Effects of RF Signal Eventization Encoding on Device Classification Performance

Abstract

The results of first-step research activity are presented for realizing an envisioned “event radio” capability that mimics neuromorphic event-based camera processing. The energy efficiency of neuromorphic processing is orders of magnitude higher than traditional von Neumann-based processing and is realized through synergistic design of brain-inspired software and hardware computing elements. Relative to event-based cameras, the development of event-based hardware devices supporting Radio Frequency (RF) applications is severely lagging and considerable interest remains in obtaining neuromorphic efficiency through event-based RF signal processing. In the Operational Technology (OT) protection arena, this includes efficient software computing capability to provide reliable device classification. A Random Forest (RndF) classifier is considered here as a reliable precursor to obtaining Spiking Neural Network (SNN) benefits. Both 1D and 2D eventized RF fingerprints are generated for bursts from N_Dev = 8 WirelessHART devices. Average correct classification (%C) results show that 2D fingerprinting is best overall using detected events in burst Gabor transform responses. This includes %C ≥ 90% under multiple access interference conditions using an average of N_EPB ≥ 400 detected events per burst. This is sufficiently promising to motivate next-step activity aimed at (1) reducing fingerprint dimensionality and minimizing the required computational resources, and (2) transitioning to a neuromorphic-friendly SNN classifier—two significant steps toward developing the necessary computing elements to achieve the full benefits of neuromorphic processing in the envisioned RF event radio.

1. Introduction

As the use of wireless Operational Technology (OT) expands to support nearly all Critical Infrastructure (CI) sectors, so does the need for increased communication network reliability, security, and resiliency [1,2,3]. A majority of today’s OT technology evolved from information technology applications, with cost reduction and performance benefits of information technology adaptation leading to the development and deployment of various smart technologies throughout numerous CI sectors. This includes the complementary use of Internet of Things (IoT) and Industrial Internet of Things (IIoT) devices to produce an integrated mesh of physical systems supporting (1) healthcare, transportation, energy, and industrial control system sectors [4], and (2) other OT-dominated sectors that include critical manufacturing, defense industrial base, emergency service, and water/wastewater treatment sectors [5]. Enabling OT is vital to cross-sector critical infrastructure operations and the communications interconnectivity has driven the need for ensuring resilience, safety, and security.

Various Radio Frequency (RF) fingerprinting methods have been considered over the past decade to improve the security of communication systems supporting OT networks. Among these methods are those identified in [6] where the authors have aptly summarized different RF fingerprint generation, extraction, and discrimination methods that can be considered to boost physical layer protection. A majority of the methods noted in [6] can be categorized as passive methods where the fingerprint features are extracted from collected RF emissions of operationally installed devices performing their by-design function. This differs from active fingerprinting methods, whereby the features are extracted from externally stimulated RF emissions collected from uninstalled devices that may or may not be functionally operating.

Fingerprinting methods based on Distinct Native Attribute (DNA) features are duly noted in [6] and have demonstrated potential for enhancing physical layer security in wireless OT networks [7,8,9]. This includes demonstrations using WirelessHART communication devices, which (1) have rapidly proliferated throughout OT application spaces, (2) are among the two most widely used industrial international standards, and (3) have fielded numbers approaching tens of millions [10]. The statistical DNA-based fingerprinting methods have employed both passive [11,12,13] and active [8,14] approaches for exploiting WirelessHART DNA features. These works have predominantly employed Multiple Discriminant Analysis (MDA) and ensemble-based Random Forest (RndF) classifiers to perform device discrimination.

1.1. Research Motivation

Advances in neuromorphic computing [15] and the use of Spiking Neural Network (SNN) classification architectures [16] have enabled near-equivalent classification performance as obtained with traditional von Neumann-based artificial neural network architectures at a fraction of the energy consumption. While neuromorphic computing has shown energy reduction approaching 1000× in selected applications [17,18,19], its impact on radio-frequency (RF) applications remains largely uninvestigated.

RF sensing systems stand to gain considerable benefit from new energy-efficient neuromorphic processing. This includes upgrades to RF receiver processing that historically requires analog-to-digital conversion of continuous signals and sample decimation to reduce the amount of data presented to downstream processing elements. RF signal “eventization” holds promise for decreasing the overall required power by reducing the amount of data required by downstream processes. For RF fingerprinting applications [14], this includes reducing the amount of data required for fingerprint generation and device discrimination by using features extracted from information-bearing event data.

Neuromorphic event-based camera processing is orders of magnitude more energy efficient than traditional frame-based camera processing [20]. The envisioned “event radio” concept seeks to bring these advantages into the RF processing arena. The belief that similar benefits may be realized for an RF event radio is motivated by (1) the existence of hardware such as the Intel Loihi neuromorphic chip [21] that provides an energy-efficient speed improvement when processing RF signals [22], and (2) the use of computationally efficient deep machine learning algorithms in RF electronic warfare applications [23].

Potential benefits of neuromorphic computing are considered here in light of previously demonstrated DNA fingerprinting methods. This includes comparing non-eventized and eventized RF fingerprinting performance using features from experimentally collected signals for eight WirelessHART devices—some of the same devices that are proliferating throughout various OT application spaces. The WirelessHART signals are adopted from [14] and are representative of communications using Frequency-Hopped, Time Division Multiple Access (FH-TDMA) to provide multi-user, multi-channel operation. The WirelessHART FH-TDMA demonstration signals include the effects of multi-device, multi-channel interference, which significantly increases the fingerprint discrimination challenge when compared with single-device, single-channel operation.

The RF eventization work here represents the first step toward transitioning to a neuromorphic-friendly, low power-consuming, SNN classification capability of enhancing edge device operational protection. This includes consideration for implementing SNN-based neuromorphic processing in Field Programmable Gate Array (FPGA) hardware being hosted on Software-Defined Radio (SDR) platforms. Several RF eventization encoding methods are considered here using WirelessHART one-dimensional Time Domain (1D-TD) signals and their corresponding two-dimensional Gabor transform (2D-GTX) responses. Classification results are generated for N_Dev = 8 devices using fingerprints from selected eventization methods to highlight the potential for realizing event radio capability—this is envisioned as being an SDR-based solution hosting FPGA hardware to achieve low-power SNN-based neuromorphic processing objectives.

1.2. Relationship to Prior Research

The concept of an “event” occurring within time-series data has been studied in multiple applications and includes events at the signal waveform level as well as the machine-processing level [24,25,26]. A key issue with time-series processing is dealing with vast amounts of data generated by continuously sampled univariate or multivariate processes. For the purpose of RF eventization, as defined in this work, a large sequence of real-valued numbers (raw signal samples) is transformed into a shorter length sequence of binary-valued “spikes”, which are either positive or negative, for use in neuromorphic processing. Various methods have been devised to implement this type of eventization encoding and are broadly categorized as rate coding and temporal coding methods [27]. For a given application, a preferred encoding method may be empirically selected based on information loss of the original signal [28], classifier accuracy [29], or some other metric. As achieved in the event camera arena [20], key eventization advantages include very high temporal resolution, low latency, very high dynamic range, and low power consumption [20]. It is desired to achieve similar advantages in neuromorphic RF systems.

For the purpose of this work, we used a threshold-based temporal coding method given its successful application in the event-based classification of Free-Spoken Digit (FSD) audio datasets in [30]. Audio is perhaps the most similar signal type to the WirelessHART data used here. This earlier work addresses pre-processing encoding techniques for lower-frequency, narrowband (100 < f < 1000 Hz), and time-varying audio signals. The pre-processing of raw input signal samples includes multi-channel Butterworth filtering followed by temporal spike encoding prior to feature extraction and classification. Of the various temporal encoding methods considered in [30], it was concluded that Temporal Contrast encoding was best overall and yielded the highest average classification accuracy with minimum accuracy variance. Temporal Contrast encoding generates spikes by comparing absolute signal variation with a fixed detection threshold and assigning resultant positive (+1) and negative (−1) spikes to the encoded sequence.

Given its success in [30] with audio signals, threshold-based contrast encoding was adopted here for initial RF eventization demonstration using the higher-frequency/higher-bandwidth WirelessHART signals detailed in Section 2.1. Contributions of the work here include (1) the first application of Temporal Contrast encoding to one-dimensional Time Domain (1D-TD) WirelessHART signals as detailed in Section 2.2.1, and (2) the introduction and demonstration of a Temporal–Spectral Contrast encoding approach using two-dimensional Gabor Transform (2D-GTX) responses of WirelessHART signals in Section 2.2.2.

1.3. Paper Contribution

There is a wide range of RF fingerprinting methods surveyed in [6] that can be used for device classification. The effectiveness of these methods is directly related to fingerprint “profile” features, which yield best-case performance when the features are ideally unique across the pool of devices to be classified. While the numerous fingerprint features noted in [6] are influenced by waveform level “events” (turn-on/turn-off transients, intentional/unintentional amplitude, phase, frequency modulation, etc.), none of the noted methods in [6] use RF fingerprints comprised of event-based features such as used here.

As completed here, the use of RF signal eventization coding and characterizing its effect on device classification performance is believed to be a first-of-a-kind activity for higher RF frequency (10 s of MHz) event processing. The work in [30] is perhaps the most related but considered much lower frequency signals, including very low-frequency signals (10 Hz to 1 KHz) as occurs in smart device biometric applications and mid-audio frequency signals (500 Hz to 2 KHz) as occurs in human voice recognition applications. As noted in Section 1.2, the success in [30] with these lower frequency signals is achieved using a threshold-based contrast encoding method, which was adopted here for higher frequency RF signal consideration.

Of equal importance, the RndF accuracy benchmark (%C ≥ 90%) established here and the identification of the average number of RF Events-Per-Burst (N_EPB ≥ 400) required to achieve this accuracy sustain motivation for continuing the development and demonstration of an RF event radio capability. The RndF classifier is a reliable precursor for subsequent RndF-to-Convolutional Neural Network (CNN) classifier transition activity that is currently underway. The RndF-to-CNN transition activity will provide the baseline for the final CNN-to-SNN transition activity with the resultant neuromorphic-friendly SNN classifier holding the most promise for meeting high accuracy, low latency, and high energy efficiency objectives when implemented in hardware.

1.4. Paper Organization

The remainder of this paper is organized as follows. The Demonstration Methodology is presented in Section 2 and includes selected details on WirelessHART signals, RF signal eventization encoding, and fingerprint formation using non-eventized and eventized features. Summary details for the implemented MDA/ML and RndF classifiers are presented in Section 3. The device classification results are presented in Section 4 and predominantly focus on RndF classifier performance, which provides the basis for drawing conclusions and declaring demonstration success. The paper ends with a research summary and conclusions in Section 5.

2. Demonstration Methodology

This section provides selected details for key processes and activities used for conducting the experimental demonstrations and generating the classification results presented in Section 4. Selected details are provided for the following:

• WirelessHART Signals in Section 2.1—provides details for the WirelessHART adapters being discriminated, the Frequency-Hopped Time Division Multiple Access (FH-TDMA) process used to add multi-channel Cross-Channel Interference (CCI) effects, and the Signal-to-Interference-plus-Noise (SINR) ratio scaling process used to induce varying channel effects. The use of CCI-laden bursts here for the initial demonstration was (i) a matter of experimental convenience given that the single-channel WirelessHART bursts and the FH-TDMA process for coherently combining them were available [14]; and (ii) it was believed that discrimination using CCI-laden bursts presented a greater challenge when compared with single-channel discrimination;
• RF Signal Eventization Encoding in Section 2.2—provides details for the threshold-based contrast encoding used for one-dimensional Time Domain (1D-TD) and two-dimensional Gabor Transform (2D-GTX) fingerprinting demonstrations. This includes encoding the WirelessHART FH-TDMA signal responses into event sequences used for fingerprint generation;
• Fingerprint Formation in Section 2.3—provides details for forming the non-eventized statistical DNA and eventized fingerprint vectors that are input to the classifiers to assess device discriminability. These vectors are often referred to as input “samples” within the machine learning community. However, the term fingerprints is used exclusively herein to help minimize potential confusion between classifier input samples and experimentally collected time domain samples in the FH-TDMA signals.

2.1. WirelessHART Signals

The experimental signals used here for eventization demonstrations were originally collected in support of work in [13] and subsequently processed to support work in [14] that added multi-channel Cross-Channel Interference (CCI) effects. Selected experimental collection details from these previous works are included here for completeness. The signal collections were performed in a typical laboratory environment using the four Siemens AW210 [31] and four Pepperl+Fuchs Bullet [32] devices listed in

Table 1. Details for the N_Dev = 8 WirelessHART adapters (D1, D2, …, D8) used for demonstration [13,14] showing two different manufacturers and models with the indicated serial number (S/N).

Device ID	Manufacturer	Model	S/N
D1	Siemens	AW210	003095
D2	Siemens	AW210	003159
D3	Siemens	AW210	003097
D4	Siemens	AW210	003150
D5	Pepperl+Fuchs	Bullet	1A32DA
D6	Pepperl+Fuchs	Bullet	1A32B3
D7	Pepperl+Fuchs	Bullet	1A3226
D8	Pepperl+Fuchs	Bullet	1A32A4

. Note that while two different manufacturers are listed, which is based on labels affixed to the devices, all devices were actually manufactured in a single plant located in Twinsburg Ohio, USA. The change in labeling and serial number sequencing is a result of Pepperl+Fuchs acquiring the manufacturing facility from Siemens.

As illustrated in Figure 1, the devices communicate directly with an Emerson 1410 gateway [33] one at a time while a USRP X310 Software Defined Radio (SDR) [34] collects the device emissions. The devices were placed 8 ft. from the gateway, and the SDR collection antenna was positioned 18 in. from the operating device. Each device was operated in non-overlapping 5.0 MHz WirelessHART channels (Chn#1–Chn#15) in the 2.4 GHz industrial, scientific, and medical frequency band [35]. The channel center frequencies include f_c(m) = 2405 + 5m MHz for m ∈ {1, 2, …, 15} and span [f_c(m) − 2.5, f_c(m) + 2.5] MHz. The devices use preamble-based signaling with Offset Quadrature Phase-Shift Keyed (O-QPSK) data modulation.

The X310 collection receiver was manufactured by Ettus Research in Austin, TX, USA. It uses an RF bandwidth of BW_Col = 100 MHz and was set to a center frequency of f_Ctr = 2.440 GHz, which was sufficient for collecting signals in all WirelessHART frequency channels. The collection receiver employed an f_S = 100 Mega-Samples per second (MSps) sample rate and a total of 2500 experimental bursts were collected per device in each of the 15 WirelessHART channels. Post-collection Signal-to-Noise Ratio (SNR) analysis in [13] showed that an average collected SNR_Col ≈ 41.4 dB was realized across all devices, all channels, and all collected bursts. The effects of real-world CCI were added post-collection through coherent re-combination using a Frequency-Hopped, Time Division Multiple Access (FH-TDMA) process [14]. This process was used to (1) mimic WirelessHART network operation that includes multiple adapters simultaneously transmitting in multiple frequency channels [36], and (2) enable classification performance assessment under conditions that are expected to increase the device discrimination challenge. As detailed below, the induction of CCI necessitated the need for an alternate Signal-to-Interference-plus-Noise Ratio (SINR) metric.

The FH-TDMA processing in Figure 2 was implemented such that N_Frq = 8 adjacent Frequency Slots (FS) were occupied within each Time Slot (TS). The frequency assignment of device D4 across time slots is highlighted in blue to illustrate the frequency hopping nature of the process when considering the FH-TDMA assignment for a given device. The FH sequential TS-by-TS processing included (1) random assignment of collected signals from all N_Dev = 8 devices to 1-of-8 FH frequency slots corresponding to WirelessHART Chn#8–Chn#15 operation; (2) coherent summation of the eight assigned bursts, one from each of the users operating in their assigned frequency channel—this effectively induces the cross-device CCI effects; (3) FS-by-FS slot (channel-by-channel) filtering using a 5.0 MHz bandpass channel filter to extract and segregate individual user signals; (4) device-by-device down-conversion and filtering using a 2.5 MHz baseband filter; and (5) factor-of-20 sample decimation for a final sample rate of f_S = (100 MSps)/20 = 5 MSps.

The FH-TDMA processing was repeated until a total of N_Brst = 8576 CCI-bearing responses, denoted as $s_{\mathrm{F}\mathrm{h}\mathrm{T}\mathrm{d}}\left(t\right)$, were generated for each of the eight devices. The SINR of the channel-filtered $s_{\mathrm{F}\mathrm{h}\mathrm{T}\mathrm{d}}\left(t\right)$ was scaled prior to eventization and DNA fingerprint generation. The input signal to the eventization and fingerprinting processes is given by

$$s_{\mathrm{F}\mathrm{h}\mathrm{T}\mathrm{d}}\left(t\right)=filter\left[ s_{\mathrm{W}\mathrm{H}}\left(t\right)+s_{\mathrm{C}\mathrm{C}\mathrm{I}}\left(t\right)+n_{\mathrm{B}\mathrm{c}\mathrm{k}}\left(t\right) \right] ,$$

(1)

where filter [ ] denotes the WirelessHART channel filtering used to segregate individual user signals, $s_{\mathrm{W}\mathrm{H}}\left(t\right)$ is the experimentally collected WirelessHART signal, $s_{\mathrm{C}\mathrm{C}\mathrm{I}}\left(t\right)$ accounts for the induced CCI contribution, and $n_{\mathrm{B}\mathrm{c}\mathrm{k}}\left(t\right)$ represents background noise that was present during the collection. The SINR of the $s_{\mathrm{F}\mathrm{h}\mathrm{T}\mathrm{d}}\left(t\right)$ responses in Equation (1) were scaled on a channel-by-channel basis using channel-filtered Additive White Gaussian Noise (AWGN) to induce channel variation effects according to

$$\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}\equiv \frac{{\mathrm{S}}_{\mathrm{W}\mathrm{H}}}{\left({\mathrm{I}}_{\mathrm{C}\mathrm{C}\mathrm{I}}+{\mathrm{N}}_{\mathrm{B}\mathrm{c}\mathrm{k}}+{\mathrm{N}}_{\mathrm{A}\mathrm{W}\mathrm{G}\mathrm{N}}\right)} ,$$

(2)

$$\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}\left(\mathrm{d}\mathrm{B}\right)={\mathrm{S}}_{\mathrm{W}\mathrm{H}}\left(\mathrm{d}\mathrm{B}\right)-10\times {\mathrm{L}\mathrm{o}\mathrm{g}}_{10}\left({\mathrm{I}}_{\mathrm{C}\mathrm{C}\mathrm{I}}+{\mathrm{N}}_{\mathrm{B}\mathrm{c}\mathrm{k}}+{\mathrm{N}}_{\mathrm{A}\mathrm{W}\mathrm{G}\mathrm{N}}\right) ,$$

(3)

where S_WH is the average collected WirelessHART signal power, I_CCI is the average induced CCI power, N_Bck is the average collected background power, and N_AWGN is the average channel-filtered noise power that is added to set the desired analysis SINR. It was empirically determined that the average (cross-device, cross-burst, cross-channel) power levels before FH-TDMA processing (N_Bck only contributes) and after FH-TDMA processing (both I_CCI + N_Bck contribute) resulted in an approximate +8.5 dB increase in the noise floor of $s_{\mathrm{F}\mathrm{h}\mathrm{T}\mathrm{d}}\left(t\right)$. The noise floor was further increased by varying N_AWGN to set the simulated range of +6.5 > SINR(dB) > +26.5 dB used for results presented in Section 4.

2.2. RF Signal Eventization Encoding

Threshold-based contrast encoding [30] was adopted here for initial RF eventization demonstration using the WirelessHART signals detailed in Section 2.1. The methodology here includes (1) the first application of Temporal Contrast encoding to one-dimensional Time Domain (1D-TD) WirelessHART signals in Section 2.2.1, and (2) the introduction of a Temporal–Spectral Contrast encoding approach using two-dimensional Gabor Transform (2D-GTX) responses in Section 2.2.2.

Effects of RF eventization on device classification performance were investigated using the experimentally collected WirelessHART burst responses. Figure 3a,b show the 1D-TD amplitude and 2D-GTX magnitude responses generated from the sequence of samples $\left\{b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$ for a representative WirelessHART burst. Elements of the $b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)$ sequence are sample values of the real-valued continuous burst response $b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(t\right)$ taken at the $t_n$-th time instant. There are various eventization processes that could be considered and a select few were considered here for initial assessments. As detailed in the next two sub-sections, the threshold-based contrast encoding processes used here include (1) eventization of 1D-TD non-transformed $\left\{b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$ sample sequences, and (2) eventization of transformed 2D-GTX sequences of the $\left\{b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$ sequence.

For both the 1D-TD and 2D-GTX demonstrations, a threshold-based eventization process is used. For 1D-TD, a given threshold value (Thr) is applied to centered (mean removed) and normalized (values scaled to span [−1 +1]) responses. For all of the 1D-TD and 2D-GTX responses to be eventized, with CtrNrm(m) representing a given element of the centered-normalized response, the detection of an event using CtrNrm(m) includes comparing abs[CtrNrm(m)] with the Thr value and declaring one of two conditions: (1) for abs[CtrNrm(m)] ≥ Thr, a detection is declared and an eventization value of sign[CtrNrm(m)] = ±1 is assigned to the mth element where sign[x] is the sign of x—this is the detection of what are called positive (+1) and negative (−1) events; and (2) for abs[CtrNrm(m)] < Thr, a value of zero is assigned for the mth element to indicate no event was detected.

2.2.1. One-Dimensional Time Domain (1D-TD) Eventization

The 1D-TD eventization processing included (1) Direct Eventization using the centered-normalized $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{D}\mathrm{i}\mathrm{r}}\left(n\right)\right\}$ sequence samples for threshold-based event detection; (2) Integral Eventization using the centered-normalized integrated $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{I}\mathrm{n}\mathrm{t}}\left(n\right)\right\}$ sequence samples for threshold-based event detection; and (3) Derivative Eventization using the centered-normalized first derivative $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{D}\mathrm{e}\mathrm{r}}\left(n\right)\right\}$ sequence samples for threshold-based event detection. The 1D-TD centering (mean removal), normalization, thresholding, and eventization process are illustrated in Figure 4 using the first derivative $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{D}\mathrm{e}\mathrm{r}}\left(n\right)\right\}$ sequence of samples for the representative WirelessHART response in Figure 3.

The threshold-based eventization process illustrated in Figure 4 was applied to the 1D-TD direct $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{D}\mathrm{i}\mathrm{r}}\left(n\right)\right\}$, integrated $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{I}\mathrm{n}\mathrm{t}}\left(n\right)\right\},$ and first derivative $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{D}\mathrm{e}\mathrm{r}}\left(n\right)\right\}$ sequences using selected threshold values (+/− Thr). The event declaration assignments of e(n) ∈ [−1 0 +1] were made and used to form eventized fingerprints per Equation (7) in Section 2.3.2 and used for RndF classifier training and testing. Apart from the actual eventization detections, i.e., assignment of ±1 detection values at specific n indices, results for the other 1D-TD $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{D}\mathrm{i}\mathrm{r}}\left(n\right)\right\}$ direct and $\left\{b_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{1\mathrm{D}-\mathrm{I}\mathrm{n}\mathrm{t}}\left(n\right)\right\}$ integral sequences would appear similar.

2.2.2. Two-Dimensional Gabor Transform (2D-GTX) Eventization

A detailed discussion of GTX processing is omitted here for brevity. The reader is referred to the many works that have addressed GTX development and its application for improving signal joint time–frequency resolution. The GTX application trail is diverse and spans from some of the earliest signal processing development activity [37,38,39] to some of the most recent work [40,41]. Of most relevance here is the Gabor-based DNA fingerprinting work, with early demonstrations occurring in [42,43] and the most recent demonstrations being performed in [8]—the GTX processing implemented here was based on these works. Elements of the complex GTX matrix are denoted by GTX(k,m) for k = 1, 2, …, KTim and m = 1, 2, …, MFrq. The full GTX matrix generation parameters included KTim = 16, MFrq = 128, with N_Δ = 64 time sample shifts between transformations. The analysis Gaussian window width was set to W_GW = 0.01. Following the generation of GTX(m,k) for a given input burst, there were two 2D-GTX eventization encoding processes considered:

• Direct Eventization: Elements of the (MTim × KFrq)-dimensional GTX matrix such as shown in Figure 5a were generated from collected $\left\{b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$ sequence samples. Centering and normalization were applied to the resultant GTX matrix such that −1 ≤$\mathrm{a}\mathrm{b}\mathrm{s}\left[{\mathrm{G}\mathrm{T}\mathrm{X}}_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{\mathrm{D}\mathrm{i}\mathrm{r}}(m,k)\right]$ ≤ +1 for all m, k.
• Derivative Eventization: The (MTim × KFrq)-dimensional GTX matrix was used with row-wise (row-by-row) differencing followed by centering and normalization such that −1 ≤ $\mathrm{a}\mathrm{b}\mathrm{s}\left[{\mathrm{G}\mathrm{T}\mathrm{X}}_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{\mathrm{D}\mathrm{e}\mathrm{r}}(m,k)\right]$ ≤ +1 for all m, k.

The previously detailed threshold-based eventization detection process was applied to elements of the centered-normalized matrices, i.e., CtrNrm(m,k) = $\mathrm{a}\mathrm{b}\mathrm{s}\left[{\mathrm{G}\mathrm{T}\mathrm{X}}_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{\mathrm{D}\mathrm{i}\mathrm{r}}(m,k)\right]$ and CtrNrm(m,k) = $\mathrm{a}\mathrm{b}\mathrm{s}\left[{\mathrm{G}\mathrm{T}\mathrm{X}}_{\mathrm{C}\mathrm{t}\mathrm{r}-\mathrm{N}\mathrm{r}\mathrm{m}}^{\mathrm{D}\mathrm{e}\mathrm{r}}(m,k)\right]$, respectively. These CtrNrm(m,k) were compared with specified threshold values (0 < Thr < 1) and event declaration assignments of e(n) ∈ [−1 0 +1] made. The e(n) assignments were used to form eventized fingerprints per Equation (7) in Section 2.3.2 and used for RndF classifier training and testing.

Sequential stages of the GTX eventization process are illustrated in Figure 5 for derivative eventization of the GTX matrix in Figure 3b—the graphic illustration would be similar for direct eventization. The illustration includes (1) Figure 5a, which is the derivative GTX matrix response with the event detection ROI highlighted; (2) Figure 5b, which is an expanded view of the event detection ROI in Figure 5a; (3) Figure 5c, which is the eventized GTX derivative matrix for the ROI using a threshold value of Thr = 0.6; and (4) Figure 5d, which is the vectorized form of the GTX event matrix in Figure 5c.

2.3. Fingerprint Formation

For consistency with a majority of AFIT’s historically related fingerprinting work [8,9,11,13,14,42,43], the classifier input “samples” are referred to herein as fingerprints—this helps minimize the potential confusion between classifier input “samples” and experimentally collected time domain samples in the $\left\{b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$ sequence. Three different types of fingerprints were formed using ${\mathrm{N}}_{\mathrm{C}\mathrm{o}\mathrm{l}}$ samples of the collected burst sequence $\left\{b_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$. These include (1) the non-eventized as-collected $\left({\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{C}\mathrm{o}\mathrm{l}}\right)$ and non-eventized statistical $\left({\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}\right)$ fingerprints detailed in Section 2.3.1, and (2) the eventized $\left({\overrightarrow{\mathbf{F}}}_{\mathrm{E}\mathrm{v}}\right)$ fingerprints detailed in Section 2.3.2.

2.3.1. Non-Eventized Fingerprint Formation

Classification assessments were performed using two different Non-Eventized (NonEv) fingerprint types. The non-eventized as-collected fingerprints $\left({\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{C}\mathrm{o}\mathrm{l}}\right)$were formed as vectors having elements equaling the ${\mathrm{N}}_{\mathrm{C}\mathrm{o}\mathrm{l}}$ sample values of the collected burst sequence $\left\{{\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)\right\}$ according to

$${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{C}\mathrm{o}\mathrm{l}}={\left[ {\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(1\right) {\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(2\right) \dots {\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right) \dots {\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n_{{\mathrm{N}}_{\mathrm{C}\mathrm{o}\mathrm{l}}-1}\right) {\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n_{{\mathrm{N}}_{\mathrm{C}\mathrm{o}\mathrm{l}}}\right) \right]}_{1\times {\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}}$$

(4)

where ${\mathrm{b}}_{\mathrm{C}\mathrm{o}\mathrm{l}}\left(n\right)$ is the nth collected sample for n = 1, 2, …, N_Col, and ${\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}={\mathrm{N}}_{\mathrm{C}\mathrm{o}\mathrm{l}}$ is the total number of fingerprint features. This produces the highest-dimensional non-eventized fingerprints and generally requires the highest computational intensity (energy consumption) to perform classification.

The non-eventized statistical DNA fingerprints $\left({\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{D}\mathrm{N}\mathrm{A}}\right)$were formed from statistical features of non-transformed 1D-TD and 2D-GTX responses as illustrated in Figure 3a and Figure 3b, respectively. This process is consistent with previous DNA fingerprint generation where the fingerprint features include statistical metrics of variance (σ²), skewness (γ), and kurtosis (κ). These statistics are calculated using samples within selected sub-regions of (1) 1D-TD amplitude (Amp), phase (Phz), and/or frequency (Frq) responses as detailed in [14], and (2) 2D-GTX transform matrices as detailed in [8,42,43]. For each of the selected 1D-TD responses (centered-normalized amplitude, phase, and/or frequency) and 2D-GTX response (centered-normalized magnitude), the response is divided into N_SRgn sub-regions, and the non-eventized statistical DNA fingerprint is formed according to

$${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{D}\mathrm{N}\mathrm{A}}={\left[{ \mathbf{f}}_{{\mathrm{S}\mathrm{R}}_1} ⋮ {\mathbf{f}}_{{\mathrm{S}\mathrm{R}}_2} ⋮ { \mathbf{f}}_{{\mathrm{S}\mathrm{R}}_3} ⋮ \dots { \mathbf{f}}_{{\mathrm{S}\mathrm{R}}_i} \dots ⋮ {\mathbf{f}}_{{\mathrm{S}\mathrm{R}}_{{\mathrm{N}}_{\mathrm{S}\mathrm{R}\mathrm{g}\mathrm{n}}}-1} ⋮{ \mathbf{f}}_{{\mathrm{S}\mathrm{R}}_{{\mathrm{N}}_{\mathrm{S}\mathrm{R}\mathrm{g}\mathrm{n}}}} \right]}_{1\times {\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}},$$

(5)

where the $⋮$ symbol denotes vector concatenation, index i = 1, 2, …, N_SRgn, and ${\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}$ is the total number of fingerprint features. Considering the noted ${\mathrm{N}}_{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}=3$ statistical features (σ², γ, κ), the${ \mathbf{f}}_{\mathrm{S}\mathrm{R}i}$ in Equation (5) are calculated using ith sub-region samples according to

$${ \mathbf{f}}_{{\mathrm{S}\mathrm{R}}_i}={\left[{\mathsf{\sigma }}_{{\mathrm{S}\mathrm{R}}_i}^2{\mathsf{\gamma }}_{{\mathrm{S}\mathrm{R}}_i} {\mathsf{\kappa }}_{{\mathrm{S}\mathrm{R}}_i}\right]}_{1\times 3}.$$

(6)

This yields a total of ${\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}={\mathrm{N}}_{\mathrm{S}\mathrm{R}\mathrm{g}\mathrm{n}}\times {\mathrm{N}}_{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}\times {\mathrm{N}}_{\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{p}}$ features when substituting Equation (6) back into Equation (5) where ${\mathrm{N}}_{\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{p}}$ is the total number of instantaneous responses used (amplitude, phase, and/or frequency). Statistical DNA fingerprints generated per Equation (6) are the lowest-dimensional non-eventized fingerprints and require lower computational intensity (energy consumption) to perform classification.

2.3.2. Eventized Fingerprint Formation

The Eventized (Ev) classification assessments were performed using fingerprints formed directly from e(n) ∈ [−1 0 +1] assignments such as illustrated in the eventization vectors shown in Figure 2 and Figure 5. The eventized fingerprint is formed according to

$${\overrightarrow{\mathbf{F}}}_{\mathrm{E}\mathrm{v}}={\left[ \mathrm{e}\left(1\right) \mathrm{e}\left(2\right) \mathrm{e}\left(3\right)\dots \mathrm{e}\left(n\right) \dots \mathrm{e}\left({\mathrm{N}}_{\mathrm{E}\mathrm{v}}\right) \right]}_{1\times {\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}},$$

(7)

where n = 1, 2, …${\mathrm{N}}_{\mathrm{E}\mathrm{v}}={\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}$. Given a total number of${\mathrm{N}}_{\mathrm{E}\mathrm{v}}$ detected events, the nth fingerprint feature in Equation (7) is assigned as either (1) $\mathrm{e}\left(n\right)=+/-1$ for a Positive/Negative event or (2) $\mathrm{e}\left(n\right)=0$ when no event is detected. The ${\mathrm{N}}_{\mathrm{E}\mathrm{v}}$ events used to form the ${\overrightarrow{\mathbf{F}}}_{\mathrm{E}\mathrm{v}}$ fingerprint in Equation (7) equals either (1) the total number of 1D-TD eventized response samples, e.g., the total number of samples in Figure 4b, or (2) the total number of elements in the eventized 2D-GTX response, e.g., the total number of 2D-GTX elements (KTim × MFrq) in Figure 5d.

3. Device Classification

Both 1D-TD and 2D-GTX fingerprints were generated per Section 2.3 for the eventization methods in Section 2.2 and used to discriminate the WirelessHART devices listed in Table 1. For consistency with prior non-eventized DNA fingerprinting works [8,9,11,13,14,42,43], classification results are first generated for a Multiple Discriminant Analysis, Maximum Likelihood (MDA/ML) classifier adopted from these earlier works. Some fundamental details for MDA/ML processing are provided next in Section 3.1—the reader is referred to cited works therein for additional details. A Random Forest (RndF) classifier is then introduced and used to generate the primary results used for drawing conclusions related to similarity and/or differences between Non-Eventized (NonEv) and Eventized (Ev) fingerprinting performances. Fundamental details for the RndF classifier used here are provided below in Section 3.2—the reader is referred to cited works therein for additional details.

Regardless of the classification method used, the classification results reported herein are based on a classification confusion matrix, as illustrated in

Table 2. Classification confusing matrix for 2D-GTX derivative eventized fingerprints for an N_Cls = 8 class (device) classifier using N_TST = 1716 testing fingerprints per device. The bold diagonal entries are correct device estimates and yield an overall average cross-class percent correct of %C ≈ 95.38. The bottom row shows the individual per-class %C_Cls performance.

	Estimated Class (%)
Actual Class	D1	D2	D3	D4	D5	D6	D7	D8
D1	1708	2	5	0	0	0	0	1
D2	3	1695	13	0	0	3	0	2
D3	0	31	1677	0	0	7	1	0
D4	0	0	0	1695	2	0	19	0
D5	0	0	1	4	1630	64	14	3
D6	6	21	30	0	109	1494	9	47
D7	0	0	63	30	65	19	1539	0
D8	12	10	0	0	1	37	0	1656
%CCls	99.53%	98.78%	97.73%	98.78%	94.99%	87.06%	89.69%	96.50%

. This shows classification testing results using fingerprints for the 2D-GTX derivative eventization process illustrated in Figure 5. The entries are used to calculate the average cross-class percent correct %C, which is a less rigorous metric than that used herein to enhance appreciation for the work across a broader, cross-discipline readership [11]. A more detailed analysis of confusion matrix results for a multi-class classifier may be performed using the methods in [44]. The Table 2 classification results are for an N_Cls = 8 class (device) model using a total of N_TST = 1716 held-out testing fingerprints for each device. The sum of the bold diagonal entries is divided by the total number of trials represented in the confusion matrix to provide an estimated %C ≈ [13,094/(8 × 1716)] × 100 ≈ 95.38%. The last row in Table 2 also provides the per-class average percent correct %C_Cls, which is calculated using the number of correct estimates for the class divided by N_TST = 1716.

3.1. MDA/ML-Based Classification

The MDA/ML designation is used to reinforce that there are two fundamental processes involved, including MDA model development and ML class estimation. A few summary details of MDA and ML processing are provided here for completeness and are primarily taken from [11]. MDA is a multi-class (N_Cls > 2) form of Fisher’s linear discriminant processing. The process takes in N_TNG $\left(1\times {\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}\right)$-dimensional training fingerprints $\left({\mathbf{F}}_{\mathrm{T}\mathrm{N}\mathrm{G}}\right)$ and outputs an $\left[{\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}\times \left({\mathrm{N}}_{\mathrm{C}\mathrm{l}\mathrm{s}}-1\right)\right]$-dimensional projection matrix ($\mathbf{W}$) and training fingerprint statistics—the collection of ($\mathbf{W}$, μ_F, σ_F, μ_k, Σ_k) for k = 1, 2, …, N_Cls that is returned from MDA processing is known as the model.

The generation of $\mathbf{W}$ is analytically driven by optimization conditions that include the pool of input N_TNG fingerprint features being normally distributed. The resultant matrix $\mathbf{W}$ effectively projects the N_TNG fingerprints into an $\left({\mathrm{N}}_{\mathrm{C}\mathrm{l}\mathrm{s}}-1\right)$ decision space where the inter-class mean separation distance is maximized and the intra-class spread is minimized [45]. Given the trained MDA model, the MDA projection vector for a given testing fingerprint ${\mathbf{F}}_{\mathrm{U}}$, i.e., an “unknown” fingerprint for one of the classes that was not used for model development, the $\left({\mathrm{N}}_{\mathrm{C}\mathrm{l}\mathrm{s}}-1\right)$-dimensional projection vector is calculated using ${\mathbf{p}}_{\mathrm{U}}=\left[\left({\mathbf{F}}_{\mathrm{U}}-{\mathsf{\mu }}_{\mathbf{F}}\right)⨀{\mathsf{\sigma }}_{\mathbf{F}}^{-1}\right]\mathbf{W}$ where $⨀$ denotes a Hadamard product.

The resultant projection vector ${\mathbf{p}}_{\mathrm{U}}$ is used for class estimation, a one-versus-all best match assessment where ${\mathbf{p}}_{\mathrm{U}}$ is declared (rightly or wrongly) as coming from/belonging to the kth-class (k = 1, 2, …, NCls). The declaration of a class estimate can be made using many measures of similarity, including (1) a distance-based Euclidean distance measure where the class estimate is based on the minimum geometric distance between fingerprint projection ${\mathbf{p}}_{\mathrm{U}}$ and the model training class mean μ_k across all classes; and (2) probability-based measure where ${\mathbf{p}}_{\mathrm{U}}$ is mapped to the a-posterior probabilities (likelihoods) of all classes and the class yielding the maximum likelihood is the estimated class. When performed under Bayesian conditions of equal a priori probabilities for all classes and equal costs for making an estimation error, the resultant probability-based estimate is referred to as a Maximum Likelihood (ML) estimate.

3.2. RndF-Based Classification

For RndF classification decisions each “unknown” ${\mathbf{F}}_{\mathrm{U}}$ testing fingerprint is classified by each tree in the ensemble. The final output class estimate is made through a plurality vote, whereby the class receiving the most votes across the ensemble is declared as the estimate [46]—a majority of the ensemble classifiers do not have to agree with the estimate. This requires that a large ensemble of classifiers be used to ensure an unbiased and accurate classification estimate is made. In general, the use of more trees can increase classification performance but at the expense of increased estimation time. To minimize both bias and between-tree correlation across the ensemble, the trees can be grown to be full-length (maximum depth). For all RndF results presented in Section 4, the RndF classifier was implemented in a Python-based Scikit-Learn environment using the following:

• Number of Trees: 100;
• Epoch Termination Criterion: Gini Impurity;
• Maximum Tree Depth: None; resulting in full-length trees with pure leaves;
• Minimum Number of Fingerprints to Split: 2;
• Minimum Number of Fingerprints in a Leaf: 1;
• Number of features for random subspace selection: $\sqrt{{\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}}=\sqrt{1000}\approx 32$.

One unique benefit is that RndF processing enables the calculation and output of Gini index relevance values for all features. The Gini index value reflects the relative importance of a given feature on the final classification estimate—a higher Gini Index value indicates a greater influence on the final class estimate. Gini index ranking was successfully exploited in previous DNA-based fingerprinting work [12] using the same WirelessHART devices being used here. This work demonstrated fingerprint dimensional reduction that included Gini-based identification and removal of the lowest-ranked, most irrelevant 80% of the fingerprint features while sacrificing a marginal 1% < %C_Δ < 2% degradation in overall classification performance.

Representative Gini index values are presented in Figure 6 for an N_Cls = 8 RndF classifier using 1D-TD eventized fingerprints. The eventized fingerprints from Equation (7) included a total of N_Feat = 1000 features and an average number of detected Events-Per-Burst equaling N_EPB = 206 events—as introduced here the N_EPB average is calculated across eventized fingerprints for all N_Brst = 8576 bursts from each of the N_Dev = 8 devices. Figure 6a shows the sorted (highest-to-lowest) Gini values and Figure 6b shows the non-sorted Gini values for each feature index number. The feature-by-feature retention/removal of higher/lower significant features is clearly supported and suggests that the dimensional reduction benefit demonstrated in [12] may be realizable for the eventized fingerprints being considered here—this investigation remains a topic for future research.

4. Device Classification Results

Both 1D-TD and 2D-GTX fingerprints were generated per Section 5 and used to discriminate WirelessHART signals. For consistency with prior non-eventized DNA fingerprinting works [8,9,11,13,14,42,43], classification was first performed with a Multiple Discriminant Analysis, Maximum Likelihood (MDA/ML) classifier—the reader is referred to the noted references for MDA/ML-based device discrimination details. The RndF classifier detailed in Section 3.2 was then introduced and an MDA/ML vs. RndF classification comparison was performed.

Figure 7 shows classification results for both classifiers and N_Cls = N_Dev = 8 classes using both non-eventized (NonEv) 1D-TD and 2D-GTX DNA fingerprint features. The sets of N_FP = N_Brst = 8576 1D-TD and 2D-GTX DNA fingerprints per device were generated using Equations (5) and (6). The total number of available fingerprints was then divided into an 80% training subset and a 20% testing subset. Each subset was stratified and balanced to ensure an equal number of class representations. Ultimately, 54,880 fingerprints were used for training, and 13,728 fingerprints were used for testing.

For 1D-TD DNA fingerprinting results in Figure 7, the statistical ${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}$ fingerprints in Equation (6) were formed using (1) N_Resp = 3 (Amp, Phz, Frq) non-eventized burst responses; (2) N_SRgn = 16 fingerprinting regions per response; and (3) N_Stat = 3 statistics (σ², γ, κ) to form vectors per Equation (5). The statistical vectors from Equation (6) were used in Equation (5) to form the final composite ${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{1\mathrm{D}-\mathrm{T}\mathrm{D}}={\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}$ fingerprints. The resultant ${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{1\mathrm{D}-\mathrm{T}\mathrm{D}}$ fingerprints used for Figure 7 results had a total of ${\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}^{1\mathrm{D}-\mathrm{T}\mathrm{D}}=3\times 16\times 3=144$ features.

For 2D-GTX DNA fingerprinting results in Figure 7, the statistical ${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}$ fingerprints in Equation (5) were formed by (1) dividing non-eventized 2D-GTX matrices into$\left({{\mathrm{N}}_{\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{B}\mathrm{l}\mathrm{k}}\times \mathrm{N}}_{\mathrm{F}\mathrm{r}\mathrm{q}\mathrm{B}\mathrm{l}\mathrm{k}}\right)$-dimensional sub-matrices where ${\mathrm{N}}_{\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{B}\mathrm{l}\mathrm{k}}$ and ${\mathrm{N}}_{\mathrm{F}\mathrm{r}\mathrm{q}\mathrm{B}\mathrm{l}\mathrm{k}}$ denote the number of time and frequency blocks, respectively; (2) calculating N_Stat = 3 statistics (σ², γ, κ) for each of the $\left({\mathrm{N}}_{\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{B}\mathrm{l}\mathrm{k}}=9\right)\times \left({\mathrm{N}}_{\mathrm{F}\mathrm{r}\mathrm{q}\mathrm{B}\mathrm{l}\mathrm{k}}=6\right)=54$sub-matrices; and (3) forming the statistical feature vectors per Equation (6). The statistical vectors from Equation (6) were used in Equation (5) to form the final composite ${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}={\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}}$ fingerprints. The resultant ${\overrightarrow{\mathbf{F}}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}$ fingerprints used for Figure 7 results had a total of ${\mathrm{N}}_{\mathrm{F}\mathrm{e}\mathrm{a}\mathrm{t}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}=9\times 6\times 3=162$ features.

In light of next-step performance assessments in the following sub-sections using eventized fingerprints, there are two conclusions to be considered from Figure 7:

• 2D-GTX fingerprinting outperforms 1D-TD fingerprinting for both classifiers across a majority of the SINR ≥ 10.5 dB considered—the 2D-GTX vs. 1D-TD benefit here is consistent with prior 2D-GTX DNA fingerprinting findings [8,42,43];
• For best-case 2D-GTX fingerprints, MDA/ML (unfilled ★) outperforms RndF (unfilled ✶) by an average of ${\mathrm{\%}\mathrm{C}}_{∆}^{\mathrm{G}\mathrm{T}\mathrm{X}-\mathrm{T}\mathrm{D}}\approx +2.97\mathrm{\%}$ across the range of SINR(dB) considered. This includes operating under lower ${\mathrm{S}\mathrm{I}\mathrm{N}\mathrm{R}}_{∆}^{\mathrm{G}\mathrm{T}\mathrm{X}-\mathrm{T}\mathrm{D}}\approx -4 \mathrm{d}\mathrm{B}$ channel conditions to achieve an arbitrary performance benchmark of %C = 90%.

In transitioning to eventized classification performance results in the following sub-sections, it is noted that the eventized ${\overrightarrow{\mathbf{F}}}_{\mathrm{E}\mathrm{v}}$ fingerprints are formed using Equation (7) and contain zero-valued elements. Thus, the statistical distribution of eventized fingerprint features is binary and not well-suited for MDA/ML classification—the development of MDA models and classification performance is dependent upon the input features being normally distributed. This is accounted for in MDA projection matrix formation, which requires the inversion of a composite input fingerprint matrix. As the number of zero-valued fingerprint features increases, the matrix becomes non-invertible (determinant approaches zero) and projection matrix formation is not possible. Thus, all results in the following sub-sections were obtained using an RndF classier with the parameters noted in Section 3.2.

4.1. Eventized Classification

Classification performance using 1D-TD and 2D-GTX eventized fingerprints was next considered for the eventization methods detailed in Section 2.2. The results were generated using the same RndF classifier detailed in Section 3.2 and used for the non-eventized results in Figure 7. The 1D-TD vs. 2D-GTX RndF classification results are presented in Figure 8. The eventized ${\overrightarrow{\mathbf{F}}}_{\mathrm{E}\mathrm{v}}^{1\mathrm{D}-\mathrm{T}\mathrm{D}}$ and ${\overrightarrow{\mathbf{F}}}_{\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}$ fingerprints were formed using Equation (7) for each of the Direct, Derivative, and Integral eventization methods considered. The fingerprint features included the detected eventization values (−1, +1) such as those illustrated in Figure 4b (TD-DNA) and Figure 5d (GTX-DNA), and zero values at remaining indices where no event is detected.

One operational implementation objective includes minimizing the number of fingerprint features, which in turn minimizes the required computational resources. This is supported by (1) setting eventization thresholds to minimize the number of detected Events-Per-Burst (N_EPB), while (2) achieving a given %C classification performance. As indicated in

Table 3. Method-dependent threshold values and resultant minimum N_EPB required to achieve the indicated maximum %C classification performance.

Eventization Method		Threshold (Thr)	Minimum NEPB	Maximum %C
1D-TD	Direct (●)	0.60	482	89.71
	Integral ()	0.40	368	74.77
	Derivative ()	0.60	295	87.43
2D-GTX	Direct (◆)	0.05	738	92.06
	Derivative (■)	0.10	526	91.62

, the resultant N_EPB and %C classification performance is a function of the eventization method employed (method-dependent) and the specific threshold value (threshold-dependent) used with a given method. The results in Table 3 are a selected subset of results obtained for a range of empirical thresholds spanning 0.01 < Thr < 0.75 in ΔThr = 0.05 increments. Table 3 shows the threshold value yielding the minimum N_EPB to achieve the maximum asymptotic %C for that threshold. As first used in Table 3, the color coded symbology for the various eventization methods is retained throughout the remainder of the paper in tables and figures to assist in tracking per-method performances.

The %C classification results in Figure 8 were obtained for the indicated average (cross-burst, cross-device) number of N_EPB using a given eventization method. Relative to achieving a minimum N_EPB demonstration objective, there are several conclusions drawn from Figure 8.

• The 1D-TD Integral () fingerprinting performance does not achieve the arbitrary performance benchmark of %C = 90% for all 50 < N_EPB < 900 considered—integral-based eventization was henceforth removed from further consideration;
• The 1D-TD Direct (●) fingerprinting performance is second-best and approaches the %C = 90% benchmark for N_EPB > 480. Of note here is the poorer performing 1D-TD Derivative () fingerprints, which do achieve the %C = 90% benchmark for any N_EPB considered. Thus, the penalty in classification performance for taking a time domain derivative is severe, and the computational cost for doing so should be avoided;
• The 2D-GTX Derivative (■) fingerprinting performance is best overall across the entire range of 50 < N_EPB < 850 considered. This includes the %C = 90% benchmark being achieved for N_EPB > 380 detected events—the previously demonstrated benefit of eventized over non-eventized fingerprinting in Figure 7 is retained.

The classification performance for both 1D-TD () and 2D-GTX (■) Derivative fingerprints is statistically equivalent over an approximate range of 50 < N_EPB < 215. For N_EPB > 215, the 2D-GTX (■) derivative fingerprints provide a clear benefit that includes an increase in performance of 1% < %C_Δ < 12.2%. This benefit is realized at the expense of performing one additional processing step that included taking a row-wise derivative of the input GTX matrix before performing eventization. There are other processing alternatives that may be considered (e.g., a column-wise derivative) to achieve similar or even greater benefit—alternatives remain on the list for future consideration.

4.2. Non-Eventized vs. Eventized Classification

To directly highlight the effect of eventization on device classification performance, a comparison of Non-Eventized (NonEv) vs. Eventized (Ev) RndF classification was performed. As presented in Figure 9, the comparisons were performed for SINR = 16.5 dB channel conditions using eventized fingerprints based on N_EPB = 600 events. A selection of these values is based on RndF achieving the %C = 85% benchmark, with SINR selected from Figure 7 and N_EPB selected from Figure 8 where all fingerprinting methods achieved the benchmark. The performance degradation resulting from eventization is reflected in the eventization difference metric ${\mathrm{\%}\mathrm{C}}_{∆\mathrm{E}\mathrm{v}}\equiv {\mathrm{\%}\mathrm{C}}_{\mathrm{E}\mathrm{v}}-{\mathrm{\%}\mathrm{C}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}$ shown in

Table 4. Comparison of non-eventized and eventized classification performance is shown in Figure 9 for each of the eventization methods considered.

Eventization Method		${\mathbf{\%}\mathbf{C}}_{\mathbf{N}\mathbf{o}\mathbf{n}\mathbf{E}\mathbf{v}}$	${\mathbf{\%}\mathbf{C}}_{\mathbf{E}\mathbf{v}}$	${\mathbf{\%}\mathbf{C}}_{∆\mathbf{E}\mathbf{v}}$
1D-TD	Direct (●)	90.22	89.50	−0.72
	Integral ()	80.55	75.60	−4.95
	Derivative ()	88.02	87.00	−1.02
2D-GTX	Direct (◆)	90.70	95.66	−4.96
	Derivative (■)	92.50	95.38	−2.88

where ${\mathrm{\%}\mathrm{C}}_{\mathrm{E}\mathrm{v}}$ is the performance using eventized fingerprints and ${\mathrm{\%}\mathrm{C}}_{\mathrm{N}\mathrm{o}\mathrm{n}\mathrm{E}\mathrm{v}}$ is the performance using non-eventized fingerprints.

As indicated in Table 4 ${\mathrm{\%}\mathrm{C}}_{∆\mathrm{E}\mathrm{v}}$ results, all eventization methods degraded performance to some degree with the GTX-based eventization methods degrading performance by ${\mathrm{\%}\mathrm{C}}_{∆\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{D}\mathrm{i}\mathrm{r}}\approx -4.96\mathrm{\%}$ and ${\mathrm{\%}\mathrm{C}}_{∆\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{D}\mathrm{e}\mathrm{r}}\approx -2.88\mathrm{\%}$. It is not unreasonable to expect that this level of degradation will ultimately be acceptable when considering other benefits provided by eventization. For example, achieving the %C = 90% benchmark in Figure 8 requires N_EPB ≈ 380 events using the 2D-GTX derivative ${\overrightarrow{\mathbf{F}}}_{\mathrm{D}\mathrm{e}\mathrm{r}-\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}$ fingerprints that include an average of (N_S = 1250) − (N_EPB ≈ 380) = 870 zero-valued elements. It is envisioned that a form of dimensional reduction (compression) may be possible for the derivative ${\overrightarrow{\mathbf{F}}}_{\mathrm{D}\mathrm{e}\mathrm{r}-\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}$ fingerprints by removing zero-valued elements that are common across the pool of device fingerprints being used. If this can be done, there will be an approximate [(1250 − 380)/1250] × 100 ≈ 70% reduction in the number of eventized fingerprint features—this would decrease the computational processing requirements and may sufficiently offset the $-3\%<{\mathrm{\%}\mathrm{C}}_{∆\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{D}\mathrm{e}\mathrm{r}}<-4\mathrm{\%}$ loss observed here with the RndF classifier. Furthermore, this level of degradation is considered marginal in light of the energy savings demonstrated by using SNN classification architectures [15].

5. Summary and Conclusions

This paper summarizes first-step research activity aimed at realizing an envisioned “event radio” capability that mimics neuromorphic event-based camera processing. The energy efficiency of neuromorphic processing is orders of magnitude higher than traditional von Neumann-based processing architectures (10× to 1000× [17,18,19]) and realized through synergistic design of brain-inspired software [47] and hardware [22] computing elements. The development and availability of event-based hardware devices supporting Radio Frequency (RF) applications are severely lagging when compared with activity in the event-based camera arena. Despite this lag, there remains considerable interest across the technical community in obtaining neuromorphic efficiency benefits through event-based RF signal processing. For the Operational Technology (OT) protection needs addressed here, this processing includes efficient software computing capability to provide reliable device classification.

While not envisioned as the final solution, a Random Forest (RndF) classifier is first considered here as a reliable precursor to using a Convolutional Neural Network (CNN) classifier, which is, in turn, a precursor to eventual demonstrations using the desired neuromorphic-friendly Spiking Neural Network (SNN) classifier. The event-based RF fingerprints used for RndF device classification were generated from experimentally collected signals for N_Dev = 8 WirelessHART devices. The signals were pre-conditioned prior to fingerprint generation to induce the generally adverse effects of Cross-Channel Interference (CCI). The induced CCI is a result of the N_Dev = 8 devices simultaneously operating in N_Ch = 8 different FH-TDMA network channels [14]. For completeness, classification performance for non-eventized fingerprints was performed as well and used as a baseline for characterizing the effects of eventization on classifier performance. The average %C correct classification results show the following:

• 2D-GTX non-eventized fingerprinting performs best with an MDA/ML classifier across the range of the 6.5 < SINR< 26.5 dB considered;
• 2D-GTX eventized derivative fingerprinting performs best with a RndF classifier under SINR = 16.5 dB channel conditions across the range of the 50 < N_EPB < 900 considered;
• 2D-GTX derivative-based eventization suffers a marginal performance penalty of ${\mathrm{\%}\mathrm{C}}_{∆\mathrm{E}\mathrm{v}}^{2\mathrm{D}-\mathrm{G}\mathrm{T}\mathrm{X}}\approx -2.88\mathrm{\%}$ when compared with non-eventized performance;
• An arbitrary performance benchmark of %C ≥ 90% is achieved under SINR = 16.5 dB channel conditions using an average of N_EPB ≥ 400 detected events per burst.

While RndF is not envisioned as being the final solution for achieving neuromorphic benefits in an event radio, the 2D-GTX eventized classification performance is promising and sufficiently motivates next-step demonstration activity, which includes (1) fingerprint dimensional reduction (compression) supported using rank-ordered RndF Gini feature relevance values such as illustrated in Figure 6—such a reduction minimizes the required computational generation, storage, transfer, complexity, etc.; and (2) transitioning to a Convolutional Neural Network (CNN) classifier as a precursor to near-end-game demonstrations using the desired neuromorphic-friendly Spiking Neural Network (SNN) classifier—RndF performance has historically provided a reliable baseline for highlighting the classification improvement that is achievable using a CNN classifier with similarly structured signals. It is believed that classification performance will remain favorable and represent one significant step toward identifying the software computing elements required to implement an event radio. It is also hoped that this will motivate researchers and designers to develop complementary hardware computing elements so that the full benefits of neuromorphic processing may be realized in the envisioned event radio.