed a Python-based simulator. We have done that, in
contrast to using some (mostly ns-3 based) of the established and readily
available simulators (e.g., TeraSim [50]) for evaluating the performance of
THz-operating nanonetworks, as such simulators feature a fairly heterogeneous
simulation capabilities, resulting in much worse execution time and
scalability for the problem at hand. Utilization of the in-house Python
simulator allowed us to increase the number of considered system parameters
and derive a number of insights in a reasonable time-frame. Our simulator
consists of four main modules: channel modeling, two-way ToF-based
trilateration, nanonode’s energy consumption and harvesting, and performance
metrics calculation). The output of the channel modeling module of our
simulator has been compared to the same output of TeraSim [50] and are
comparable, suggesting that our implementation of the module is correct. The
fact that the other three main modules would have to be implemented regardless
of the simulator makes us confident that our simulator is able to derive the
same insights for the problem at hand as TeraSim.

In the simulator, we have initially defined a set of 625 (25x25) nanonodes and
controllers in a grid-like fashion. If not stated differently, the four
controllers are positioned in the corners of the grid. The default distance
between neighboring nanonodes was set to 9.0 mm, which correlates to spacing
needed for controlling electromagnetic waves in the mmWave frequencies (i.e.,
with the operational frequency of 25 GHz, assuming the spacing equals to 3/4
of the wavelength). Hence, they were not power-constrained and (if not stated
differently) their locations were known and fixed. The other nanonodes are
assumed to be powered through energy harvesting, with their energy levels
modeled using Equations 1 and 2. Moreover, we assumed that the energy is
harvested from two different environmental sources, specifically air-
vibrations and RF-based power transfer. We have selected these two harvesting
options with the following intuitions. The air-vibrations represent an
ubiquitous energy harvesting source that can be utilized in a large variety of
deployment environments and conditions. The RF-based power transfer using
metamaterial elements themselves [51] is tightly related to one of the most
prominent applications of SDMs, namely the intelligent wireless environments.
In the intelligent wireless environments, the SDMs will be used for
controlling the properties of RF waves, hence it is natural that the energy of
these waves can also be utilized for powering the power-constrained nanonodes
[22]. In agreement with the existing literature, we have specified the default
harvesting cycle duration of 20 and 1.71 ms for air-vibrations [46] and RF
power transfer [52], respectively. Moreover, [46, 52] report the average
harvesting charge $\Delta Q$ of 6 pC for one ZnO nanowires’ compress-and-
release cycle. As commonly done in the literature (e.g., in TeraSim [50]), we
model these charges using Gaussian distributions with 6 pC as the mean value
and 0.6 pC as the standard deviation. We consider a capacitor with the energy
storage capacity of 800 pJ, which is in correspondence to the existing
literature [46]. The initial energy levels of the nanonodes have been drawn
from a uniform distribution bound by the energy storage capacity.

In order to establish the availability of the localization service, we have
also considered the energy required for the necessary signaling between the
controllers and nanonodes whose location is to be estimated. In TS-OOK, the
information is transmitted by short time-spread pulses or silences, where the
vast majority of energy is spent in their transmission and reception, as
originally shown by Jornet and Akyildiz [46], which is also the assumption we
utilize in this work. Specifically, the energies consumed in transmitting
($E_{T_{Xpulse}}$) and receiving ($E_{R_{Xpulse}}$) a TS-OOK pulse are set to
1 and 0.1 pJ [46, 50], respectively. Furthermore, the transmit power is set to
$-20$ dBm, which is again in line with the existing literature [46, 50]. The
energy is assumed to be consumed during the operational, localization
announcement, and localization phases of a nanonode. During the localization
phase, the energy can be consumed in the reception and retransmission of a TS-
OOK pulse (or multiple TS-OOK pulses) for deriving the two-way ToF. In the
operational phase, the energy is, if not stated otherwise, assumed to be
consumed in the reception of an 8 bits long packet, with the bits (i.e.,
logical “0”s and “1”s) being drawn from a uniform distribution. The reception
of such a packet mimics an instruction sent to a nanonode for which an 8 bits
long packet is usually sufficient [1, 2]. Note that we also consider various
other relevant energy consumption patterns such as the nanonodes transmitting
packets, performing sensing and actuation, and various combinations of these
operations, as in more details discussed in the following section.
Acknowledging that other types of sequences are possible, we assume the
localization announcement is performed by transmitting a sequence of three TS-
OOK pulses. Hence, we model the nanonode’s energy consumption in the
localization announcement phase with the energy consumed in reception of three
TS-OOK pulses. The default operational bandwidth is set to 1 THz, equaling the
theoretical limit derived in [40], in order to demonstrate the theoretically
achievable localization accuracy in SDMs. Note that, although 1 THz of
bandwidth (implying comparable sampling frequency at the nanonode level) is
not practically feasible, different approaches exist for two-way ToF sampling
that could be used for mitigating this limitation and effectively result in
two-way ToF ranging errors that could be achieved for the THz-frequent
sampling, as in more details discussed in Section 6.

If not stated otherwise, from the initial grid-like distribution the nanonodes
are “moved” randomly in the area of sizes $(x,y,z)=(d,d,d/2)$, with $d$ being
the distance between two controllers on the same edge. This random selection
of locations inside a bounded area resembles a scenario in which a flexible
SDM is attached to an uneven convex surface, such as in the smart textiles
[10]. In addition, we consider the mobility of the nanonodes resembling a
half-spherical and half-cylindrical patterns bound by the same area
$(x,y,z)=(d,d,d/2)$ (Figure 17). These patterns are relevant as they mimic the
mobility of SDMs bent around different types of elastic structures for e.g.,
structural health monitoring [53] or mitigating the exposure to
electromagnetic radiation [54].

Two-way ToF measurements are derived from the true distances between each
nanonode and each controller, to which bandwidth-dependent zero-mean Gaussian-
drawn variabilities are added. The standard deviation of the variability is
derived as the ratio between the speed of light and bandwidth (i.e., the raw
resolution), which is an often utilized method for simulating the ToF
variability [55, 35].

Location estimates can be generated if the two-way ToF measurements between a
given nanonode and all 4 controllers are obtained. This is characterized by
comparing the strength of the received signal with the receiver sensitivity,
i.e., if the received signal strength is higher than the receiver sensitivity,
the signal is considered as received. The received signal strength $P_{Rx}$ is
obtained by subtracting frequency-selective absorption and spreading losses
from the transmit power $P_{Tx}$, which is a THz nanoscale channel modeling
method often used in the literature (e.g., [56, 57]). The received signal
strength is given as follows, with $d$, $f$, and $c$ being respectively the
distance between devices, operating frequency, and the speed of light.
Moreover, $k(f)$ is a frequency-dependent medium absorption coefficient, with
its values obtained from the HITRAN database [58]:

$P_{Rx}[dBm]=P_{Tx}-k(f)d10log_{10}(e)-20log\left(\frac{4\pi fd}{c}\right).$
(3)

The modeled attenuation as a function of operating frequency, bandwidth, and
distance between the devices is given in Figure 5. As visible from the figure,
the attenuation increases with the increase in the operating frequency and
distance between the devices, which is an intuitively expected behaviour.
Moreover, the utilized bandwidth affects the attenuation due to the frequency
selectivity in the propagation channel, which is again an expected behaviour
aligned with propagation modeling in TeraSim, as visible from the figure.
Finally, the error of our implemented propagation model is well below 1%
compared to TeraSim in all cases. We hypothesize this small error to be due to
differences in rounding and precision between the two used programming
languages (i.e., Python and C++).

Figure 5: Attenuation (absorption and spreading losses) as a function of
operating frequency, bandwidth, and distance between the devices

Given that the flexible SDMs will in the majority of cases be “attached” to a
certain surface, we also consider an environment-specific attenuation
contribution $A_{ENV}$ to the received signal strength. With the environment-
specific attenuation contribution $A_{ENV}$, we are also abstracting various
imperfections that are certainly to be expected in reality, but cannot be
fully captured using a simulation-based approach. Some examples of abstracted
imperfections include the antenna coupling effects, imperfections in the
omnidirectional radiation, potential interferences, etc. Given that this
attenuation contribution is hardly quantifiable based on the existing
literature and will intuitively depend on the utilized hardware (e.g., antenna
coupling efficiency) and the deployment environments (e.g., type of surface to
which the SDM is attached), we characterize the effect of an increasing
environment-specific attenuation contribution $A_{ENV}$ on the performance of
the proposed localization system. We consider such modeling to be appropriate,
as it encapsulates different types of signal degradations (e.g., scattering,
absorption) and establishes their effects, thus also the effects of different
surfaces, on the performance of the proposed system. The received signal
strength is finally characterized as:

$P_{Rx}[dBm]=P_{Tx}-k(f)d10log_{10}(e)-20log\left(\frac{4\pi
fd}{c}\right)-A_{ENV}.$ (4)

##  5 Evaluation Results

###  5.1 Localization Accuracy and Availability

Figures 6 and 7 depict the accuracy and availability of the localization
service as a function of the energy harvesting rate and location update
period, respectively. As depicted in the figures, the energy harvesting rate
and location update period do not significantly affect the localization
accuracy. This is because all the nanonodes are in the default setup in the
range of all controllers, regardless of the energy harvesting rate and
location update period. Hence, these parameters only affect the probability of
generating two-way ToF measurements, and not their quality. In other words, if
the measurements are obtained, location can be estimated with a consistent
accuracy. The localization service achieves less than 1 mm in terms of average
localization error, which demonstrates the feasibility of the two-way ToF-
based trilateration in SDMs. Moreover, the outliers (95th percentile of all
estimates) experience localization errors of less than 12.0 mm, which again
shows the promise of the two-way ToF-based trilateration service.

For the parameters reported in Table 2, the availability of the service is
around 90%, with the only reason for not being able to estimate the locations
resulting from the depletion of the available energy. This again demonstrates
the potential of the proposed system for localization in SDMs. As shown in the
figures, the availability of the localization service is enhanced as the
energy harvesting rate or location update period increase. For example, if the
harvested charge is increased from 2 to 10 pJ per cycle, the availability is
increased by roughly 10%. Similarly, if the localization update period
increases from 20 to 260 ms, the availability increases from 80 to 100%. The
reason for that is the fact that higher harvesting rates represent more
harvested energy, while less frequent location updates yield less energy
consumed over time. Therefore, the nanonodes more often have sufficient energy
to generate two-way ToF measurements and consequently estimate the location,
which enhances the availability of the localization service. Though the
results depicted in Figures 6 and 7 are intuitive, we present them to serve as
an argument demonstrating the correct implementation of our simulation setup.

Figure 6: Accuracy and availability vs. energy harvesting rate Figure 7:
Accuracy and availability vs. location update period

Figures 8 and 9 depict the localization accuracy and availability in relation
to the utilized bandwidth and spacing between nanonodes. As shown in the
figures, both parameters have an impact on the localization accuracy, while
not influencing the availability of the service. This is because the increase
in the utilized bandwidth increases the achievable signal sampling rate. This
in turn reduces the variability of the two-way ToF measurements, benefiting
the accuracy of localization. For example, if the utilized bandwidth is
increased from 0.1 to 1 THz, the average localization error is reduced from
roughly 5 to less than 1 mm. Similarly, the spacing between the nanonodes
affects the localization accuracy, however in this case only the outliers are
affected. This is because as the spacing increases, the sizes of the
localization area increase as well, which in turn results in larger errors of
the outliers. This is a well-known behavior in more traditional localization
approaches, e.g., [59, 60].

Figure 8: Accuracy and availability vs. operational bandwidth Figure 9:
Accuracy and availability vs. spacing between nanonodes

We argue that the results presented in Figure 8 demonstrate that the proposed
localization approach can provide solid performance even with constrained
bandwidth (in the THz context), which could be a beneficial feature for
avoiding interference in case of multiple closely-located SDMs by utilizing
non-overlapping frequency bands. Note that it is well-established that RF-
interference (even only data transmission in the same frequency band) can
significantly degrade the performance of RF-based localization solutions [34,
61]. Moreover, based on the results shown in Figure 9, we argue that the
proposed localization solution can operate well across different frequencies
of the electromagnetic waves that are being manipulated by the SDM.
Specifically, assuming that the spacing between metamaterial elements equals
3/4 of the wavelength, we show that localization is feasible for SDMs used for
controlling electromagnetic waves with frequencies ranging from cc. 9.4 (i.e.,
spacing of 24 mm) to 75 GHz (i.e., spacing of 3 mm), thus encapsulating the
most interesting (at least currently) mmWave frequencies.

Figure 10: Accuracy and availability vs. receiver sensitivity

As depicted in Figure 10, the receiver sensitivity does not significantly
affect the localization accuracy and availability in the default setup for the
sensitivity levels below roughly -105 dBm. This is because all the nanonodes
are in the range of the controllers and experience relatively high received
powers. The effect on the accuracy and availability becomes more pronounced
when the receiver sensitivity is low (i.e., above -105 dBm) or when the
spacing between nanonodes further increases. This is depicted in Figure 11,
where we show the interplay between spacing and receiver sensitivity for the
spacings of 3 mm and 18 mm, while Figure 10 depicts the same for the spacing
of 9 mm. As visible in the figures, the availability of the localization
service experiences a rapid drop if the receiver sensitivity is reduced below
a certain value. This value, however, depends on the spacing between
nanonodes, hence for relatively small spacings this drop is experienced for
very low receiver sensitivities (e.g., around -92 dBm for the spacing of 3 mm,
Figure 11a) not expected in practice. As the spacings increase, the receiver
sensitivity starts playing an important role, i.e., the drops in availability
are experienced at the receiver sensitivity levels expected (cf., Figures 10)
or even unfeasible in practice (cf., Figure 11b). We believe a careful design
of the localization system, accounting for the receiver sensitivity and
spacings between metamaterial elements, will be needed for guaranteeing high
availability of localization. In case the spacings are too large and the
availability of localization is not satisfiable, as is the case in Figure
11b), introducing additional localization anchors will be required, which is a
well-known approach in increasing the accuracy and availability of more
traditional RF-based localization services [59].

(a) 3 mm spacing between neighboring nanonodes

(b) 18 mm spacing between neighboring nanonodes

Figure 11: Accuracy and availability vs. receiver sensitivity for different
spacings between nanonodes Figure 12: Accuracy and availability vs.
deployment-specific attenuation Figure 13: Accuracy and availability vs.
number of TS-OOK pulses used for two-way ToF derivation

The derivations presented above assume that the signal propagation in THz
frequencies is not affected by the attenuation from a surface to which an SDM
is mounted (i.e., Equation 3), which is not a realistic assumption for some of
the envisioned applications. Hence, in Figure 12 we also consider the
environmental attenuation $A_{ENV}$ as a high-level approximation of all
absorption and scattering losses from the surface on which an SDM is mounted
(i.e., Equation 4). As depicted in the figure, for the default simulation
parameters from Table 2, there is no significant effect of the environmental
attenuation $A_{ENV}$ until roughly 8 dB when the availability of the
localization service drops rapidly. Similar as before, the effect is only
visible in case a nanonode is not in the range of some of the controllers,
hence two-way ToF trilateration cannot be performed. In this case, additional
localization anchors will have to be introduced in the system to cope with
strong attenuation from the surface on which an SDM is mounted. In more
general terms, in the design of a system for localization in SDMs, one will
have to account for the scattering and absorption losses from a particular
surface, and the design of such a system will have to be environment specific
for attenuation-heavy environments. Nevertheless, initial studies in the
literature report around 5 dB scattering and absorption losses for different
types of sands [62], and less than 5.6 dB for losses in ordinary clothing
materials [63], suggesting that for some of the potential use-cases the
environment-specific designs might not be needed.

In Figure 13, we depict the localization accuracy and availability as a
function of the number of TS-OOK pulses used for two-way ToF estimation. As
mentioned before, each controller is envisioned to transmit a TS-OOK pulse
followed by its retransmission by a particular nanonode, which is then used
for estimating two-way ToF for that controller/nanonode pair. The same
procedure can be repeated multiple times (x-axis in Figure 13) for obtaining a
number of two-way ToF estimates for a given controller/nanonode pair. In the
consequent step, these estimates can be averaged into a single two-way ToF
estimate with lower expected variability, which in turn increases the
localization accuracy, as depicted in the figure. Example-wise, the
utilization of three averaged TS-OOK pulses instead of one reduces the maximum
localization errors in the outliers from roughly 12 to 8 mm. As shown in the
figure, the effect of increasing the number of TS-OOK pulses on the average
localization accuracy is minor, while the latency of producing location
estimates experiences a significant increase (more details in Section 5.2). In
addition and perhaps counterintuitively, the availability of localization
slightly decreases with the increase in the number of TS-OOK pulses, as show
in the figure. This is because of the increase in the number of pulses results
in higher energy consumption of the nanonodes (i.e., multiple transmissions
and receptions needed for performing two-way ToF estimation), in turn
increasing the chances of energy depletion. These observations have two
important implications. First, in the design of a localization solution for
SDMs, one should consider the requirements that the application(s) to be
supported pose on the underlying localization service. Only if the
localization accuracy with a single TS-OOK pulse cannot meet the requirements
from the applications, one should aim at increasing the number of pulses, as
this increase will inevitably affect the availability and latency of providing
location estimates. Second, the above discussion amplifies the importance of
considering multiple evaluation metrics for characterizing the performance of
localization in SDMs. In this particular case, the interplay between
localization accuracy and latency of providing location estimates has been
emphasized, although additional metrics could be considered, as in more
details discussed in Section 6.

The above results have been derived assuming the metamaterial elements are
utilized as instruction-receiving entities only, with the energy in their
operational phase being consumed for receiving an 8 bits long packet.
Additionally, we have assumed that the nanonodes are powered by harvesting the
environmental energy from air-vibrations. In Figure 14, we evaluate the
effects of different energy harvesting and energy consumption options on the
accuracy and availability of localization in SDMs. Specifically, we consider
RF-based power transfer as a harvesting option, in addition to air-vibrations.
This has been done as the SDMs are envisioned to be used for manipulating RF
signals, hence harvesting the energy from such signals becomes a feasible and
intuitive aim. Moreover, we consider the nanonodes being used for transmitting
packets to controllers, as well as the combination of sensing/actuation and
transmission. These have been selected as they reflect the SDM usage patterns
outlined in the literature [1, 2]. The transmission-only pattern has been
modeled by assuming that a nanonode transmits an 8 bits long packet in its
operational phase. For the transmission and sensing/actuation-focused
patterns, we assumed the energy is consumed in transmission (modeled in the
same way as before), as well as sensing/actuation. The energy consumed in,
respectively, sensing and actuation is assumed to be two times lower than and
equal to the energy consumed in transmission of an 8-bit packet, which is in
line with the existing literature [52].

Figure 14: Accuracy and availability vs. energy harvesting and consumption
profiles (R: receive-only; T: transmit-only; T+S: transmission and sensing;
T+A: transmission and actuation)

As shown in Figure 14, all usage patterns of a nanonode can be supported in
case of RF power transfer. This is indicated by the fact that there is no
change in the availability of the localization service for this energy
harvesting options, suggesting that the nanonodes always have enough energy to
perform localization. However, in case of air-vibrations, which is a
significantly weaker harvesting option than RF-based power transfer, the
localization service cannot be fully available, regardless of the operational
pattern of the nanonodes, which is a direct consequence of a weak harvesting
process. Moreover, the availability experiences a downward trend as the energy
consumed by the nanonodes in their operational phase increases. For example,
the availability drops from roughly 90 to 40% if the nanonodes are utilized
for actuation and transmission, instead for reception-only purposes. The above
observations shows that in the design of SDM localization one should account
for the energy consumption patterns of the nanonodes, as well as for the
amounts of energy the nanonodes are expected to harvest. If these
considerations result in imperfect availability of the localization service,
as it is the case for air-vibrations-based harvesting in Figure 14, one should
further consider the requirements from the application(s) to be supported. If
the application prioritizes the availability over the localization frequency,
one should increase the location update period. This would allow more time for
energy harvesting and result in the increased availability of the service, as
demonstrated in Figure 7.

Also note that, although we have considered that the nanonodes utilize (i.e.,
transmit or receive) an 8 bits long packet for communication in their
operational phases, the results depicted in Figure 14 can easily be translated
to packets with more or less bits. For example, the transmit-only results in
the figure are depicted for the operational phase in which the nanonodes
transmit 8 bits long packets. The same characterization would follow for the
reception of 80 bits long packets, given that the nanonodes consume an order
of magnitude less energy in the reception than in the transmission of a TS-OOK
pulse. For this reason, we argue that the performance in case of larger
packets in different operational states can be directly interpolated from the
results depicted in Figure 14. Thus, the localization accuracy and
availability as a function of a number of bits in such a packet were not
considered.

Until now, we have assumed that the controllers’ locations are known and
perfectly accurate. As mentioned, we base this assumption on the fact that
there are use-cases where an SDM can be mounted on a surface in a way that the
controllers’ locations are fixed and can be measured. For the use-cases where
that is not the case, we have argued that, given that the controllers are not
power-constrained, their locations can potentially be estimated by some other
more traditional localization approach or by the same approach as the one
utilized for localization of metamaterial elements, only with increased
transmit power. Whatever the method for localizing the controllers, it will
inevitably feature a certain level of localization errors.

Figure 15: Accuracy and availability vs. error in controllers’ localization

In Figure 15, we demonstrate the effects of imperfect accuracy of controllers’
localization. The per-axis localization errors have been modeled as zero-mean
Gaussian random variables, which is an established method frequently used in
the literature (e.g., [59, 64]). Note that in the figure, we depict the per-
axis standard deviation of the localization error, not the standard deviation
of the overall localization error in the controllers’ localization. As
depicted in the figure, the accuracy of nanonodes’ localization decreases with
the increase in the localization errors of the controllers’ localization.
Nonetheless, as we have shown before that two-way ToF-based trilateration can
achieve sub-millimeter level accuracy of localization of the nanonodes, it is
intuitive that comparable (potentially even better) accuracy can be achieved
in the controllers’ localization. This is because the controllers are not
power-constrained, thus they can utilize higher transmit powers in their
localization. If we assume the average localization error in controllers’
localization to be 1.4 mm, which is considerably higher than the one
demonstrated for nanonodes’ localization, the per-axis error in a 3D space
roughly equals 0.8 mm. As depicted in Figure 15, such a per-axis error
increases the average localization error from roughly 1 to 2 mm, with most
affects being visible in the outliers. For example, if the controllers’
locations are not perfectly accurate but feature a per-axis error of 0.8 mm,
the errors of outliers in SDM localization increase to around 20 mm, in
contrast to such errors being consistently lower than 12 mm for perfectly
accurate controllers’ locations. We argue that only a slight increase in the
average errors due to the imperfect localization of the controllers shows that
the system can operate well even if the controllers are not fixed and their
locations are not known with perfect accuracy.

Figure 16: Accuracy and availability vs. number of controllers

In Figure 16, we depict the effects of different number of controllers on the
accuracy and availability of localization in SDMs. As shown in the figure, the
accuracy increases with the increase in the number of controllers used as
anchors for localization. However, this benefit comes at the cost of a more
complex design due to the increased number of controllers, as well as an
increased latency of SDM localization. Also note that, because of the
increased chances of nanonodes’ power depletion, the availability of
localization slightly decreases with the increase in the number of
localization anchors. Similar as with the increasing number of TS-OOK pulses
used for two-way ToF estimation (cf., Figure 13), increasing the number of
controllers should be attempted only if the application to be supported
requires higher localization accuracy than the one that can be delivered by
using the minimum required number of controllers (i.e., four for localization
in a 3D space).

Figure 17: Accuracy and availability vs. mobility patterns of the nanonodes

Finally, Figure 17 depicts the effects of the nanonodes’ mobility patterns on
the accuracy and availability of localization in SDMs, respectively.
Specifically, the figure shows that the localization accuracy of the outliers
decreases in case of cylindrical and spherical mobilities compared to fully
random one. We argue this can be attributed to the fact that trilateration-
based localization in general yields better performance for locations closer
to the center of a deployment environment, while the performance degrades
closer to the edges of the environment [34, 65]. In case of the random
mobility, more nanonodes are located closer to the center of the localization
environment, while for the cylindrical and especially spherical patterns the
nanonodes are, generally speaking, located closer to the edges of the
environment. Note that if the mobility pattern is to an extent predictable, as
is the case for the spherical and cylindrical ones, the accuracy of
localization could potentially be improved by imposing certain constrains on
the nanonodes’ estimated locations based on the estimated locations of their
neighboring nanonodes. Despite the slight increase in the outliers’
localization errors for the spherical and cylindrical patterns, the results
demonstrate that the proposed approach can work well for different types of
nanonodes’ mobility.

###  5.2 Latency of Location Estimation

From traditional RF-based localization research, it is known that the latency
of generating and reporting location estimates is hardware-specific [66, 47,
34, 67]. Thus, without hardware implementations it is arguably impossible to
quantify the latency of localization. Nonetheless, qualitative
characterizations or trends can still be derived. Hence, in the following we
aim at deriving the qualitative latency of localization as a function of the
number of nanonodes to be localized, the number of controllers used for their
localization, and the number of TS-OOK pulses used for deriving a single
controller/nanonode two-way ToF estimate.

Let us assume that the time needed to obtain a two-way ToF estimate for one
controller/nanonode pair equals $t_{ToF}$, while the time needed to perform
trilateration for one nanonode once all ToF estimates are obtained equals
$t_{tr}$. Moreover, let $m$, $n$, and $k$ be the number of nanonodes,
controllers, and TS-OOK pulses used for two-way ToF estimation for one
controller/nanonode pair. The latency of localization then consists of the
time needed to obtain two-way ToF estimates for all controller/nanonode pairs,
as well as the time needed to perform trilateration, multiplied by the number
of nanonodes to be localized. In the first approximation, we can assume that
the time to perform trilateration for one nanonode is constant and does not
depend on the number of controllers or TS-OOK pulses used in localization. We
consider this to be a reasonable assumption, given that this computation time
is in practice much lower than the time needed for obtaining the necessary
signal features [55, 68], in this case two-way ToF estimates. Under these
assumptions, the latency $t_{loc}$ of localization of all nanonodes whose
location is to be estimated can be written as:

$t_{loc}=m(nkt_{ToF}+t_{tr}).$ (5)

As expected, the localization latency increases with the increase in the
number of nanonodes, controllers, and TS-OOK pulses used for deriving a two-
way ToF estimate. A graphical representation of the qualitative localization
latency characterization is given in Figure 18, assuming $t_{ToF}>>t_{tr}$.
Given that the latency increases linearly with the increase in the number of
nanonodes, anchors, and TS-OOK pulses, it is intuitive that the increase in
the number of TS-OOK pulses used for estimating two-way ToF for one
controller/nanonode pair has the most significant negative effect on the
latency of localization. This is because the increase in the number of TS-OOK
pulses scales up the latency proportionally to the number of
controller/nanonode pairs. Adversely, increases in the number of controllers
and nanonodes affect the localization latency in proportion to the number of
nanonodes and controllers, respectively. Thus, in the attempt to increase the
accuracy of localization, one should first aim at increasing the number of
controllers, followed by increasing the number of TS-OOK pulses used for
deriving one two-way ToF estimate. One should also keep in mind that the
latency of localization will increase with the increase in the number of
nanonodes. In order to maintain the localization latency below a certain
threshold if an application to be supported requires that, one could aim at
increasing the number of SDM subsystems (one such subsystem depicted in Figure
1) instead of increasing the number of nanonodes in one subsystem.

Figure 18: Qualitative characterization of localization latency

##  6 Open Challenges

Again grounded in the novelty of localization in SDMs, we consider it
beneficial to provide our perspective on the remaining open challenges in the
realization of such systems.

Novel Use-Cases: Although we have outlined several high-level example use-
cases where localization in SDMs could be beneficial, we believe a more
comprehensive and detailed overview is needed. Providing an exhaustive
overview of the potential benefits would make the topic more tangible and,
therefore, more attractive to the wider research community. By stating
“providing a more detailed overview” we primarily refer to an overview that
specifies the performance requirements that the use-cases pose on the
underlying localization service. This would address the problem that we will
illustrate with the following example. In this work, we have demonstrated a
sub-millimeter achievable accuracy and relatively high availability of the
proposed localization service. However, at this point we cannot provide
scientifically accurate statements about the sufficiency of such a service in
enabling all the envisaged use-cases, or any for that matter. Hence, the
specifications of the potential use-cases should be detailed in the sense that
they quantitatively characterize the requirements that a certain use-case
poses on the underlying localization service.

System-level Perspective: A system-level solution for localization in SDMs is
also required, which could be designed by specifying the signaling
requirements and protocols. For example, we assumed that two-way ToF
measurements can be derived for each controller-nanonode pair. In reality,
deriving such measurements will require a protocol that defines a sequence
according to which the nanonodes should transmit signals for ToF estimation.
In this direction, one should realize that, although the SDMs will support
structural deformations, the network structure will not change, apart from the
nanonodes potentially going out of range or turning off due to the energy
depletion. In other words, the controllers will always be controlling the same
sets of nanonodes (i.e., metamaterial elements). This suggests that the two-
way ToF estimation between a controller and the nanonodes could be done
sequentially, potentially even without the need for physical-layer preambles
and MAC-layer headers. We consider the evaluation of this hypothesis to be an
open challenge.

We also believe the time needed for obtaining the required ToF measurements
could be significantly reduced along two main directions. First, by properly
designing the system one could potentially parallelize the ToF measurements
from the standpoint of the controllers, i.e., all controllers could at the
same time be performing ToF estimations if there is no interference between
the one-controller subsystems. Second, one could also embed ToF estimations
from a number of nanonodes in a fixed time interval $\beta$ between
transmission of two consecutive TS-OOK pulses (or silences). Specifically, in
TS-OOK the time between transmissions is fixed and much longer than the pulse
duration (usually two to three orders of magnitude) [44], which is a feature
originally designed so that the communicating devices do not have to be
tightly synchronized, as well as to reduce the effects of interference from
collocated transmissions. By carefully designing the reactions of the
nanonodes to the pulse transmitted by the controller, one could achieve a
number of ToF estimations by transmitting only a single TS-OOK pulse on the
controller level. Note that such an approach would also benefit the energy
efficiency of the solutions, as the nanonodes would consume energy for
receiving only one TS-OOK pulse, in contrast to a number of them if the
estimation is done by sending a pulse by the controller for each
controller/nanonode pair.

Localization Approaches: In this work, we have considered the main instances
of traditional RF-based localization approaches and argued that two-way ToF-
based trilateration is the most suitable among them for enabling localization
in SDMs. In other words, we believe that the traditionally utilized
alternatives, primarily AoA-based triangulation and RSS-based trilateration
approaches, cannot be utilized for localization in SDM in the near future due
to the specifics of the nanoscale scenario at hand. In a hypothetical example
of achieving the AoA resolution of 0.75 degrees and RSS variability
characterized with a zero-mean Gaussian distribution with standard deviation
of 0.3 dB, one would be able to localize the SDM elements with the accuracies
as shown in Figure 19. Note that the selected resolution and variability
values are significantly lower than what the state-of-the-art macro-scale THz
systems are able to achieve [69, 70]. Comparable AoA resolutions and RSS
variabilities at nanoscale are, therefore, hardly achievable in the near
future, hence we portray these results only as a hypothetical example. In
addition, in the derivation of the results depicted in the figure, we did not
consider the energy consumption of each of the approaches, but assumed that
the nanonodes have sufficient energy for localization. This is mainly due to
inability of modeling energy consumption in AoA-based triangulation, given
that such a system intrinsically cannot be built assuming omnidirectional TS-
OOK-based nanoscale communication. The other simulation parameters are
consistent for all three approaches from Figure 19 and summarized in Table 2.
As depicted in Figure 19, the ToF-based localization yields more than an order
of magnitude lower localization errors than the two considered alternatives.
This is a direct result of a large available bandwidth at THz frequencies,
which, we believe, makes an argument for further developments of ToF-based
localization approaches for THz-operating TS-OOK-based nanoscale communication
systems.

Figure 19: Localization accuracy in comparison to AoA-based triangulation and
RSS trilateration-based localization

However, in our evaluation we have assumed large channel bandwidth (implying
extreme sampling rates and fine-grained time discrimination on the level of a
nanonode) that are hard to achieve in practice. We have done this because our
aim was to demonstrate the potential of localization in SDMs by showing its
theoretical performance limits. Nonetheless, there are several approaches in
the existing literature aiming at generating accurate two-way ToF measurements
under limited sampling frequencies [71, 55], as well as for tight pulse-based
synchronization at the nanoscale [72, 73]. The applicability of such
approaches for the problem at hand is yet to be established.

Given that the traditional RF-based localization research is at this point
abundant, we believe there are other lessons to be learned from those efforts.
Hence, more advanced SDM localization approaches could be developed, which
would in turn further advance the performance of localization in SDMs. One
approach we have considered is multi-dimensional scaling [74], a localization
approach that assumes the existence of an interconnected graph between
(nano)nodes. Based on the graph, the approach is able to estimate the
locations with higher accuracy than regular trilateration [75], and it works
particularly well for structured grid-like graphs, hence it is intuitively
suitable for SDMs. However, we have observed that the energy consumed in the
process of obtaining and delivering all ToFs (distances) between connected
nanonodes to the controller level makes the approach infeasible for the
primarily considered nanonodes with air vibration-based energy harvesting.
Nonetheless, this does not imply that other approaches could not advance the
currently reported performance metrics.

One could also consider entirely replacing RF-based localization with other
types of approaches. For example, a inductive coupling-based localization
approach has been shown to yield promising performance at the microscale [76].
However, it is currently unclear if such a solution can be further downscaled
and if the power consumption of such a miniaturized solution would be
acceptable from the perspective of energy harvesting nanonodes.

Anchor/controller Localization: In this work, we have assumed the localization
anchors are either fixed or their locations can be estimated with high levels
of accuracy. Although we believe the assumption of the anchors’ locations
being fixed, therefore measurable and perfectly accurate, is feasible for some
use-cases such as e.g., structural monitoring, for others there will certainly
be a need for estimating the locations of the anchors. The question on how to
perform such localization is currently not clear, given that in order to
localize the nanonodes, the accuracy of the anchors’ localization should be
higher than what the existing approaches (mostly using sub-6 GHz frequencies)
can achieve. We believe the answer here lies in the utilization of high
frequency and high bandwidth localization approaches (i.e., mmWave and THz)
that show a high promise in enhancing the accuracy of localization [35, 77].
However, the question of the feasibility of such approaches is, to the best of
our knowledge, still open, especially for the challenging environments (e.g.,
smart textiles worn by a person) relevant in this context.

Prototypical Implementations: By modeling and simulating a new localization
solution one can obtain initial insights on its performance in realistic
deployments. For example, [35] is an early work on mmWave macro-scale
localization, where the authors utilize a simulation-based approach for
demonstrating that trilateration-based localization in mmWave frequencies can
achieve the accuracy on a decimeters-level. The utilized simulation approach
is similar in its degree of realism to the one utilized in this work. These
initial implications have been experimentally confirmed by [77], where the
authors demonstrated the average localization error of around 30 cm for ToF
and AoA-based trilateration. Prototypical implementations of localization-
enabled THz-operating power-constrained SDMs will be needed for confirming (or
discarding) the insights made in this and potentially future simulation-
oriented works. In this direction, pioneering efforts on developing graphene-
based antennas [41, 78] and transceivers [79, 80], micro and nanoscale energy-
harvesters [81, 82, 83, 84], as well as SDMs prototypes [3, 85, 86, 87, 88,
89, 90] are worth emphasizing.

Performance Evaluations: Similar as in traditional localization utilizing RF
signals, in the context of nanoscale localization in SDMs multiple performance
metrics will be needed to fully characterize the performance of newly proposed
localization systems. For example, the EVARILOS Benchmarking Handbook [49]
provides the specifications of an exhaustive set of such metrics, encompassing
among others the localization accuracy, reliability (i.e., availability),
latency, energy efficiency, deployment overhead, scalability, etc. In
addition, the handbook aims at standardizing the experimentation conditions
required for the benchmarking of new solutions, so that the obtained
benchmarks can later on be compared among each other in a meaningful way. In
the context of nanoscale localization in general, such specifications and
benchmarking guidelines do not exist, which could result in incomparable
performance results with low utility.

In the consequent step, experimental benchmarking should ideally be performed
under the same conditions (e.g., same environment, same hardware, evaluation
points), which is an issue that has been recognized in the community focused
on traditional RF-based localization, resulting in a number of localization
competitions and similar events aiming at comparative benchmarking of
localization solutions (e.g., [91, 34, 67]). Consequently, the data obtained
in the experimentation started becoming available and even accessible through
web services and platforms, so that the only thing an experimenter has to do
is to upload the code of a localization solution, while the service deals with
feeding it unified experimental data, gathering and processing of the outputs
provided by the solution, and positioning of the solution in the context of
already benchmarked ones [92, 47, 48, 93]. Similar tools and methodologies are
needed for nanoscale localization to avoid the “status quo” where various
parties claim the general superiority of their localization solution based on
incomplete and incomparable performance benchmarks.

Finally, if the applications require that the localization errors of all
estimates are below a certain threshold, one could attempt to develop a system
for estimating localization errors on a per-estimate basis, followed by
discarding the estimates whose errors are predicted to be higher than the
threshold. In this direction, it is worth emphasizing [38], where the authors
utilize machine learning for solving this problem. They show that the system
can achieve the accuracy of estimation of localization errors of an per-
estimate basis that is significantly higher than the one that can be obtained
through static benchmarks. Nevertheless, the proposed system is focused on the
macroscale, considers a different localization approach (i.e., fingerprinting
vs. trilateration) and different networking technologies (i.e., SigFox and
LoRa vs. in-body nanonetwork), among others. Hence, the utility of such or
similar systems for the considered setup is yet to be established.

##  7 Conclusion

We have shown that the two-way Time of Flight (ToF)-based trilateration has a
potential for enabling accurate localization in Terahertz (THz)-operating and
power-constrained Software-Defined Metamaterials (SDMs). We base our
indication on the sub-millimeter accuracy and high availability of
localization for the system parameterizations expected in real-life SDM
implementations. Moreover, we have qualitatively characterized the effects of
several relevant system parameters. Example-wise, we have shown that the
utilized bandwidth significantly affects the localization accuracy, while the
energy harvesting rate and location update period play an important role in
the service availability. Finally, we have shown that the proposed
localization solution can be introduced to energy-harvesting (and therefore
power-wise highly constrained) nanonodes without incurring significant energy-
related constraints to the operation of the nanonodes.

In conclusion, we argue that this work provides a new argument for the
utilization of THz-based wireless solutions for the control and programming of
SDMs, in contrast to the utilization of wired solutions. This is because a
wireless solution, in addition to being form-factor-wise superior, would allow
localizing the metamaterial elements under mobility, which in turn could be an
enabler of novel applications, as well as novel approaches for location-based
optimization of the nanonetwork for controlling SDM elements. Future work will
focus on addressing some of the challenges outlined in this paper.

## Acknowledgments

This work was supported by the EU Marie Curie Actions Individual Fellowship
(MSCA IF) project Scalable Localization-enabled In-body Terahertz Nanonetwork
(SCaLeITN), grant nr. 893760. Filip Lemic’s research stay at the Terahertz
Wireless Communications Lab at Shanghai Jiao Tong University, China was
supported by the Research Foundation - Flanders (FWO) in the form of a grant
for a long stay abroad (grant nr. V406320N). This work also received support
from the European Union via the Horizon 2020 Future Emerging Topics call
(FETOPEN, grant no. 736876).

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  *[2D]: 2-Dimensional
  *[THz]: Terahertz
  *[WSN]: Wireless Sensor Network
  *[IoT]: Internet of Things
  *[RF]: Radio Frequency
  *[ToF]: Time of Flight
  *[TS-OOK]: Time-Spread ON-OFF Keying
  *[SDMs]: Software-Defined Metamaterial
  *[WSNs]: Wireless Sensor Network
  *[LoS]: Line of Sight
  *[RSS]: Received Signal Strength
  *[AoA]: Angle of Arrival
  *[3D]: 3-Dimensional