# A Holistic Investigation on Terahertz Propagation and Channel Modeling
Toward Vertical Heterogeneous Networks

Kürşat Tekbıyık, Ali Rıza Ekti, Güneş Karabulut Kurt, Ali Görçin, Halim
Yanikomeroglu K. Tekbıyık and G.K. Kurt are with the Department of Electronics
and Communications Engineering, İstanbul Technical University, İstanbul,
Turkey, e-mails: {tekbiyik<EMAIL_ADDRESS>Tekbıyık, A.R. Ekti, and A.
Görçin are with Informatics and Information Security Research Center (BİLGEM),
TÜBİTAK, Kocaeli, Turkey, e-mails: {kursat.tekbiyik, aliriza.ekti,
<EMAIL_ADDRESS>Ekti is with the Department of
Electrical–Electronics Engineering, Balıkesir University, Balıkesir, Turkey,
e-mail<EMAIL_ADDRESS>Görçin is with the Department of Electronics
and Communications Engineering, Yıldız Technical University, İstanbul, Turkey,
e-mail<EMAIL_ADDRESS>Yanikomeroglu is with the Department of
Systems and Computer Engineering, Carleton University, Ottawa, Canada, e-mail:
<EMAIL_ADDRESS>
###### Abstract

User-centric and low latency communications can be enabled not only by small
cells but also through ubiquitous connectivity. Recently, the vertical
heterogeneous network (V-HetNet) architecture is proposed to
backhaul/fronthaul a large number of small cells. Like an orchestra, the
V-HetNet is a polyphony of different communication ensembles, including
geostationary orbit (GEO), and low-earth orbit (LEO) satellites (e.g.,
CubeSats), and networked flying platforms along with terrestrial communication
links. In this study, we propose the Terahertz (THz) communications to enable
the elements of V-HetNets to function in harmony. As THz links offer a large
bandwidth, leading to ultra-high data rates, it is suitable for backhauling
and fronthauling small cells. Furthermore, THz communications can support
numerous applications from inter-satellite links to in-vivo nanonetworks.
However, to savor this harmony, we need accurate channel models. In this
paper, the insights obtained through our measurement campaigns are
highlighted, to reveal the true potential of THz communications in V-HetNets.

##  I Introduction

Flexible wireless communication architectures including small cells, cell-free
designs, heterogeneous networks, and multi-band connectivity are widely
aspired by the telecommunication industry for the user-centric system designs
toward 6G and beyond to provide the required quality of service (QoS) levels
among users [1]. Even though free-space optics (FSO) and mmWave technology
have been discussed over the years, they are not capable of making this dream
possible on their own. THz wireless communication will be a critical enabler
for 6G since it proposes a solution for the unlicensed band scarcity below
$100$ GHz and it can be employed by not only macro-scale networks (e.g.,
inter-satellite links) but also by nano-scale networks (e.g., nanonetworks)
[2]. The small cell concept has not been fully deployed yet because of the
backhaul and fronthaul cost. It is thought that along with the development of
non-terrestrial networks, the pervasive connectivity can be provided, as well
as the backhaul and fronthaul required by small cell and cell-free topologies
[3]. This 3D-network structure, depicted in Fig. 1, is termed as the V-HetNet.
As THz communications can offer an enormous bandwidth enabling ultra-high data
rates, it stands out among the competing solutions that are likely to be used
in V-HetNets. Although the transceiver costs for THz communication are
currently high, a cost reduction is expected with the developments in
semiconductor technologies.

This study presents an overview of the THz-enabled V-HetNets framework. Below,
we explain the motivation behind the THz communications in V-HetNet and
address challenges. By interpreting THz channel behavior with measurement
results, tips are given on how the system design and requirements will be
affected by channel behavior in V-HetNets. Finally, we pinpoint the open
issues for the realization of THz-enabled V-HetNets by considering the
measurement results.

Figure 1: The THz-enabled V-HetNet framework including GEO, and LEO
satellites, and NFPs along with terrestrial communication links. Furthermore,
THz networks will be a crucial enabler for the nanonetworks due to antenna
size, while enabling the operation of HetNets in harmony to support e-health
applications.

##  II Why Terahertz band?

Besides being a candidate technology for 6G, THz communications imply a
remarkable potential for the future of wireless communications as detailed
below.

###  II-A Utilizing the not Fully-explored Frequencies

There is a need to push the carrier frequency beyond the mmWave band to
overcome the spectrum scarcity below $100$ GHz. The THz band allows wireless
communication through tens of GHz bandwidth. Even though the path loss
increases with frequency, the antenna gain is related to the square of the
operating frequency. Therefore, high gain antennas can cope with the extreme
path loss in the THz band. As known, antennas with high operating frequency
have relatively narrow beams compared to lower frequencies; hence, THz
antennas can be utilized in point-to-point links to backhaul small-cells.
Moreover, since the antenna size decreases with frequency, it is possible to
place a massive number of antennas on small surfaces. For example, it is
possible to cover $1$ $\mathrm{mm}^{2}$ area with four antennas at $300$ GHz.
Beyond the massive-multiple-input multiple-output (mMIMO), namely ultra-
massive-MIMO (UM-MIMO) [4], can be employed to leverage the communication
distance as well as the data rate enhancement. Although today’s technology is
in scarcity for high power THz transmitters, it is expected that signal
generators with high power can be created in the near future considering
studies on graphene and InGaAs mHEMT MMICs.

###  II-B Revolutionary Network Design Towards 6G

####  II-B1 Cell-free Networking

It is widely acknowledged that an architectural revolution is needed in 6G and
beyond [5]. Tiny cells and a cell-free architecture are demanded to cater the
data-hungry end-users. In this regard, the high path loss, which is the main
drawback of the THz band, can be turned to account for the cell-free design.
In other words, the THz band is the region with the highest frequency reuse
factor. Thus, it can be concluded that the THz band is ideally suited for the
cell-free networking. Not only backhaul from access points to core network but
also links between AP and user equipments can utilize THz waves to build up a
cell-free network and satisfy the high data rate for backhaul. To support
cell-free networking, a user-centric approach can be adopted for the spatial
multiplexing by using UM-MIMO. Additionally, distributed APs are required
fronthauling to the central processing unit. Therefore, cell-free networking
can utilize the THz waves to avoid fiber construction to every AP.

####  II-B2 Vertical Heterogeneous Networks

Recently, since aerial APs such as unmanned aerial vehicles, NFPs, and high-
altitude platform stations attract considerable attention, there has been an
unprecedented vertical directional expansion in the wireless network.
Furthermore, it seems that data flow between satellites and earth will
increase more than ever in the coming years [6]. Although a dense satellite
network has started to be established with the Starlink project and the
Keppler project, the studies in this area are still nascent. FSO and mmWave
technologies have been proposed for the inter-satellite and satellite-to-X
links. However, mmWave can only serve through a total of $9$ GHz bandwidth of
the available unlicensed bands. On the other hand, as CubeSats are designed
for LEO operation, they need to move with a velocity of $28\times 10^{3}$ kph
to keep their orbits. This velocity necessitates fast beam steering; hence,
FSO with a mechanical gimbaled beam steering mechanism is susceptible to track
the moving target. However, one face of $1$U CubeSat can be theoretically
covered by $10^{4}$ antennas operating at $300$ GHz. Furthermore, to the
extent allowed by the flight dynamics, the bottom of the NFP’s wings can be
covered with hundreds of antenna. Therefore, THz enables to fast track a
moving receiver with the help of electronic steering.

THz mMIMO setups can be grouped to serve a different number of users according
to demand as illustrated in Fig. 2. These enable a flexible communication
network that can be dynamically shaped in conformity with the need [7]. For
example, the capacity demand possibly exceeds the target demand when event
times or stadiums serve as an emergency assembly area. Here, THz-aided HAPSs
can be used as a flexible communication structure to meet the increasing
demand. Given the effort of each new generation to make the network more
flexible, THz communications has the potential to be a crucial enabler for 6G
and beyond.

Figure 2: THz networks can employ ultra-massive antenna arrays; hence, it can
be turned into an advantage by dynamically adjustable beam pattern and
multiple spot flexibility.

####  II-B3 Multi-connectivity

Ultra-reliable and low-latency communications in 5G require a high QoS due to
stringent requirements on availability and latency. Diversity and network
availability increase as the user communicates with more than one AP to
improve QoS. We infer that 6G and beyond systems can employ different
technologies to enhance the QoS levels. For example, in the THz band,
different sub-bands/windows can be used for communication at the same time, or
complementary technologies such as mmWave, FSO, and THz can be used
simultaneously.

###  II-C Applications from Planetary-scale to Nano-scale

In the V-HetNet framework toward 6G and beyond, it is envisioned that the
world, which was previously connected by ground and undersea fiberoptic
cables, is now connected over a wide space network. The near future
communication technology pushes the limits of science-fiction. With the
development of e-health technologies, billions of nanodevices and sensors need
to be connected to the medical center over a unified and seamless network to
enable low-latency communications. It is envisaged that using the THz band in
V-HetNets will be useful to meet the latency and data rate required by
e-health and haptic applications due to extremely short THz pulses on the
order of femtoseconds [8]. For example, the THz band paves the way for
unprecedented applications initially suffering from the size, weight, and
power (SWaP) constraints. The size of nanomachines can only be satisfied by
the THz antennas. As illustrated in Fig. 1, THz waves can be employed in the
harmony of nanonetworks, body area network (BAN), and wireless local area
network (WLAN). For instance, nanomachines communicate with each other and
sensors with THz waves. BAN can utilize either IEEE 802.15.62 or mmWave (e.g.,
WiGig). The backhaul of AP can be a directional THz beam.

###  II-D Economic Feasibility

To achieve resilient and reliable connectivity, mmWave and THz band connection
are needed as described in Section II. Furthermore, the mmWave technology
market in the telecommunication industry, which is anticipated to reach
$\$10.92$ billion by 2026 with a growing compound annual growth rate of
$36.3\%$ per year, along with the corresponding industrial ecosystem, makes it
attractive for the network operators and semiconductor companies [9].
Therefore, adopting mmWave and THz band communication will stimulate the
economy along with supporting Tbps data rates, novel usage scenarios, and
applications. Thus, network operators exhibit particular interest in the
proper adoption of the THz band communication, which can further reduce the
total cost of ownership, capital expenditures, and operational expenditures.
Deploying a macro base station in a crowded and populated location such as
downtown and providing seamless high-speed data rate connectivity to the
remote islands and rural/suburban areas can be quite challenging and also very
expensive due to the harsh geographical conditions. Thus, extending the
wireless connectivity with the help of existing infrastructure to the areas
beyond the reach of the fiberline by using the THz band is anticipated to
reduce the total cost. First, no additional or significant upgrades are needed
for the backhaul traffic by the network operators since already existing
infrastructure will be used for the traffic offloading which will ease the
traffic congestion problem. Second, as for the software and hardware of the
radio access network, there is no need for extreme modifications. Furthermore,
the recent advances in the semiconductor technology enable to design at THz
frequencies; thus, antenna and chip can be integrated into the same package to
reduce the production cost.

##  III Operational Challenges

Attractive properties of THz wireless communication can make it possible to
build up the wireless communication network of the future. Nevertheless, there
are many challenges to overcome. The state-of-the-art semiconductor technology
cannot generate high power THz waves. However, some promising transceiver
designs have been proposed. It seems that a high output power transceiver will
be designed by discovering the essence of graphene and complementary metal-
oxide semiconductor (CMOS). Although the transmit power of CMOS power
amplifiers is about $1$-$10$ mW, they are in line with SWaP constraints [10].
Fortunately, it is possible to design high gain antennas in this spectra to
recover the signal power.

In V-HetNets, we do not expect THz waves to suffer a severe loss in inter-
satellite communication. The main problem is the operating temperature of the
satellites. The temperature fluctuates concerning the position of Earth and
Sun. Satellites already have a thermal control system (TCS) to maintain stable
operation against changes in operating temperature. However, it may require to
review the design of TCS. Recently, NASA-JPL has pushed receiver design limits
toward CubeSats. THz-enabled satellite communication in the near future is not
pie in the sky.

Since HAPSs fly above the troposphere, which $99\%$ of the water vapor in the
atmosphere is at this layer, no severe path loss is expected between HAPSs and
LEO satellites. But, the relatively high speed between HAPSs and satellites,
and the sharp beam of THz antennas require stringent tracking of transmitter
and receiver. The electronic steering functionality of UM-MIMO can provide
fast and accurate tracking with the cost of large antenna arrays.

A high attenuation rate is observed between HAPSs and ground stations since
water vapor absorbs most of the power of the THz wave, and the region where
the water vapor is most dense in the atmosphere is up to $20$ km above the
Earth. The atmospheric attenuation coefficient at $300$ GHz is around $3$
dB/km and $30$ dB/km for very light and dense humidity levels, respectively.
The attenuation coefficients imply that the THz wave is more advantageous than
FSO in terms of path loss [3, 11].

Another challenge lies in UAV communication. UAVs with high mobility vibrate
slightly, even when they are suspended in the air, due to flight aerodynamics.
This poses a serious challenge to THz communication, which has a very narrow
antenna beam. The loss due to misalignment between THz antennas is known to be
severe [12]. The beam search may take a long time after the antenna alignment
deteriorates. At this point, we think that it would be appropriate to make THz
communication with wider beams using beam broadening. Also, the phased array
can be adaptively controlled with the help of a Kalman filter and gyroscope on
the UAV; however, this can cause energy scarcity for battery-dependent UAVs.

As high data rate THz pulses have very short-times; multipath components may
not overlap with the first-path component. However, the propellers’ periodic
behavior may give rise to rotor modulation. As the wavelength is much smaller
than propellers, a simple blockage model can be utilized to analyze the effect
of the rotor modulation.

There are additional challenges that may occur in each layer of V-HetNet.
These include beam steering, high-performance computation, and low-complexity
tracking. Also, ultra-large antenna array configuration, mutual coupling among
antennas, and correlation among sub-channels should be jointly considered in
the design of UM-MIMO [2]. One of the main challenges is to estimate the
propagation channel for UM-MIMO THz communication. Since it is expected to use
UM-MIMO systems with thousands of antennas, novel intelligently designed
channel acquisition algorithms are needed. Deep learning (DL)-based channel
estimation techniques can be utilized ubiquitously. The sparse nature of THz
wireless channels allows using compressed sensing so that the complexity of
acquisition methods can be reduced.

##  IV Overview of Measurement Studies

###  IV-A Channel Modeling Methodologies

Wireless channel modeling is mainly categorized under two approaches:
deterministic and stochastic methods. The deterministic methods are
propagation medium-specific. They require the model of the environment in-
depth with the material characteristics and dimensions. Although an accurate
channel model is obtained for a given environment, the computation complexity
is extremely high, and it exponentially increases with the dimensions of the
environment. Ray-tracing is the most used deterministic technique for channel
modeling. Ray-tracing models the scattering, diffraction, and reflection
effects in with geometric optics. Finite-difference time-domain, method of
moments (MoM), and finite element method (FEM) are some of the other
deterministic channel modeling techniques. Since MoM and FEM are working in
the frequency domain, these methods do not seem to be the best approach as
they require excessively complex computations in channel modeling for a huge
THz band, but geometric optics that become more accurate due to the stronger
corpuscular behavior in the THz band.

Unlike deterministic modeling, stochastic channel modeling aims to create a
channel model independent of the environment as much as possible. For this
purpose, a statistical average of many measurements is used to create the
channel model. For the stochastic channel modeling, measurements are usually
carried out with a vector network analyzer (VNA) or channel sounder. The main
difference between these devices is the domain where they perform operations.
Channel sounder computes the channel impulse response by using an uncorrelated
m-sequence, but VNA composes many narrowband measurements to create channel
transfer function. VNA performs more accurate channel modeling due to
calibration for each narrowband and encountering low noise, but the
measurement time is long [13]. Another difference is that VNA-assisted
measurement does not require extra clock synchronization due to two ports in
the same device, whereas channel sounder requires a strict external clock to
sync two distinct ports.

Due to the presence of the colossal bandwidth, multipath components can be
distinguished. The nature of the THz band leads to severe frequency
selectivity. As a result, conventional small scale flat fading models are not
appropriate, and the broadening effect cannot be ignored.

###  IV-B Measurement Setup and Results

In this section, we detail the THz measurement campaigns and results. Firstly,
VNA-assisted measurements are carried out to observe THz channel behavior with
high spectral resolution. Afterward, pulse-based measurements for short-range
THz communication will be addressed since on-off keying (OOK) is seriously
envisaged for use in THz wireless communications [8]. The VNA-assisted
measurement provides high spectral resolution at the cost of long measurement
time while the pulse-based method lacks high resolution, but it allows taking
measurements in a short time.

####  IV-B1 VNA-assisted Channel Modeling

An experimental measurement setup is constructed in the anechoic chamber with
dimensions of $7\mathrm{m}\times 3\mathrm{m}\times 4\mathrm{m}$ as seen in
Fig. 3. To eliminate the specular effects, the perimeter of the system is
covered with absorbent material. The measurement setup consists of a VNA,
WR-03 waveguided extension modules, and an extender controller. WR-03
extension modules expand the VNA, whose upper limit is $67$ GHz, to THz band
by multiplying RF input signal with $18$. In cases where an extender module is
used, it should be preferred to use as few frequency multipliers as possible.
This is observed due to the increasing number of striking, phase distortion,
and intermodulation product effect increases. A single multiplier, if
possible, is preferred to avoid mentioned distortions. The extender module
employed in this setup includes single frequency multiplier.

Figure 3: The measurement setup consists of VNA equipped with THz extender
modules with WR-03 waveguide, and extender controller.

Driving VNA with the input signal in between $13.34$ GHz and $16.67$ GHz
results in THz waves with carrier frequencies in between $240$ GHz and $300$
GHz. To protect the phase and amplitude stability, instead of using all the
band provided by the extender, measurement is taken in the band between $240$
and $300$ GHz by not using the edge points of the band [12]. The IF signals
downconverted at transmitter and receiver are used to find channel transfer
function by comparing them to acquire scattering parameters (i.e., $S_{21}$).
VNA-assisted channel modeling provides high-frequency resolution by taking
measurements. $4096$ frequency points are employed within the operation band
demarked by the VNA. As a result, $14.648$ MHz spectral resolution is provided
by the measurement setup.

By using measurement results, the frequency dependency of the path loss is
revealed in [12]. The measurement results indicate similar channel behavior at
varying distances. However, the loss in some frequency intervals is higher
than in others. For example, there is a noticeable reduction in the power of
the received signal between $270$ GHz and $290$ GHz. As stated above, antenna
alignment is crucial for THz communication because of the relatively narrow
beamwidth. It is shown that the pointing error in antenna alignment gives rise
to a sharp fall in the received power. Since the received power decreases
exponentially, it is reasonable to model this decay as an exponential
distribution. The pointing errors between receiver and transmitter are pointed
as challenges in Section III. Thus, how pointing error degrades the received
power is investigated by tilting the antennas. As seen in Fig. 4, the antenna
misalignment causes a decrease in the received peak power. The power decrease
concerning the peak power corresponding to the line-of-sight (LOS) path is
approximately $2.3$ dB and $13$ dB for $10^{\circ}$ and $20^{\circ}$ tilts,
respectively. These results clearly demonstrate the need for precise alignment
between the transceivers. Similar to [11], the humidity has no significant
effect on the received signal power. In the light of measurement results, it
is proved that THz-enabled V-HetNets strictly need an accurate resolution in
the beam steering as well as beam broadening before fine-tuning. However,
considering that the eavesdroppers cannot be aligned with the transmit antenna
due to the narrow beam, power loss due to misalignment increases communication
security.

Figure 4: The VNA-assisted measurements show the severe effect of misalignment
on the received signal power which decreases $13$ dB the in case of
$20^{\circ}$ tilt.

####  IV-B2 Pulse-based Channel Modeling

As OOK modulation is mainly considered for THz communication, specifically in
nanonetworks, we prepare a measurement campaign to analyze the channel
behavior for a pulse train [14]. The measurement setup detailed above is used
without a change except for using a signal generator and a spectrum analyzer
rather than VNA. As two ports are on distinct devices, the synchronization is
ensured by connecting the reference clock of the signal generator to the
external clock input of the spectrum analyzer via a cable. The band between
$275$ GHz and $325$ GHz is measured by feeding the extender module with a
pulse train generated by the signal generator. The width of the pulse is
limited with a minimum of $140$ ns due to signal generator capability. At the
receiver side, the pulse train is recorder during $1$ms by taking $100,000$
I/Q samples. The study focuses on path loss relations with frequency and
distance. In this regard, Fig. 5 denotes both frequency and distance related
path loss. The same pattern through the band is observed for each range.

Due to a frequency dependency, a linear path loss model may not be adequate in
such a wide band. We denote that the path loss obeys the two-slope model [14].
It is the evidence that for THz the distance is another determinant along with
the frequency. By employing the two-slope model, the normalized received power
is illustrated in Fig. 6 for the unit power transmitter at $300$ GHz. These
results imply that the distance-dependent channel characteristics require
distance-aware medium access control (MAC) to control physical layer
parameters such as modulation order and coding rate.

The high frequency reuse factor due to high path loss enables the design of
small cell networks and cell-free architectures. The measurement results point
that the most challenging part of THz-enabled V-HetNets is the link between
HAPSs and terrestrial APs as the main path loss arises through the long
distance, where the majority of water molecules in the atmosphere are found
and the antenna alignment is compelling over the long-distance. Because of the
frequency selectivity, the THz band can be divided into sub-bands; thus, using
different sub-bands can support the multiple connections in the V-HetNets.

Figure 5: The received power with respect to frequency obtained by pulse train
driven measurements. The $95\%$ confidence intervals are denoted with error
bars.

##  V Open Issues and Research Directions

Owing to the fact that THz is one of the key enablers of V-HetNets, in this
early stage of the technology, there are many open issues to be addressed to
make it viable.

##### Cell-free Networking

To construct the user-centric network of the future, it is required to satisfy
a decentralized seamless connection. Therefore, promising tools such as radio
stripes, metasurfaces (e.g., reconfigurable intelligent surfaces), and
holographic beamforming are needed to meet THz wireless communication.
Moreover, DL can be employed for the efficient operation of cell-free networks
(e.g., controlling transmitter power in UM-MIMO).

##### Software-defined and Self Organizing Networks

The software-defined network (SDN) and self-organizing network (SON) pave the
way for not only ubiquitous connection but also low-cost network operation.
SDNs and SONs require dynamic MAC, spectrum sharing, and spectrum switching,
DL, and deep reinforcement learning (DRL) enable to improve the elasticity of
networks by considering feedback from the medium to find optimal network
policy owing to the fact that hundreds of billions of devices will be
connected. DRL and blockchain are promising techniques to meet this demand
[15] by utilizing intelligent spectrum sharing protocols. Moreover, federated
learning allows to distribute the computation cost over the thousands of the
connected devices, and therefore the central processing unit may not be
needed. Multi-band antennas and RF chains are also required to support
spectrum switching.

Figure 6: The normalized received power considering the two-slope path loss
model with unit power transmitter.

##### Channel Modeling and Estimation

In the absence of the LOS link, the communication may be carried out through a
non-line-of-sight link; hence, reflection and scattering of THz waves must be
investigated in the V-HetNet framework. Few studies model the spatial
correlation in UM-MIMO channels. Low-complexity methods with compressed
sensing by utilizing the sparsity of THz channels can be investigated. Also,
it is expected that DL-based approaches will be useful for understanding
channel characteristics. For instance, generative adversarial networks are
able to generate infinitely many channel states, so we can model the channel
estimation methodology, which is due to the effect of fast changes in channel
characteristics. It is noted that the weather conditions such as rain, fog,
and clouds have crucial impacts on the channel characteristics. Therefore,
they should be considered in the models. Although the channel modeling
document by IEEE 802.15.3d Task Group points to some weather impacts on the
channel, it needs further investigation. Furthermore, for the feasibility of
the operations of HAPSs, thorough airborne channel modelling activities are
needed.

##### Multiple Access Techniques

The severe frequency selectivity plays an important role when choosing
multiple access technology. For example, code-division multiple access suffers
from high-cost equalizer to recover the received signal. However, we believe
that subcarrier-based access technologies, like orthogonal frequency division
multiple access, are suitable to employ in the THz networks. Yet, it is seen
that peak-to-average power ratio reduction methods are required owing to an
excessive number of nodes. Non-orthogonal multiple access (NOMA), proposed to
increase spectral efficiency, is likely to be used in THz systems, but there
is a trade-off between the additional complexity that NOMA would bring and the
increase in efficiency. Due to mMIMO and pencil-sharp beams, the beam division
multiple access is highly welcome in THz communications. As in IEEE 802.11ad,
single-carrier frequency division multiple access can be used for THz
communications.

##### Beam Alignment

It seems that utilizing UM-MIMO in user equipment is formidable owing to the
high computational complexity of beamforming algorithms and space limitations
for antennas. Hence, a situation-aware MAC layer is required, which allows
adaptively utilization of THz and mmWave. Further, intelligent surfaces can be
key enablers for THz user equipment because the computations are made on the
medium rather than user equipment.

##  VI Summary

THz-enabled V-HetNets provide not only ubiquitous connection but also
relatively low-cost dense networks. As projected, different wireless
communication technologies, including FSO, mmWave, and THz, will be
orchestrated for 6G and beyond; however, THz technologies will be the maestro
due to widespread application strategies. Howbeit, novel approaches
considering channel behavior should be adopted from satellite to in-vivo THz
communications.

## References

  * [1] P. Yang, Y. Xiao, M. Xiao, and S. Li, “6G Wireless Communications: Vision and Potential Techniques,” _IEEE Network_ , vol. 33, no. 4, pp. 70–75, Jul. 2019.
  * [2] K. Tekbıyık, A. R. Ekti, G. K. Kurt, and A. Görçin, “Terahertz Band Communication Systems: Challenges, Novelties and Standardization Efforts,” _Physical Communication_ , vol. 35, Aug. 2019\.
  * [3] M. Alzenad, M. Z. Shakir, H. Yanikomeroglu, and M.-S. Alouini, “FSO-Based Vertical Backhaul/Fronthaul Framework for 5G+ Wireless Networks,” _IEEE Commun. Mag._ , vol. 56, no. 1, pp. 218–224, Jan. 2018.
  * [4] I. F. Akyildiz, C. Han, and S. Nie, “Combating the Distance Problem in the Millimeter Wave and Terahertz Frequency Bands,” _IEEE Commun. Mag._ , vol. 56, no. 6, pp. 102–108, Jun. 2018.
  * [5] S. Chen, Y.-C. Liang, S. Sun, S. Kang, W. Cheng, and M. Peng, “Vision, Requirements, and Technology Trend of 6G: How to Tackle the Challenges of System Coverage, Capacity, User Data-Rate and Movement Speed,” _IEEE Wireless Commun._ , pp. 1–11, Feb. 2020.
  * [6] I. F. Akyildiz and A. Kak, “The Internet of Space Things/CubeSats,” _IEEE Network_ , vol. 33, no. 5, pp. 212–218, Sep. 2019.
  * [7] C. Lin and G. Y. L. Li, “Terahertz Communications: An Array-of-Subarrays Solution,” _IEEE Commun. Mag._ , vol. 54, no. 12, pp. 124–131, Dec. 2016\.
  * [8] J. M. Jornet and I. F. Akyildiz, “Femtosecond-Long Pulse-Based Modulation for Terahertz Band Communication in Nanonetworks,” _IEEE Trans. Commun._ , vol. 62, no. 5, pp. 1742–1754, May 2014.
  * [9] Stratistics Market Research Consulting Pvt Ltd, “Millimeter Wave Technology \- Global Market Outlook (2017-2026),” Available: https://bit.ly/33LztPC, Accessed on Apr. 20, 2020.
  * [10] A. Tang, T. Reck, and G. Chattopadhyay, “CMOS System-on-Chip Techniques in Millimeter-Wave/THz Instruments and Communications for Planetary Exploration,” _IEEE Commun. Mag._ , vol. 54, no. 10, pp. 176–182, Oct. 2016\.
  * [11] G. A. Siles, J. M. Riera, and P. Garcia-del Pino, “Atmospheric Attenuation in Wireless Communication Systems at Millimeter and THz Frequencies,” _IEEE Antennas Propag. Mag._ , vol. 57, no. 1, pp. 48–61, Feb. 2015.
  * [12] A. R. Ekti, A. Boyaci, A. Alparslan, İ. Ünal, S. Yarkan, A. Görçin, H. Arslan, and M. Uysal, “Statistical Modeling of Propagation Channels for Terahertz Band,” in _IEEE Conf. on Standards for Communications and Networking (CSCN)_ , 2017, pp. 275–280.
  * [13] S. Priebe, M. Kannicht, M. Jacob, and T. Kürner, “Ultra Broadband Indoor Channel Measurements and Calibrated Ray Tracing Propagation Modeling at THz Frequencies,” _J. Commun. Netw._ , vol. 15, no. 6, pp. 547–558, 2013.
  * [14] K. Tekbıyık, E. Ulusoy, A. R. Ekti, S. Yarkan, T. Baykaş, A. Görçin, and G. K. Kurt, “Statistical Channel Modeling for Short Range Line-of-Sight Terahertz Communication,” in _IEEE Int. Symp.on Personal, Indoor and Mobile Radio Communications (PIMRC)_ , 2019, pp. 1–5.
  * [15] Y. Dai, D. Xu, S. Maharjan, Z. Chen, Q. He, and Y. Zhang, “Blockchain and Deep Reinforcement Learning Empowered Intelligent 5G beyond,” _IEEE Network_ , vol. 33, no. 3, pp. 10–17, 2019.

## Biographies

KÜRŞ̧AT TEKBIYIK [StM’19]<EMAIL_ADDRESS>is pursuing his Ph.D. degree
in Telecommunication Engineering at Istanbul Technical University and is also
researcher at TUBITAK BILGEM.

ALİ RIZA EKTİ received Ph.D. degree in Electrical Engineering from Department
of Electrical Engineering and Computer Science at Texas A&M University in
2015. He is currently an assistant professor at Balikesir University and also
senior researcher at TUBITAK BILGEM.

GÜNEŞ̧ KARABULUT KURT [StM’00, M’06, SM’15]<EMAIL_ADDRESS>received the
Ph.D. degree in electrical engineering from the University of Ottawa, Ottawa,
ON, Canada, in 2006. Since 2010, she has been with Istanbul Technical
University. She is serving as an Associate Technical Editor of IEEE
Communications Magazine.

ALİ GÖRÇİN received his Ph.D. degree in University of South Florida. He is
currently assistant professor at Yildiz Technical University in Istanbul and
also manager at BILGEM BTE.

HALIM YANIKOMEROGLU [F]<EMAIL_ADDRESS>is a full professor in the
Department of Systems and Computer Engineering at Carleton University, Ottawa,
Canada. His research interests cover many aspects of 5G/5G+ wireless networks.
His collaborative research with industry has resulted in 37 granted patents.
He is a Fellow of the Engineering Institute of Canada and the Canadian Academy
of Engineering, and he is a Distinguished Speaker for IEEE Communications
Society and IEEE Vehicular Technology Society.

  *[V-HetNet]: vertical heterogeneous network
  *[GEO]: geostationary orbit
  *[LEO]: low-earth orbit
  *[THz]: Terahertz
  *[V-HetNets]: vertical heterogeneous network
  *[QoS]: quality of service
  *[FSO]: free-space optics
  *[NFPs]: networked flying platform
  *[HetNets]: heterogeneous network
  *[mMIMO]: massive-multiple-input multiple-output
  *[UM-MIMO]: ultra-massive-MIMO
  *[AP]: access point
  *[APs]: access point
  *[NFP]: networked flying platform
  *[HAPSs]: high-altitude platform station
  *[SWaP]: size, weight, and power
  *[BAN]: body area network
  *[WLAN]: wireless local area network
  *[CMOS]: complementary metal-oxide semiconductor
  *[TCS]: thermal control system
  *[UAV]: unmanned aerial vehicle
  *[UAVs]: unmanned aerial vehicle
  *[DL]: Deep learning
  *[MoM]: method of moments
  *[FEM]: finite element method
  *[VNA]: vector network analyzer
  *[OOK]: on-off keying
  *[LOS]: line-of-sight
  *[MAC]: medium access control
  *[DRL]: deep reinforcement learning
  *[NOMA]: Non-orthogonal multiple access


# Image-level Classification in Hyperspectral Images using Feature
Descriptors, with Application to Face Recognition

###### Abstract

Image-level classification from hyperspectral images (HSI) has seldom been
addressed in the literature. Instead, traditional classification methods have
focused on individual pixels. Pixel-level HSI classification comes at a high
computational burden though. In this paper, we present a novel pipeline for
classification at image-level, where each band in the HSI is considered as a
separate image. In contrast to operating at the pixel level, this approach
allows us to exploit higher-level information like shapes. We use traditional
feature descriptors, i.e. histograms of oriented gradients, local binary
patterns, and the scale-invariant feature transform. For demonstration we
choose a face recognition task. The system is tested on two hyperspectral face
datasets, and our experiments show that the proposed method outperforms the
existing state-of-the-art hyperspectral face recognition methods.

##  1 Introduction

A hyperspectral image (aka. hyperspectral cube) consists of two spatial
dimensions and a spectral dimension. The latter contains information pertinent
to the intrinsic material properties of the object. This spectral information
in HSI makes them well suited for classification tasks, such as scene
recognition [1], 3D reconstruction [2], saliency detection [3], pedestrian
detection [4, 5], material classification [6], cultural heritage [7] and many
more. In this paper, we propose a framework for hyperspectral image
classification, where each band in the HSI is considered as a separate image.
Treating the problem at the image-level allows us to exploit high-level
information, like shapes, that help to improve the classification performance.
We use traditional feature descriptors (i.e. SIFT [8], HOG [9], LBP [10]) for
image-level feature extraction and classification (See Fig. 1 for
illustration). For the demonstration of our method, we investigate into face
recognition using wavelengths ranging from the visible ($380-700nm$) to the
near-infrared ($750-1100nm$) spectrum.

Fig. 1: For a given hyperspectral image, with $\eta$ the number of spectral
bands, several features are extracted from each of the $\eta$ mono-spectral
images. Fig. 2: An overview of our image-level classification chain in the
hyperspectral images. Each band in the HSI is treated as a mono-spectral image
(or band). Features ($Feat$) are extracted for each image using a feature
extraction method (e.g. HOG, LBP, and SIFT), and then these features are fed
to linear one vs all SVM classifier, where $\eta$ SMVs are trained on $\eta$
bands. For the final label prediction, we merge the predictions of all SVM
learners trained on different bands using majority voting.

The availability of more bands than the usual three RGB bands has been shown
advantageous in disambiguating objects. In literature, the common tendency to
exploit the hyperspectral data has been addressed at pixel-level. As the
spatial and spectral dimensions in HSI increase, it is difficult to separate
hyperspectral data at the pixel-level for large classes dataset using
statistical methods [11, 12]. However, in our method classification is done at
the image-level, where from each image we extracted a limited number of
features, far fewer than the number of pixels. With such smaller numbers of
features at hand, we can afford to not further reduce the number of spectral
bands that are considered. This allows us to exploit the entire input space
without losing information for feature extraction. We show that the entire
feature space information leads to significantly improved performance in a
face recognition task.

Recently, deep learning (DL) a learning-based representation has outperformed
traditional descriptors for deriving distinctive features in image
classification task [13, 14], but DL has a major shortcoming: it requires many
samples for the training process and an insufficient number of training
samples quickly leads the network to overfitting. As we already know, in HSI
the spectral bands are very unique and discriminative. Thus, we believe
traditional feature descriptors can effectively exploit this spectral
information and help to generate powerful feature representation of their
content that characterize the object better. In this work, we have explored
the hand-crafted HSI features in V-NIR images and also have shown improvement
in the classification performance by a significant margin for a face
recognition task.

The rest of the paper is organized as follows. In Section 2, we discuss the
related work, and Section 3 describes our proposed method. Experiments and
analysis are given in Section 4, and Finally, the conclusions are drawn in
Section 5.

##  2 Related Work

There is an extensive work on HSI classification, but here we mention a few
relevant papers on face recognition task only. During the last decade, face
recognition has achieved great success. The research has tended to focus on
RGB or b/w images, rather less attention has been paid to hyperspectral
images. In this paper, we focus on HSI face recognition. The idea of face
recognition in hyperspectral images, started with Pan et al. [15], who
manually extracted the mean spectral signatures from the human face in the NIR
spectrum, and were then compared using Mahalabonis distance. Further in [16]
Pan et al. extended their work [15] by incorporating spatial information in
addition to spectral. Similarly, Robila et al. [17] also uses spectral
signatures but their comparison criterion was spectral angle measurements.
Almost all the existing proposed HSI face recognition methods perform
dimensionality reduction and the low-dimensional feature space are extracted
for classification. Di et al. [18] projected the hyperspectral image into low
dimensional space using 2D-PCA for feature extraction, and were then compared
using Euclidean distance. In recent works, Shen and Zheng [19] apply 3D Gabor
wavelets with different central frequencies to extract signal variances in the
hyperspectral data. Liang et al. [20] utilize 3D high-order texture pattern
descriptor to extract distinctive micro-patterns which integrate the spatial-
spectral information as features. Uzair et al. [21] apply 3D discrete cosine
transformation and extract the low frequency coefficients as features, where
Partial Least Squares Regression is used for classification. Uzair et al. most
recent work in [22] extended their previous study [21] and employed 3D
cubelets to extract the spatio-spectral covariance features for face
recognition. In contrast, in our work, the hyperspectral image is fully
exploited without losing information by performing feature extraction and
classification at the image-level.

(a) PolyU-HSFD: Visible Range (440-690nm). Bands with a step size of 40nm are
shown.

(b) CMU-HSFD: V-NIR Range (450-1090nm). Bands with a step size of 50nm are
shown.

Fig. 3: Example hyperspectral image for a subject with its corresponding RGB
image.

##  3 Proposed Method

In the last two decades, researchers have developed robust descriptors
(feature extraction methods) to extract useful feature representations from
the image that are highly distinctive and are perfect for an efficient and
robust object recognition. The traditional feature descriptors (SIFT, HOG, LBP
and more) have several advantages. These features are invariant to image
scaling, geometric and photometric transformations: translations or rotations,
common object variations, minimally affected by noise and small distortions,
and to a great extent invariant to change in illumination. These descriptors
when combined with hyperspectral images, make the extracted features even more
robust and powerful. We believe that the extracted new class of features
obtained from hyperspectral images shall give near-perfect separation because
these features are generated from highly discriminative bands (Fig. 3) in HSI
that are captured in different wavelengths. These images captured in different
wavelength range, contain discriminative information that characterize the
object better with great precision and detail.

Fig. 2 shows the schematic layout of our framework for hyperspectral image
classification. In our work, each mono-spectral band in the HSI is treated as
a separate image. Treating the mono-spectral bands as separate images, allows
us to exploit: the discriminative texture patterns present in the images
captured in different wavelengths, hence able to utilize the entire space
without losing information for feature extraction. Then, the features are
extracted for each mono-spectral band using a feature extraction method (e.g.
HOG, LBP, and SIFT). This allows us to capture the high-level information like
shapes and abstract concepts from images: making it more suitable for high-
level visual recognition tasks, similar is not possible at pixel-level.
Classification at the pixel-level (think of raw pixel values) comes at high
computational burden, and it turns out that, it is difficult to disambiguate
objects with large classes dataset by simple concatenating of multi-spectral
data into single pixel-related vectors using statistical methods. Thus, we
extract from each image a limited number of features, far fewer than the
number of pixels. With such smaller numbers of features at hand, we show that,
we achieve better recognition results, significantly outperforming pixel-level
features (see Table 2), and can afford to not further reduce the number of
spectral bands that are considered. Then, the extracted feature vectors are
fed to linear one vs all SVM classifier, where we have a SVM for each band.
For the final label prediction, we merge the predictions of all SVM learners
trained on different bands using majority voting.

For feature extraction of each mono-spectral image, we use a fixed-size
representation to extract SIFT, LBP and HOG features. The parameters for
feature extraction (i.e. window size, step size, number of oriented bins,
number of clusters, and more) contribute to the good results, and play a
crucial role in improving the recognition performance. In Section 4, we
describe the implementation setup in detail.

The performance of the the proposed approach is demonstrated for face
recognition in HSI. Excellent results show that these robust feature
descriptors are perfect for reliable face recognition in hyperspectral images.

##  4 Experiments

The proposed method in the previous section was tested on two standard
hyperspectral face datasets [18, 23] for a face recognition task. Our
experiments consist of two parts. In the first part, we compare our proposed
method with the state-of-the-art HSI face recognition methods. Then in the
second part, we compare the usefulness of the discriminative spectral bands
with the RGB image representation of HSI. We now introduce the datasets used
and then we move onto training/testing protocol, and implementation details.

###  4.1 Experimental Setup

For the experimental evaluation, we used a desktop with Intel i7-2600K CPU at
3.40GHZ, 8GB RAM. All experiments were performed using vlfeat library [24].

#### Hyperspectral Face Datasets:

Hong-Kong Polytechnic University Hyperspectral Face Dataset (PolyU-HSFD) [18]
(see Fig. 3 and Table 1) is acquired using the CRI’s VariSpec LCTF with a
halogen light source. The database contains data of 48 subjects acquired in
multiple sessions, with 1-7 cubes over all sessions. Following the same
experimental protocol of [20, 21, 22], only first 25 subjects were used for
evaluation. The acquired images for the first 6 and the last 3 bands are noisy
(i.e. very high shot noise). So they are discarded from the experiment, as
suggested in the previous work. In all, 24 spectral bands were used with
spectral interval (i.e. step size) of 10nm. The database has significant
appearance variations of the subjects because it was constructed over a long
period of time. Major changes in appearance variation were in hair-style and
skin condition.

Carnegie Mellon University Hyperspectral Face Dataset (CMU-HSFD) [23] (see
Fig. 3 and Table 1) is acquired using the CMU developed AOTF with three
halogen light sources. The database contains data of 54 subjects acquired in
multiple sessions, with 1-5 cubes over all sessions. Following the same
experimental protocol of [20, 21, 22], only first 48 subjects were used for
evaluation. Each subject maintains a still pose with negligible head movements
and eye blinks, due to of that a slight misalignment error exists between
individual bands because the image capturing process takes several seconds.

Dataset | Spectral Range | Bands | Spatial Range | Step Size
---|---|---|---|---
PolyU-HSFD | 400-720nm | 33 | $220\times 180$ | 10nm
CMU-HSFD | 450-1090nm | 65 | $640\times 480$ | 10nm

Table 1: Hyperspectral Face Dataset

#### Training and Testing Protocol:

Following the same training and testing protocol as defined in [20, 21, 22],
only frontal view has been considered for evaluation of both datasets. When
only one sample per subject is used for training and two samples per subject
are used for testing. Both gallery set (or training set) and probe set (or
testing set) were constructed for 5 times by random selection and the average
recognition accuracy was reported.

#### Data Preprocessing:

All images were cropped and resized to size $263\times 263$ in spatial
dimension. Due to of low signal-to-noise ratio (i.e. high shot noise) in the
datasets, we apply a median filter of size $3\times 3$ to remove shot noise.

#### Implementation Details:

To extract the HOG and LBP features, we use a window size of $8\times 8$, and
number of orientation bins of 9 for HOG. For SIFT, we use a bin size of 4,
step size of 8, then the extracted SIFT-features are Fisher encoded. To
compute Fisher encoding, we build a visual dictionary using GMM with 100
clusters. We normalize the features using L2-normalization. We denote dense
SIFT Fisher vectors by DSIFT-FVs. These parameters are fixed for all
descriptors. We use linear SVM with $C=10$ from LIBSVM [25] to train
classifier with features.

###  4.2 Results

#### Comparison with state-of-the-art methods:

In Table 2, we quantitatively evaluate the recognition accuracy of our
proposed method, and compare it with state-of-the-art hyperspectral face
recognition methods reported in the literature. We observe from the results
that among the traditional feature descriptors, as expected DSIFT-FVs
outperforms the LBP and HOG recognition accuracy by a significant margin.
Also, it should be noted that DSIFT-FVs outperforms all the traditional
methods listed in the literature and achieve state-of-the-art accuracy with
96.1% on PolyU-HSFD dataset. Though, DSIFT-FVs is inferior to Band fusion+PLS
[22], but is still better than all the other methods on CMU-HSFD dataset.
Furthermore, this examination reveals that SIFT shows the same trend of
performing better in face recognition in hyperspectral images as in RGB
images.

Methods | Accuracy |
---|---|---
| PolyU-HSFD | CMU-HSFD
Spectral Signature [15] | 24.6 | 38.1
Spectral Angle [17] | 25.4 | 38.1
Spectral Eigenface [16] | 70.3 | 84.5
2D PCA [18] | 71.1 | 72.1
3D DCT [21] | 84.0 | 88.6
LBP (ours) [10] | 85.6 | 86.1
3D Gabor Wavelets [19] | 90.1 | 91.6
HOG (ours) [9] | 92.3 | 91.5
3D LDP [20] | 95.3 | 94.8
Band fusion+PLS [22] | 95.2 | 99.1
DSIFT-FVs (ours) [8] | 96.1 | 96.9

Table 2: Recognition rates of different methods using all bands on both
datasets.

#### Comparison of HSI with RGB Image:

For this evaluation, we generate an RGB image for each of the hyperspectral
image 111For transforming the HSI to RGB color space, we use (a) CIE 2006
tristimulus color matching functions, (b) CIE standard daylight illuminant
($D_{65}$), (c) and Silicon sensitivity of Hamamatsu camera. In this regard,
we refer the reader to the book by Ohta and Robertson [26] for detailed steps.
Then, we apply the proposed method to an RGB image (with three channels) in
the same way as we applied to the hyperspectral image, discussed earlier in
Section 3.

In Table 3, we quantitatively evaluate the recognition accuracy of the whole
band set in the hyperspectral cube, and compare it with a three channels RGB
image. It is evident from the comparison that the classification performance
for the computed features from HSI images is significantly better than the
computed features from RGB images on both datasets. In the literature, it has
been shown by Pan et al. [15], NIR images exhibit a distinct spectral
properties of the skin and this information leads to more accurate
classification in comparison to retained information in RGB images (i.e.
visible range). The reason being, in NIR range the spectral responses of the
tissues are more discriminative due to larger penetration depth, which is
dependent on the portion of melanin and hemoglobin [27] in the human skin.

| HOG | LBP | DSIFT-FVs
---|---|---|---
PolyU-HSFDRGB | 85.0 | 78.8 | 85.4
PolyU-HSFDAll-Bands | 92.3 | 85.6 | 96.1
CMU-HSFDRGB | 85.9 | 80.5 | 83.8
CMU-HSFDAll-Bands | 91.5 | 86.1 | 96.9

Table 3: Comparison of hand-crafted HSI features with RGB image features for
both datasets.

##  5 Conclusion

In this paper, we proposed a novel pipeline for image-level classification in
the hyperspectral images. By doing this, we show that the discriminative
spectral information at image-level features lead to significantly improved
performance in a face recognition task. We also explored the potential of
traditional feature descriptors in the hyperspectral images. From our
evaluations, we observe that SIFT features outperform the state-of-the-art
hyperspectral face recognition methods, and also the other descriptors. With
the increasing deployment of hyperspectral sensors in a multitude of
applications, we believe that our approach can effectively exploit the
spectral information in hyperspectral images, thus beneficial to more accurate
classification.

## References

  * [1] Matthew Brown and Sabine Süsstrunk,  “Multi-spectral sift for scene category recognition,”  in CVPR, 2011.
  * [2] Ali Zia, Jie Liang, Jun Zhou, and Yongsheng Gao,  “3d reconstruction from hyperspectral images,”  in WACV, 2015.
  * [3] Jie Liang, Jun Zhou, Xiao Bai, and Yuntao Qian,  “Salient object detection in hyperspectral imagery,”  in ICIP, 2013.
  * [4] Soonmin Hwang, Jaesik Park, Namil Kim, Yukyung Choi, and In So Kweon,  “Multispectral pedestrian detection: Benchmark dataset and baseline,”  in CVPR Workshops, 2015.
  * [5] Yun Luo, Jeffrey Remillard, and Dieter Hoetzer,  “Pedestrian detection in near-infrared night vision system,”  in Intelligent Vehicles Symposium, 2010.
  * [6] Neda Salamati, Clément Fredembach, and Sabine Süsstrunk,  “Material classification using color and nir images,”  in CIC, 2009.
  * [7] Costas Balas, Vassilis Papadakis, Nicolas Papadakis, Antonis Papadakis, Eleftheria Vazgiouraki, and George Themelis,  “A novel hyper-spectral imaging apparatus for the non-destructive analysis of objects of artistic and historic value,”  Journal of Cultural Heritage, 2003.
  * [8] David G Lowe,  “Object recognition from local scale-invariant features,”  in ICCV, 1999.
  * [9] Navneet Dalal and Bill Triggs,  “Histograms of oriented gradients for human detection,”  in CVPR, 2005.
  * [10] Timo Ojala, Matti Pietikäinen, and Topi Mäenpää,  “Multiresolution gray-scale and rotation invariant texture classification with local binary patterns,”  PAMI, 2002.
  * [11] David A Landgrebe,  Signal theory methods in multispectral remote sensing,  John Wiley & Sons, 2005.
  * [12] John A Richards and JA Richards,  Remote sensing digital image analysis,  Springer, 1999.
  * [13] Yaniv Taigman, Ming Yang, Marc’Aurelio Ranzato, and Lars Wolf,  “Deepface: Closing the gap to human-level performance in face verification,”  in CVPR, 2014.
  * [14] Ken Chatfield, Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman,  “Return of the devil in the details: Delving deep into convolutional nets,”  arXiv preprint arXiv:1405.3531, 2014.
  * [15] Zhihong Pan, Glenn Healey, Manish Prasad, and Bruce Tromberg,  “Face recognition in hyperspectral images,”  PAMI, 2003.
  * [16] Zhihong Pan, Glenn Healey, and Bruce Tromberg,  “Comparison of spectral-only and spectral/spatial face recognition for personal identity verification,”  EURASIP, 2009.
  * [17] Stefan A Robila,  “Toward hyperspectral face recognition,”  in Electronic Imaging 2008. International Society for Optics and Photonics, 2008.
  * [18] Wei Di, Lei Zhang, David Zhang, and Quan Pan,  “Studies on hyperspectral face recognition in visible spectrum with feature band selection,”  Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 2010.
  * [19] Linlin Shen and Songhao Zheng,  “Hyperspectral face recognition using 3d gabor wavelets,”  in ICPR, 2012.
  * [20] Jie Liang, Jun Zhou, and Yongsheng Gao,  “3d local derivative pattern for hyperspectral face recognition,”  in FGR, 2015.
  * [21] Muhammad Uzair, Arif Mahmood, and Ajmal Mian,  “Hyperspectral face recognition using 3d-dct and partial least squares,”  in BMVC, 2013.
  * [22] Muhammad Uzair, Arif Mahmood, and Ajmal Mian,  “Hyperspectral face recognition with spatiospectral information fusion and pls regression,”  TIP, 2015.
  * [23] Louis J Denes, Peter Metes, and Yanxi Liu,  Hyperspectral face database,  Carnegie Mellon University, 2002.
  * [24] Andrea Vedaldi and Brian Fulkerson,  “Vlfeat: An open and portable library of computer vision algorithms,”  in Proceedings of the international conference on Multimedia, 2010\.
  * [25] Chih-Chung Chang and Chih-Jen Lin,  “Libsvm: A library for support vector machines,”  ACM Transactions on Intelligent Systems and Technology (TIST), 2011\.
  * [26] Noboru Ohta and Alan Robertson,  Colorimetry: fundamentals and applications. Chapter 3: CIE Standard Colorimetric System,  John Wiley & Sons, 2006.
  * [27] Takanori Igarashi, Ko Nishino, and Shree K Nayar,  “The appearance of human skin: A survey,”  Foundations and Trends® in Computer Graphics and Vision, 2007.