Enhancing internet of things security using entropy-informed RF-DNA fingerprint learning from Gabor-based images

Abstract

Internet of Things (IoT) deployments are anticipated to reach 29.42 billion by the end of 2030 at an average growth rate of 16% over the next 6 years. These deployments represent an overall growth of 201.4% in operational IoT devices from 2020 to 2030. This growth is alarming because IoT devices have permeated all aspects of our daily lives, and most lack adequate security. IoT-connected systems and infrastructures can be secured using device identification and authentication, two effective identity-based access control mechanisms. Physical Layer Security (PLS) is an alternative or augmentation to cryptographic and other higher-layer security schemes often used for device identification and authentication. PLS does not compromise spectral and energy efficiency or reduce throughput. Specific Emitter Identification (SEI) is a PLS scheme capable of uniquely identifying senders by passively learning emitter-specific features unintentionally imparted on the signals during their formation and transmission by the sender’s radio frequency (RF) front end. This work focuses on image-based SEI because it produces deep learning (DL) models that are less sensitive to external factors and better generalize to different operating conditions. More specifically, this work focuses on reducing the computational cost and memory requirements of image-based SEI with little to no reduction in performance by selecting the most informative portions of each image using entropy. These image portions or tiles reduce memory storage requirements by 92.8% and the DL training time by 81% while achieving an average percent correct classification performance of 91% and higher for SNR values of 15 dB and higher with individual emitter performance no lower than 87.7% at the same SNR. Compared with another state-of-the-art time-frequency (TF)-based SEI approach, our approach results in superior performance for all investigated signal-to-noise ratio conditions, the largest improvement being 21.7% at 9 dB and requires 43% less data.

1 Introduction

Internet of Things (IoT) deployments reached 15.14 billion in 2023 and may reach 29.42 billion by the end of 2030 with an average Compound Annual Growth Rate (CAGR) of 16% [1, 2]. These numbers may not appear impressive in and of themselves; however, if the projections are correct, they represent an overall growth of 201.4% in operational IoT devices from 2020 to 2030. This growth is alarming due to the level at which IoT devices have and continue to permeate all aspects of our daily lives and that most lack adequate security [3,4,5]. Lack of adequate security is due to weak or missing encryption and insufficient or missing authentication mechanisms. Both of which make IoT devices and their associated infrastructure susceptible to attack and exploitation [6,7,8,9,10,11,12,13]. The identification and authentication of IoT devices are two best practices in security that are essential for access control in connected systems and IoT infrastructures [5]. Physical Layer Security (PLS) is an alternative or augmentation to cryptographic and other higher-layer security schemes. PLS does not compromise spectral and energy efficiency or reduce throughput. One such PLS scheme is known as Specific Emitter Identification (SEI).

Specific Emitter Identification (SEI) is a PLS approach initially focused on providing electronic warfare systems the ability to detect, characterize, and identify radar systems using inherent and unique features that the radar’s radio frequency (RF) front-end circuits, sub-systems, and systems unintentionally impart upon the signals during their formation and transmission. These unintentional signal features are sufficient to achieve serial number discrimination (a.k.a., differentiate between emitters of the same manufacturer and model number) but sufficiently benign not to impede normal communication operations (e.g., detection, synchronization, and channel estimation). SEI is an advantageous PLS technique because it is a passive technique; thus, the exploited features are generated and imparted upon the transmitted signals during normal operations without the need for external stimuli, and the exploited features persist across time, settings, and location; thus, SEI presents an opportunity to identify and authenticate IoT devices without the need for encryption or other more traditional security approaches, such as passwords.

For its existence, SEI has primarily focused on feature-engineered or handcrafted features and traditional machine learning algorithms such as random forests and support vector machines. These “hand-crafted” SEI processes rely heavily on the proficiency and knowledge of the person or persons designing them, which can lead to suboptimal results. During the past 6 to 7 years, deep learning (DL) has received a lot of attention within the SEI community due to its demonstrated successes in the areas of modulation detection [14], system design [14,15,16,17,18], and spectrum management [19, 20] areas. Also, DL thrives under increasing information scenarios and can learn SEI exploitable features directly from a signal’s raw In-phase and Quadrature (IQ) samples [15, 21, 22]. Despite this, the lack of expert knowledge is not always good, as its incorporation can improve DL performance. An example is the Radio Transformer Network (RTN), which uses expert-defined algorithms to enhance the demodulation performance of a DL-based communications receiver [14]. The work in [23] further supports the justification for including expert knowledge in DL-based SEI processes. The authors of [23] perform multipath correction before DL-based SEI because the average accuracy is only nine percent without it.

Our SEI-based IoT identification approach is inspired by the work presented by the authors of [24], which uses entropy and a convolutional neural network (CNN) to determine whether or not an artwork is fake. Identification of faked artwork requires a skilled expert, and in some instances, even that is insufficient. Identification of faked artwork is comparable to discriminating between two emitters of the same manufacturer and model number. An artwork’s high-resolution image is too large to be processed by a standard CNN; thus, the authors of [24] divided it into “tiles,” and tiles with entropy values more significant than the entire image’s entropy are retained. This entropy-based tile selection approach is a form of data reduction, and due to its success, we incorporate it into an image-based SEI process to strengthen IoT security by providing a means of identity-based access control by authenticating the identity of IoT device emitters while keeping computational complexity and memory storage requirements to a minimum. Image-based SEI is advantageous because it results in DL models that are less sensitive to external factors such as RF device power cycling [25] and generalize better to different operating channels and moving emitters/devices [26]. However, image-based SEI has received little attention within the community, and even less attention has been paid to reducing its computational cost and memory needs with little to no performance reduction.

This work reduces the computational cost and memory requirements of image-based SEI with little to no reduction in performance by selecting the most informative portions of each image using entropy. These image portions or tiles reduce memory storage requirements by 92.8% and the DL training time by 81% while achieving an average percent correct classification performance of 91% and higher for signal-to-noise ratio (SNR) values of 15 dB and higher with individual emitter performance no lower than 87.7% at the same SNR. Compared with a state-of-the-art (SoTA) time-frequency (TF)-based SEI approach, our approach results in superior performance for all investigated signal-to-noise ratio conditions, the largest improvement being 21.7% at 9 dB and requires 43% less data. The next section provides greater detail on how our work compares to the current SoTA and the contributions of our work in greater detail.

The rest of the paper is organized as follows: Section 2 summarizes relevant, related works and describes the contributions of this work relative to them; Section 3 discusses the signal of interest, Gabor transform calculation, and CNN architecture; Section 4 explains the signal collection, detection, and post-processing processes, signal preparation that includes entropy calculation, alternate signal representations and tile selection approaches, CNN configuration, and specifications of the computer used to generate all of the results presented in Section 5, while Section 6 concludes the paper.

2 Related works and contribution

The authors of [27] use entropy to select the most informative features before classification via k-nearest neighbors (kNN). The features come from the spectral elements of the Universal Mobile Telecommunications System (UMTS) emitters’ Random Access CHannel (RACH) preambles. SEI features are generated from the spectrally averaged RACH preamble, which combines multiple RACH preambles transmitted by the same emitter to increase the SNR. In [27], the authors calculate the entropy of each spectral component in the RACH preambles of all emitters. An emitter’s averaged RACH preamble spectral component is selected if its entropy value is greater than or equal to that calculated across the corresponding spectral component of the averaged RACH preambles of all emitters. Our work differs from that in [27] through the use of a DL-driven SEI process that learns an optimal set of emitter discriminating features, single preamble instead of the average of multiple preambles, entropy as a data reduction technique and not feature selection, and emitter-specific features are learned from high entropy tiles extracted from the preamble’s time-frequency (TF) representation. In addition, all the signals used in our research are gathered in a standard laboratory setting; therefore, they contain interference and other channel imperfections. Lastly, we evaluate our SEI process under degrading SNR channel conditions.

The authors of [28] compare ten TF signal representations to investigate SEI’s robustness to interference. Each TF representation is assessed under increasing interference conditions modeled using a Gaussian pulse centered at the emitter’s carrier frequency of 2.4 GHz. The authors show that the continuous wavelet transform (CWT) magnitude is the TF representation most resilient to increasing wireless interference [29, 30].

The authors of [31] enhance SEI performance using nonlinear, dynamic elements known as the multidimensional approximate entropy (MApEn) feature that provides SEI-enabling information. A window slides along each signal, and MapEn is calculated over each window to reduce computational complexity. SEI is performed using a kNN classifier. Our work differs from that of [31] because we do not use entropy as a feature and perform DL-based SEI instead of handcrafted SEI.

The authors of [32] perform SEI using the bispectrum’s color moments, known as the bispectrum-based energy entropy and color moments (BEECM) and support vector machines (SVM). BEECM quantifies the bispectrum’s evenness to determine the similarity between different grayscale images generated from the signals’ bispectrum representations. Unlike the author of [31], the authors of [32] use entropy as a feature, which differs from our use of entropy for data reduction.

In [33], the authors investigated the robustness of an image-based SEI approach to adversarial machine learning (AML) attacks. The authors employ the generative adversarial network (GAN) and fast gradient sign method (FGSM) for AML attacks. The GAN-based attack reduces the percent correct identification performance to less than 32% for three of the seven known/authorized emitters. For the FGSM-based attack, the authors observe that increasing the FGSM perturbation intensity results in higher attack success. It is important to note that even the lowest perturbation intensity prevents the identification of the fifth known emitter within the set of seven. The used emitters are seven USRP X310 Software-Defined Radios (SDRs). The X310 is a high-performance SDR starting at $9634 per unit, which means these SDRs do not reflect the typical low-cost and low-computation IoT device [34]. The authors also collect all signals using a wired set-up; thus, there are no channel effects, and the adversary’s ability to learn SEI features is maximized. Our work differs from that of [33] because we use commercial off-the-shelf emitters that cost $20 per unit, a better analog for operational IoT devices. Additionally, we collect all signals over the air, aligning more with an operationally deployed SEI scenario. Furthermore, the authors of [33] use the entire $224{\times }224{\times }3$ color image, generated in accordance with the methods in [25, 26]. In contrast, we use tiles selected, via entropy, from the grayscale images, which reduces the DL’s input to a smaller $140{\times }140$ image. Lastly, the authors of [33] do not evaluate their work under noisy channel conditions.

Table 1 Comparison of the content of this paper versus related works within the SEI area

Our prior work in [35] presents the initial entropy-driven data reduction approach to facilitate SEI on resource-constrained Internet of Things (IoT) devices and associated infrastructure. This work differs from our previous work in [35] in the following ways.

• Conducts an exhaustive search to select the most informative tiles drawn from the signals’ grayscale images to enhance SEI performance at an SNR of 9 dB.

• Introduces a neighborhood search approach to select the most informative tiles drawn from the signals’ grayscale images to enhance SEI performance at an SNR of 9 dB.

• Investigates using Red, Green, and Blue (RGB) images instead of grayscale images.

• Integrates online learning to create a more efficient DL-based SEI process robust to noise for improved individual emitter identification accuracy.

• Conducts comparative SEI assessment using tiles selected from grayscale images via the exhaustive and neighborhood search approaches to tiles selected from RGB images using the approach from [35].

Our work in [36] explores entropy-informed SEI focused on device identity (ID) verification, a one-to-one approach, versus the one-to-many classification approach used herein. Classification is advantageous because only a single DL model is needed to authenticate device identities, while ID verification requires a DL model for every to-be-authenticated authorized device. Table 1 provides a direct comparison between the contributions of this work versus those prior relevant works highlighted in this section.

Our results show that entropy-informed tile selection, implemented using a neighborhood search-based approach, selects $140{\times }140$ pixel-sized tiles with the highest entropy among their neighbors. Ensemble learning achieves the highest SEI performance at an SNR of 9 dB¹. The average percent correct classification performance is 91% and higher for SNR values of 15 dB and higher with individual emitter performance no lower than 87.7% at the same SNR. Memory storage requirements are reduced by 92.8%, and the DL training time is at least 81% shorter. The results also show that when using DGT tiles and ensemble learning, the performance is 21.7% greater than a CWT-based SEI approach at an SNR of 9 dB while using 43.3% less data

3 Background

This section describes the signal of interest, the transform that converts the IEEE 802.11a Wi-Fi preambles into their two-dimensional TF representations, entropy, the CNN algorithm, and computer specifications. Table 2 defines the notations used.

Table 2 Notations

3.1 Signal of interest

Emitter-specific features are learned from the grayscale image representations of IEEE 802.11a Wireless-Fidelity (Wi-Fi) preambles. IEEE 802.11a Wi-Fi is an Orthogonal Frequency Division Multiplexing (OFDM) signal that enables information communication rates up to fifty-four megabits per second using Binary Phase-Shift Keying (BPSK), Quadrature PSK (QPSK), 16-ary Quadrature Amplitude Modulation (QAM), or 64-ary QAM. IEEE 802.11a Wi-Fi emitters operate within the 5 GHz Industrial, Scientific, and Medical (ISM) band. Every IEEE 802.11a Wi-Fi frame begins with a sixteen-microsecond preamble constructed using known, fixed sequences of OFDM symbols. Wi-Fi receivers use these symbol sequences to perform frequency and phase offset correction, channel equalization, and synchronization [38]. The preamble’s structure consists of ten 0.8 µs Short Training Symbols (STS) designated as $t_{1}$ through $t_{10}$, a Guard Interval (GI), and two Long Training Symbols (LTS) that are designated $T_{1}$ and $T_{2}$. Figure 1 shows the structure of an IEEE 802.11a Wi-Fi preamble. The use of IEEE 802.11a Wi-Fi is for the following reasons:

• The IEEE 802.11 Wi-Fi family is one of, if not the world’s most widely deployed wireless standards.

• IEEE 802.11 Wi-Fi accounts for 31% of the total IoT connections, which equates to roughly 4.7 billion devices [2].

• Allows extension of our work to other preamble-based standards such as IEEE 802.11ac, IEEE 802.11ad, IEEE 802.11ax (a.k.a., Wi-Fi 6), IEEE 802.11p, ZigBee, Z-Wave, and Bluetooth [39].

• The use of OFDM by other 4G and 5G communications standards such as Long Term Evolution (LTE), Worldwide Interoperability for Microwave Access (WiMAX), and 5G-New Radio (5G-NR) [40].

• Numerous SEI publications have used this signal [21, 23, 41,42,43,44].

• An on-hand, commercial off-the-shelf (COTS) set of IEEE 802.11 Wi-Fi compliant emitters.

Fig. 1

IEEE 802.11a Wi-Fi preamble structure that comprises the first 16 µs of a frame [38]

3.2 Gabor transform

Our SEI process uses transformed versions of the IEEE 802.11a Wi-Fi preambles. This transformation is achieved using the discrete Gabor transform (DGT) that is calculated by [45]

$$\begin{aligned} G_{mk}=\sum \limits _{n=1}^{MN_{\Delta }}s(n)W^{*}(n-mN_{\Delta })exp^{-j2\pi kn/K_{G}}, \end{aligned}$$

(1)

where $G_{mk}$ are the complex-valued, Gabor coefficients, $s(n)=s(n + lMN_{\Delta })$ is the periodic input signal, $W(n)=W(n + lMN_{\Delta })$ is the periodic analysis window, $N_{\Delta }$ is the total number of shifted samples, $m=1,2,\dots ,M$ for M total shifts, $k=1,2,\dots ,K_{G}-1$ for $K_{G}\ge N_{\Delta }$, and $mod(MN_{\Delta },K_{G})=0$ satisfied. The Gaussian analysis window is,

$$\begin{aligned} W(n) = \exp \left\{ \left( -\dfrac{\pi }{pN_{s}^{2}}\right) \cdot \left[ n - \dfrac{1}{2}\left( N_{s} - 1\right) ^{2}\right] \right\} , \end{aligned}$$

(2)

where the analysis window width is roughly $N_{s}\sqrt{p}$ and $N_{s}$ is the number of discrete-time samples comprising the input signal s(n) [45]. The Gaussian window’s bandwidth decreases as p increases in the time domain. If $K_{G} > N_{\Delta }$, then the DGT is considered to be “oversampled” and is advantageous when processing noisy data. Since SEI is performed using signals with SNR values of 9 dB and higher, DGT is calculated to satisfy the oversampled criterion. The DGT is the Short Time Fourier Transform (STFT), in which a Gaussian analysis window replaces the rectangular analysis window. The DGT is advantageous because it does not suffer the resolution pitfalls of the STFT, such that good time resolution results in the loss of frequency resolution and vice versa. The DGT produces a TF representation that captures the frequency content of signal segments (i.e., the signal within the Gaussian analysis window) as a function of time, thus ensuring instantaneous TF variations are presented to the CNN. Variations that the SEI process’ CNN may miss.

The DGT coefficients are then converted to a TF surface by computing their magnitude, squaring the magnitude, and then normalizing the resulting magnitude-square representation to ensure all of the TF surface values are in the range of zero and one, which is expressed by,

$$\begin{aligned} \overline{|G_{mk}|}= \dfrac{|G_{mk}|-min\{|G_{mk}|\}}{max\{|G_{mk}|\}-min\{|G_{mk}|\}}. \end{aligned}$$

(3)

3.3 Entropy

The entropy calculation used in this work comes from Information Theory, which defines entropy as a message’s average uncertainty [46]. The amount of information in a message is determined by its rarity, and the more information, the less uncertainty; thus, entropy measures the amount of uncertainty a message eliminates. The more times a piece of information is communicated leads to a proportional reduction of that piece of information’s total entropy [46]. In our work, the Gabor-based images and their extracted tiles are the messages, and entropy determines the information they contain. The entropy of image I is,

$$\begin{aligned} \epsilon (I) = -\sum \limits _{i=0}^{255}{f_{I}[i]\log (f_{I}[i])}, \end{aligned}$$

(4)

where i is a pixel’s intensity within the image I, and $f_{I}[i]$ is the chance that a given pixel’s intensity lies within I [46].

3.4 Convolutional neural networks

Artificial intelligence (AI) pertains to the domain of computer science, which revolves around the investigation of intelligent agents. These agents encompass any technology capable of perceiving its external environment and devising strategies to optimize its actions, ultimately increasing the likelihood of attaining specific objectives [47]. Deep learning (DL) represents a specialized branch within AI that offers a potent framework for supervised and unsupervised learning tasks. DL Neural Networks (NN) encompass complex multi-layer architectures designed to approximate the mapping function $y = f(x)$ for an input (x) and an output (y). DL leverages augmented layers and units per layer to approximate complex functions in Deep NN [48]. Among the fundamental DL architectures are Multi-Layer Perceptrons (MLPs), also known as feed-forward NN, which serve as the elementary structure for estimating a mapping function $f(x;\theta )$, wherein $\theta$ denotes the learning parameters.

Convolutional neural networks (CNNs) represent supervised learning, MLP-based neural networks tailored to handle multi-dimensional data within a grid-like framework. These networks can process various data formats, including one-dimensional vectors like time-interval data and two-dimensional and three-dimensional pixel grids, such as images [48]. By employing the back-propagation algorithm, CNNs learn the parameters $\theta$ to estimate a discriminative model’s mapping function while minimizing a loss function. The loss function measures the discrepancy between the model’s predictions and the ground truth. The CNN network comprises a multi-layer perceptron (MLP) preceded by convolutional and pooling layers. The convolutional layers are constructed with a grid-like arrangement of multiple neurons, where each neuron is linked to the outcome of element-wise multiplication between a multidimensional kernel (also known as a filter) and a region within the input data, matching the size of the kernel. The kernel elements are referred to as weights and are shared among all neurons in the layer [49]. Within a CNN, the convolutional layer(s) play a crucial role in detecting and extracting features from various regions of the input data, consequently generating feature maps. Further, an activation function is applied to each neuron within the convolutional layer to non-linearly transform the corresponding element of the feature map [49, 50]. Pooling layers typically follow convolutional layers to reduce the dimensionality of the activated feature map. This reduction is achieved by computing a statistical summary, such as the maximum, minimum, or average, of nearby outputs [48]. Max Pooling is the most commonly used method in CNN networks. In this context, Max Pooling is applied to extract the maximum-value features within rectangular frames of the activated feature maps. Subsequently, after one or more stages of convolutional and pooling layers, fully connected layers, also known as dense layers, come into play. These fully connected layers detect high-level features and transmit them to the output layer [51].

The primary purpose of the output layer in a neural network, particularly in the context of CNNs, is to make predictions about the label or category to which the extracted features belong. It serves as the final stage of the network, responsible for transforming the high-level features derived from the preceding layers into meaningful output.

3.5 Computer specifications

All results are generated using a high-performance computing cluster comprising four compute nodes and MATLAB^® R2020b [52]. Each node has two Intel^® Xeon^® Gold 6148 CPUs, four NVIDIA^® Tesla^® 32 GB V100s, 192 GB of error correction code RAM, and 64-bit Redhat Linux release 8.3.2011 operating on top of driver version 450.80.02.

Fig. 2

Block diagram illustrating the methodology steps

4 Methodology

This section describes the signal collection, detection, and post-processing, the steps that prepare the signal data set for entropy-informed tile selection, the entropy-informed tile selection approaches investigated, the DL configuration, and the technical requirements for the computer that produced all the results. An illustration of the methodology is presented in Fig. 2. Each block corresponds to a specific subsection within the methodology and is labeled accordingly.

4.1 Signal collection, detection, and post-processing

The IEEE 802.11a Wi-Fi signals are transmitted by eight TP-Link Archer T3-U USB Wi-Fi dongles and captured using an Ettus Research Universal Software Radio Peripheral (USRP) B210 Software-Defined Radio (SDR) at a sampling frequency of 40 MHz [53]. The average SNR of the collected signals is between 27 dB and 30 dB. Signal post-processing begins by removing the channel noise segments between each Wi-Fi frame. Next, course preamble detection is performed by generating an ideal IEEE 802.11a preamble (i.e., this preamble is not tainted by channel and hardware imperfections) with the same sampling frequency as that of the USRP B210 SDR. The ideal preamble’s magnitude is slid along the collection record’s magnitude, and the Mean Squared Error (MSE) is calculated. Magnitude is used because it is not impacted by the presence of carrier frequency offset (CFO), which can impede accurate preamble detection. A preamble is “detected” whenever the MSE is minimized. The IQ samples of each detected preamble are extracted from the collection record and stored for further processing.

Ten thousand preambles are detected and stored for each of the eight Wi-Fi emitters. Each detected preamble is then downsampled to 20 MHz to be compliant with the IEEE 802.11a Wi-Fi standard [38], corrected for CFO in accordance with [54], filtered using a fourth-order, lowpass elliptic filter that has a cutoff frequency of 8.865 MHz, a passband ripple of 0.5 dB, and 20 dB of stopband attenuation, and normalized to be of unit energy.

4.2 Data preparation

The average SNR of the filtered preambles is between 28 dB and 31 dB. Each filtered preamble has like-filtered additive white Gaussian noise (AWGN) added to it to achieve a desired SNR value, with the resulting noisy preamble expressed as

$$\begin{aligned} r(n) = s(n) + \beta ~\eta (n), \end{aligned}$$

(5)

where $\eta (n)$ is the complex-valued, filtered noise, and $\beta$ is the factor used to scale $\eta (n)$ to achieve a particular SNR value. This process is repeated ten times for each preamble to facilitate Monte Carlo simulation at the selected SNR. SEI assessment is conducted for SNR values ranging from 9 to 30 dB in increments of 3 dB between consecutive values. Achieving a specific SNR value through the use of like-filtered AWGN agrees with digital communications assumptions [55, 56] and is in line with prior SEI work [57,58,59,60]. Following the generation of the noisy preambles, the TF representation of each preamble is generated using Eqs. (1), (2), and (3) with $M=320$, $K_{G}=320$, $N_{\Delta }=1$, and $p=0.03$. Each preamble’s normalized, magnitude-squared TF representation is converted into a grayscale image with pixel values ranging from zero to two hundred fifty-five and the pixel intensities divided by two hundred fifty-five to ensure they are between zero and one. The resulting image is designated a Gabor-based image.

Fig. 3

Flowchart showing the general process used to select a tile $\tau$ from the Gabor-based image I using entropy ${\epsilon }$

4.3 Entropy-informed tile selection

The process followed for entropy-informed tile selection is shown in Fig. 3. Entropy-informed tile selection begins by computing the entropy of a normalized, grayscale, Gabor-based image using Eq. (4) and designated the “image entropy,” ${\epsilon (I)}$. The selected Gabor-based image is partitioned into $N_{\tau }$, non-overlapping, and equally sized tiles. The entropy of each tile is calculated using Eq. (4). The entropy of tile $\tau$ extracted from the ith normalized, grayscale, Gabor-based image is designated ${\epsilon ^{\tau }(I)}$. A tile is retained for subsequent CNN-based SEI processing if its entropy value is greater than or equal to its image entropy, ${\epsilon (I)}$,

$$\begin{aligned} \epsilon ^{\tau }(I) \ge \epsilon (I). \end{aligned}$$

(6)

If the tile entropy is less than the entropy of its entire image, then that tile is rejected. An example of this tile selection process is illustrated in Fig. 4. Figure 4 shows a tile with an ${\epsilon ^{1}(I)=7.86}$ entropy larger than the image entropy of ${\epsilon (I)=6.5}$ being retained for subsequent SEI processing. In contrast, a second tile with a ${\epsilon ^{2}(I)=3.10}$ entropy is rejected because its entropy value is lower than that of the entire image.

Fig. 4

Non-overlapping tile selection approach: Representative illustration showing a tile with an ${\epsilon ^{1}(I)=7.86}$ entropy greater than the ${\epsilon (I)=6.5}$ entropy of the entire image being retained. While a second tile—whose ${\epsilon ^{2}(I)=3.10}$ entropy is less than ${\epsilon (I)=6.5}$—is rejected. This figure is adopted from [36]

4.3.1 Alternate tile selection approach: enhanced entropy

The use of “enhanced” entropy is presented in our prior work [35] and is incorporated here for completeness and continuity. Enhanced entropy focuses on the strengthening of Eq. (6) through the use of another statistic such as mean $\mu$, standard deviation $\sigma$, variance $\sigma ^{2}$, skewness $\gamma$, or kurtosis $\kappa$. Including this additional statistic simultaneously requires the tile to satisfy Eqs. (6) and (7).

$$\begin{aligned} \gamma ^{\tau }(I) \ge \gamma (I), \end{aligned}$$

(7)

where $\gamma ^{\tau }(I)$ is the skewness calculated over tile $\tau$ of image I and $\gamma (I)$ is the skewness calculated over the entire image I. This enhanced entropy process is performed using each of the above statistics by substituting for $\gamma$ and $\gamma ^{\tau }$ in Eq. (7) using the desired statistic and is performed as part of the “${\epsilon ^{\tau }(I){\ge }\epsilon (I)}$” decision block in Fig. 3 when enhanced entropy tile selection is performed.

4.3.2 Alternate tile selection approach: neighborhood search

The non-overlapping process described in Section 4.3 does not ensure the tiles retained contain the most emitter-specific information in the normalized, grayscale, Gabor-based images from which the tiles are drawn. This may lead to degraded SEI performance at lower SNR values or overall. A neighborhood-based search is introduced to address the noted shortcoming of the tile selection process described in Section 4.3. The neighborhood-based search approach is the same as the tile selection approach in Section 4.3 up to the point that a tile is designated for retention due to its tile entropy value being greater than or equal to that of its image entropy. Once a tile meets the image entropy criterion of Eq. (6), its neighbors are selected by shifting by one pixel in each cardinal direction, which creates eight additional tiles (see the “Select tile $\tau$’s neighbors” process block in Fig. 3). The entropy value of each neighboring tile is calculated using Eq. (4) (see the “Calculate each neighbor’s entropy ${\epsilon }$” process block in Fig. 3). The neighbor tile with the highest overall entropy value—amongst its peers and the initially selected tile—is retained for subsequent SEI processing. Figure 5 provides a representative illustration of the neighborhood search-based tile selection approach, which is performed by the “Choose the tile with the largest ${\epsilon }$ amongst the neighborhood” process block in Fig. 3).

Fig. 5

Neighborhood Search-based Tile Selection Approach: Representative illustration showing entropy-informed tile selection from a neighborhood of tiles. In this example, the center-most tile–whose entropy is ${\epsilon ^{\tau }(I) = 7.85}$ and selected using the approach described in Section 4.3 and illustrated in Fig. 4–is shown with its eight neighbors whose entropy values (starting from the top, right-most tile and moving clockwise) are ${\epsilon ^{ru}(I) = 7.52}$, ${\epsilon ^{r}(I) = 7.86}$, ${\epsilon ^{rd}(I) = 7.92}$, ${\epsilon ^{d}(I) = 7.93}$, ${\epsilon ^{ld}(I) = 7.91}$, ${\epsilon ^{l}(I) = 7.84}$, ${\epsilon ^{lu}(I) = 7.51}$, and ${\epsilon ^{u}(I) = 7.53}$. Note that the entropy value of the center-most tile is greater than the entire image’s entropy value of ${\epsilon (I) = 6.5}$ but not the largest entropy value concerning its neighbors. The highest overall entropy value–amongst the neighbors–is ${\epsilon ^{d}(I) = 7.93}$ and is associated with the bottom tile enclosed in the green ellipse and marked “Retained Tile”. The step size amongst the neighbors shown in Fig. 5a is enlarged to enhance clarity. This figure is adopted from [36]

In Fig. 5a, the tile selected following the process in Section 4.3—with an entropy of ${\epsilon ^{\tau }(I)=7.86}$—is highlighted in the normalized, grayscale, Gabor-based image—with an entropy of ${\epsilon (I) = 6.5}$—using a solid, green square. The positions of the initially selected tile’s neighbors are also highlighted within the normalized, grayscale, Gabor-based image, Fig. 5a. Figure 5b shows the neighborhood tiles’ corresponding entropy values. Each neighborhood tile is highlighted using the same line style and colored squares used to identify their positions in Fig. 5a. Although the initially selected tile does have a tile entropy value, ${\epsilon ^{\tau }(I)=7.86}$, greater than that of the image entropy value, ${\epsilon (I) = 6.5}$, it does not have the highest entropy value within its neighborhood. A higher entropy value is achieved by the bottom, center tile that is enclosed by a green ellipse in Fig. 5b with an entropy value of ${\epsilon ^{d}(I) = 7.93}$; thus, it is the tile selected and used for later SEI while all others are discarded. This process is repeated for every tile selected from a normalized, grayscale, Gabor-based image using the approach described in Section 4.3 and all normalized, grayscale, Gabor-based images.

4.3.3 Alternate tile selection approach: exhaustive search

Even the neighborhood search-based tile selection approach does not guarantee that the tiles selected for SEI are associated with the highest possible entropy values of the normalized, grayscale, Gabor-based image being processed. The only way to ensure this is true is to search the entire normalized, grayscale, Gabor-based image exhaustively. The best way to explain the exhaustive search-based tile selection approach is to use a sliding window of the exact dimensions of the tiles. Initially, the window is placed in the top left corner of the normalized, grayscale, Gabor-based image. The tile that falls within the window is extracted, its entropy is calculated via Eq. (4), and it is selected or rejected for later SEI processing based on the tile selection approach described in Section 4.3. The window is advanced one pixel to the right, and the process is repeated for the tile that falls under the updated window location. The window slides one pixel each time until it travels across the entire width of the normalized, grayscale, Gabor-based image. The window is then repositioned to the far left edge of the image and moved down one pixel from its initial starting location when the search began. Again, the window slides one pixel to the right each time until it travels across the entire width of the normalized, grayscale, Gabor-based image. Each time the window is advanced, the tile selection approach in Section 4.3 is performed. This process is repeated until the window traverses the entirety of the normalized, grayscale, Gabor-based image. This tile selection approach significantly increases the number of tiles that are selected per image and emitter while simultaneously guaranteeing the tiles with the highest entropy values are selected. However, the number of tiles chosen would either surpass the available memory on resource-constrained devices, necessitate expanding the amount of onboard memory, or necessitate using edge or cloud resources that result in increased V2X communications overhead and latency. None of these are desirable; thus, only the tiles associated with the highest two overall entropy values are selected and used for SEI.

4.4 Deep learning configuration and training

The CNN has four layers with eight, eight, sixteen, and thirty-two filters per layer, respectively. Each filter is $35{\times }35$ in size. CNN training is performed by randomly selecting 90% of the selected tiles, and the remaining 10% is used for “blind” testing of the trained CNN. The CNN is trained using $\chi$-fold cross-validation to ensure model generalization. The error performance of each “fold” is tracked within and across noise realizations at a given SNR value. The CNN model that achieves the lowest error across all folds and noise realization for each SNR is designated the “best” model, used to classify its corresponding SNR’s “blind” test set of tiles, and the results presented in Section 5.

4.4.1 Online augmentation

We incorporate online augmentation into the CNN training process to improve entropy-informed, data-reduced SEI performance by creating a CNN model that is robust to noise and generalized across training samples. Online augmentation was first introduced by the authors of [61]. During the online augmentation process, we introduce AWGN into every minibatch selected from the training set. This addition occurs immediately after the necessary data preparation steps are implemented but before generating each preamble’s TF representation using the Gabor Transform. Figure 6 shows the difference between the online augmentation in [61] and the offline augmentation explained in Section 4.2.

Fig. 6

Flowchart showing the difference between online and offline augmentation processes when applied to the neighborhood search-based tile selection approach

5 Results

The initial goal is to identify the tile sizes and entropy-informed data reduction strategy that results in the highest SEI performance using average percent correct classification performance at an SNR of 30 dB. Table 3a provides the number of tiles retained for four tile sizes, and the corresponding average percent correct classification performance is shown in Table 3b. Entries in Table 3b of “–” signify cases in which too few tiles are retained to facilitate CNN training. The $135{\times }135$ tile size yields the highest average percent correct classification performance amongst the four tile sizes when tiles are selected using entropy $(\epsilon )$, entropy and mean $(\epsilon ~ \& ~\mu )$, or entropy and kurtosis $(\epsilon ~ \& ~\kappa )$. Based upon the $135{\times }135$ tile size results in Table 3b, SEI performance for each of the eight IEEE 802.11a Wi-Fi emitters is shown in Fig. 7 using confusion matrices for the entropy $(\epsilon )$, entropy and mean $(\epsilon ~ \& ~\mu )$, and entropy and kurtosis $(\epsilon ~ \& ~\kappa )$ informed tile selection approaches along with the full, $320{\times }320$ DGT image confusion matrix for comparison. For the full, $320{\times }320$ DGT image results, the normalized images are used in their entirety. In other words, no form of entropy-informed data reduction is performed. Regardless of whether entropy (see Fig. 7b) or enhanced entropy (see Fig. 7c and d) are used to select the $135\times 135$ tiles, individual emitter SEI performance never falls below 95% for any of the emitters. When comparing the SEI results of the three entropy-informed tile selection approaches to that of the full, $320{\times }320$ DGT image results, average percent correct classification performance drops by 0.86%, 0.76%, and 1.21% when using entropy $(\epsilon )$, entropy and mean $(\epsilon ~ \& ~\mu )$, and entropy and kurtosis $(\epsilon ~ \& ~\kappa )$ informed tile selection, respectively. The real advantage of entropy- and enhanced entropy-informed tiles is the memory and training time reductions achieved over the full, $320{\times }320$ DGT image case, Table 4. The amount of RAM needed to store the entropy and enhanced entropy selected tiles data sets is reduced by 92.8%, 91.3%, and 98.5% for the entropy $(\epsilon )$, entropy and mean $(\epsilon ~ \& ~\mu )$, and entropy and kurtosis $(\epsilon ~ \& ~\kappa )$ informed tile selection approaches when compared to the memory needed to store the full, $320{\times }320$ DGT image data set. The CNN is trained 80.7%, 76.6%, and 95.5% faster for the entropy $(\epsilon )$, entropy and mean $(\epsilon ~ \& ~\mu )$, and entropy and kurtosis $(\epsilon ~ \& ~\kappa )$ informed tile selection data sets than when the CNN is trained using the full, $320{\times }320$ DGT image data set. Less memory and faster training times are advantageous if the SEI process CNN model needs to be re-trained as more information becomes available, new emitters join the network, or operating conditions change. This is also important if the data set or a portion needs to be shared with other entities within the IoT infrastructure because it lowers communications requirements (e.g., data rate and throughput).

Table 3 Entropy and enhanced entropy for four tile sizes at an SNR of 30 dB. Table entries of “–”correspond to cases with insufficient tiles to train the CNN

Fig. 7

Entropy and enhanced entropy tile selection: Confusion matrices showing percent correct classification of the eight IEEE 802.11a Wi-Fi emitters associated with the three highest average percent correct values–for $135\times 135$ tiles—in Table 3b at an SNR of 30 dB

Based on the number of tiles in Table 3a and the SEI performance results shown in Table 3b and Fig. 7, entropy ${\epsilon }$ and enhanced entropy-based—via ${\epsilon ~ \& ~\mu }$, and ${\epsilon ~ \& ~\kappa }$—tile selection selects a sufficient number of tiles per approach to train a CNN for each and facilitate comparative assessment. Overall, entropy and mean (${\epsilon ~ \& ~\mu }$) based tile selection achieves the highest average percent correct classification performance amongst the three entropy-informed tile selection approaches; however, the use of entropy and kurtosis (${\epsilon ~ \& ~\kappa }$) requires the least amount of memory and has the lowest CNN training time because it selects the fewest number of tiles of 815 versus over 4,000 using the other two entropy-based approaches. This is an important consideration if data reduction is the primary purpose of implementing an SEI process that uses entropy-informed tile selection. It is also worth emphasizing the fact that the use of entropy and kurtosis (${\epsilon ~ \& ~\kappa }$) based tile selection does result in the lowest average percent correct classification performance amongst the three entropy-informed tile selection approaches. Still, the difference is negligible, with a reduction of only 0.35% versus that of entropy only and 0.68% lower than the entropy and mean-based tile selection approaches. Despite this information, further investigation is needed to determine the effectiveness of each tile selection approach under degrading SNR conditions using the $135\times 135$ tile size. The number of tiles retained by each of the three entropy-informed tile selection approaches is shown in Table 5a, and the corresponding average percent correct classification performance is shown in Table 5b.

Table 4 Memory needed to store the full, $320 \times 320$ DGT image data set and the time needed to train its CNN for a single noise realization across all ten cross-validation folds at SNR of 30 dB versus the $135 \times 135$ tiles selected using entropy and enhanced entropy. The numbers in parentheses denote the percent reduction in memory and time concerning the full, $320 \times 320$ DGT image case

Table 5a shows that the number of tiles selected decreases as SNR degrades until the SNR reaches 9 dB. At 9 dB, the number of tiles selected increases for all three entropy-informed tile selection approaches. We believe this is due to the noise power beginning to dominate the preambles and DGT-based grayscale images, negatively impacting the entropy- and enhanced entropy-measured preamble-specific information. The noise power’s influence at 9 dB influences the images’ entropy and enhanced entropy values and their extracted tiles’ entropy and enhanced entropy values to the point that more tiles satisfy the thresholds of Eqs. (6) and (7).

Table 5 Entropy ($\epsilon$), entropy and mean $(\epsilon\ \&\ \mu)$, and entropy and kurtosis $(\epsilon\ \&\ \kappa)$ results for the $135 \times 135$ tile size as SNR degrades from 30 to 9 dB in increments of 3 dB between consecutive values

Fig. 8

Entropy and entropy and mean tile selection: Confusion matrices showing percent correct classification performance for the eight IEEE 802.11a Wi-Fi emitters. Each emitter is represented by $135{\times }135$ tiles extracted from the grayscale image of a preamble’s normalized, magnitude-squared DGT representation. Tile selection is performed using entropy (${\epsilon }$, left column of sub-figures) or entropy and mean (${\epsilon \& \mu }$, right column of sub-figures)

At 12 dB and 15 dB, the average percent correct classification performance of the entropy and entropy and mean selected tiles is superior to the full, $320{\times }320$ DGT image case, Table 5b. At SNRs for 18 dB and higher, the full, $320{\times }320$ DGT image average percent correct classification performance is higher than both entropy-informed tile selection approaches; however, the difference between the full, $320{\times }320$ DGT image performance and that of the entropy-informed tile selection approaches is never greater than 1%. SEI performance for each emitter is shown for SNRs of 9 dB, 12 dB, 15 dB, and 18 dB in Fig. 8. Individual emitter performance using entropy-selected tiles is shown in the left column of sub-figures (a.k.a., Figs. 8a, c, e, and g). In contrast, the right column of sub-figures (a.k.a., Figs. 8b, d, f, and h) presents individual emitter performance generated using entropy and mean selected tiles. Entropy and mean (${\epsilon ~ \& ~\mu }$) informed tile selection achieves superior performance to that of the entropy (${\epsilon }$) informed tile selection case at SNR values of 9 dB, 12 dB and 18 dB but not at 15 dB. The small difference between the SEI performance of the two selection approaches is within the statistical variability of the experiments.

The 9 dB results in Table 5b show that the average percent correct classification performance drops by at least 10% using the ${\epsilon \& \mu }$ tile selection approach and 12.82% when ${\epsilon }$-informed tile selection is performed. To improve SEI performance at 9 dB, the tile size is re-investigated using eleven tile sizes ranging from $100{\times }100$ up to $160{\times }160$. Tile selection using ${\epsilon ~ \& ~\kappa }$ is neglected because too few tiles are selected at SNR values of 12 dB, 15 dB, 18 dB, and 21 dB to facilitate CNN training at these SNRs, Table 5a. Table 6a shows that the number of tiles selected decreases as the SNR falls from 30 to 9 dB, but at 9 dB, the number of tiles selected increases. This trend was also seen in Table 5a, and as previously stated, the reason for the increase is attributed to the increased noise power that influences the image’s and tiles’ ${\epsilon }$ and ${\epsilon ~ \& ~\mu }$ values. Table 6b presents the average percent correct classification performance for the tiles set numbers shown in Table 6a. As SNR decreases from 30 to 9 dB, the average percent correct classification performance also decreases. However, the average percent correct classification performance increases as tile size increases to a tile size of $140{\times }140$ for four out of the eight SNR values investigated (i.e., SNR values of 12 dB, 15 dB, 18 dB, and 27 dB). No other tile size results in more than one instance of achieving superior average percent correct classification performance. It is important to note that the highest average percent correct classification performance for each SNR is annotated using green colored cells and bold typeset font. These results show that the optimization of SEI performance is connected to tile size at each SNR. For example, ${\epsilon ~ \& ~\mu }$ tile selection and a $155{\times }155$ tile size lead to the selection of 3835 tiles and an average percent correct classification performance of 78.78% at 9 dB, which is the highest average percent correct classification performance at that SNR across all tile sizes and both tile selection approaches. When ${\epsilon }$ informed tile selection is performed, the highest average percent correct classification performance at 9 dB corresponds to a $160{\times }160$ tile size and 1,018 tiles being selected. SEI performance for each emitter is provided using confusion matrix for ${\epsilon ~ \& ~\mu }$ selected $155{\times }155$ tiles in Fig. 9a and b presents the confusion matrix for the ${\epsilon }$-selected $160{\times }160$ tiles.

Fig. 9

Entropy and entropy and mean tile selection: Confusion matrices showing percent correct classification performance for each IEEE 802.11a Wi-Fi emitter using ${\epsilon ~ \& ~\mu }$ selected tiles at an SNR of 9 dB

5.1 Results: neighborhood search-based tile selection

To improve SEI performance at 9 dB, tile selection is performed using the neighborhood-based tiles selection approach described in Section 4.3.2, and the corresponding SEI results are presented here. Neighborhood-based tile selection leads to performing SEI using all neighborhood tiles that satisfy Eq. (6) or using only the tile with the highest entropy value amongst its neighborhood. The first case is designated as Entire Neighborhood, and the second is designated Highest Neighbor.

Table 6 The number of tiles retained and SEI performance when entropy ($\epsilon$) or entropy and mean $(\epsilon\ \&\ \mu )$ informed tile selection is performed using each of eleven tile sizes at SNR values ranging from 9 to 30 dB in increments of 3 dB between consecutive values. Each SNR’s highest average percent correct classification performance is annotated using bold text and green-filled cells

5.1.1 Results: entire neighborhood

The number of tiles selected for the entire neighborhood selection case and the eleven tile sizes from Table 6 are shown in the top row of Table 7a. The top row of Table 7b presents the average percent correct classification performance for the entire neighborhood selected tiles at an SNR of 9 dB. Compared to the original tile selection procedure described in Section 4.3, the entire neighborhood tile selection approach results in more tiles being selected for subsequent SEI, increasing CNN training by 76.7%. The highest average percent correct classification performance is achieved using $140{\times }140$ entire neighborhood selected tiles, which is 10.54% higher (93.87% versus 83.33%) than the $160{\times }160$ tile size. Interestingly, the $160{\times }160$ tile size corresponds to the highest average percent correct classification performance when using the entropy-informed tile selection approach of Section 4.3.

Table 7 Neighborhood search-based tile selection: The number of tiles retained and SEI performance when using entropy ($\epsilon$) for eleven tile sizes at an SNR of 9 dB. Each selection procedure’s highest average percent correct classification performance is denoted using bold text and green-filled cells

5.1.2 SEI results: highest neighbor

The middle rows of Table 7a and b present the number of tiles and average percent correct classification performance associated with the highest neighborhood tile selection case at an SNR of 9 dB. The results in Table 7b show that selecting the tile with the highest entropy among the neighborhood results in a superior SEI performance when using tiles sized $140{\times }140$. The highest neighbor case achieves an average percent correct classification performance that is only 0.62% lower than what is achieved using the entire neighborhood tile selection approach while reducing the number of tiles needed to achieve an average percent correct classification performance above 93% by nearly 75%. For a tile size of $140{\times }140$, the highest neighbor tile selection approach increases the average percent correct classification performance by 23. 49% (a.k.a., 93. 25% versus 69. 76% compared to the tile selection approach based on entropy in Section 4.3.

Fig. 10

Neighborhood search-based tile selection: Confusion matrices showing percent correct classification performance for each IEEE 802.11a Wi-Fi emitter. Each emitter is represented by $140{\times }140$ (left column figures) and $160{\times }160$ (right column figures) tiles, extracted from the grayscale image of a preamble’s normalized magnitude-squared DGT representation. Tile selection is performed using entropy (${\epsilon }$) only

SEI performance for each IEEE 802.11a Wi-Fi emitter is presented using confusion matrices in Fig. 10. The right column of sub-figures—in Fig. 10—corresponds to $140{\times }140$ sized tiles, while the results for the $160{\times }160$ sized tiles are presented in the left column of sub-figures. Regardless of the case, the neighborhood-based tile selection approach increases SEI performance over the entropy-informed tile selection approach of Section 4.3. When considering the highest neighbor-selected results in Fig. 10e, the average percent correct classification performance is higher when using the entire neighborhood-selected tiles, Fig. 10e, but the highest neighbor-selected tiles result in fewer misclassification per emitter. An example of this is shown when considering Emitter #2 and Emitter #7, and the phenomenon is present in the $140{\times }140$ and $160{\times }160$ tile size results.

5.2 Results: exhaustive search-based tile selection

As stated in Section 4.3.3, the only way to ensure optimal SEI performance using entropy-informed tile selection to reduce the amount of data needed is to exhaustively search for the highest entropy tiles within the entire grayscale DGT-based image. Exhaustive search-based tile selection is performed using entropy-only tile selection for $140{\times }140$ and $160{\times }160$ sized tiles. The number of tiles selected for both tile sizes is over 94% larger than the tile set selected using the entropy-informed tile selection approach described in Section 4.3; thus, only the highest two entropy tiles for each grayscale image are used to perform SEI. SEI performance for the exhaustive search-based tile selection approach is presented for each IEEE 802.11a Wi-Fi emitter using confusion matrices shown in Fig. 11. In comparison to the original entropy-informed tile selection approach, the exhaustive search-based tile selection approach’s average percent correct classification performance is decreased by 7.2% and 7.15% when using $140{\times }140$ and $160{\times }160$ sized tiles, respectively. It is important to note that the entropy of the full, $320{\times }320$ DGT-based grayscale image is not used to select the tiles; thus, the exhaustive search selected tile set contains tiles that are not part of the original entropy-informed tile selected set. These additional tiles may be impeding SEI performance. Also, only the tiles associated with the highest two entropy values are added to the exhaustive search selected tile set, so further research is needed to determine if increasing the number of selected tiles would improve SEI performance.

Fig. 11

Exhaustive search-based tile selection: Confusion matrices showing percent correct classification performance for the eight IEEE 802.11a Wi-Fi emitters. Each emitter is represented by $140{\times }140$ and $160{\times }160$ tiles, extracted from the grayscale images of the preambles’ normalized, magnitude-squared DGT representation. Tile selection uses the original entropy-informed tile selection algorithm (first row) of the exhaustive search-based tile selection approach (second row)

5.3 Results: red, green, and blue images

This section presents results generated using RGB images to facilitate comparative assessment with other SEI works that use Red, Green, and Blue (RGB) images, such as that presented in [33]. The data preparation remains largely the same, except for the final step, Section 4.2. Instead of converting each normalized, magnitude-squared DGT representation into a grayscale image, it is converted into an RGB image by translating the one to two hundred fifty-five valued pixels into RGB-compatible hues. The original entropy-informed tile selection approach in Section 4.3 is still used. Still, it is slightly modified because each RGB image has three layers (one for each color) instead of only one. In the modified approach, each color layer is processed separately. For example, entropy-informed tile selection is performed using only the red layer, and tiles whose entropy values satisfy Eq. (6) are retained for subsequent SEI while all others are discarded. The entropy-informed tile selection process is then repeated for the green and blue colored layers of the RGB image, and their selected tiles are added to the red layer’s tiles. The result is a selected tile set up to three times larger than the grayscale images’ tile set. The $140{\times }140$ and $160{\times }160$ sized tile sets are 88.02% and 94.93% larger than their corresponding grayscale image counterparts, respectively. The CNN’s input layer is also modified to accept a three-dimensional input. The RGB images average percent correct classification performance is 58.03% when using $140{\times }140$ sized tiles and 57.93% when $160{\times }160$ sized tiles are used. This represents a 34.19% and 38.87% reduction in average percent correct classification performance compared to their grayscale counterparts’ SEI performance results, respectively. Figure 12’s confusion matrices present SEI performance for each IEEE 802.11a Wi-Fi emitter using entropy-selected tiles of size $140{\times }140$ or $160{\times }160$, extracted from the RGB images converted from the preambles’ normalized, magnitude-squared DGT representations at an SNR of 9 dB. The top row of sub-figures presents the grayscale image-based results for tiles sizes of $140{\times }140$ (Fig. 12a) and $160{\times } 160$ (Fig. 12b). While the RGB image-based SEI results are presented in the bottom row of sub-figures in which Fig. 12c presents the $140{\times }140$ sized tiles results and Fig. 12d presents the results for the $160{\times }160$ sized tiles. The confusion matrices in Fig. 12 show that SEI performance is lower when using tiles selected from RGB images.

Fig. 12

Red, green, and blue (RGB) images: Confusion matrices showing percent correct classification performance for the eight IEEE 802.11a Wi-Fi emitters. Each emitter is represented by a $140{\times }140$ or $160{\times }160$ sized tiles extracted from the RGB image of a preamble’s normalized, magnitude-squared DGT representation at an SNR of 9 dB. Tile selection is performed using entropy (${\epsilon }$)

5.4 Results: online augmentation

The final attempt at improving the SEI performance associated with performing data reduction via entropy-informed tile selection involves the use of online augmentation within the CNN training process (see Section 4.4.1 and Fig. 6). Based on the results presented up to this point, the online augmentation investigation is performed using the second case of neighborhood search-based tile selection and $140{\times }140$ sized tiles. In the second case of neighborhood search-based tile selection, only the neighbor with the highest entropy is retained, and all others are discarded. Online augmentation results are generated using a single CNN model and four CNNs trained using ensemble learning.

Fig. 13

Online augmentation: Individual percent correct classification performance for each IEEE 802.11a Wi-Fi emitter at SNR values ranging from 9 to 30 dB increasing by 3 dB between consecutive values and a tile size of $140{\times }140$

Figure 13a shows the percent correct classification performance for each IEEE 802.11a emitter along with the average percent correct classification performance calculated for the eight emitters generated using a single CNN at SNR values of 9 to 30 dB in steps of 3 dB between consecutive values. The online augmentation results shown in Fig. 13a are generated using the process depicted in Fig. 6a. This process is inherently sequential, involving a series of data pre-processing steps, such as adding white Gaussian noise, followed by entropy-informed tile selection. Each step is performed sequentially on individual mini-batches, and the selected tiles are prepared for training a single classification model. Analyzing the results presented in Fig. 13a, it becomes evident that Emitter #2 demonstrates the highest percent correct classification performance compared to all other emitters, exhibiting a peak value of 100% at SNR levels of 27 dB or higher, and a minimum of 90.25% at an SNR of 9 dB. Conversely, Emitter #3, Emitter #5, and Emitter #6 fall below the average percent correct classification performance for all SNR values within the range of 9 to 30 dB. The average percent correct classification performance across all emitters reaches a peak of 96.63% at an SNR of 30 dB and a minimum of 85.72% at an SNR of 9 dB. Based on the results in Fig. 13a, our attention turns to ensemble learning due to its potential to improve the SEI performance of certain emitters by addressing overfitting and improving the generalization of the model between training samples.

5.4.1 Results: online augmentation via ensemble learning

The key objectives behind exploring ensemble learning are twofold: (i) to reduce the training process’ computational complexity, which includes minimizing the time consumed by a single data processing pipeline and reducing the training time of a single classification model, and (ii) to enhance model generalization, thus enabling better performance on unseen data. We aim to achieve these goals by employing ensemble learning techniques and optimizing the classification process for improved efficiency and individual emitter identification accuracy.

Ensemble learning techniques leverage the capabilities of multiple machine learning algorithms to generate predictions by extracting features through diverse data projections. These results are combined using various voting mechanisms to achieve superior performance compared to any individual constituent algorithm [62]. This section describes an initial attempt to apply ensemble learning, where the ensemble learning bagging scheme is integrated into the online augmentation process depicted in Fig. 6a. The training set is divided into four equally sized subgroups, with preambles randomly assigned to each subgroup. Each of these subgroups undergoes separate data processing pipelines and is used to train an individual classification model. Importantly, all four processing pipelines and model training procedures are executed in parallel, reducing overall processing and model training times. As a result of this ensemble learning bagging scheme, four identical models are generated, each being trained on 25% of the original training set, by leveraging parallel processing and breaking down the training process into subgroups to improve efficiency and potentially enhance the overall performance and generalization of the classification models. The procedure involves passing the test preamble through each of the four models obtained through ensemble learning to predict the final label for a test preamble. Consequently, each model generates its prediction for the test preamble. A voting scheme is employed to arrive at the final label, where the label with the highest number of votes among the four individual predictions is selected as the ultimate prediction for the test preamble. This voting-based approach helps make a more robust and accurate classification decision by considering the collective predictions of the ensemble models.

Figure 13b shows the percent correct classification results for each of the IEEE 802.11a emitters using the highest neighbor tile selection approach, tiles of size $140{\times }140$, and the ensemble learning scheme described above. Comparing Fig. 13b to the single model scheme in Fig. 13a, it is evident that the average percent correct classification performance has shown improvement across all SNR values. In particular, the ensemble learning scheme improves performance, with the maximum average percent correct classification performance reaching 98.4% at 30 dB. These encouraging results motivate the authors to explore other ensemble learning schemes in their future research, incorporating different models, transformation functions, and feature spaces.

5.4.2 Results: online augmentation versus state of the art

This section presents results comparing our ensemble learning-based SEI approach using entropy-selected tiles extracted from Gabor-based grayscale images, Fig. 13b, with two SoTA SEI approaches using features learned or extracted from a signal’s (i) CWT [28,29,30], and (ii) IQ representations [51]. This comparison is presented in Fig. 14 using average percent correct classification performance with 95% confidence intervals. The CWT is implemented using MATLAB R2020b’s “|cwt|” function and results in a $[56{\times }320{\times }2]$ complex image in which the third dimension’s first and second entries are the positive and negative frequency components, respectively [52]. A $[108{\times }320]$ complex image is created by concatenating the positive and negative frequency entries along the first dimension and the magnitude calculated to create a grayscale image similar to that described in Section 4.2. All CWT- and IQ-based SEI results are generated using the DL network in [28] and [21], respectively. Regardless of signal representation, the corresponding DL architectures are trained and tested for SNRs ranging from 9 to 21 dB in increments of 3 dB between consecutive values.

Compared to the CWT and IQ-based SEI approaches, the results in Fig. 14 show that our ensemble learning-based SEI approach using entropy-selected tiles results in superior average percent correct classification performance for all investigated SNR values. The superiority of DGT-based SEI over CWT-based SEI is consistent with prior research [63]. As noted in Section 3.2, the DGT captures the frequency content of a signal as a function of time, ensuring that TF variations, behaviors, and related features are presented to CNN. Such variations, behaviors, and features are not directly present within the IQ representation and may contribute to poorer performance. Lastly, our approach uses entropy to select the most information containing portions of the grayscale images, while the other two approaches use the entirety of the signals or their representation. Using the entire signal or representation includes portions that would be removed by our entropy selection process but are not, thus presenting confusing information to the classifier and leading to increased misclassifications.

Fig. 14

Comparison with the state of the art: Average percent correct classification performance with 95% confidence intervals across the eight IEEE 802.11a Wi-Fi emitters at SNR values ranging from 9 to 21 dB increasing by 3 dB between consecutive values. Note that $140{\times }140$ sized tiles are used to generate the ensemble learning-based SEI approach using entropy-selected tiles

6 Conclusion

This work investigates entropy and enhanced entropy-informed tiles selection, three tile selection approaches, DL, and ensemble learning to reduce the data and time needed to train an SEI model capable of securing IoT devices and the corresponding infrastructure. Our results show that entropy-informed tile selection using tiles with the highest entropy among their neighbors, tiles of size $140{\times }140$ pixels, and four CNN models trained using ensemble learning results in the best SEI performance while simultaneously reducing the amount of data and time needed to achieve that performance. The result is an average percent correct classification performance of 91% and higher for SNR values of 15 dB and higher with individual emitter performance no lower than 87.7% at the same SNR. The memory needed to store the data is reduced by 92.8%, and the DL training time is at least 81% shorter. Compared with another state-of-the-art TF-based SEI approach, our approach results in superior performance across all investigated signal-to-noise ratio conditions, with the largest improvement being 21.7% at 9 dB and requiring 43% less data. Future work will investigate the modification of the neighborhood search-based tile selection approach by increasing the number of neighbors selected and increasing the neighborhood’s size.