# Cross-Modal Terrains: Navigating Sonic Space through Haptic Feedback

Gabriella Isaac

Lauren Hayes

Todd Ingalls

Arts, Media + Engineering  Arizona State University  Tempe, AZ 85287, USA
<EMAIL_ADDRESS>Arts, Media + Engineering  Arizona State University
Tempe, AZ 85287, USA<EMAIL_ADDRESS>Arts, Media + Engineering
Arizona State University  Tempe, AZ 85287, USA<EMAIL_ADDRESS>
###### Abstract

This paper explores the idea of using virtual textural terrains as a means of
generating haptic profiles for force-feedback controllers. This approach
breaks from the para-digm established within audio-haptic research over the
last few decades where physical models within virtual environments are
designed to transduce gesture into sonic output. We outline a method for
generating multimodal terrains using basis functions, which are rendered into
monochromatic visual representations for inspection. This visual terrain is
traversed using a haptic controller, the NovInt Falcon, which in turn receives
force information based on the grayscale value of its location in this virtual
space. As the image is traversed by a performer the levels of resistance vary,
and the image is realized as a physical terrain. We discuss the potential of
this approach to afford engaging musical experiences for both the performer
and the audience as iterated through numerous performances.

###### keywords:

Haptic interfaces, cross modal mapping, performance, multimodal interaction,
terrain

††conference: NIME’17, May 15-19, 2017, Aalborg University Copenhagen,
Denmark.

1998 H.5.5 [Information Interfaces and Presentation] Sound and Music
Computing, H.5.2 [Information Interfaces and Presentation] User
Interfaces—Haptic I/O.

##  1 Introduction

The introduction of digital musical instruments (DMIs) has removed the need
for the existence of a physically resonating body in order to create music,
leaving the practice of sound-making often decoupled from the resulting sound.
The inclination towards smooth and seamless interaction in the creation of new
DMIs has led to the development of musical instruments and interfaces for
which no significant transfer of energy is required to play them. Other than
structural boundaries, such systems usually lack any form of physical
resistance, whereas the production of sounds through traditional instruments
happens precisely at the meeting of the performer’s body with the instrument’s
resistance: “When the intentions of a musician meet with a body that resists
them, friction between the two bodies causes sound to emerge" [10, p1]. Haptic
controllers offer the ability to engage with digital music in a tangible way.
Previous work with force-feedback has derived haptic profiles from physical
models of acoustic instruments and real-world interactions (see [1] for a
discussion of this). Relying on these sources becomes an issue when working
with digital signal processes that have no real-world correspondence. By
exploring other methods of generating force-feedback profiles, purely digital
information can become physically realized in a genuine and engaging manner.

Figure 1: Using basis functions to generate haptic terrains for the NovInt
Falcon.

##  2 Background

Dynamic relationships occur and are ongoing between the performer, the
instrument, and the sounds produced when playing musical instruments. These
exchanges depend upon the sensory feedback provided by the instrument in the
forms of auditory, visual, and haptic feedback [9]. Because digital interfaces
based around an ergonomic HCI model are generally designed to eliminate
friction altogether, the tactile experience of creating a sound is reduced.
Even though digital interfaces are material tools, the feeling of pressing a
button or moving a slider does not provide the performer with much physical
resistance, whereas the engagement required to play an acoustic instrument
provides musicians with a wider range of haptic feedback involving both
cutaneous and proprioceptive information, as well as information about the
quality of an occurring sound [9]. This issue is recognized in Claude Cadoz’s
work regarding his concept of ergoticity as the physical exchange of energy
between performer, instrument, and environment [3]. A possible solution to
these issues is the use of haptic controllers. As has been previously noted,
“we are no longer dealing with the physical vibrations of strings, tubes and
solid bodies as the sound source, but rather with the impalpable numerical
streams of digital signal processing" [5, p1]. In physically realizing the
immaterial, the design of the force profile is crucial because it determines
the overall characteristics of the instrument.

###  2.1 Instrumental Modeling

Previous work on the design of haptic profiles has been focused around
modeling, enhancing, or augmenting pre-existing musical interactions. Leonard
and Cadoz’s physics-based system GENESIS-RT allows users to design virtual
musical instruments and engage with them in a way that resembled interaction
with traditional instruments [8]. Ber-dahl’s work with the physically
intuitive haptic drumstick builds off and extends real-world physics, allowing
a drummer to play a drum roll either in the usual manner with two drumsticks,
or single-handedly with the aid of force-feedback. It is the direct engagement
with the synthetic haptic feedback that allows the percussionist to perform in
this way yet the “physics of the performer’s basic interaction with the
instrument remain similar," rendering the instrument “physically intuitive"
[2, p363].

Further recent developments include actuated instruments that “produce sound
via vibrating element(s) that are co-manipulated by humans and
electromechanical systems" [9, p155]. Physical instruments such as the
Feedback Resonance Guitar, the Electromagnetically Prepared Piano, the
Overtone Fiddle, and Teleoperation with Robothands have been extended through
virtual qualities while conforming to real-world physics in their structural
design.

###  2.2 Sound Sculpting

Hayes’ Running Backwards, Uphill was a performance for a piano trio that
explored the relationship between “touch, gesture and timbre by examining the
sonic qualities of the acoustic instruments," as well as the electronics.
Musicians utilized the absolute extremes of their instruments and were
“directed to lurch and fall off the keys; or, create the most delicate airy
bowed sounds" [6, p402]. Unlike acoustic instruments, which require physical
force and highly skilled action to reach the edges of their sonic potential,
the extremes of most digital controllers can be reached almost instantaneously
due to their lack of resistance [10, p1]. With the Falcon’s resistance, Hayes
was able to use various force-feedback profiles to both assist her in reaching
desired effects, such as short, staccato-like samples of a recording and
longer segments that flowed together, and fight against her to make certain
sounds more difficult to reach. Throughout the performance, she notes that the
haptic feedback gave her a “feeling of moving through the sound" and the means
to shape the sound accordingly [6, p403]. Her use of haptics allowed an
extensive range of gestures and levels of engagement to occur in this
performance.

###  2.3 Cross-Modal Approaches

Others have noticed that it is useful to transfer auditory and visual
perceptual information to the tactile realm. The Haptic Wave is an interface
that allows “cross-modal mapping of digital to audio to the haptic domain"
[11, p2150] and provides a platform for visually impaired users to navigate
and edit digital audio. Instead of translating existing representations of
digital audio, such as visual waveforms, the initial iterations of this
project used the NovInt Falcon to “directly access qualities of the sound"
[11, p2153]. By mapping the horizontal axis of the Falcon to the length of a
sound file and the amount of resistance to the amplitude—higher amplitude
increased resistance—users were able to scan through the soundfile from left
to right and feel the amplitude of the soundfile at every point in time.

Other work has explored the use of visual information within the realm of
digital signal processing. James maps 2D visual textures to the distribution
of “timbre spatialization in the frequency domain" [7, p128]. Filatriau and
Arfib’s work presents three different tactics for linking “visual and sonic
textures using similar synthesis processes" [4, p31]. The first two methods
use a visual texture as the material basis for sound generation. Their
approach titled “image from a sound" considers the texture as a sonogram and
uses this image to “derive from a static image an evolving sound" [4, p32].
This process involves scanning over the static image to generate an evolving
sound, using the horizontal axis as the time value and the vertical value at
that time as the sinusoid to reproduce. The “pixel image sonification
technique" employs an image that is constantly changing and constantly
producing a sound. This could be exemplified by movement in front of a camera
or by moving through a static image at a small scaled viewpoint, viewing the
visual texture as composed of small sections, kernels, or pixels. The final
process of “equivalent processes" expresses the texture-generating algorithm
in visual and sonic mediums instead of using the image as the starting point.
Both the visual and sonic processes are expressions of the texture-generating
algorithm.

In our work with the Falcon, we have utilized both the “pixel image
sonification" and the “equivalent processes" technique by using a texture-
generating algorithm to create a visual expression and move through this image
on a pixel-to-pixel basis. Working in this direction avoids issues of physical
modeling because it is not concerned with using images or interactions as true
or exact models as a means to expressively sculpt sound.

##  3 Methodology

In this section we describe an iterative approach to the development of a
terrain-based haptic instrument. We outline both the technical considerations,
along with autoethnographic accounts of its role in numerous performances by
Gabriella Isaac over a period of several months.

###  3.1 Case Study: Constant Resistance Model

The first iteration of the instrument involved applying a constant force
profile to a single dimension of the NovInt Falcon. This would exert a
constant physical force back on the performer’s hand in one dimension. In
turn, the same z-index of the Falcon’s position was mapped to the the start
point of a grain’s position within a sound file and, by pushing and pulling
the ball-grip of the controller, the performer was able to physically scrub
through a buffer containing that file while granulating the sound. The force-
feedback of the controller remained at a static level throughout the piece and
provided a constant background resistance, allowing the performer to fine tune
their movement and focus in on points of interest by stabilizing their
actions.

In addition, parameters of other DSP processes were map-ped to the x-y
position of the Falcon’s ball-grip, including the x-y coordinates of an
amplitude envelope—which could be drawn in real-time—and the selection and
speed of playback of a corpus of samples. Furthermore, the sound output was
recorded into a looping buffer and fed to a granulator. Using a button on the
ball grip, haptics could be turned on and off: when off, the sound would be
recorded into the buffer; when on, recording stopped and granulation started,
allowing the performer to hone in on interesting parts of the recorded buffer,
and move back through time.

This iteration was used in two solo performances and one collaborative
performance. In the former, the mappings did not change over time, and
therefore the extremes of the piece were reached after about five minutes.
Isaac felt that the collaborative performance was more successful as the
presence of two performers allowed the sounds produced to occur over a greater
period of time and at different intervals. In this context, the limitations of
the instrument could be explored further. Additionally, audience feedback from
both scenarios suggested that although the audience members could see the
performer actively struggling with the Falcon, they did not understand what
was actually happening and how the sounds were being produced. With the
controller facing forward and the knob pointed towards the performer, the
audience could not see the full range of motion exerted during the performance
because the body of the controller blocked the view of the performer’s
gestures.

This first model was a helpful starting point due to the simplicity of the
audio-haptic mappings involved. It resulted in a physically-demanding
controller, which invited further exploration into the types of performer-
instrument relationships it might afford. This approach was also useful in
drawing out the sonic characteristics of the specific granular patch that had
been implemented.

Isaac found that without the additional resistance, potentially interesting
sonic details were more likely to be skimmed over and lost due to the ease of
movement. The physical difficulty of moving the controller’s ball grip with
the added resistance initially provided a more interesting mode of engagement
between the performer and the digital sonic material. However, the fixed
amount of resistance became too predictable in practice. This suggested that
implementing a wider and more dynamic range of resistances should be explored
next, along with an investigation into how the relationships between sound and
physical resistance could be developed further.

###  3.2 Case Study: Haptic Terrain (Version 1)

The second case study builds upon the constant resistance model for using the
NovInt Falcon as a controller for performing granular synthesis, and
implements an early version of a virtual physical terrain. In this version,
rather than working with a constant force in a single dimension, multiple
zones of resistance are constructed and placed in arbitrary locations within a
virtual 2D space. Max/MSP’s nodes object is a visual panel of circular nodes
that can be resized and placed in various locations. A cursor can then be
moved through the panel and the object will output whether or not the cursor
is within a node’s region, as well as its distance from the center of each
node. By mapping the Falcon’s x and y position to the coordinates of the
cursor, the performer is able to control the cursor’s location within a
collection of nodes, and traverse the terrain. Using IRCAM’s MuBu for Max, a
sound file is segmented by an onset threshold and each segment is associated
with a specific node (see Figure 2). When the coordinates of the Falcon’s
ball-grip position are over a node, the specific segment is triggered and sent
through a granular synthesizer for further processing. Although the nodes
would sometimes overlap due to their varying radii and placement within 2D
space, the sound segment selected for playback would always be the segment
whose center was closest to the cursor. The output of the node was scaled to
the highest resistance value of the Falcon and sent to the force parameter of
the z-index—the plane associated with a forward and backward motion for the
performer. In this configuration, the performer would receive a low amount of
force-feedback towards the outskirts of the node’s region, and high amount of
feedback towards the center, thus producing the feeling of moving over a bump.

Figure 2: Haptic Terrain Version 1 using nodes and audio segmentation.

Because each node was circular, any position at or around the circumference of
a node would receive the same amount of feedback. The resistance sent to the
Falcon was also scaled and mapped to the density of the grains being played.
This meant that if the performer wanted to create a more intense and abrasive
sound, they would have to hold the Falcon in the most physically resistant
spot. In performance Isaac noted that while this was difficult, it still
remained a stable and predictable terrain. While the bumpy resistance created
through the nodes improved on the constant resistance model, Isaac felt that
this still became predictable when performing because the textures were
essentially the same, differing only in scale. This iteration lacked different
types of textures and therefore variation in the qualities of the force-
feedback. It offered a completely different sensation than the original patch,
yet it remained a pre-determined and somewhat stable terrain. Despite this,
the nodes could be used in future iterations to access different regions of
internal processes within the patch. This iteration could also be used as
potential material for an additional visual element for the audience.

###  3.3 Case Study: Haptic Terrain (Version 2)

The second iteration of this idea uses the Max/MSP object jit.bfg to create
terrains based on different noise textures. The jit.bfg object “evaluates and
exposes a library of procedural basis functions"111See the jit.bfg reference
page in the Max/MSP documentation. and by changing the noise basis, different
textures can be generated. The basis function that generated Voronoi cells was
favoured during initial tests because, on a close up zoom, it creates crater-
like textures with ridges and dips (see Figure 3). On a higher scale (zoom
out), the cells become tiny, bumpy surfaces with defined edges.

The jit.bfg object outputs a grid of texture that is rendered from a range of
values from 0 to 1. This range was first normalized, and then mapped onto the
maximum and minimum force-feedback values for the NovInt Falcon. Again, the x
and y coordinates received from the location of the Falcon’s ball-grip were
used to scroll through the cells of the 2D matrix generated by jit.bfg and
return the greyscale value of that cell. The scaled value was mapped to the
force-feedback input of the Falcon. By mapping the highest force of the Falcon
to the highest value—the lightest areas of the texture map—and the lowest
values to the lowest force of the Falcon—the darkest areas on the texture
map—the computationally generated virtual textures were physically realized
through haptic interface (see Figure 1).

The sonic result of this patch follows the texture maps generated. The source
of the sound is generated by two phasors with controllable frequencies that
are run through a comb filter. The x and y coordinates change the delay and
feedforward of the comb filter. As such, the sound changes drastically
depending on the controller position, yet maintains some recognizable
characteristics. These sounds are then processed further using granulation and
the gain of the grains also mapped to the Falcon’s x and y coordinates. In
this way, sound will only occur when the performer is hovering over a lighter
area of the texture.

Figure 3: A haptic terrain generated using Voronoi basis functions.

Additionally, all of the sound was sent through a noise gate. The threshold of
the noise gate was determined by the z position of the Falcon, and
simultaneously multiplied by the z force being sent to the Falcon. In this
way, the fullest sounds can only be heard if the performer is hovering over a
light, forceful area and if they are exerting a strong force on this area.
Even if the performer applies the same force in a darker area, they will not
be able to hear the fullest sound. It is only through a strong force in a
physically demanding area that the performer can hear all of the frequencies
at full volume. Even though there is a relatively large range between the
weakest and strongest forces of the Falcon’s resistance, it does not take a
large amount of effort to merely slide over the different zones. The force-
feedback is really only felt when the user pushes forwards. The Falcon is
comparable to a joystick controller and, unlike a traditional instrument, its
extremities are easily reached. According to Parker, “grafting the joystick’s
physical extremes to the limits of software parameters can result in an
unrewarding musical experience" [10, p1]. Therefore, it was more fruitful to
explore the affordances of the physical extremities offered by the haptic
terrains. Desirable sounds were still able to occur within the range of these
limits. Multiplying the current resistance being output from the Falcon by the
force received required the performer to exert significant effort in order to
reach the full range of dynamics that the system had to offer.

Isaac felt that this version of the sonic terrain was the most exciting to
work with because of the diverse range of textures and resistances that it
afforded. The interaction between gesture and sound seemed to correspond to
the texture in a meaningful way. By mapping the combined resistance from the
terrain and the performer’s force to the threshold of the noise gate, dark
areas of low resistance seemed to let small particles of the sound seep
through, while light areas that required heavy force gave the sensation of
physically pushing the full sound through the gate. The fact that feedback was
no longer static, but became dependent on the response of the performer was
also highly engaging.

##  4 Conclusions and Future Work

We have described the iterative development of a haptic DMI through the
implementation of different strategies for generating force-feedback profiles.
The first strategy involved a constant resistant force that made movement in
one dimension more difficult. While this allowed the performer to more
expressively explore regions of their sonic material in more detail, the
uniformity of the resistance was deemed to be undesirable after numerous
performances. The second strategy explored the idea of cross-modal terrains,
generated as visual planes, and mapped to both haptic and sonic parameters. In
particular, the Voronoi terrains generated by the basis functions afforded
rich and varied haptic profiles.

These nonuniform terrains can be generated on the fly, allowing for
instantaneous re-mapping to take place. Future work will explore this by
changing force-feedback profiles during performance. The nodes-based model
will also be repurposed as an audio processing routing strategy, running
concurrently with the Voronoi technique. We will also experiment with
projecting the terrains for the audience so that they can watch the performer
attempt to navigate space both physically, as well as digitally.

## References

  * [1] E. Berdahl, G. Niemeyer, and J. O. Smith.  HSP: A simple and effective open-source platform for implementing haptic musical instruments.  In Proceedings of the International Conference on New Instruments for Musical Expression, pages 262–263, 2009.
  * [2] E. Berdahl, B. Verplank, J. O. Smith III, and G. Niemeyer.  A physically-intuitive haptic drumstick.  In Proceedings of the International Computer Music Conference, pages 363–366, 2007.
  * [3] C. Cadoz.  Instrumental gesture and musical composition.  In ICMC 1988-International Computer Music Conference, pages 1–12, 1988.
  * [4] J.-J. Filatriau, D. Arfib, J.-M. Couturier, and B. Yeti.  Using visual textures for sonic textures production and control.  In Proceedings of the International Conference on Digital Audio Effects, pages 31–36, 2006.
  * [5] L. Hayes.  Vibrotactile feedback-assisted performance.  In Proceedings of the International Conference on New Instruments for Musical Expression, pages 72–75, 2011.
  * [6] L. Hayes.  Performing articulation and expression through a haptic interface.  In Proceedings of the International Computer Music Conference, 2012\.
  * [7] S. James.  Multi-point nonlinear spatial distributions of effects across the soundfield.  In Proceedings of the International Computer Music Conference, 2016\.
  * [8] J. Leonard and C. Cadoz.  Physical modelling concepts for a collection of multisensory virtual musical instruments.  In Proceedings of the International Conference on New Instruments for Musical Expression, pages 150–155, 2015.
  * [9] D. Overholt, E. Berdahl, and R. Hamilton.  Advancements in actuated musical instruments.  Organised Sound, 16(02):154–165.
  * [10] M. Parker.  Joys of travel: Introducing the spectral tourist.  Leonardo Electronic Almanac, 15.
  * [11] A. Tanaka and A. Parkinson.  Haptic wave: A cross-modal interface for visually impaired audio producers.  In Proceedings of the ACM Conference on Human Factors in Computing Systems, pages 2150–2161. ACM, 2016.


# Statistical Analysis Based Feature Selection Enhanced RF-PUF with $>$99.8%
Accuracy on Unmodified Commodity Transmitters for IoT Physical Security

Md Faizul Bari 1,∗, Parv Agrawal 1, Baibhab Chatterjee 1 and Shreyas Sen 1

###### Abstract

## 1

Due to the diverse and mobile nature of the deployment environment, smart and
connected commodity devices are vulnerable to various attacks which can grant
unauthorized access to a rogue device in a large, connected network and lead
to data theft and malicious activities. Traditional digital signature-based
authentication methods are vulnerable to key recovery attacks, cross-site
request forgery, etc. To circumvent the inherent weakness of the digital
signature-based authentication system, RF-PUF had been proposed as a promising
alternative that utilizes the inherent nonidealities of the devices as
physical signatures that arise from the manufacturing process variation. RF-
PUF offers a robust authentication method that is resilient to key-hacking
methods due to the absence of secret key requirements and does not require any
additional circuitry on the transmitter end, eliminating the need for
additional power, area, and computational burden. In this work, for the first
time, we analyze the effectiveness of RF-PUF on commodity devices, purchased
off-the-shelf, without any modifications whatsoever. Data were collected from
30 Xbee S2C modules used as transmitters and released as a public dataset for
the whole community. A new feature has been engineered through PCA and
statistical property analysis. With a new and robust feature set, it has been
shown that 95% accuracy can be achieved using only $\sim$1.8 milliseconds of
test data fed into a lightweight neural network (with 10 neurons in 1 layer),
reaching $>$99.8% accuracy with more data and network of higher model capacity
(1 layer with 70 neurons), for the first time in literature without any
assisting digital preamble. The design space has been explored in detail and
the effect of the wireless channel on the network performance has been
determined. The performance of some popular machine learning algorithms has
been tested and compared with the neural network approach in terms of device
numbers. A thorough investigation on various PUF properties has been done and
both intra and inter-PUF distances have been calculated. With extensive
testing of 41238000 cases, the detection probability for RF-PUF for our data
is found to be 0.9987, which, for the first time, experimentally establishes
RF-PUF as a strong authentication method. Finally, the potential attack models
and the robustness of RF-PUF against them have been discussed.

##  2 Keywords:

IoT, machine learning, physical security, PUF, neural network (NN), radio
frequency, authentication, Xbee

##  3 Introduction

The fourth industrial revolution, powered by low-power, high-speed modern
communication systems has ushered in a new era of immersive and unprecedented
user experience through smart devices that are connected with each other and
to the cloud, popularly known as the Internet of Things (IoT). The global IoT
market is experiencing a rapid boost and according to a prediction by Norton,
there will be around $21$ billion connected devices by $2025$ [1]. We are
already talking about the Internet of Everything (IoE) which essentially
refers to people, data, and smart things connected to form an ecosystem that
ensures a better and smarter lifestyle. The diverse application environment of
the smart devices has rendered them vulnerable to a wide attacking surface.
The weakest point in a network defines its security and for IoT networks, the
resource-limited, user-end devices are the weakest points where a security
compromise can provide access to a rogue device that can pose a massive threat
to the whole network. So, the question of secure authentication before
granting access to a large network is of increasing importance.

Figure 1: The concept of RF-PUF exploits the inherent physical signature
embedded in the device which manifests itself as different imperfections,
which are used as features to train a neural network at the receiver end for
authentication. The challenges involve developing a proper feature set,
choosing a proper neural network architecture, and evaluating the concept in
real, commodity devices.

Traditional methods such as symmetric-key cryptography and asymmetric-key
cryptography use secret private keys or public/private key pairs respectively,
for encryption/decryption. Key-based methods require the storage of a secret
key in a nonvolatile memory (NVM) or SRAM. However, they are vulnerable to
different invasive/semi-invasive key-hacking attacks and side-channel attacks
[2, 3, 4]. Multi-factor authentication (MFA) [5, 6] requires one or more
verification factors (e.g., biometric factor, two-factor code from
authentication app, etc.) along with the secret key. The widely-used open
authentication (OAuth 2.0) protocol [7] for current IoT networks suffer from
cross-site request forgery (CSRF) attacks [8, 9]. Both OAuth and MFA are
inconvenient for large networks as they require manual verification. In
addition to these vulnerabilities, the use of digital signatures also puts
additional power and area burden which are typically small but could be
significant for extremely energy and resource constraint edge devices.

To circumvent this, the idea of radio frequency physical unclonable function
(RF-PUF) has been recently proposed [10] using physical signature instead of
or in addition to the digital signature. The concept of RF-PUF is explained in
Fig. 1. RF-PUF exploits the inherent device imperfections due to manufacturing
process variation and other system-level nonidealities (e.g. LO frequency
offset, I-Q mismatch, DC offset, attenuation, fading, Doppler shift, etc.) as
unique physical signatures. These signatures are used as features and fed to a
neural network at the receiver to train it. Once trained, this network can be
employed at the receiver for authentication. RF-PUF does not demand any
additional preamble, digital keys, or assistive communication medium for
authentication purposes. The absence of an external security key or preamble
makes RF-PUF highly resilient to different types of key-hacking attacks and
alleviates the need for preamble obfuscation [11]. Also, it does not require
any secured memory block for key storage. Thus, both power and area overhead
is reduced on the resource-constrained edge-node side of an asymmetric IoT
network.

In [10], the idea of RF-PUF was presented primarily based on simulation data
using I-Q samples as features. However, the PUF output is stochastic in nature
and it is very hard to accurately capture the device nonidealities in
simulation. This calls for addressing the open research needs of experimental
validation of RF-PUF and demonstration of high-accuracy on devices found ‘in-
the-wild’. In this work, we address both these research problems by a)
analyzing the efficacy of RF-PUF on unmodified commodity devices and b)
introducing effective feature selection to increase RF-PUF accuracy $>99.8\%$.
To achieve this, an improved and robust feature set is necessary to provide a
reliable authentication method. We purchased commercially available $30$ Xbee
S2C devices and used them as unmodified commodity COTS (Components off-the-
self) devices to experimentally validate RF-PUF. 155.4 GB of data have been
collected from the Xbee transceiver systems and 2.5 GB of data have been used
for experimentation. This dataset has also been made public on GitHub along
with this paper, for further development and validation by the RF-Security
community.

It has been shown that $95\%$ accuracy can be achieved even with a
lightweight, single-layer neural network with $10$ neurons and $\sim 1.8$
$\mathrm{ms}$ ($30\text{\,}\mathrm{kB}$) of test data, which ensures the
feasibility of RF-PUF in a low-latency network. With statistical analysis, a
new feature has been augmented that massively boosts the performance of the
network. The impact of the variation in neural network model capacity and the
amount of training data on detection accuracy has been explored. Along with
artificial neural networks, experiments have been performed with multiple
traditional machine learning algorithms, and their performance is compared in
terms of the number of devices. A detailed analysis of the PUF properties has
been done to evaluate the eligibility of RF-PUF as a PUF. Inter-PUF and intra-
PUF hamming distances have been calculated and it has been proved that for
commodity COTS (Components off the self) devices without any modification, RF-
PUF shows strong identifiability with a very high ($99.87\%$) detection
probability. As an authentication method, possible vulnerabilities and attack
models for RF-PUF have been investigated and the robustness of RF-PUF against
them has been proved. The insights gathered from these analyses and
experiments may prove to be extremely important for the design and
implementation of RF-PUF in the future in realistic application scenarios with
‘in-the-wild’ devices.

###  3.1 Our Contribution

In this work, through thorough statistical analysis of unmodified commodity
devices we have found an optimum feature that improves the accuracy of RF-PUF
significantly on a suite of commodity hardware devices leading to $>99.8\%$
accuracy, along with PUF property analysis and security vulnerability
analysis. Detailed contributions are as follows:

1) Feature engineering: Principal component analysis has been performed on the
existing feature set found in the literature to find the dominant feature.
Through moment analysis on the dominant feature (i.e. carrier frequency
offset) we demonstrate that the addition of a feature called COV (ratio of
standard deviation and mean of carrier frequency offset) significantly helps
in achieving high ($>99.8\%$) accuracy (Section 6.3).

2) Highest accuracy achieved with unmodified COTS devices: $30$ Xbee S2C
modules have been used without the help of any assisting communication
preamble or any modification to the devices whatsoever. Using data received
over a wireless channel with a suitable feature set and a lightweight neural
network, $99.8\%$ accuracy can be achieved which, to our best knowledge, is
the highest accuracy using this many commodity COTS devices considering the
wireless channel (Section 6.4).

3) RF-PUF established as a strong PUF: Any distinct PUF class is identified
through some properties that make it a separate class. They include
constructability, evaluability, uniqueness, reliability, and identifiability.
We have explored these properties for RF-PUF in detail, calculated intra-PUF
and inter-PUF hamming distances and in an extensive test of $41238000$ cases,
we have shown that the probability of proper identification of an RF-PUF
instance is $0.9987$. This is the first time analysis of RF-PUF as a PUF class
which experimentally demonstrates RF-PUF as a strong and unique PUF class by
itself (Section 8).

4) Performance evaluation using popular machine learning algorithms and
comparison with neural network (NN) based approach. It has been shown that
even a lightweight NN with a single hidden layer can handle $>$300 devices
with 99.9% accuracy, unlike ML algorithms (Section 7.4).

5) Wireless channel variability analysis on the accuracy of RF-PUF and the
effect of network depth on accuracy with and without wireless channel has been
presented. Discussion on possible important attack models and the robustness
of RF-PUF against such attacks (Section 7.5).

6) Public Dataset: Our collected data have been released as a public dataset
for the whole community to explore and experiment with (Section 5.3).

Figure 2: (a) Commodity off-the-shelf devices (30 Xbee S2C modules) used for
data collection. (b) Conceptual experimental setup. (c) Actual experimental
setup in the lab. The TX and RX are placed $1\text{\,}\mathrm{m}$ apart (they
are close here for image capturing purpose only) and a HackRF module was used
to collect data either from the TX (case 1) or RX (case 2). GNU Radio records
the collected data and shows a live constellation (visible on-screen). The
rotating constellation is later processed in MATLAB through coarse and fine
frequency compensation. Figure 3: Grouping collected data in a number of
frames and filtering of data for acceptable frames. This step is required as
the Xbee module transmits data on an interval.

##  4 Related Works

Time and frequency domain properties of individual transmitters have been used
for RF fingerprinting [12, 13, 14, 15, 16, 17, 18, 19, 20]. However, both time
and frequency domain analysis have their limitations in the form of detecting
the start and end of the transients, high oversampling ratios, and the need
for fixed preambles to avoid data dependency. MAC layer and other upper layers
of the communication protocol have also been used for RF-fingerprinting [21].
However, device identifiers in upper layers like IMEI number, IP address, MAC
address, etc. can be spoofed [22, 23, 24, 25]. Hanna et al. utilized power
amplifier nonlinearity to fingerprint RF devices [26] using simulation data.
Recently, there have been a growing number of works that use raw RF data and
depend on complex neural networks to classify devices [27, 28, 29, 30]. This
method has one weak point. As wireless data are contaminated with noise and
interference, any use of the RF data without processing always posits a risk
of huge performance drop in scenarios where environmental nonidealities can go
beyond the estimation that was used while designing the network. Contaminated
data can render faulty predictions, especially if the training environment is
significantly different from the test environment. Another concern in this
approach is that it is somewhat blind and does not provide intuition on
different design parameters and their effects. Processing data, extracting a
proper feature set, and unraveling the mystery of the design space can render
a robust authentication method that is less vulnerable to environmental
factors and provides more flexibility to the designer. That’s why RF-PUF
performs better than the CNN-based approach as is shown in [31]. Brik et al.
[32] used IEEE 802.11 devices to show $99\%$ detection accuracy. However, the
wireless channel was ignored completely. In our work, using data from $30$
commercial Xbee devices and considering the wireless channel in conjunction
with a lightweight NN, we have shown that we can achieve $>99.8\%$ accuracy.

##  5 Experimental Setup

###  5.1 Physical Device Setup

For experimental validation, 30 XBee S2C modules are chosen (IEEE 802.15.4
standard) which is designed for industrial and commercial use. Fig. 2(a) shows
the Xbee devices whereas Fig. 2(b), and Fig. 2(c) show the block diagram and
the actual setup. The TX and RX are kept 1 m apart. Using SMA cable, a HackRF
One software-defined radio (SDR) module has been connected either to the TX
(case 1) or to the RX (case 2) to extract data excluding (case 1) or including
(case 2) wireless channel.

###  5.2 Data Collection and Filtering Noise

A 31-bit pseudo-random bit sequence (PRBS) is generated in MATLAB and fed to
each TX which transmits this data for 60 sec with QPSK modulation at 2.465 GHz
and 230400 bps baud rate. These data were captured in a Xbee RX module.
Simultaneously, data were also captured by a HackRF one software-defined radio
(SDR) module, sampled at 6 MSps, and stored by GNU Radio. The captured data
are divided into several frames, each containing a number of samples. From the
constellation diagram of the frame data (Fig. 3), it is found that some frames
have no significant data points and contain only noise as the Xbee devices
transmit data intermittently due to its buffer limitation. These blank frames
containing only noise were discarded.

###  5.3 Public Dataset

This dataset contains raw data collected from 30 Xbee S2C transmitters for
both cases (excluding and including the channel) in binary format. The total
size of the dataset is 155.4 GB (each transmitter data is $\sim$2.5 GB). It
can be downloaded from ‘Sparclab RF-PUF Dataset [33]’.

Figure 4: (a) Accuracy vs the number of neurons in each hidden layer. Even
after increasing the number of hidden layers, the accuracy remains $<75\%$.
(b) Principal Component Analysis (PCA) reveals that first principal component
(PC) causes most variation, which in turn depends mostly on the carrier
frequency offset, CFO. (c) Mean ($\mu$) and standard deviation ($\sigma$) of
the dominant feature (CFO) analyzed in search of a new feature. It reveals
that these statistical parameters vary significantly among transmitters. So,
their ratio or coefficient of frequency offset variation, COV =
$\frac{\text{standard deviation ($\sigma$) of CFO}}{\text{mean ($\mu$) of
CFO}}$ is taken as the tenth feature. (d) Inclusion of COV shows significant
improvement in the detection accuracy. Using a single hidden layer with only
$10$ neurons, $95\%$ accuracy is achieved, and $>99\%$ accuracy is reached for
$>50$ neurons.

##  6 Feature Extraction

###  6.1 Initial Feature Set

In our work, CFO and I-Q data are taken as features just as in the original
RF-PUF paper[10]. The previously generated frames are filtered using matched
filtering, frequency compensated (both fine and coarse), and finally
synchronized using timing recovery. In this process, CFO is found as a
byproduct. Along with CFO, the compensated in-phase and quadrature-phase
components in four quadrants are used as features. The $9$ features (CFO $+$ 4
I-components $+$ 4 Q-components) from each frame and $1000$ frames from each
TX lead to a feature set of $9\times 1000$. The final feature matrix is a
combination of these feature sets from all $30$ devices and has a size of
$9\times 30000$.

###  6.2 Accuracy with Carrier Frequency Offset and I-Q Features

The whole feature data are divided into $70\%$, $15\%$, and $15\%$
respectively for training, validation, and test purposes and fed into a neural
network (NN). The performance of the neural network is tested by varying the
number of neurons and hidden layers. Fig. 4(a) shows the accuracy of the
trained model for different neural networks. The accuracy is less than $75\%$
in all test cases. Since exploring different NN configurations does not
provide expected accuracy, our choice here is to: (i) form an improved feature
set to be used with the NN (ii) use different machine learning (ML) algorithms
(iii) use more data. We first search for an improved feature set for better
accuracy. Later, effect of more data is shown in subsection 7.1, 7.2 and a
comparison of different ML algorithm and NN is discussed in subsection 7.4.

###  6.3 Statistical Analysis

####  6.3.1 Principal Component Analysis

We start the investigation by performing Principal Component Analysis (PCA)
with feature matrix as input (each feature represents one input dimension).
Fig. 4(b) shows the principal components and their contribution to the
variances. The first principal component (PC) contributes to most of the
variances and the input to PC mapping reveals that the CFO is the most
dominant feature. So, an in-depth statistical property analysis of the CFO can
help in deriving a new feature.

####  6.3.2 Moment Analysis

Since, CFO varies from frame to frame (i.e., with time), it is intuitive to
look at the moments of their distribution. Specifically, we want to look at
first and second-order moments (mean and variance). Fig. 4(c) shows the
absolute values of mean and standard deviation (square root of variance) of
CFO. These parameters vary significantly from TX to TX in most cases. And even
if for any two TX, the mean is similar, the standard deviation is different,
and vice versa. If they can be combined to form a new feature, that can
provide significant discrimination among transmitters and lead to much better
accuracy. In statistics, the ratio of standard deviation and mean is known as
the coefficient of variation. So, using this statistical parameter, we form a
new feature named the coefficient of frequency offset variation (COV) which is
defined as:

$COV=\left|\frac{\textit{Standard deviation of CFO}}{\textit{Mean of
CFO}}\right|$

###  6.4 Performance using COV feature

COV is included as the tenth feature in our existing feature matrix. From PCA
analysis, it is already revealed that the I-Q features contribute to much
fewer variances and can be discarded by trading some accuracy. Since our goal
is to achieve maximum possible accuracy, we still keep them as features. Also,
I-Q values contain channel information, which will help the NN to compensate
for the wireless channel (channel effect is explained in subsection 7.5).

After including COV as the tenth feature, our neural network was trained,
validated, and tested again with the new feature matrix. Fig. 4(d) shows that
the performance of the network has improved drastically. With just a single
hidden layer, $>95\%$ accuracy can be achieved using $10$ neurons and can hit
$99.9\%$ accuracy by increasing the number of neurons.

##  7 Evaluation of Design Parameters

Figure 5: (a) Detection accuracy vs the number of samples per frame for
different neural networks which shows a trend of accuracy improvement
(indicated by red arrow) with the increase in sample number. (b) Detection
accuracy for different frame numbers shows higher frame number renders better
performance. (c) Detection accuracy versus the number of neurons per layer.
The general trend shows that accuracy improves with the increase in the number
of neurons in each layer. Also, accuracy typically improves with more hidden
layers until the higher model order causes overfitting and degrades
performance.

###  7.1 Effect of number of samples

Fig. 5(a) shows the plot of detection accuracy versus the number of samples in
each frame for different neural networks. The general trend is that, for each
NN configuration, detection accuracy improves with the increase in the number
of samples (along the x-axis). This is expected because a higher number of
samples provide more information and hence better performance. Also, $>95\%$
accuracy point is reached at around $150$ samples per frame which is
equivalent to $12.5\text{\,}\mathrm{ms}$ of total data (or
$1.8\text{\,}\mathrm{ms}$ test data). Hence, we can reach the $95\%$ accuracy
bar using small test data.

###  7.2 Effect of the Number of Frames in Feature Set

Fig. 5(b) shows accuracy for two different frame numbers, $500$ and $1000$.
With a higher frame number, the information content of each transmitter device
increases and so their detection gets better as shown by the blue ($1000$
frames) and brown lines ($500$ frames) respectively. We can generalize the
previous subsection (sample number effect) and this subsection as more data
render better performance.

###  7.3 Effect of the Neural Network Parameters

Fig. 5(c) shows the plots of accuracy versus the number of neurons in each
hidden layer. As the number of neurons increases along the x-axis, accuracy,
in general, gets better. Also, as the number of hidden layers increases, the
network performs better initially, but later it creates an overfitting problem
where the model capacity is too large compared to data. This phenomenon
directly manifests itself as a degradation in performance. Hence, there is an
optimum model capacity up to which accuracy increases, and beyond that
accuracy drops.

Figure 6: (a) Popular ML algorithms show high accuracy for 30 Xbee devices.
(b) The accuracy of simple ML networks drops when the number of TX is large,
wherein the neural network still holds up with $>99.9\%$ accuracy.

###  7.4 Using Simple Machine Learning (ML) Algorithm

It has been observed that the COV values vary significantly among different
transmitters. When a simple feature displays a significant separation among
different classes, it can be modeled with a complex if-else ladder structure.
This implies that even simple ML algorithms (e.g. Tree) can show good results.
Fig. 6(a) shows that some popular ML algorithm achieves $>95\%$ accuracy.

The true power of the neural network comes into play when the number of TX
increases as shown in Fig. 6(b). For this, features are generated for $300$ TX
devices following a Gaussian distribution (as in [10]) with the same mean and
variance as that of the original $30$ TX devices, for both inter and intra-
class variations. Fig. 6(b) shows that as the number of TX increases, accuracy
falls after a certain point ($\sim 100$ TX) even for support vector machines
(SVM), and it fails to converge for $>150$ TX.

###  7.5 Effect of Wireless Channel

Figure 7: Comparison of the network performance in the cases of including and
excluding the wireless channel data. The network needs 15 neurons compared to
10 neurons in a hidden layer to achieve $95\%$ accuracy for the case where the
channel is considered. But with higher model capacity, both lines converge and
the network learns the channel effect on data. d the network learns the
channel effect on data. The light red box shows the region where the network
fails to learn transmitter variation, light yellow box shows the region where
the network learns transmitter variation but fails to learn the variation due
to the wireless channel. The light green box shows the region where the
network learns both the transmitter and channel variation properly.

So far, nonidealities due to TX were considered and the wireless channel was
ignored (TX, RX connected via SMA cable). But the channel itself adds some
nonidealities. Here, the effect of a static wireless channel
($1\text{\,}\mathrm{m}$ of fixed TX-RX separation) has been analyzed. Fig. 7
shows accuracy versus neuron number in a single layer, with and without the
wireless channel. For iso-accuracy of $95\%$, wireless channel demands
slightly higher model capacity ($10$ vs $15$ neurons). But when the number of
neurons increases ($>50$), both curves merge and render similar accuracy.

In one of our recent works [31], we applied RF-PUF on the ORACLE dataset which
contains data for 16 USRP X310 TX for both static and quasi-static (variable
TX-RX separation) cases with a channel length varying from 2ft to 62ft. We
have shown that RF-PUF achieves $100\%$ accuracy up to 38ft and $>95\%$
accuracy even at 62ft channel length. This result confirms that the RF-PUF
approach can make the channel compensation with the help of NN and render high
performance even in a long wireless channel. On a side note, that work
combined with current work, also confirms that RF-PUF achieves high accuracy
on experimental data in different platforms (XBee vs USRP radios using WiFi)
for different devices.

##  8 Analysis of PUF Properties

PUF response to a particular challenge is a probabilistic function. In this
section, we will determine intra-PUF hamming distance and inter-PUF hamming
distance and discuss various PUF properties ([roel2012physically,
HOST_course]) in light of those distances.

###  8.1 Constructability

A PUF class $\mathbb{P}$ is constructible if we can create a new PUF instance
$puf_{m}\in\mathbb{P}$ through a process, $\mathbb{P}$.Create :
$puf_{m}\leftarrow\mathbb{P}\text{.Create}$, where $puf_{m}$ has entropy that
makes it distinct from other PUF instances $puf_{n,n\neq m}$. In the case of
RF-PUF, the source of entropy is the manufacturing process variation. During
fabrication of ICs, we have within die and die-to-die variation which is due
to the limitation of the manufacturing process. In contrast to many other PUF
classes where we need a separate mechanism for PUF instance creation, the
manufacturing process of the integrated circuit itself serves as the creation
process for RF-PUF which is one of its advantages.

###  8.2 Evaluability

A PUF class $\mathbb{P}$ is evaluable if for a random PUF instance
$puf_{m}\in\mathbb{P}$ and a random challenge $(x)$, we can evaluate a
response $y:y\leftarrow puf_{m}(x)$. In our case, the challenge is a randomly
generated bitstream in MATLAB that is fed into the transmitter and the
corresponding response is the analog signal that contains the unique physical
signature of the transmitter.

###  8.3 Inter PUF Distance - Uniqueness

Uniqueness refers to how different each instance of a PUF class $\mathbb{P}$
is from each other. A measurement metric that is used to represent PUF
uniqueness is called inter-PUF hamming distance and is defined as:

$HD_{inter}\cong distance[Y_{m}^{\alpha}(x),Y_{n}^{\alpha}(x)]$

Here, $Y_{m}^{\alpha}(x)$ and $Y_{n}^{\alpha}(x)$ are the responses from
$puf_{m}$ and $puf_{n}$ (two instances of PUF class $\mathbb{P}$) under same
environmental condition $\alpha$ and same challenge x. Ideally, these inter-
chip hamming distances should be much greater than any intra-chip hamming
distances to distinguish them separately. In our experiment, our PUF class
$\mathbb{P}$ = RF-PUF and $puf_{i},(\text{where }i=1,2,...30)$ are the
instances of that class (30 Xbee devices).

To calculate $HD_{inter}$, the first $1000$ frames from each of the
transmitters are taken. Each frame contains $3600$ samples. Our features
remain unchanged: CFO, eight I-Q component values, and COV. But after taking
$10$ features from each of $1000$ frames, instead of using them as a feature
matrix for each transmitter, the mean values of the features are taken across
all the frames. This means that instead of representing each transmitter as a
$10\times 1000$ feature matrix, it is represented as a $10\times 1$ feature
vector. The reason for taking the average value across the frames is that the
frames have an associated timestamp with them i.e., each frame data are
collected from time to time. So, each frame faces slightly different
environmental conditions such as heating of the transmitter due to data
transmission for a long time, external interference, noise, etc. Averaging the
feature values across a large number of frames mitigates the environmental
factors, especially noise. Also, taking the first $1000$ frames from each
transmitter ensures the same initial heating pattern across devices. So the
final outcome is that the feature vector for each transmitter has a very
similar environmental factor $\alpha$, which is one of the conditions of
inter-chip hamming distance calculation.

After taking feature vector from each transmitter, the Euclidean distance was
calculated in ten dimensional feature space as hamming distance. For
$puf_{m}$, let us denote $CFO_{m}$ = carrier frequency offset, $COV_{m}$ =
coefficient of frequency offset variation, $I_{k,m}$ = in-phase component in
the $k-th$ quadrant and $Q_{k,m}$ = quadrature-phase component in the $k-th$
quadrant. Then distance $d_{m,n}$ between $puf_{m}$ and $puf_{n}$ instances is
given by:

$\begin{split}d_{m,n}^{2}=&(CFO_{m}-CFO_{n})^{2}+(COV_{m}-COV_{n})^{2}+\\\
&\sum_{k=1}^{4}(I_{k,m}-I_{k,n})^{2}+\sum_{k=1}^{4}(Q_{k,m}-Q_{k,n})^{2}\end{split}$
(1)

The inter-chip distances were calculated for each transmitter with respect to
all $30$ transmitters (including the chip under test), which leads to a
$30\times 30$ symmetric matrix (upper and lower triangular matrices with same
values since $d_{m,n}=d_{n,m}$ = inter-chip distance between $puf_{m}$ and
$puf_{n}$) with a principal diagonal of zeros (self-distance). It is found
that the worst case scenario with minimum distance, $HD_{inter,min}=0.2307$
and the best case scenario with maximum distance, $HD_{inter,max}=10.149$.

Figure 8: Data distribution of (a) intra-PUF hamming distances and (c) inter-
PUF hamming distances. Due to skewness, Weibull distribution fitting is a more
accurate representation in these cases. (b) The two Weibull curves are
superimposed on top of each other. It is seen that there is a very slight
overlap (yellow region) between the curves which is shown in a zoomed inset.
Although trivial, this overlapping is the source of the detection error.

In literature, often a mean inter-puf distance, $\mu_{inter}$, is reported
which is the average of all $HD_{inter}$. The formula is:

$\begin{split}\mu_{inter}&=\overline{HD_{inter}}\\\
&=\frac{2}{N_{puf}\times(N_{puf}-1)\times N_{chal}}\sum HD_{inter}\end{split}$

Where $N_{puf}$ is number of puf instances ($N_{puf}=30$ for us), and
$N_{chal}$ is the number of challenges ($N_{chal}=1$, since we are not varying
our challenge). Using this formula, we find that $\mu_{inter}=3.703$.

Fig. 8(c) shows the probability mass function distribution of $435\text{
}(=\frac{30\times 29}{2})$ inter-PUF distances. The density function is right-
skewed, that’s why Weibull fitting (which is exponential in nature) fits it
more accurately than normal distribution fitting. This fitting shows that on
the right side the curve is more sparse but on the left side it is more
centered instead of being sparse, which is good because that will ensure that
the inter-PUF values don’t go to overlap intra-PUF distances which should
ideally be at zero.

###  8.4 Intra PUF Distance - Reliability

PUF responses are in general dependent on various environmental factors that
render any PUF instance response as a probabilistic function. This means that
a particular PUF instance can provide slightly different values of features
based on varying environmental conditions. For authentication purposes, this
poses an issue. Reliability refers to how resilient a PUF instance is against
environmental factors e.g. noise, interference, temperature, supply voltage,
etc.

A measurement metric that is used to represent how reliable a particular
instance of a PUF class $\mathbb{P}$ is intra-puf hamming distance and is
defined as:

$HD_{intra}\cong distance[Y_{m}^{\alpha}(x),Y_{m}^{\beta}(x)]$

Here, $Y_{m}^{\alpha}(x)$ and $Y_{m}^{\beta}(x)$ are the responses from
$puf_{m}$ under two distinct environmental conditions $\alpha$ and $\beta$ and
same challenge x. Many $HD_{intra}$ distances are calculated at different
environmental conditions. Ideally this intra-chip hamming distances should be
zero.

To calculate $HD_{intra}$, we follow two steps. Let us consider one particular
PUF instance $puf_{m}$. On step 1, the first $1000$ frames (frame number $1$
to frame number $1000$) were taken from $puf_{m}$, each frame containing
$3600$ samples. Then mean values of the previously mentioned ten features were
taken just as before to represent it as a $10\times 1$ feature vector. Let us
represent this vector as $f_{v,1}$. Then on step 2, first $5$ frames are
skipped and the next $1000$ frames are taken from frame number = $6$ to frame
number = $1005$. Step 1 is repeated here to get next feature vector $f_{v,2}$.
Then next $1000$ frames are taken from frame number = $11$ to frame number =
$1010$ and a feature vector $f_{v,3}$ is formed. This process is repeated $80$
times to form $80$ different feature vectors $f_{v,\alpha};\text{
}\alpha=1,2,...,80$. These $10\times 1$ feature vectors are stacked together
to form a feature vector set $f_{set,m}$ of size $10\times 80$ for $puf_{m}$.
The whole process is then repeated for all $30$ devices.

The purpose of taking frame-shifted or time-shifted frame groups is to
consider the time factor. Each frame has a duration of $0.6ms$, so $5$ frames
gap in between two frame groups renders a time difference of at least $3ms$
(in reality the difference is much larger since the transmitter transmits data
for a small time and most of the frames are just noise which are filtered in
data pre-processing step). The $80$ time-spaced frames, in reality, cover
almost half a minute. Our $2.4GHz$ clock will have LO drift cycle time in the
nanoseconds range. Hence, half-minute data can incorporate significant
environmental factors into frame data. So, it can be assumed that the feature
vectors $f_{v,\alpha};\text{ }\alpha=1,2,...,80$ in feature vector set
$f_{set,m}$ of $puf_{m}$ represents $\alpha=80$ different environmental
conditions.

Now, for each instance $puf_{m}$, Euclidean distance is calculated in $10$
dimensional feature space among the feature vectors in the feature vector set
using Eq. 1. This results in a symmetric matrix of size $80\times 80$ with a
principal diagonal of zeros. This process is repeated for other transmitters
as well. Essentially it gives us $30$ matrices of size $80\times 80$ for
intra-PUF distances. In the best-case scenario, the minimum distance is
$HD_{intra,min}=7.23\times 10^{-5}$ and in the worst case scenario, the
maximum distance is $HD_{intra,max}=0.73$.

Fig. 8(a) shows the probability mass function distribution of $94800\text{
}(=\frac{30\times 80\times 79}{2})$ intra-PUF distances. The density function
is right-skewed and Weibull distribution gives better fitting for it just like
inter-PUF cases. This fitting shows that on the left side the curve is
strongly centered towards zero, but has a diminishing trail on the right. this
trail goes on to overlap inter-puf distances slightly and causes a few
detection errors. Detection probability is discussed in the next subsection.

Finally, a mean intra-PUF distance, $\mu_{intra}$, is calculated which is the
average of all $HD_{intra}$. The formula is:

$\begin{split}\mu_{intra}&=\overline{HD_{intra}}\\\ &=\frac{2}{N_{puf}\times
N_{chal}\times\alpha\times(\alpha-1)}\sum HD_{intra}\end{split}$

Where $N_{puf}$ is number of puf instances ($N_{puf}=30$ for us), $N_{chal}$
is the number of challenges ($N_{chal}=1$, since we are not varying our
challenge) and $\alpha$ is number of environmental conditions ($\alpha=80$ in
our study). Using this formula, it is found that $\mu_{intra}=0.136$.

###  8.5 Identifiability

In the previous two subsections, both inter-PUF and intra-PUF hamming
distances and their mean values: $\mu_{inter}=3.703$ and $\mu_{intra}=0.136$
are calculated. Their comparison shows that $\mu_{inter}>\mu_{intra}$, which
establishes that on average the PUF instances can be distinguished from each
other. But the mean value does not depict the full story. Fig. 8(b) shows the
fitted distribution curves superimposed on each other. The brown curve (intra-
PUF distribution) is skewed to the left and the blue curve (inter-PUF
distribution) is skewed to the right and they mostly cover different regions.
However, there is slight overlapping between them which is shown in the inset
as a zoomed version of the overlapping area. Ideally, there should be no
overlapping. But in a practical scenario, this overlapping region is the
source of detection error.

From the definition of identifiability, a PUF class $\mathbb{P}$ is
identifiable if it is reliable as well as unique, and if the probability of
inter-PUF variation being greater than intra-PUF variation is very high.
Mathematically:

$Probability(HD_{inter}>HD_{intra})\approx 1$

In previous two subsections, $94800\text{ }(=\frac{30\times 80\times 79}{2})$
intra-PUF distances and $435\text{ }(=\frac{30\times 29}{2}$ inter-PUF
distances have been calculated. Now, each of these inter-puf distances is
compared with each of the intra-PUF distances that leads us to $435\times
94800=41238000$ cases, among which, $HD_{inter}>HD_{intra}$ is found in
$41184206$ cases.

$\bm{Probability(HD_{inter}>HD_{intra})=0.9987}$

This is a very high probability and close to $1$. This proves that RF-PUF has
strong identifiability and this property along with reliability, uniqueness,
constructability, and evaluability manifests RF-PUF as a distinct PUF class.
This is the first-ever experimental validation of RF-PUF as a distinct and
strong PUF class by itself.

##  9 Possible Attack Models on RF-PUF

Figure 9: Heatmap of unsupervised learning in the attacker using k-means
clustering. (a) The worst case accuracy of $0.09\%$ and (b) the best case
accuracy of $6.8\%$. Repeated clustering for $1000$ times shows $3.63\%$
accuracy on average.

RF-PUF does not store any digital key and hence, is not susceptible to
malicious PUF models which assume that the adversary can have access to all
the challenge-response pairs through a built-in logger software/implanted
Trojan. However, there is a possibility of a machine learning-based attack
that needs to be discussed (Fig.10). For RF-PUF, ML attack is a two-step
process:

  * •

Step 1: model/profile the victim TX (Unsupervised)

  * •

Step 2: use that model for spoofing/replay attacks

In step 1, the rogue device tries to learn the feature/parameter values of the
victim TX. Unlike the intended RX, this is an unsupervised problem for the
attacker. We have utilized k-means clustering to divide the feature map into
$30$ clusters and compare the predicted and true labels (Fig. 9). The process
was repeated $1000$ times as k-means isn’t unique without specific conditions.
Our analysis shows that clustering achieves $\sim 3.63\%$ accuracy on average,
which is very close to the probability of random detection
$(\frac{1}{30}=3.3\%)$. So, practically it is almost impossible to get the
right feature value and label.

Figure 10: ML attack model. Adversary ML network cannot undo the effect of ADC
and DAC which requires extremely high precision and resolution, making the
attack impractical.

If somehow the attacker succeeds in step 1, then in step 2, the attacker needs
to produce an RF signal that contains the same imperfections as the victim TX
with high accuracy. This requires a high speed and high-resolution circuitry.
Fig. 10 shows that the physical signature of the transmitter, $S$, goes
through transformation $T_{TX}$ at TX and $T_{RX}$ at RX. The transformations
in the attacker are $T_{A}$, $T_{ML1}$, $T_{ML2}$, and $T_{D}$ respectively.
Full transformation for the original device is $T_{RX}$($T_{TX}$($S$)) and for
the adversary is
$T_{RX}$($T_{D}$($T_{ML2}$($T_{ML1}$($T_{A}$($T_{TX}$($S$)))))). The adversary
ML2 framework needs to make these two transformations equal by undoing the
effect of its ADC/DAC which requires almost infinite resolution, rendering it
practically impossible (typical ADC/DAC are 8/16-bit). This Resolution
limitation in ADC/DAC and bandwidth limitation in filters and other RF
components also prevent replay attack, which requires the attacker to convert
the TX signal in the digital domain, incorporate malicious contents and then
transform it back into the RF domain with very high precision. Further
analysis of precision requirements for a practical attack will be included in
future work. The robustness of RF-PUF against malicious PUF model, ML attack,
and replay attack proves its strong candidacy of employment for RF security.

##  10 Conclusion

In this work, data collected from off-the-shelf commodity components ($30$
Xbee modules) were used to develop a new feature called the coefficient of
frequency offset variation (COV) through PCA and moment analysis. The new
feature leads to $95\%$ accuracy for a single hidden layer with $10$ neurons
and $>99.8\%$ accuracy for a single hidden layer with $>50$ neurons, for the
first time in literature without any assisting digital preamble. The dataset
containing 155.4 GB of data has also been released for public use. The design
space has been explored and the effect of the wireless channel is analyzed to
provide design insights. The scalability issue of simple ML algorithms for
high accuracy has also been explored. The PUF properties of RF-PUF have been
explored in detail. The inter-PUF and intra-PUF hamming distances are
calculated and with their distribution, it has been shown that they have
trivial overlapping. A detailed analysis reveals that the probability of
$HD_{inter}>HD_{intra}$ = $0.9987$, which resonates with the claim that RF-PUF
has a very high device authentication probability. Finally, possible important
attack models are discussed and the robustness of RF-PUF against them is
analyzed. This work experimentally validates RF-PUF with high accuracy, which
can contribute to a secure authentication system using inherent physical
signatures without extra power, area, or computational overhead on the
resource-constrained IoT transmitter side.

## Funding

This work was supported in part by the National Science Foundation, under
Grant 1935573.

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