nestedcomment IEEEexample:BSTcontrol

# Machine Learning in NextG Networks via
Generative Adversarial Networks

Ender Ayanoglu  Fellow, IEEE  Kemal Davaslioglu  Member, IEEE
Yalin E. Sagduyu  Senior Member, IEEE E. Ayanoglu is with the Center for
Pervasive Communications and Computing (CPCC), Dept. of EECS, UC Irvine, CA,
USA, K. Davaslioglu is with UTS Inc., MD, USA, and Y. E. Sagduyu is with
Intelligent Automation, A BlueHalo Company, MD, USA.

###### Abstract

Generative Adversarial Networks (GANs) are Machine Learning (ML) algorithms
that have the ability to address competitive resource allocation problems
together with detection and mitigation of anomalous behavior. In this paper,
we investigate their use in next-generation (NextG) communications within the
context of cognitive networks to address i) spectrum sharing, ii) detecting
anomalies, and iii) mitigating security attacks. GANs have the following
advantages. First, they can learn and synthesize field data, which can be
costly, time consuming, and nonrepeatable. Second, they enable pre-training
classifiers by using semi-supervised data. Third, they facilitate increased
resolution. Fourth, they enable the recovery of corrupted bits in the
spectrum. The paper provides the basics of GANs, a comparative discussion on
different kinds of GANs, performance measures for GANs in computer vision and
image processing as well as wireless applications, a number of datasets for
wireless applications, performance measures for general classifiers, a survey
of the literature on GANs for i)–iii) above, and future research directions.
As a use case of GAN for nextG communications, we show that a GAN can be
effectively applied for anomaly detection in signal classification (e.g., user
authentication) outperforming another state-of-the-art ML technique such as an
autoencoder.

Generative adversarial networks (GANs), conditional GANs, generative modeling,
spectrum sharing, anomaly detection, outlier detection, wireless security,
unsupervised learning.

##  1 Introduction

The number of radios and their use are increasing exponentially. Over the last
several years, wireless data transmission has grown up by approximately 50%
per year [1, 2]. This increase in demand has largely been driven by novel
applications such as streaming videos and social media on smart devices, and
has strained the ability of the limited available wireless spectrum to support
it. The coming era of the Internet-of-Things (IoT) and its anticipated goal of
connecting tens of billions of devices via wireless will make this situation
even more challenging for next-generation wireless communication networks
(NextG). Classical methods for medium access control and physical layer
operation, designed to handle a relatively small number of users in a given
space-time-frequency resource, will soon be overwhelmed and alternatives must
be sought.

Wireless systems of the future are anticipated to share the available spectrum
rather than operating with exclusive assigned frequencies. It is generally
expected that this sharing will be across all possible dimensions, including
space, time, and frequency, and will involve a huge quantity of interactions
among a very large number of radios. Flexible methods will be needed to
efficiently use the limited available resources, quickly adapting themselves
to changing environments and Quality-of-Service (QoS) requirements. This will
be true even as wireless systems move to higher frequencies (such as
anticipated for mmWave and THz bands) where available bandwidth is more
abundant. Due to shorter propagation distances and the increased prevalence of
blockages, it will require networks to continually reconfigure themselves via
handoffs, cooperative relaying, beamforming, and so on. Given the
exponentially increasing demand for wireless connectivity and the inevitable
increase in the complexity of the networks that will supply it, it is no
surprise that research is turning towards data-driven techniques of Artificial
Intelligence (AI) and Machine Learning (ML) techniques for help in addressing
these issues by learning from the spectrum data and solve complex tasks.

The Defense Advanced Research Projects Agency (DARPA) recently built a testbed
named Colosseum for testing shared-spectrum communication systems [1, 2]. The
vision is to emulate more than 65,000 unique interactions, such as text
messages or video streams, among 128 radios at once. This testbed is built
with the full expectation that the type of complicated spectrum sharing
scenario described above is likely and can be efficiently managed by AI [1,
2].

There are two possible ways of sharing spectrum. One is an open access model,
that is similar to an unlicensed band, such as the Industrial, Scientific, and
Medical (ISM) band. A more desirable model from an interference viewpoint is
known as the hierarchical access model, or the cognitive radio network. When
the cognitive radio concept was first proposed, learning was already
considered to be essential for its operation [3, 4]. There are three reasons
why considering ML for cognitive radio is important. First, as discussed in
[1, 2], due to the expected numbers of wireless devices and the complexity of
the services they provide, the learning process suggested in [3, 4] cannot be
managed by classical model-based techniques, and will need to employ ML
algorithms. Second, for complex radios with many inputs and many outputs, a
very large number of actions will be necessary to account for all possible
radio states. In the past, most cognitive radio research focused on radios
that are hard-coded to manage these states. ML provides an opportunity for a
learning engine to auto-generate these actions, rather than pre-programming
them [5]. Third, ML provides a framework in which to incorporate memory from
past actions and results into current operations, and thus more quickly adapt
to changing conditions in the future [5].

As ML techniques rely on the availability of representative data, it has
become imperative to generate and curate data samples for training and testing
of spectrum operations. To that end, synthetic data can be generated to help
with ML training and testing processes, when there is a lack of sufficient
number of real data samples. Building upon recent advances in deep neural
networks, Generative Adversarial Networks (GANs) have been originally
introduced to generate synthetic data that cannot be distinguished from real
data [6]. One direct use case of GANs is to generate synthetic training data
samples for data augmentation purposes to strengthen the training process of
ML algorithms. Later, the use of GANs has been extended to support domain
adaptation, defend against adversarial attacks, enable unsupervised learning
of data, detect anomalies embedded in rich data representations, and security
applications. As far as defending against adversarial attacks, GANs are
capable of generating adversarial samples. These can be used for network
attacks that may be missed by the ML detector. Or, they can be added to the
training set to help the ML detector adjust its classification boundary in
order to acquire better detection capabilities.

While these use cases also apply in wireless communication systems, their
effective application hinges upon careful account of wireless communication
characteristics:

  1. 1.

Training data for wireless communications is typically limited. There are
sensing limitations regarding sampling rate (due to hardware effects) and time
spent for sensing (balancing the sensing-communication tradeoff). Therefore,
GANs can be used to augment the training data for wireless applications, such
as spectrum sensing and wireless signal detection and classification (e.g.,
jammer identification) when the Radio Frequency (RF) data typically involves
uncertainties due to noise, channel, traffic, and interference effects [7].

  2. 2.

Wireless data is heavily environment dependent. For example, the training data
collected in a laboratory environment (e.g., indoor) does not necessarily
match channel characteristics in test time (e.g., outdoor). Therefore, the
adaptation of test or training data to channel conditions raises the need for
domain adaptation with GANs [8].

  3. 3.

Signal spoofing is a key element of wireless security that poses threats for
infiltration through signal/user authentication systems, and can be
alternatively used to set up decoys/honeypots from the defense point of view
[9, 10].

  4. 4.

Wireless communication systems are subject to attacks due to the open nature
of wireless spectrum and anomalies due to hardware impairments and
intended/unintended interference. GANs can be used to protect wireless
communications against attacks and detect anomalies.

The unique characteristics of wireless communication systems that need to be
considered for the GAN applications are summarized as follows.

  1. 1.

The input to the GAN is (real) RF data that is highly complex and dynamic,
subject to noise, channel, traffic, and interference effects. Statistical
modeling may not be effective to represent the spectrum data. Therefore, the
complex structures of deep neural networks in the GAN formulation can be
effectively used to represent the spectrum data [11, 12, 13].

  2. 2.

The format of the RF data is not universal (like pixels in computer vision)
and may vary from time series of in-phase/quadrature components (I/Qs) or
Received Signal Strength Indicators (RSSIs) to frequency domain
representations.

  3. 3.

The generator and the discriminator of the GAN may need to be distributed at
transmitter and receiver, respectively, as data transmission and the
corresponding reception need to be separated through a wireless channel in
online applications. In this context, the message exchange between the
generator and the discriminator may be executed over noisy wireless channels.

  4. 4.

While training the GAN, the RF data itself as well as communication channels
between the generator and the discriminator may change due to the limited
coherence time of channel conditions [9, 10].

Contributions of the paper are as follows. Sec. 2 introduces the basics of
GANs and a number of alternative GAN structures, together with their
underlying mathematics. GAN structures were originally developed for computer
vision and image processing. This paper is on adopting them for applications
in NextG wireless communications. To that end, Sec. 3 first discusses
performance measures used in computer vision and image processing. It
introduces performance measures that can be used in wireless applications
since the former measures cannot be used in this field. It introduces public
datasets that can be employed in wireless applications. It also discusses
performance measures for general classifiers, including wireless classifiers.
It discusses the use of GANs to extend a given dataset, called data
augmentation. Furthermore, Sec. 3 introduces a number of GAN techniques that
have been used in spectrum sharing, anomaly detection, and security for NextG
wireless. A summary of these is available in Table 7. Sec. 4 presents an
anomaly detection problem for the modulation classification task and presents
our results where we solve this problem using two unsupervised deep learning
methods, a GAN-based and an autoencoder-based algorithm. We also provide
interpretations of the results, tradeoffs between the two approaches, and
implementation details. Sec. 5 provides a discussion of a number of potential
future research directions, including their challenges. Finally, Sec. 6
provides our conclusions.

##  2 Preliminaries on Generative Adversarial Networks

Figure 1: Generative Adversarial Network (GAN) with image generation
application [14].

GANs were introduced in 2014 [14, 6], and belong to the class of deep-
learning-based generative models. Generative modeling is an unsupervised ML
task that involves automatically discovering the regularities or patterns in
input data in such a way that the model can be used to generate new samples
that cannot be discriminated from the original dataset. Facebook’s Director of
Artificial Intelligence Research Yann Le Cunn is famously known to have said
in June 2016 that “GANs and the variations that are now being proposed is the
most interesting idea in the last 10 years in ML, in my opinion.” Given the
many subsequent applications of GANs in different fields, some of which we
discuss below, it is difficult to argue with this opinion.

GANs train a generative model by decomposing the problem into two sub-models,
as depicted in Fig. 1. The first is a generator network trained to generate
new examples, while the second is a discriminator network that tries to
classify examples as either real (from the domain) or fake (generated). The
two models are jointly trained that continues until the generator network
learns to synthesize plausible samples that cannot be distinguished from real
data.

GANs and their variations have been used in a variety of applications. A few
examples include creation of synthetic human faces [15, 16, 17] and
transforming images from one domain (e.g., real scenery) to another domain
(paintings by famous painters) [18]. Other examples of image-to-image
translation in [18] include conversion of horse pictures to pictures of zebras
and vice versa, pictures of summer scenery to pictures of the same scenery in
winter, etc. Further applications include face aging [19], creation of super-
resolution images from those of low resolution [20], music generation [21],
audio synthesis [22], and video synthesis [23]. More relevant to this paper,
GANs have been applied to problems in spectrum sensing and security in
wireless networks, e.g., [8, 24, 25, 9, 26, 27, 11], and these will be
discussed in more detail below. A list of the many different applications of
GANs is available in [28].

To describe how GANs are trained, let x belong to the manifold of the real
input data with distribution $p_{\rm data}({\bf x})$, and let z belong to the
latent or noise prior space with distribution $p_{\bf Z}({\bf z})$. Further,
let $G$ be a differentiable function representing the generator with input z,
and let $D$ be a differentiable function representing the discriminator with
input x or $G({\bf z})$, where the output of $D$ is mapped to the interval
$[0,1]$. Now consider the function

$\begin{split}V(D,G)=&\mathbb{E}_{{\bf x}\sim p_{\rm data}({\bf x})}[\log
D({\bf x})]\\\ &+\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf z})}[\log(1-D(G({\bf
z})))]\;.\end{split}$ (1)

The first term increases when the real samples are more correctly classified,
while the second term increases as the discriminator more successfully
identifies the generated samples as fake. Thus, the discriminator $D$ acts to
maximize (1). On the other hand, $G$ attempts to minimize (1), that is
equivalent to minimizing just the second term, which increases the likelihood
that the discriminator is fooled. This leads to a minimax optimization in
which $D$ and $G$ work against each other to achieve the equivalent of a Nash
equilibrium point [6, 29]:

$\min_{G}\max_{D}V(D,G)\;.$ (2)

The two optimizations in (2) are carried out by employing neural networks and
backpropagation via gradient ascent and gradient descent, which is possible
since $D$ and $G$ are differentiable.

Given a batch $\\{{\bf x}_{i},{\bf z}_{i}\\}_{i=1}^{n}$ of training data and
samples from the latent space, we can convert the optimization expressed via
(1) and (2) into the optimization of two cost functions, for $D$ and $G$,
respectively, as

$\begin{split}J_{D}&=-\frac{1}{2}\big{(}\sum_{i=1}^{n}\log D({\bf
x}_{i})+\sum_{i=1}^{n}\log(1-D(G({\bf z}_{i}))\big{)},\\\
J_{G}&=-\frac{1}{n}\sum_{i=1}^{n}\log D(G({\bf z}_{i})).\end{split}$ (3)

Details on implementing (3) with a neural network and gradient ascent and
descent to train the GAN can be found in [6, Algorithm 1]. Note that by
substituting the criterion in (1)–(2) with that in (3), an implicit assumption
of ergodicity, or ensemble averages being equal to time averages, is made.
This assumption, common in signal processing and communications, will be made
again in the sequel.

Additional information that is correlated with the input data, such as class
labels, can be used to improve GAN performance, either in the form of more
stable or faster training, or generated images that have better quality. Such
conditional GANs (CGANs) are trained in such a way that both the generator and
the discriminator models are conditioned on the class label, so that when the
trained generator is used as a standalone model to generate samples in the
domain, samples of a given type can be generated [30]. For example, in the
synthesis of faces one could focus on generating a female face, or one could
convert a summer scene into a winter scene, etc. Popular face aging
applications are also based on this principle. To describe this approach, let
$y$ represent extra information on which the generator and discriminator are
conditioned. One can perform the conditioning by feeding $y$ into both the
discriminator and generator as additional input layer. As mentioned above, the
information $y$ could be in the form of a class label, leading to a so-called
class-conditional GAN, or some other kind of input such as a single image, in
the case the GAN is performing an image-to-image translation task. Letting
${\bf y}$ represent a potentially multidimensional label from a distribution
$p_{\bf Y}({\bf y})$, the optimization in (1) and (2) becomes

$\begin{split}\min_{G}\max_{D}\quad&\mathbb{E}_{{\bf x},{\bf y}\sim p_{\rm
data}({\bf x},{\bf y})}[\log D({\bf x},{\bf y})]\\\ &+\mathbb{E}_{{\bf y}\sim
p_{\bf Y}({\bf y}),{\bf z}\sim p_{\bf Z}({\bf z})}[\log(1-D(G({\bf z,{\bf
y}),{\bf y}}))]\end{split}$ (4)

for CGANs, with (3) updated in a straightforward fashion based on (4).

A number of other GAN formulations exist beyond those mentioned above. For
example, in the Least-Squares GAN (LSGAN) [31], the objective functions become

$\begin{split}\min_{D}&\\{\mathbb{E}_{{\bf x}\sim p_{\rm data}({\bf
x})}[(D({\bf x})-a)^{2}]\\\ &+\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf
z})}[(D(G({\bf z}))-b)^{2}]\\},\\\ \min_{G}&\mathbb{E}_{{\bf z}\sim p_{\bf
Z}({\bf z})}[(D(G({\bf z}))-c)^{2}],\end{split}$ (5)

where $a$ and $b$ represent labels for real data and fake data, respectively,
and $c$ be the value that $G$ wants $D$ to believe for fake data. Reference
[27] employs an LSGAN with $a=-b=1$ and $c=0$. Another variation is known as
Wasserstein GAN (WGAN) [32], which employs the loss function

$\min_{G}\max_{D\in{\cal D}}\mathbb{E}_{{\bf x}\sim p_{\rm data}({\bf
x})}[D({\bf x})]-\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf z})}[D(G({\bf z}))],$
(6)

where ${\cal D}$ is a set referred to as the set of 1-Lipshitz functions.
Reference [33] removes the condition $D\in{\cal D}$ but adds an additional
term for stability, repeatability, and predictable behavior during the
training process. Reference [11] employs a WGAN with the additional term
proposed in [33]. An alternative way to enforce the Lipshitz constraint is to
add a penalty on the gradient norm for random samples ${\hat{\textbf{x}}}\sim
p_{\hat{X}}$, and the updated loss function can be expressed as

$\begin{split}\min_{G}\max_{D\in{\cal D}}\quad&\mathbb{E}_{{\bf x}\sim p_{\rm
data}({\bf x})}[D({\bf x})]-\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf
z})}[D(G({\bf z}))]\\\ &+\lambda\mathbb{E}_{{\hat{\textbf{x}}}\sim
p_{\hat{X}}(\hat{\bf
x})}\left[\left(\|\nabla_{\hat{\textbf{x}}}D(\hat{\textbf{x}})\|_{2}-1\right)^{2}\right].\end{split}$
(7)

This approach is known as WGAN with gradient penalty (WGAN-GP) [33] and it
provides stability and predictable behavior during the GAN training process.

###  2.1 Anomaly Detection by Using GANs

One area of particular importance where GANs have been applied is in anomaly
detection, which is the task of discovering anomalies, or patterns in the data
that do not conform to “normal behavior.” While the use of GANs is based on
modeling normal behavior using the adversarial training process, an anomaly
score based on this model can be calculated and employed for anomaly
detection. Several GAN-based approaches for anomaly detection have been
published, all of which employ the technique of Adversarial Feature Learning
idea [34]. This idea makes use of a novel architecture referred to as
bidirectional GANs, or BiGANs.

Figure 2: The structure of BiGAN [34].

BiGANs add an inverse mapping from the data space to the latent distribution,
from which regular GANs generate artificial samples. The overall model is
depicted in Fig. 2. A BiGAN includes an encoder $E$ which maps data x to
latent representations z, in addition to the generator $G$ employed by the
standard GAN architecture [34]. The BiGAN discriminator $D$ discriminates not
only in data space (x versus $G({\bf z})$), but jointly in both the data and
latent space (tuples $({\bf x};E({\bf x}))$ versus $(G({\bf z});{\bf z}))$,
where the latent component is either an encoder output $E({\bf x})$ or a
generator input ${\bf z}$.

The two modules $E$ and $G$ do not directly “communicate” with one another:
the encoder never “sees” generator outputs ($E(G({\bf z}))$ is not computed),
and vice versa. However, it is shown in [34] that the encoder and generator
must learn to invert one another in order to fool the BiGAN discriminator. In
other words, $E$ learns the inverse of the generator $E=G^{-1}$. The encoder
$E$ is a nonlinear parametric function in the same way as $G$ and $D$, and can
be trained using a standard learning algorithm such as gradient descent. A
latent representation z may be thought of as a “label” for x, but one which
came for “free,” without the need for supervision. As discussed in [34],
BiGANs make no assumptions about the structure or type of data to which they
are applied.

In this paper, we will focus on three GAN architectures that conceptually
employ the inverse generator concept of BiGANs. These are the AnoGAN [35],
Efficient GAN-Based Anomaly Detection (EGBAD) [36], and a GAN + autoencoder
approach [37]. AnoGAN is a deep convolutional GAN that learns a manifold of
normal variability, together with a scoring scheme that labels anomalies based
on the mapping from the image to the latent space. For results on medical
imaging data, see [35]. Given a query image ${\bf x}$, the algorithm iterates
through points in the latent space to find a representation $G({\bf z})$ that
is close to ${\bf x}$. The algorithm begins by choosing a random point ${\bf
z}_{1}$ in the latent space, and generates a data sample $G({\bf z}_{1})$. The
algorithm then proceeds through a number of points ${\bf z}_{1},{\bf
z}_{2},\ldots,{\bf z}_{\Gamma}$ based on the following loss function:

${\cal L}({\bf z}_{\gamma})=(1-\lambda){\cal L}_{R}({\bf
z}_{\gamma})+\lambda{\cal L}_{D}({\bf z}_{\gamma})\;,$ (8)

where

${\cal L}_{R}({\bf z}_{\gamma})=\|{\bf x}-G({\bf z}_{\gamma})\|_{1}$ (9)

is the residual loss, and

${\cal L}_{D}({\bf z}_{\gamma})=\|f({\bf x})-f(G({\bf z}_{\gamma}))\|_{1}$
(10)

is the discriminator loss, where $f$ is the output of one of the layers of the
multilayer perceptron and $0<\lambda<1$ is an interpolation coefficient. The
residual loss enforces similarity between the query data ${\bf x}$ and the
generated data $G({\bf z}_{\lambda})$, while the discrimination loss
constrains the generated data to lie near the learned manifold ${\cal X}$
[38]. For each $\gamma=2,3,\ldots,\Gamma$, ${\bf z}_{\gamma}$ is calculated by
iteratively minimizing (8) via backpropagation steps. The iteration is on
${\bf z}_{\gamma}$, the coefficients of $G$ and $D$ are not changed. The
approach of using a linear combination of two loss functions (9) and (10) that
employ the $L_{1}$ norm for training a deep neural network is different than
the approaches discussed earlier for training GANs and CGANs. This approach
originated with [39] and was adapted in [35].

Implementing the AnoGAN optimization over $\Gamma$ steps results in a
relatively high computational load. The EGBAD approach [36] was developed as a
more efficient alternative and is based on the methods in [34, 40], which
enable learning an encoder $E$ by mapping input samples to their latent
representation during adversarial training. GANomaly [37] is designed to be an
improvement over [34, 35, 36] in terms of both performance and speed. The
algorithm trains a generator network to learn the manifold of the input
samples while at the same time training an autoencoder to encode the data in
their latent representation. This approach uses a discriminator, a decoder,
and two encoders, but the encoders have the same architecture. We describe
this approach in more detail below.

Figure 3: Simplified single-dimensional architecture representation of
GANomaly. Multiple blocks in series represent two-dimensional convolutional
encoders and single blocks are for providing two-dimensional input-output
[37]. Figure 4: Comparison of GANs for anomaly detection for computer vision
and image processing applications, A: AnoGAN [35], B: EGBAD [36], C: GANomaly
[37]. Two-dimensional convolutional encoders and input-output devices are
depicted as single-dimensional blocks for simplicity without any loss in
functionality.

As shown in Fig. 3–4, the generator network has three elements in series: an
encoder $G_{E}$, a decoder $G_{D}$, and another encoder $E$. The combination
of $G_{E}$ and $G_{D}$ forms an autoencoder that functions as the generator
$G$. The encoder $E$ has the same structure as $G_{E}$. $G_{E}$ takes the data
sample ${\bf x}$ and generates an encoded version ${\bf z}$ in the latent
space. Then $G_{D}$ employs ${\bf z}$ to create $\hat{\bf x}$, which is a
reconstructed form of ${\bf x}$. Finally, $\hat{\bf x}$ is used to generate
another point in the latent space, $\hat{\bf z}$. Three loss functions are
defined, which are combined to generate the overall generator loss. The first
is the adversarial loss ${\cal L}_{\rm adv}$,

$\begin{split}{\cal L}_{\rm adv}&=\mathbb{E}_{{\bf x}\sim p_{\bf X}({\bf
x})}\|f({\bf x})-\mathbb{E}_{{\bf x}\sim p_{\bf X}({\bf x})}f(G({\bf
x}))\|_{2}\\\ &=\|f({\bf x})-f(\hat{\bf x})\|_{2}\;,\end{split}$ (11)

where $f$ is the output of an intermediate layer in the multi-layer
perceptron. The second loss function is the contextual loss and is given by

${\cal L}_{\rm con}=\mathbb{E}_{{\bf x}\sim p_{\bf X}}\|{\bf x}-G({\bf
x})\|_{1}=\|{\bf x}-\hat{\bf x}\|_{1}\;,$ (12)

and the third is the encoder loss

${\cal L}_{\rm enc}=\mathbb{E}_{{\bf x}\sim p_{\bf X}({\bf x})}\|G_{E}({\bf
x})-E(G({\bf x}))\|_{2}=\|{\bf z}-\hat{\bf z}\|_{2}.$ (13)

Finally, the generator loss is given as

${\cal L}=w_{\rm adv}{\cal L}_{\rm adv}+w_{\rm con}{\cal L}_{\rm con}+w_{\rm
enc}{\cal L}_{\rm enc}\;,$ (14)

where $w_{\rm adv}$, $w_{\rm con}$, and $w_{\rm enc}$ are coefficients between
0 and 1 that sum to 1. During the test stage, the model uses ${\cal L}_{\rm
enc}$ given in (13) for scoring the abnormality $A(\hat{\bf x})$ of a given
image:

$A(\hat{\bf x})=\|G_{E}(\hat{\bf x})-E(G(\hat{\bf x}))\|_{1}.$ (15)

In order to make the anomaly score easier to interpret, [37] proposes to
compute it for every sample $\hat{\bf x}$ in the test set $\hat{D}$ to obtain
the set $S=\\{s_{i}:A(\hat{\bf x},\hat{\bf x}\in\hat{D}\\}$ of individual
anomaly scores, and then apply a scaling to force the scores to lie within the
range $[0,1]$:

$s_{i}^{\prime}=\frac{s_{i}-\min(S)}{\max(S)-\min(S)}.$ (16)

Abbreviation | Application | Comment | Reference
---|---|---|---
GAN | General | Employs (1)-(3). Structure in Fig. 1. | [6], [14]
CGAN |  | Conditional GAN. Employs (4). | [30]
LSGAN |  | Least Squares GAN. Employs (5). | [31]
WGAN |  | Wasserstein GAN. Employs (6). | [32]
WGAN-GP |  | Gradient Penalty WGAN. Employs (7). | [33]
BiGAN | Anomaly Detection | Bidirectional GAN. Structure in Fig. 2. | [34]
AnoGAN |  | Anomaly GAN. Employs (8)-(10). | [35]
EGBAD |  | Efficient GAN-Based Anomaly Detection. | [36]
GANomaly |  | GAN+Autoencoder. Employs (11)-(16). Structure in Fig. 3. | [37]
Table 1: Different versions of GANs used in computer vision and image
processing applications. Note that Fig. 4 compares the structures of AnoGAN,
EGBAD, and GANomaly. Which of GAN, CGAN, LSGAN, WGAN, or WGAN-GP is preferable
depends on the application. For the tradeoffs among the versions used in
anomaly detection, see the text.

Fig. 4 shows a comparison of the architectures of the three GAN-based anomaly
detection algorithms discussed above. Experiments show that EGBAD is faster
than AnoGAN, and that GANomaly achieves better performance and speed than
EGBAD [37, 41]. Table 1 provides a summary of GAN versions used for computer
vision and image processing applications.

##  3 Application of GANs to 5G and Beyond

In what follows, we will first discuss, in Sec. 3.1, measures of performance
and specific issues that have to do with applying GANs first to computer
vision and image processing and then to wireless applications. We will discuss
public datasets available for enabling the training and benchmarking the
performance of GANs in the wireless domain. In the same section, we will
discuss measures for general classifier performance. We will specifically use
these measures in wireless classifier applications. In Sec. 3.2, we will
discuss the technique of data augmentation by using GANs, which can be
employed in the following three sections. Then, in Sec. 3.3–Sec. 3.5, we will
discuss fast, accurate, and robust methods for analyzing large quantities of
spectrum data in order to identify opportunities for i) spectrum sharing, ii)
detecting anomalies, and iii) mitigating security attacks, respectively.

###  3.1 Performance Measures for GANs and General Classifiers

We will now discuss performance measures for GANs, first for computer vision
and image processing, and then for wireless applications, and finally, general
classifiers. There are basically two measures of the quality of images
generated by GANs for computer vision and image processing applications. These
are Inception Score (IS) [38] and Fréchet Inception Distance (FID) [42, 43].
IS offers a way to objectively and quantitatively evaluate the quality of
generated images by a GAN. It is generally considered that this score is well-
correlated with scores from human observers. Similarly, FID is used to
evaluate the quality of images generated by GANs. FID compares the mean and
standard deviation of one of the deeper layers in a Convolutional Neural
Network (CNN) named Inception-v3. These layers are closer to output nodes and
are believed to mimic human perception of similarity in images. Clearly, these
two measures are useless for wireless applications. They need to be replaced
with measures meaningful in the context of wireless communications.

For wireless applications, the goal is to calculate the similarity of two
probability densities. A commonly used measure towards that end is the Jensen-
Shannon distance, which is the square root of the Jensen-Shannon divergence
[44]. Jensen-Shannon divergence, on the other hand, is a symmetric form of the
well-known Kullback-Leibler divergence [45].

In passing, we would like to state that to facilitate the training of GANs in
the wireless domain and benchmark the performance of GANs, there are
increasingly more public datasets available. Examples of such sets are RADIOML
2016.04C, RADIOML 2016.10A, RADIOML 2018.01A by DeepSig [46], RFMLS 2016a by
DARPA [47], CBRS by NIST [48], and synthetic data generated by GNU Radio [49].

To measure the performance of any classifier, Probability of Detection
($P_{D}$) and Probability of False Alarm ($P_{FA}$) are calculated. Then, the
Receiver Operating Characteristics (ROC), which plot $P_{D}$ against $P_{FA}$
are drawn [50]. A commonly used measure is Area Under Curve of the ROC
(AUROC). Accuracy (ACC) is defined as the ratio of the correct classifications
to the total classifications. It can be calculated as Accuracy = (True
Positives + True Negatives)/ (True Positives + False Positives + True
Negatives + False Negatives). Furthermore, the variables Precision, Recall,
and F1 Score determine the success of a binary classification problem.
Precision equals the ratio of the true positives to total (true and false)
classified positives. Recall equals the number of true positives to the sum of
true positives and false negatives. Precision is a good measure to employ when
the cost of the false positive is high whereas Recall is a good measure when
the cost of the false negative is high. F1 Score, the harmonic mean [51] of
Precision and Recall [52], is employed when it is desired to have a balance
between Precision and Recall. All three measures take values between 0 and 1.
For a given classification system, it is desirable that each be as close to 1
as possible. Please see Sec. 4 for combinations of these quantities and the
definitions of Density and Coverage in [53].

An important lesson learned in this subsection is that while it is desirable
to employ GAN structures from computer vision and image processing for NextG
wireless applications, the performance measures in the two fields are
different.

###  3.2 Data Augmentation via GANs for NextG

By recognizing that supervised ML requires significant number of training data
samples and it is expensive and likely even infeasible to collect a
sufficiently comprehensive and representative set of training data, [8]
provides training data augmentation by adding synthetic data to an existing
training set. This is achieved by a workflow of three steps. In the first
step, a CGAN is trained using real training samples. In this step, the
generator learns to synthesize new data samples. In the second step, the
synthetic data samples are used along with the real samples to train a
classifier. In the third step, as new data comes in, the classifier is used
for classification purposes. The authors of [8] show that this approach
significantly improves the adaptation time and accuracy of the resulting
spectrum sensing.

In an attempt to come up with a good modulation recognition technique, [54]
employs Auxiliary Classifier GANs (AC-GANs) [55] after a density
transformation of the signal called Contour Stellar Image to enhance the
performance of CNNs. Although employing a training sequence whose length is
10% of another algorithm, [54] achieves up to 6% gain in the recognition
performance of the test sequence.

Reference [13] investigates training data augmentation for deep learning RF
systems by asking basic questions about the augmentation process. The paper
concentrates on the Automatic Modulation Classification (AMC) problem. These
questions are: i) how useful a synthetically trained system will be when
deployed without considering the environment within the synthesis, ii) how can
augmentation be leveraged within the RF ML domain, and iii) what impact
knowledge of degradations to the signal caused by the transmission channel
contributes to the performance of a system. The results show that for data
generation to a higher fidelity, the propagation path from the Digital-to-
Analog Converter (DAC) to the Analog-to-Digital Converter (ADC) must be
investigated and modeled. Second, although augmentation provides savings in
terms of time and money, the authors suggest a cost analysis to achieve a
balance between the two. Finally, a methodology is established for the
quantity of data needed.

A lesson that should be derived here is that GANs can generate synthetic
training data and thus augment the training set in ML. We will discuss this
topic in more detail in Sec. 5.

###  3.3 Spectrum Sharing

As NextG networks rely on the co-existence of heterogeneous networks such as
cellular and non-terrestrial networks, and radar systems, spectrum sharing is
expected to play a major role in NextG communications and radar systems, while
relying on ML techniques to identify and make use of spectrum opportunities.
One particular example is Citizens Broadband Radio Service (CBRS) band at 3.5
GHz where the cellular wireless system needs to share the spectrum with the
tactical radar while avoiding mutual interference [56]. As such, the use of ML
for spectrum sensing problems is currently a growing area of interest, as
evidenced in the survey [57] which summarizes results from [58, 59, 60, 61,
62, 63, 64, 65, 66, 67]. The work reported in [58, 59, 60, 61] focuses on ML
issues including optimization of supervised classifiers, reduction of the
feature space dimension, reduction of interference, and minimization of the
number of sensors, respectively. Attacker detection and minimization of
sensing time, delay, and operations in collaborative spectrum sensing are
discussed in [62, 63]. Techniques that target Spectrum Sensing Data
Falsification (SSDF) are developed in [64, 65, 66, 67]. Furthermore, [68, 69,
70, 71] discuss the use of neural networks for spectrum sensing under low
Signal-to-Noise Ratio (SNR) conditions. References [72, 73] discuss employing
neural networks for spectrum sensing in the face of parameter uncertainties in
the transmitted signals.

Spectrum sharing techniques can be broadly characterized as belonging to open
sharing or hierarchical access models [74, 75, 76]. In the open sharing model,
each network accesses the same spectrum without any interference constraint
from one network to its peers. The unlicensed band is an example of this
model. The hierarchical or cognitive radio model consists of a primary network
and a secondary network that accesses the primary spectrum without interfering
with the Primary Users (PUs). We will focus on the concept of cognitive radio
networks in order to achieve efficient spectrum sharing via ML, using the
classification from [77] to organize potential approaches to spectrum sharing
in cognitive radio networks. In this classification, spectrum sharing
techniques are categorized as either underlay, overlay, or interweave.

Underlay | Overlay | Interweave
---|---|---
SU knows the channel strengths | SU knows the channel gains, | When PU is not using the spectrum,
of PU | codebooks, and messages of PU | SU knows the spectral holes in
|  | space, time, or frequency
As long as the interference is below | SU can simultaneously transmit | SU can simultaneously transmit
an acceptable limit, SU can | with PU; interference to PU | with PU only in the case of false
simultaneously transmit with PU | can be offset by using part of | spectral hole detection
| SU’s power to relay PU’s message |
SU’s transmit power is limited by | SU can transmit at any power; | SU’s power is limited by the
the interference constraint | the interference to PU can be | range of its spectral holes
| offset by relaying PU’s message |
Table 2: Characteristics of underlay, overlay, and interweave techniques for
cognitive radio networks [76, 77].

Table 2 summarizes the basic characteristics of underlay, overlay, and
interweave techniques [77]. In the underlay technique, a Secondary User (SU)
needs to be aware of the channels for all active PUs in order to know if the
interference it generates will be below an acceptable limit. This
consideration limits its transmit power. For the overlay technique, in
addition to the PU channel characteristics, the SU also knows the codebooks
and messages of the active PUs. The SU can transmit at

!b

Figure 5: Holes in frequency and time domains [78]. Figure 6: Spectrum usage
in a shared band and spectrum holes in the frequency (vertical) and time
(horizontal) domains enabling dynamic spectrum access. For the figure,
spectrum sensing is done by HackRF Software Defined Radio (SDR), and
QSpectrumAnalyzer library is used for the real-time data visualization.

any power, but to offset the interference it causes to the PUs, it relays
their transmitted messages. In the interweave technique, the goal is to
opportunistically communicate in the spectrum holes, or more generally the
space-time-frequency voids that are not in use by either licensed and
unlicensed users. As depicted in Fig. 6, these voids change with frequency and
time. The interweave technique requires periodic monitoring of the spectrum
for detection of user activity, so that the SU can transmit opportunistically
over the space-time-frequency voids with minimal interference. All of the
above approaches can benefit from SUs employing directional antennas or
beamforming for more flexible control of the interference. Fig. 6 depicts
spectrum sensing by a Software Defined Radio (SDR) in an actual setting.

For this research topic, implementing the spectrum sensing task using a GAN-
based technique as in [8] is an interesting and potentially useful first step.
It provides domain adaptation by creating synthetic data that enables the
classifier to quickly adapt to changes in the spectrum environment. The
approach in [8] can be extended to exploit voids in all possible dimensions
including space, time, and frequency, which is of particular importance to
interweave cognitive radios. To extend the research in this direction, an
approach based on CGANs that emphasizes specific subsets of the space, time,
and frequency spectrum using specific domain knowledge can be employed. For
example, an approach based on CGANs, conditioned on specific subsets of the
space, time, and frequency using specific domain knowledge can be employed.
Such a CGAN will be able to generate synthetic data that is specific to
certain “labels” that correspond for example to known locations (e.g., hot
spots), time periods (e.g., rush hour), or occupancy patterns of certain
frequency bands. A further step in this direction is the investigation of the
performance of the algorithms in the presence of low SNR as in [68, 69, 70,
71] and parameter uncertainties as in [72, 73].

The approach in [8] consists of the following three steps: i) training a GAN
using real training samples so that the generator learns to synthesize new
samples, ii) training of a classifier with augmented data so that the original
and limited training set is expanded with synthetic data, and, iii) regular
operation by classifying data using the trained model. It is possible to
extend this approach by training a CGAN for more typical scenarios, such as
known locations, time periods, and occupancy patterns of certain bands, as
discussed in the previous paragraph. In this context, unlike [8], it is
possible to make a comparison of this ML-based approach with conventional
narrowband spectrum sensing techniques based on energy detection,
cyclostationary feature detection, matched filter detection, and wideband
spectrum sensing techniques such as compressed sensing [79, 57] in terms of
performance and complexity, specifically in the three areas discussed in Sec.
1.

In addition to [13] discussed in Sec. 3.2, another work on the AMC problem is
provided in [80]. This work uses a modified version of CGAN and AC-GAN, which
is operated in a semi-supervised (not unsupervised) mode. The modifications
are needed to solve the following problems: i) the complexity of the
modulation signals cause non-convergence due to the mapping from the high-
dimensional parameter space to the low-dimensional classification space, and
ii) lack of diversity of the generated samples cause mode collapse. Mode
collapse is defined as the difficulty in convergence, especially during the
training process, due to conditional constraints. The modifications consist of
an encoder block $E$, a transform block $T$, and the splitting of the
classification and discrimination functions of the conventional discriminator
$D$ by adding an explicit classifier $C$ [80, Fig. 1]. The encoder $E$ and the
transform $T$ are inspired by Conditional Variational Autoencoder (CVAE) [81]
and Spatial Transformer Network (STN) [82], respectively. The definition of
the loss functions involving all the blocks and their optimization expressions
are given in [80, Eq. (10)-(20)]. To evaluate the performance of the system,
the synthetic dataset in [49] is used. This dataset contains signals of eleven
modulation modes at SNRs ranging from -20 dB to 20 dB, with channel
distortion, frequency offset, phase offset, and Gaussian noise added.
Comparisons with a number of well-known deep learning methods show gains in
classification accuracy of up to 12%.

An important implementation technique for NextG networks is Cooperative
Spectrum Sensing (CSS), where a number of SUs cooperate to improve sensing
performance. CSS can be implemented using either a centralized or a
distributed approach. In centralized sensing, the SUs send their sensing
information to a Fusion Center (FC) that makes the sensing decision and
broadcasts this information back to all SUs. In distributed sensing, the SUs
share sensing information among each other and make independent sensing
decisions locally. In both approaches, the SUs can either transmit their
individual sensing decisions or soft information in the form of partial
statistics. The information combining schemes used by the FC or SUs can be
categorized as either hard or soft combining schemes. The most common hard
combining algorithms are AND combining, OR combining, $M$-out-of-$N$
combining, and quantized hard combining, while soft combining algorithms
include selection combining, maximal ratio combining, equal gain combining,
and square law combining [83]. The soft combining approach provides the best
detection performance, but at the cost of additional control channel overhead.

It is desirable to extend the technique described above to include CSS. In one
implementation, GANs can be placed at the SUs and classifications can be
combined at the FC. An alternative is to have the SUs transmit partial
statistics to be used by a single GAN at the FC. In this regard, it is
worthwhile to investigate schemes that will employ combinations of centralized
versus distributed CSS with hard or soft decisions. The number of combinations
is high but it should be possible to reach quick conclusions. The main
interest in this activity is to determine the optimal placement for GANs in
interweave networks, and how much performance improvement they can provide.

There is an important lesson that can be drawn from this subsection. Due to
the tremendous number of users and applications in NextG networks, spectrum
sharing will need to be carried out in a dynamic environment employing
principles of cognitive networking. The goal is to determine the voids based
on time, frequency, and space and exploit them to accomodate more users. Two
specific techniques for spectrum sharing based on GANs are discussed in [8,
80] and summarized in this subsection.

###  3.4 Detecting Anomalies

In a GAN, the generator captures the distribution of the training data, and
the discriminator can detect false from real, making a GAN an attractive ML
technique for anomaly detection. This observation has led to a number of
anomaly detection techniques employing GANs [84, 85, 86, 87, 88, 89, 90, 91,
92, 93]. These applications are typically for various forms of image
processing. There are some recent applications of using adversarial networks
for anomaly detection in cyber-physical systems [94, 95], fraud detection in
banking [96, 97, 98, 99], driver assistance systems [100], air surveillance
[101], prognostics and health management in the aeronautics industry [102],
and network traffic anomaly detection [103].

We will briefly discuss [103] since it is related to network anomaly
detection. This work proposes BiGAN in conjunction with Principal Component
Analysis (PCA) for network anomaly detection using the KDDCUP-99 dataset
[104]. This database includes a wide variety of intrusions simulated in a
military network environment used for a competition during a conference to
build a network intrusion detector, a predictive model capable of
distinguishing between “bad” connections, called intrusions or attacks, and
“good” normal connections [104].

Model | Precision | Recall | F1 Score
---|---|---|---
OC-SVM [105] | 0.7457 | 0.8523 | 0.7954
DSEBM-r [105] | 0.8521 | 0.6472 | 0.7328
DSEBM-e [105] | 0.8619 | 0.6446 | 0.7399
DAGMM-NVI [106] | 0.9290 | 0.9447 | 0.9368
BiGAN [36] | 0.9363 | 0.9512 | 0.9437
PCA+BiGAN [103] | 0.9442 | 0.9592 | 0.9516
Table 3: Performance of the five anomaly detection algorithms on the KDDCUP-99
dataset [103]. OC-SVM: One-Class Support Vector Machine [105], DSEBM-r: Deep
Structured Energy-Based Model - using reconstruction error [105], DSEBM-e:
Deep Structured Energy-Based Model - using energy [105], DAGMM-NVI: Deep
Autoencoding Gaussian Mixture Model with Neural Variational Inference [106].

A number of works exist that study anomaly detection in cognitive radio
networks with conventional methods [107, 108, 109, 110, 111, 112, 113] and
with ML [114, 115, 116, 117, 118, 119, 120]. We refer the reader to [120] for
brief descriptions of [115, 116, 117, 118, 119]. These works provide an
introduction to this field, with the important observation that GAN-based
methods tend to provide better results in general. However, it is certain that
existing research in this area is still limited, and this provides an
opportunity for significant contributions.

In [114], an adversarial autoencoder was implemented for wireless spectrum
anomaly detection [121], which uses ideas similar to a GAN. We will go beyond
this approach and leverage the advantages provided by AnoGAN, EGBAD, and
GANomaly. We provide details here on an approach using GANomaly, although
similar anomaly scores can be defined for other architectures. Consider a
collection of received data vectors $X_{N}$, whose elements are for example
the I and Q components of a digitally modulated signal, or vectors of the
sampled power spectral density. We seek a model that learns the source
distribution $p(X_{N})$, so that we can detect when the vector’s distribution
is different from $p(X_{N})$. This is a hypothesis testing problem, where for
each vector ${\bf x}\in X_{T}$ in the test dataset $X_{T}$, the two hypotheses
are

$\displaystyle H_{N}\mkern-6.0mu:$ $\displaystyle\ \textrm{Sample\ data\
comes\ from\ }p(X_{N}),$ (17) $\displaystyle H_{A}\mkern-6.0mu:$
$\displaystyle\ \textrm{Sample\ data\ does\ not\ come\ from\ }p(X_{N}).$

We have three assumptions: First, the probability of anomalous behavior in
dataset $X_{N}$ is very low; second, no explicit anomaly labeling is done on
the test dataset; and third, no feature extraction is performed before feeding
the data to the model. The key insight in employing GAN-based anomaly
detection is to bring the data to the latent space, which captures relevant
features that can be used to reconstruct the actual input data, with a small
anomaly score for normal data. A GAN is trained using (1) and (2), and during
the test and operation stage, (LABEL:eqn:Ladv)–(15) are used. Once the
training process is complete, the model weights are frozen and new data are
input into the model. Anomalies are detected based on the anomaly score or the
reconstruction loss of the model.

The term anomaly covers a very broad range of possibilities in the transmitted
signal. Since the field of ML progresses based primarily on experimentation, a
number of datasets should be created to study the performance of the
algorithms under consideration. These can be in the form of time series
corresponding to I/Q data from a radio receiver after downshifting in
frequency and mixing with the local oscillator. This signal includes the
effects of fading and multipath. To create anomalous test signals, there are a
wide variety of possibilities. Reference [114] considered four types of normal
signals and four types of anomalies. The normal signals were generated as
either i) a single continuous signal with random bandwidth, SNR, and center
frequency, ii) pulsed signals with parameters similar to i), iii) multiple
continuous signals with possible frequency overlap, or iv) signals with random
bandwidths and SNR with deterministic shifts/hops in frequency. The anomalous
signals were chosen as either i) the same as normal signals in i) above, ii)
random pulsed transmissions in the given band, iii) pulsed wideband signals
covering the entire frequency band, or iv) signals from other classes in the
synthetic dataset. Normal and anomalous signals such as these can be
considered, as well as other random signal types with arbitrary power spectral
densities.

Anomaly detection within the context of cognitive radio in the mmWave band is
studied in [120], where the authors generate their own datasets with a number
of anomalies and evaluate three methods including two based on GANs for their
detection. As mmWave radios are vulnerable to malicious users due to the
shared access medium and the complex radio environment, this opens up new
threat possibilities. Moreover, since several security critical applications
in the NextG networks such as the Vehicle-to-Everything (V2X) networks are
based on mmWave communications, this problem is particularly important. In
addressing this problem, [120] makes use of three ML techniques: Variational
Autoencoder (VAE) [122], CGAN [30], and AC-GAN [55]. This work created its own
dataset by using mmWave equipment in a laboratory environment with
implementation using Field Programmable Gate Arrays (FPGAs) and building
blocks such as local oscillators, intermediate frequency modules, mmWave radio
heads, horn antennas, etc. The operation is at 28 GHz by using Cyclic-Prefix
Orthogonal Frequency Division Multiplexing (CP-OFDM) with BPSK, QPSK, 16-QAM,
and 64-QAM. Complex I/Q data is collected at baseband after the downconversion
process. There are eight channels with 100 MHz bandwidth. The normal behavior
is a fixed signal which occupies channel 4 and a sequentially moving signal
among channels 8, 6, 3, and 1. This normal behavior is used in the training
phase. For testing, three modalities are introduced. Modality 1 is a fixed
signal in channel 4, and a moving signal that jumps among channels 5, 7, 2,
and 5. Modality 2 is a fixed signal in channel 4 and a moving signal that
jumps among channels 7, 5, 2, and 1. Modality 3 is a fixed signal in channel 4
and a moving channel that jumps among channels 5, 7, 6, and 5. Performance
results are provided by AUROC and ACC. These results are given in Table 5.

| Modality | AUROC | ACC
---|---|---|---
| 1 | 0.9365 | 0.9356
VAE | 2 | 0.9577 | 0.9551
| 3 | 0.9232 | 0.9382
| 1 | 0.9566 | 0.9657
CGAN | 2 | 0.9737 | 0.9696
| 3 | 0.9545 | 0.9668
| 1 | 0.9741 | 0.9804
AC-GAN | 2 | 0.9751 | 0.9757
| 3 | 0.9742 | 0.9660

Table 4: AUROC and ACC performance of the three ML algorithms.

|  Training [mm:ss] |  Testing [mm:ss]
---|---|---
VAE | 15:09 | 01:00
CGAN | 15:16 | 01:36
AC-GAN | 30:42 | 03:16

Table 5: Computational times of the three ML algorithms.

CGAN provides better performance than VAE and AC-GAN provides better
performance than CGAN, namely, VAE performs an AUROC between 0.9365 and
0.9577, CGAN between 0.9545 and 0.9737, and AC-GAN between 0.9741 and 0.9751.
Reference [120] attributes the better performance by GANs to the fact that
they learn the relation between random noise and generated data such that the
generated data is close to real data, and as a result, they can capture the
dynamics in the real data. Whereas, VAEs return the posterior probability that
an observation belongs to a cluster. They do so by learning the latent vector
corresponding to an input, and as a result, all the dynamics in the real data
that VAEs have access to are limited to the latent vectors already modeled.
Due to a larger degrees of freedom with the former, it is generally considered
that GANs can have better performance. Computational times for the three
algorithms, performed on an NVIDIA GeForce GTX 1080 Ti GPU, are given in Table
5. Clearly, there is a big price paid for the better performance of AC-GAN (15
minutes vs. 30 minutes).

In [123], a deep learning based signal or modulation classification solution
is described, where i) signal types may change over time, ii) some signal
types are not known a priori, and therefore there is no training data
available, iii) signals are potentially spoofed such as smart jammers
replaying other signal types, iv) different signals may be superimposed due to
interference from concurrent transmissions. The authors present a CNN that
classifies the received I/Q samples as idle, in-network signal, jammer signal,
or out-network signal. Traditional approaches for signal classification
require expert design or knowledge of the signal. Modulations are classified
into i) idle, ii) in-network user signal, iii) jamming signals, and iv) out-
network user signals where there are 3, 4, and 3 different modulation
techniques corresponding to ii)–iv). There are in-network users who try to
access the channel opportunistically (SUs), out-network users with priority
channel access (PUs), and jammers that all coexist. The authors use the
dataset in [124]. There are ten modulations with SNRs from -20 dB to 18 dB in
2 dB increments. Radio fingerprinting via radio hardware imperfections such as
I/Q imbalance, time or frequency drift, and power amplifier effects are used
to identify the type of a transmitter. In addition to a CNN structure, Minimum
Covariance Determinant (MCD) , $k$-means clustering, and Independent Component
Analysis (ICA) techniques are employed. Results demonstrate the feasibility of
using deep learning to classify RF signals with high accuracy in unknown and
dynamic spectrum environments. By using the signal classification results a
distributed scheduling protocol is developed where SUs share the spectrum with
each other while avoiding interference imposed to PUs and received from
jammers.

The use of GANs that exploit the spatial domain to identify anomalous signal
sources can be considered, using data received from antennas in different
locations. In many applications, normal network operations are consistent with
users transmitting from specific locations, such as in a stadium setting, a
large hall, a shopping mall, etc. A GAN trained in this setting with an array
of antennas or widely separated receivers can be used to differentiate between
normal network traffic and signals that arrive from anomalous directions, even
if their spectral characteristics are identical to normal users. A similar
approach can be used to detect differences between mobile and stationary
sources, even if no detectable Doppler shift can be measured. Mobile sources
typically have lower power, reduced persistence, a time-varying polarization,
as well as time-varying ranges and azimuth/elevation angles. Further
differentiation is possible between ground-based and airborne sources. A
particularly important direction is to investigate whether incorporating the
spatial dimension together with the time and frequency dimensions can
significantly improve the ability of GANs to detect anomalous network
behavior.

In passing, we would like to state that more research is needed to understand
the performance vs. computational complexity of autoencoders for anomaly
detection [125, 126, 127, 128, 129], especially in terms of their performance
for given computational complexity. Tables 5 and 5 provide an interesting
comparison in this regard.

The most important lesson learned from this subsection is that the use of GANs
result in powerful techniques for anomaly detection in wireless networks. In
Sec. 4, we will expand this observation and provide more evidence to this fact
by adopting a GAN-based anomaly detection algorithm for NextG wireless
applications.

###  3.5 Security Applications of GANs in NextG

Another important application area of GANs is wireless security. In these
applications, ML can be used to create an attack, defend against an attack, or
both. Some specific cases are discussed below.

In [25], a laboratory study is carried out with eight Universal Software Radio
Peripheral (USRP) radios as trusted transmitters. The goal is to use the
imbalance in the detected I/Q components due to unique hardware differences in
each transmitter for fingerprinting, i.e., identifying which transmitter is
which. The authors use the generator $G$ of a conventional GAN to create fake
transmitters, and then the GAN classifier attempts to distinguish between real
and fake transmitters, achieving an accuracy of 99.9%. The authors also
develop approaches to distinguish between the legitimate transmitters, one
based on a CNN that obtains an accuracy of 81.6%, and another based on a Deep
Neural Network (DNN) that scores 96.6%. Although this is a simple experiment,
it shows the power of ML in wireless security.

A wireless spoofing algorithm based on a GAN architecture is proposed in [9],
split between an adversary transmitter $A_{T}$ and an an adversary receiver
$A_{R}$ placed close to the actual receiver $R$. Feedback from $A_{R}$ based
on its location allows $A_{T}$ to know the channel between the actual
transmitter $T$ and $R$ as well as between $A_{T}$ and $R$ with sufficiently
high accuracy. Then, a GAN is implemented between $A_{T}$ and $A_{R}$ in which
the generator $G$ is trained at $A_{T}$ and the discriminator $D$ is
implemented at $A_{R}$. $A_{T}$ in turn adjusts its transmission parameters
such that its signal will appear to $R$ as if they come from $T$. In this
process, $A_{R}$ trains the discriminator $D$ such that the classification
error is minimized, i.e., it attempts to achieve

$\min_{D}\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf z})}[\log(1-D(G({\bf
z})))]-\mathbb{E}_{{\bf x}\sim p_{\rm data}}[\log(D({\bf x}))].$ (18)

At the same time, $A_{T}$ trains the generator $G$ such that the
classification error is maximized, i.e., it attempts to achieve

$\max_{G}\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf z})}[\log(1-D(G({\bf z})))].$
(19)

The process is continued until convergence. Thus, although they are at
different locations, $A_{T}$ and $A_{R}$ train $G$ and $D$ while playing the
following minimax game

$\begin{split}\min_{D}\max_{G}&\mathbb{E}_{{\bf z}\sim p_{\bf Z}({\bf
z})}[\log(1-D(G({\bf z})))]\\\ &-\mathbb{E}_{{\bf x}\sim p_{\rm
data}}[\log(D({\bf x}))].\end{split}$ (20)

Simulation results show that, while the probability of successful spoofing is
only 7.9% for random signals and 36.2% in an amplify-and-forward architecture,
the GAN is able to achieve a success rate of 76.2%.

The problem of thwarting an Intrusion Detection System (IDS) is studied in
[26]. While this work is not specifically about wireless networks, the basic
results are still applicable to wireless systems. While many ML approaches
have been proposed for IDS, the authors of [26] show that such systems are
vulnerable to an attack employing a GAN. On the other hand, the paper also
shows that if the IDS system based on conventional ML is replaced by one based
on GANs, it can be made more robust against adversarial perturbations.

In [27], an interesting problem involving two Unmanned Aerial Vehicles (UAVs)
trying to communicate in the presence of an active jammer that eavesdrops
their transmissions and jams only when the two are at communicating in the
same frequency band is described. A three-way GAN is developed with the
generator $G$ present at the jammer and two classifiers $D_{s}$ and $D_{r}$
present, one at each UAV. The generator $G$ operates without access to the
classifiers. For reasons of stability, [27] does not employ the conventional
$\log$-based formulation for driving the backpropagation algorithm, but
instead, another version based on a least squares formulation called LSGAN
[31]. The performance of the algorithm is compared against two GAN-based
algorithms with three players and one non-GAN-based game theoretic approach.
The algorithm in [27] is shown to outperform the other three in terms of
average connection latency, attack probability, and packet delivery ratio in
the presence of channel switching and jamming. This paper shows the
sophistication of GAN-based approaches in wireless applications.

In addition to the GAN-based wireless security work described above, there are
many other papers in the literature that cover various aspects of wireless
security by employing other ML techniques, in terms of both designing attacks
and ways to mitigate them. A sample listing is [130, 131, 132, 133, 134, 135,
136, 137, 138, 139, 140, 141, 142, 143, 7, 144, 145, 146, 147, 148, 149, 150,
151, 10].

For spectrum sharing applications, not only traditional security threats such
as receiver jamming, but also newly emerged cognitive-radio-specific security
threats such as PU Emulation Attacks (PUEA), SSDF, common control channel
jamming, selfish users, and intruding nodes should be considered. A detailed
description of these threats can be found in [152, 153, 154, 155, 156].

Cognitive radio networks rely on a trustworthy spectrum sensing process, the
key to which is the ability to distinguish PU signals from SU signals in a
robust way. The use of licensed spectrum bands by PUs may be sporadic, so an
SU must constantly monitor for the presence of PUs in candidate bands. If an
SU detects the presence of a PU in the band under observation, it cannot use
the current band. If there is no PU currently active in the band, then SUs
employ a medium access control mechanism to share the band. In general, it is
expected that no change will be required on the part of the PU transmission
system or air interface in order to accommodate the SUs, e.g., [157], and thus
it is the responsibility of the SUs to correctly identify PUs with their
existing air interface. As a result, an SU’s ability to correctly identify PUs
becomes very important not only for avoiding interference to the PUs, but also
to be able to increase their own throughput. Distinguishing whether or not a
user is a PU is nontrivial, especially when rogue users modify their air
interface in order to mimic a PU’s signal characteristics. This is known as a
PUEA [158].

In order to mitigate the PUEA problem, it is possible to draw parallels with a
phenomenon known for adversarial attacks against classifiers that employ
neural networks. This phenomenon became apparent in classification problems in
conventional fields such as image processing, where it was observed that
certain minor variations in the input, undetectable by humans, can make a
classifier fail, see e.g., [159, 160]. An example that appeared in [160] is
very well-known. Using a 22-layer deep CNN that is able to correctly identify
a panda with 57.7% accuracy, adding a slight amount of noise results in it
being characterized as a gibbon with 99.3% confidence. This vulnerability of
deep neural networks to adversarial attacks has been well-documented, see
e.g., [161, 162, 163, 164, 165].

A number of approaches exist to deal with the problem of adversarial attacks
in the context of image processing; a good review is available in [166]. There
is a recent study which finds that generative classifiers, such as GANs, are
actually more robust to adversarial attacks [167]. Given the success of ML
techniques developed for image processing and successfully adapted to problems
in wireless networking, it is possible to leverage some of this prior work in
the context of designing GAN-based ML systems to counteract adversarial
attacks. The first such technique is described in [168], and is referred to as
Defense-GAN. In this technique, the GAN is trained to model the distribution
of unperturbed data. At inference time, it finds an output that does not
contain any adversarial changes that is “close” in some sense to the given
input data. This output is then fed to the classifier, which can employ any
model, and the result is used as the classification of the data. This
technique does not assume knowledge of the process for generating the
adversarial examples. Reference [168] empirically shows that Defense-GAN is
consistently effective against different attack methods and improves on
existing defense strategies.

Figure 7: Defense-GAN algorithm [168].

Fig. 7 illustrates the basic idea in [168]. For a given input observation x,
the system finds the closest element (in the $L_{2}$ norm) of the data space
that can be produced by the generator operating on an element of the latent
space. The resulting element of the data space, presumably free from the
affects of the adversarial perturbation, is then classified in the regular
way. Intuitively, if ${\bf x}$ is not perturbed, then the GAN can generate a
sufficiently close local copy of it to be classified as “real.” On the other
hand, a perturbed ${\bf x}$ will not be among the possible outputs of the
generator $G$ trained by using unperturbed data, and the classifier will
declare it as “fake.” There is a mathematical development that justifies this
intuition in [168]. The paper shows that the Defense-GAN technique is very
effective against both black-box and white-box attacks, i.e., attacks that do
not have any knowledge of $G$ and the classifier $C$, as well as those that do
have full knowledge of $G$ and $C$, respectively. Other works that use a
similar concept based on GANs are available in [169, 170].

In [10], the effects of a GAN-based spoofing attack to generate synthetic
wireless signals that cannot be statistically distinguished from intended
transmissions is studied. The spoofing attack can be used for various
adversarial purposes such as emulating PUs in cognitive radio networks and
fooling signal authentication systems to intrude protected wireless networks.
The adversary is modeled as a pair of transmitter and a receiver that build
the generator and discriminator of a GAN, respectively. The adversary
transmitter trains a deep neural network to generate the best spoofing signals
and fool the best defense trained as another deep neural network at the
adversary receiver. Thus, the generator and the discriminator of the GAN are
at different locations, collaborating over the air such that the GAN-generated
signals cannot be reliably discriminated from intended signals. The adversary
and the defender may have multiple transmitter or receiver antennas. Spoofing
is accomplished by jointly capturing waveform, channel, and radio hardware
effects inherent to wireless signals under attack. It is demonstrated in [8]
that a GAN-based spoofing attack can be successfully performed and its
performance is compared with random signal attack and replay attack. An
important observation is that as the attacker’s transmitter gets close to the
transmitter, the likelihood of the attacker to generate high-fidelity
synthetic signals for the spoofing attack increases. In summary, the sussess
probability of the GAN-based spoofing attack is very high. This holds for
different network topologies and when node locations change from training to
test time. This probability improves further when multiple antennas are used
at the transmitter.

It is possible to devise defensive strategies against such attacks. A simple
strategy is to change the idle and busy labels, so that the legitimate
transmitter may not transmit if it senses the channel as idle, or it may
transmit even if the channel is sensed as busy [134, 7], assuming that the
unobserved transmitter is not a PU. This can be done over a subset of the
transmit opportunities. For example, by introducing 10% of false labels, the
legitimate transmitter, as the defender, can increase the misdetection
performance of the attacker from 3.95% to 20.79% and the false alarm rate from
18.10% to 25.16%. The results for a single-input single-output (SISO) scenario
from [134] are shown in Table 6. Clearly, this simple algorithm can result in
a significant improvement.

# of defense operations | Attacker error probabilities | Transmitter performance
---|---|---
/ # of all samples | Misdetection | False alarm | Throughput | Success ratio
0% (no defense) | 3.95% | 18.10% | 0.012 | 2.91%
10% | 20.79% | 25.16% | 0.074 | 17.13%
20% | 33.88% | 40.69% | 0.124 | 28.84%
30% | 40.09% | 44.79% | 0.170 | 35.42%
40% | 45.18% | 43.75% | 0.206 | 41.53%
50% | 41.63% | 45.10% | 0.204 | 39.23%
Table 6: Results for defensive strategies against jamming attacks based on
adversarial learning [134].

It is possible to extend this work to the case where NACKs, in addition to
ACKs, are employed. ACKs are only positive acknowledgements, they do not
reveal if there was a transmission. NACKs state there was a transmission but
it was not received correctly, possibly due to a collision, but also
potentially due to other effects such as fading. This increases the state
space of the learning algorithm and may improve the performance of the
attacker. A potential direction is to investigate if there is a simple
algorithm similar to the one above that provides a defense against such
attacks.

For the case of cooperative spectrum sensing, a recent study makes adversarial
use of ML to construct a surrogate of the fusion center’s decision model
[171]. The authors then propose an algorithm to create malicious sensing data,
and show that this type of attack is very effective. Reference [171] shows,
via experiments, that with existing defenses it can achieve up to an 82%
success ratio while only manipulating a small number of malicious nodes. Then,
a mechanism referred to as an influence-limiting policy is introduced which
achieves a disruption ratio reduction of up to 80% of the attacks introduced
in [171]. An important observation that can be made based on this work is
that, as in many security problems, specific types of attacks require specific
types of solutions. It is possible to pursue attacks similar to those in [171]
and attempt to develop relevant solutions. However, it should be emphasized
that a key aspect of any defense against a particular attack is first
detecting that an attack has occurred, which is exactly the anomaly detection
problem discussed above. Strong anomaly detection is the first step in
mitigating attacks in spectrum sensing problems, both cooperative and
noncooperative. To that end, it is worthwhile to investigate the effectiveness
of the GAN-based anomaly detection techniques discussed in Sec. 2.1 against a
number of different attacks such as those described above.

While many conventional countermeasures against security attacks in cognitive
radio networks exist [172], there is very limited published work on ML
techniques for this purpose [173]. Thus, this is a potentially very fruitful
research area.

The most important lesson learned from this subsection is that GANs can be
used for security attacks or as a mechanism for defense against any security
attacks. We have discussed seven works from the literature towards both ends.

Table 7 summarizes all of the works from the literature discussed in Sec. 3.

Reference | Application | Comment
---|---|---
[8] | Spectrum Sharing | Spectrum sensing with domain adaptation and data augmentation.
[80] |  | AMC solution via modified CGAN and semi-supervised AC-GAN.
[103] | Anomaly Detection | Use of BiGAN and PCA for anomaly detection. Comparisons in Table 3.
[114] |  | Unsupervised spectrum anomaly detection via adversarial autoencoder.
[120] |  | For mmWave. Comparison of VAE, CGAN, AC-GAN in Tables 4-5.
[123] |  | Modulation classification via CNN: Idle, in- or out-network, jammer.
[25] | Security | Create and then classify fake transmitters via GAN. 99.9% accurate.
[9] |  |  Spoofing with a GAN where its $G$ and $D$ are not colocated. High success rate.
[26] |  | Intrusion detection with improved attack or defense by GANs.
[27] |  | Three-way GAN among a jammer and two UAVs trying to communicate.
[168] |  | Defense-GAN (Fig. 7). Effective against both black- and white-box attacks.
[10] |  | Effects of GAN-based spoofing to generate synthetic signals like real ones.
[7] |  | Strategy based on changing labels against GAN-based spoofing attacks. Table 6.
Table 7: Different implementations of techniques using GANs for spectrum
sharing, anomaly detection, and security applications in NextG. The main
characteristic of each application is specified as a comment. For a detailed
discussion of each of the techniques, see the text. PCA: Principal Component
Analysis, CNN: Convolutional Neural Network, UAV: Unmanned Aerial Vehicle.

##  4 Simulation Results

The problem of outlier detection in signal classification is a critically
challenging one for NextG networks. Signal classification is needed for
various NextG applications, including user equipment (UE) identification,
spectrum sharing and coexistence (as in the CBRS band), and jammer
(interference) detection. Specifically, for the case where there is no data
about unknown waveforms (that can be considered as outliers), the signal
classification problem becomes even more challenging. In this case, in
general, the outlier detection algorithms are trained using only inlier
waveforms and tested with inliers and outliers. Recent studies have shown that
GANs can help solve the outlier detection problem. AnoGAN has been proposed as
an unsupervised anomaly detection algorithm to calculate an anomaly score
[35]. Despite its good performance and relaxed assumption that does not
require labeled data, it suffers from instabilities in GAN training. In
addition, AnoGAN is an iterative algorithm which hinders its real-time
application. Fast AnoGAN (f-AnoGAN) extends AnoGAN by using a more stable GAN
architecture, WGAN, and it does not require iterations (only one forward pass)
[174]. F-AnoGAN uses an encoder to obtain the latent features of a generator.
The latent features are input to the generator. The anomaly score is
calculated as the mean squared error (MSE) of the input sample and its
reconstruction $\|{\bf x}-G(E({\bf z}))\|_{2}^{2}$ plus the MSE of the
discriminator features of the original and those of the reconstructed signal,
$\|D_{f}({\bf x})-D_{f}(G(E({\bf x})))\|_{2}^{2}$, weighted by a scaling
factor $\kappa$.

This approach can be applied to anomaly detection in RF spectrum data. As an
initial result, we used the RFMLS 2016a dataset [124] that includes eleven
different modulations collected over a wide SNR range between -20 dB and 18
dB. The f-AnoGAN algorithm is trained on only one (known) modulation and
evaluated using all eleven modulations. We expect the model to label samples
from the known (trained) modulation as inlier and samples from all others as
outliers. In contrast to [33] that uses WGAN, we used the WGAN-GP which is
known to be more stable. The f-AnoGAN model outputs an anomaly score per
sample and the AUROC figures are calculated.

In our evaluations, the f-AnoGAN model is trained in three steps:

  1. 1.

First, we trained the generator and discriminator of the WGAN-GP model, both
networks are summarized in Table 9 and Table 10 in the Appendix, respectively.

  2. 2.

Second, we trained the encoder (architecture presented in Table 11 in the
Appendix).

  3. 3.

Finally, we evaluated the performance of the anomaly detection using the
anomaly score.

This three-step procedure closely follows the f-AnoGAN implementation of
[174].111https://github.com/tSchlegl/f-AnoGAN

In evaluating the fidelity and diversity of the generative models, we compared
the use of five different measures [53]: i) sum of recall and precison (S-RP),
ii) harmonic mean of recall and precision (H-RP), iii)  sum of density and
coverage (S-DC), iv) harmonic mean of density and coverage (H-DC), and v)
Jensen-Shannon distance (JSD) [175]. In the GAN training, these measures are
evaluated every 10 epochs and if the fidelity/diversity measure has improved,
the model is saved. For the JSD metric, a lower value indicates a better
model, whereas for the remaining four measures, a higher value means a better
model. We used 500 epochs for each of the GAN and encoder training steps. For
all three networks, we used the Adam optimizer with a learning rate of 0.0002
[176].

As a comparison, we evaluated the performance of a convolutional autoencoder
(CAE) system which is again trained on the only inlier modulation. The CAE
architecture is presented in Table 12 in the Appendix. We measured the mean
and standard deviation of the reconstruction loss in the training dataset. For
any test data that has a reconstruction loss larger than a fixed threshold
(i.e., the mean reconstruction loss plus one standard deviation), the sample
is labeled as an outlier and for those samples with a reconstruction loss
smaller or equal to threshold, the sample is labeled as an inlier. Note that
to have a fair assessment between performance measures and minimize the
effects of network architecture, we have used a CAE model that is very similar
to the AE model of the f-AnoGAN.

Table 8 presents the AUROC values for the anomaly detection problem employing
different modulations. We observe that the performance of the anomaly
detection model depends significantly on the trained (inlier) modulation in
both GAN-based and CAE-based approaches. There are several reasons for this.
First, unlike image datasets, this dataset (and many other RF datasets)
include the effects of channel, noise, and hardware impairments, which make
the classification problem fundamentally challenging. Second, some modulations
in this dataset are subsets of each other in the constellation plot. For
example, AM-SSB modulation is a subset of the AM-DSB modulation. In comparing
the results in Table 8, we see that the H-RP, JSD, and S-RP measures perform
well across different modulations, whereas the S-DC and H-DC metrics did not
provide good performance. We observe that anomalies can be precisely detected
(achieving more than a 0.90 AUROC score) when f-AnoGAN models are trained on
modulations such as the AM-DSB, CPFSK, GFSK, and WBFM using any of the S-RP,
H-RP, and JSD measures. In these modulations, the f-AnoGAN method outperforms
the CAE method. However, modulations such as AM-SSB and QAM16 present
challenging problems as they are very similar to other classes (AM-DSB and
QAM64, respectively). For these modulations, the f-AnoGAN method fails to
reliably distinguish the anomalies from inliers, whereas the CAE model
performs only as good as a random classifier.

Mod. | S-RP | H-RP | S-DC | H-DC | JSD | CAE
---|---|---|---|---|---|---
AM-DSB | 0.963 | 0.964 | 0.962 | 0.965 | 0.968 | 0.899
AM-SSB | 0.088 | 0.088 | 0.088 | 0.088 | 0.273 | 0.502
BPSK | 0.797 | 0.777 | 0.349 | 0.716 | 0.439 | 0.529
8PSK | 0.558 | 0.597 | 0.540 | 0.540 | 0.636 | 0.528
CPFSK | 0.968 | 0.970 | 0.853 | 0.732 | 0.939 | 0.533
GFSK | 0.983 | 0.980 | 0.821 | 0.816 | 0.917 | 0.561
PAM4 | 0.692 | 0.728 | 0.041 | 0.707 | 0.731 | 0.587
QAM16 | 0.419 | 0.424 | 0.300 | 0.300 | 0.447 | 0.600
QAM64 | 0.549 | 0.624 | 0.285 | 0.285 | 0.545 | 0.597
QPSK | 0.664 | 0.678 | 0.547 | 0.547 | 0.559 | 0.530
WBFM | 0.937 | 0.938 | 0.934 | 0.933 | 0.939 | 0.824
Average | 0.693 | 0.706 | 0.520 | 0.603 | 0.672 | 0.608

Table 8: AUROC scores of the anomaly scores obtained using five different
fidelity measures for different modulations. S-RP stands for sum of precision
and recall, H-RP is the harmonic mean of precision and recall, S-DC stands for
sum of density and coverage, H-DC is the harmonic mean of density and
coverage, and JSD stands for Jensen-Shannon distance.

Next, we discuss some implementation details. For the WGAN-GP training, there
are two important parameters that we have tuned. The first parameter is the
number of discriminator (critic) iterations per generator iteration. We have
tested 1, 3, and 5 iterations and found that updating the generator every 3
discriminator updates provided the best results. The second parameter is the
gradient penalty coefficient $\lambda$. This parameter had a profound effect
on the performance. We tested different $\lambda$ values ($\lambda=1,5,10$)
and $\lambda=10$ provided the best results, which emphasizes the importance of
the gradient penalty. For the f-AnoGAN model, the scaling factor $\kappa$ is a
parameter that can be tuned. We have tested $\kappa=1,5,10$ values and found
that $\kappa=1$ provided the best results. Finally, as the f-AnoGAN approach
requires only one forward pass and does not need any iteration to infer a
sample, we can obtain the average inference time on hardware, which is an
important measure for the embedded implementation. Note that this is in
contrast to iterative algorithms such as AnoGAN that require setting
parameters such as the maximum number of iterations to obtain precise timing
measures. Towards this goal, we measured the average end-to-end inference time
on hardware, which includes the forward pass of the input sample to the
encoder, generator, and discriminator networks, and calculating the respective
losses to obtain the anomaly score. The results are evaluated on an NVIDIA
GeForce RTX 3060 GPU system. The average inference time is measured as
0.005784 seconds which enables us to process 172.9 samples per second without
any parallel processing.

In concluding this section, we would like to emphasize that our simulations
can only be considered as very initial results. To be able to come to more in-
depth conclusions, substantially more work by the research community should be
carried out.

##  5 Future Research Directions for GANs in NextG Communication Systems

This section is on the use of GANs for wireless applications in general terms.
This is important because the original development of GANs was in the area of
images while their straightforward application to wireless can bring up
questions. On the other hand, this feature actually makes the proposed
research nontrivial and interesting. It should be understood that what we are
proposing is not a simple translation or porting of what exists in another
field to wireless communications but rather a very careful study of how to be
inspired from a development in one field and do a careful analysis to adapt it
to a completely different area. For example, performance measures used to
compare two images do not directly translate into wireless applications. In
particular, performance measures used in image processing try to imitate human
perception. Clearly, it is questionable that they would be useful in the kind
of tasks discussed above in sections Sec 3.3–Sec 3.5. If this is the case,
then what kind of performance measures should be employed? Since ML is not a
model-based approach, finding the answer to this question will require
experimentation and thus is not a straightforward task. Another consideration
comes from the fact that GANs are known to be difficult to train, especially
for datasets other than images. Then, is there a way this difficulty can be
circumvented? In terms of datasets, there is a perception that datasets that
can be employed for wireless applications are limited in quantity.
Furthermore, in general, training of neural networks require very long
training sequences. On the other hand, the datasets available are limited in
size. Some researchers employ GANs to increase the size of the their training
sequences in a synthetic manner. But then there is a question as to whether
the generated or augmented synthetic signals contain any more information than
the training set since the GAN is able to learn the statistics of the training
sequence but it is not clear if this augmentation process can add any new
statistics. These are some of the questions that employing algorithms from the
basic exploration of GANs to their use in wireless applications will face.

A number of open problems remain in this domain. While a large number of
problems in spectrum sharing, anomaly detection, and security exist, studies
using GANs to address them have so far targeted a relatively small number of
specific problems. Scaling these solutions to a larger number of problems will
require significant effort. First, specific problems need to be identified,
for example, in anomaly detection and security, to be addressed by ML
algorithms. Second, these specific problems need to be simulated and ML
algorithms need to be trained on them. Third, the computational complexity of
this effort should be taken under consideration. There are many successful
uses of GANs, especially in image processing. While a number of these
algorithms have been successfully used in wireless applications, a number of
them are still candidates for use in that setting. For example, we have
discussed the use of BiGANs and f-AnoGANs for anomaly detection, however, a
number of other anomaly detection techniques such as EGBAD and GANomaly have
not yet been studied in the context of wireless anomaly detection. Fourth,
reliable diversity and fidelity measures for GANs to quantify the quality of
the synthetic data for RF applications need to be further explored. As it is
difficult to conduct statistical analyses over complex and high-dimensional
data, these metrics would provide the necessary reliable methods to perform
hyper-parameter optimization in training GANs and fairly compare different GAN
architectures. Towards this goal, we have investigated five of such metrics in
this paper and showed that HR-P provided the best results for the outlier
detection problem.

Yet on another subject we touched upon previously, the topic of augmentation
is controversial. Some researchers strongly hold the belief that GAN-generated
signals cannot be gainfully employed to augment the training dataset. However,
an interesting piece of news from NVIDIA, discussed in [177], together with a
short video worthwhile seeing, states that it is possible to reduce the
training sequence length 10x-20x by using data augmentation and GANs. The
particular application is the creation of synthetic images from real ones and
therefore the visual effect is strong. This was achieved by employing a
special technique with GANs, explained in [178]. Additional works show that,
by using special techniques, it is possible to achieve data augmentation
outside the statistics of the short training sequence, see, e.g., [179, 180,
181]. There exist publications that make this statement specifically for
wireless applications, see, e.g., [54, 80, 13].

An inevitable question arises when GANs are considered as a member of a large
class of ML algorithms. As shown in this paper, they have advantages in terms
performance although it is not clear that they are always the best.
Considerations such as complexity, accuracy, robustness, etc. should be taken
into account in comparing them with other ML algorithms for use in the
wireless applications considered in this paper. To the best of our knowledge,
such a study does not exist. Any step taken towards this understanding will be
very valuable.

GANs can be applied to a number of emerging areas in communications. An
example of this is communications in the mmWave and THz bands. As long as the
computational complexity of the solution can be managed, what was discussed in
this paper is applicable to communication networks in those bands. We will
discuss a number of works from the literature related to this fact. Reference
[182] discusses channel estimation for very large bandwidths operating in
mmWave and THz bands at low SNR. It proposes a GAN-based estimator that first
learns to produce channel samples from the unknown channel distribution via
training the generative network, and then uses this trained network as a prior
to estimate the current channel. This estimator has been shown to work at an
SNR of -5 dB better than Least Squares (LS) and Linear Minimum Mean Square
Estimate (LMMSE) estimators at SNR values of 20 dB and 2.5 dB, respectively.
Furthermore, this estimator reduces the required number of pilots and does not
require retraining even if the number of clusters and rays change
considerably. Channel estimation in the mmWave band is further discussed for
the unmanned aerial vehicle (UAV) applications in [183, 184] and for vehicular
systems in [185].

Another emerging area in communications is mobile edge computing. This is an
area GANs have applications in security. As discussed in [186], GANs can be
used to design a security attack for mobile edge computing. In this attack, a
malicious participant can infer sensitive information from a victim
participant even with just a part of shared parameters from the victim [187],
[186, Fig. 13]. For other applications of GANs in mobile edge computing, in
security and privacy, see, e.g., [187, 188].

##  6 Conclusion

The proliferation of wireless services, in the forms of wireless local area
networks, cellular wireless, applications of the IoT, the tactile internet,
autonomous cars, drones, factory automation, and the general expectations
under the umbrella of the Fourth Industrial Revolution place enormous demands
on wireless spectrum. Although new spectrum in the mmWave band is already
being regulated around the world, the expectations are such that spectrum
scarcity will be with us beginning in the very near future. Many experts in
the field expect that forms of spectrum sharing will be needed towards that
purpose. It is well known that a common technique under consideration for
dynamic spectrum sharing is cognitive radio which can be used to address the
problem of spectrum sharing. However, conventional forms of cognitive radio
will likely not be sufficient because of the enormous dynamics of the problem.
It is expected that the complexity of the problem will prohibit conventional
cognitive radio and forms of ML will have to be employed towards solving this
very difficult problem.

This paper addressed a particular ML solution, GANs, towards that end. GANs
are capable of generating “fake” data that cannot be differentiated from
“real” data, and thus to some extent they capture the distribution of real
signals. They are known to address competitive resource allocation problems.
Furthermore, they are known to be effective in detecting and mitigating
anomalous behavior. A survey of the use of GANs in spectrum sharing, anomaly
detection, and addressing security concerns is provided in this paper. In
several cases discussed, it is demonstrated that GANs have better performance
in addressing the concerns stated above than the other ML algorithms.

It is generally accepted that wireless applications are increasing in quantity
while wireless spectrum is scarce and that ML solutions to address this
problem are needed. GANs provide a framework for such a set of solutions with
proven success. Nevertheless, more work is needed to identify specific
problems and develop successful ML solutions, including those that involve
GANs.

##  7 Acknowledgments

The authors would like to thank the anonymous reviewers whose comments
improved the presentation in the paper.

## Appendix

In this section, we provide the parameters of the f-AnoGAN and CAE used in the
simulations in Sec. 4.

Layer Name | Details
---|---
Reshape layer |  $(N,100)$ to $(N,100,1,1)$
2D transposed | 1024 filters, kernel size of
convolution layer | (2,4), stride of (1,1), no padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D transposed | 512 filters, kernel size of
convolution layer | (2,4), stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D transposed | 256 filters, kernel size of
convolution layer | (2,4), stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D transposed | 128 filters, kernel size of
convolution layer | (2,4), stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D transposed | 64 filters, kernel size of
convolution layer | (2,4), stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D transposed | 1 filter; kernel size of
convolution layer | (2,4),stride of (2,2), padding
Table 9: Generator architecture. Layer Name | Details
---|---
2D convolution layer | 64 filters, kernel size of (2,4),
| stride of (2,2), padding
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 128 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 256 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 512 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 1024 filters, kernel size of (2,4),
| stride of (2,2), padding
Reshape layer |  $(N,1024,2,4)$ to $(N,8192)$
Linear layer |  $8192$ neurons to $1$ neuron
Table 10: Discriminator architecture. Layer Name | Details
---|---
2D convolution layer | 64 filters, kernel size of (2,4),
| stride of (2,2), padding
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 64 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 128 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 256 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 512 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 1024 filters, kernel size of (2,4),
| stride of (2,2), padding
Reshape layer |  $(N,1024,2,2)$ to $(N,100)$
Linear layer |  4096 neurons to $1$ neuron
Tanh |
Table 11: Encoder architecture of the f-AnoGAN system. Layer Name | Details
---|---
2D convolution layer | 64 filters, kernel size of (2,4),
| stride of (2,2), padding
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 64 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 128 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 256 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 512 filters, kernel size of (2,4),
| stride of (2,2), padding
Batch normalization |
Leaky-ReLU | $\alpha=0.2$
2D convolution layer | 1024 filters, kernel size of (2,4),
| stride of (2,2), padding
Reshape layer |  $(N,1024,2,2)$ to $(N,100)$
Reshape layer |  $(N,100)$ to $(N,1024,2,2)$
2D transposed | 512 filters, kernel size of (1,2),
convolution layer | stride of (1,2), padding
Leaky-ReLU | $\alpha=0.2$
Batch normalization |
2D transposed | 256 filters, kernel size of (1,2),
convolution layer | stride of (1,2), no padding
Leaky-ReLU | $\alpha=0.2$
Batch normalization |
2D transposed | 128 filters, kernel size of (1,2),
convolution layer | stride of (1,2), no padding
Leaky-ReLU | $\alpha=0.2$
Batch normalization |
2D transposed | 64 filters, kernel size of (1,2),
convolution layer | stride of (1,2), no padding
Leaky-ReLU | $\alpha=0.2$
Batch normalization |
2D transposed | 64 filters, kernel size of (1,2),
convolution layer | stride of (1,2), no padding
Leaky-ReLU | $\alpha=0.2$
2D transposed | 1 filter, kernel size of (1,2),
convolution layer | stride of (1,2), no padding
Table 12: Convolutional Autoencoder (CAE) architecture.

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