Active 2D-DNA Fingerprinting of WirelessHART Adapters to Ensure Operational Integrity in Industrial Systems

The need for reliable communications in industrial systems becomes more evident as industries strive to increase reliance on automation. This trend has sustained the adoption of WirelessHART communications as a key enabling technology and its operational integrity must be ensured. This paper focuses on demonstrating pre-deployment counterfeit detection using active 2D Distinct Native Attribute (2D-DNA) fingerprinting. Counterfeit detection is demonstrated using experimentally collected signals from eight commercial WirelessHART adapters. Adapter fingerprints are used to train 56 Multiple Discriminant Analysis (MDA) models with each representing five authentic network devices. The three non-modeled devices are introduced as counterfeits and a total of 840 individual authentic (modeled) versus counterfeit (non-modeled) ID verification assessments performed. Counterfeit detection is performed on a fingerprint-by-fingerprint basis with best case per-device Counterfeit Detection Rate (%CDR) estimates including 87.6% < %CDR < 99.9% and yielding an average cross-device %CDR ≈ 92.5%. This full-dimensional feature set performance was echoed by dimensionally reduced feature set performance that included per-device 87.0% < %CDR < 99.7% and average cross-device %CDR ≈ 91.4% using only 18-of-291 features—the demonstrated %CDR > 90% with an approximate 92% reduction in the number of fingerprint features is sufficiently promising for small-scale network applications and warrants further consideration.


Introduction
The adoption of wireless technologies is an ongoing trend that has "major implications" for achieving Internet of Things (IoT), Industrial Internet of Things (IIoT), and Fourth Industrial Revolution (IR 4.0) objectives [1]. Among the objectives is a desire to minimize or entirely eliminate human intervention through increased reliance on automation [2]. This includes using real-world virtualization in industrial system frameworks that integrate IoT/IIoT devices, computation, networking, and physical processes [3]. While the inherent efficiencies, cost savings, etc., brought about by hands-off automation, are certainly desirable, benefits are only realized if the supporting devices achieve their full life expectancy [4] and operational cyber security risks are mitigated. These risks include an increase in the number of wireless doorways for entering the operational attack surface that has expanded with the adoption and networked integration of IoT/IIoT devices [5]. This is particularly important when considering the potential for catastrophic failure in applications involving safety and the potential loss of life.
There have been decades of research and demonstration activity addressing the use of Radio Frequency Fingerprinting (RFF) to provide post-deployment operational protection of fielded electronic, electrical, and electromechanical devices. The various RF fingerprint features, extraction methods, and discrimination algorithms considered are aptly summarized by the most recent review provided in [6]. From the RF fingerprinting

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Operation based on the legacy wired HART protocol-users can take full advantage of prior experience, prior training, prior tool purchases, etc.; • Considerable reduction in deployment, installation, and maintenance cost-minimal to no additional infrastructure cabling required; • Network architectural flexibility-expansion easily accommodated by adding connectivity to additional field devices and/or other nearby networks; • Dramatic reduction in device commissioning times-device benchtop programing and field installation completed in hours versus days.
The demonstrations here are based on WirelessHART signaling given its widespread adoption and use to achieve IoT/IIoT and IR 4.0 objectives. The focus here is on relatively small-scale networks consisting of a gateway and five or more field devices. A five-device network configuration provides "sufficiently redundant mesh network operation" [22] while taking advantage of architectural flexibility to provide the required sub-network and cross-network interconnectivity within a "classical Industrial Wireless Sensor Network (ISWN) architecture" [2]. As with large-scale networks, care must be taken in small-scale WirelessHART networks supporting critical applications involving personnel safety. This is particularly important when considering the hundreds-of-thousands of WirelessHART devices that enter the supply chain annually [22].
As with all electronic devices (integrated circuits, circuit boards, sub-assemblies, etc.) entering the supply chain, there is concern that operational integrity may be compromised through the introduction of counterfeits. The extent of compromised device effects ranges from degraded functionality (slow, sluggish, inefficient operation) to premature failure (lifecycle termination)-both manifesting possible catastrophic results. The potential for this occurring can be minimized by employing near-cradle [4] pre-deployment protection measures to detect devices that have been intentionally modified or counterfeited before placing them into service. Near-cradle counterfeit protection is at one lifecycle extreme and includes two fundamentally different Radio Frequency (RF) methods: (1) active RF Identification (RFID) that exploits interrogated responses of onboard functionality that is intentionally embedded at the time of manufacture [23,24], and (2) active RF-DNA fingerprinting that exploits inherent response uniqueness resulting from component, device architecture, and manufacturing process differences [18][19][20][21].

Technical Motivation
The development and demonstration of active DNA fingerprinting methods in [19,21] to support pre-deployment protection was complementary to prior passive DNA fingerprinting works supporting post-deployment operational protection [4,11,12,[14][15][16][17]. The distinction between passive and active DNA fingerprinting is not based on device operating conditions but rather the DNA generation process employed. Passive DNA fingerprinting uses features extracted from transmitted responses (wired or wireless) of an operating device that is physically connected within a system and performing its intended function-passive DNA fingerprinting is a method for providing operational protection during a device's technical lifecycle [4]. Active DNA fingerprinting uses features extracted from externally stimulated device responses of an uninstalled non-operably connected device-active DNA fingerprinting is a method for providing near-cradle protection at the onset of a device's technical lifecycle [4].
Active DNA fingerprinting was pursued here given prior success in microwave system state estimation [18,20] and integrated circuit discrimination [21]. These previous works demonstrated benefits for using wideband (energy spanning 100s to 1000s of MHz) stimulation signals as a means to increase source-to-device electromagnetic interaction and induce fingerprint feature variability and uniqueness. The degree of source-to-device interaction is fundamentally driven by the stimulating signal characteristics (e.g., time varying amplitude, phase, and/or frequency), the device's electrical/electronic architecture complexity, and resultant higher-order multi-frequency intermodulation effects. The active DNA fingerprinting work in [21] introduced a wideband Stepped Frequency Modulated (SFM) stimulus signal that was subsequently adopted for WirelessHART adapter discrimination work in [19]. The active DNA work in [19] considered discrimination of the same four Siemens AW210 [25] and four Pepperl+Fuchs Bullet [26] WirelessHART adapters used for passive DNA discrimination assessments in [4,14].
The active DNA fingerprinting work in [19] used an SFM stimulus signal with onedimensional DNA (1D-DNA) features extracted from instantaneous time domain device responses. Considering the eight available WirelessHART adapters, 8-choose-6 = 28 different 6-class Multiple Discriminant Analysis (MDA) models were developed to represent six authentic devices. The two held-out devices were introduced as counterfeits, and a total of 28 × 6 × 2 = 336 individual counterfeit device ID verification assessments performed. Collectively considering all 28 models and the 336 individual assessments, a Counterfeit Detection Rate of %CDR ≈ 92% was demonstrated. While community feedback for work in [19] was generally favorable, there was also a clear desire to improve upon the demonstrated %CDR to better support operational motivation objectives, i.e., decrease the number of counterfeit devices installed in the field and increase the pool of certified devices that may be introduced into the supply chain.
To improve %CDR, alternate DNA features were considered here using the experimentally collected WirelessHART device responses from [19]. It was observed that non-coherent phase transitions occur as the SFM source stimulus transitions between frequency steps. These transitions appear as time domain transients in the device output responses. Thus, two-dimensional DNA (2D-DNA) features are considered here using a Gabor Transform (GT), given its prior success in [13] for signals exhibiting similar transient effects, and to obtain signal information based on the local distribution of signal energy as a function of frequency. Demonstrations are performed here in light of targeting small-scale (e.g., five sensors) IoT/IIoT and IR 4.0 implementations. Relative to results in [19], demonstrations here are based on (1) a total of 8-choose-5 = 56 different 5-class MDA models-factorof-2 increase in the number of models, with (2) three held-out counterfeit devices per model used to perform 56 × 5 × 3 = 840 individual counterfeit device ID verification assessments-factor-of-2.5 increase in the number of counterfeit assessments.

Demonstration Methodology
This section presents details for the sequence of steps taken to conduct experimental demonstrations and generate the results presented in Section 3. Summary details are provided for each step in the indicated subsection. These steps include: Dimensional Reduction Analysis (DRA) in Section 2.5-this includes final actions taken to reduce the number of fingerprint features required to achieve a given level of discrimination performance while improving computational efficiency;

Response Collection and Processing
The experimentally collected signals used here for demonstration were originally collected in support of work reported in [19] using the setup shown in Figure 1. The basic setup was adopted from integrated circuit anti-counterfeiting work originally developed and demonstrated in [21] and includes three main hardware elements: (1) a Keysight N5222B PNA microwave network analyzer [27] used to provide the DUT input stimulus s IN (t), (2) a LeCroy WaveMaster 825Zi-A oscilloscope [28] used to collect the DUT output response s OUT (t), and (3) a WirelessHART adapter serving as the DUT. The N5222B source parameters were set to produce the SFM stimulus signal s SFM (t) which was power divided and input as s IN (t) to 1-of-5 available DUT wires denoted as W j IN for j∈{1, 2, . . . , 5}. Given a goal of maximizing the SFM source-to-DUT electromagnetic interaction and increasing DUT discrimination, the SFM stimulus parameters were empirically determined based on discrete settings available on the N5222B analyzer. The resultant SFM parameters used for experimental collection included [19] (1) a total of N SFM = 9 frequency steps spanning a total frequency range of approximately 400 MHz < f < 450 MHz, with (2) the duration of each frequency step being T ∆ = 0.125 ms for a total SFM pulse duration of T SFM = 1.125 ms. The DUT s OUT (t) response was collected by the 825Zi-A oscilloscope, digitized, and stored for subsequent post-collection processing.
For the SFM stimulus applied to a given W For the SFM stimulus applied to a given W for j∈{1, 2, …, 5}, the DUT outp sponse ( ) was collected from one of the remaining wires, denoted as W 2, …, 5} for k ≠ j. Given there are five connection wires on the WirelessHART ada there are 20 order-matters permutations of W : W (stimulus input versus outp sponse) wire pairs that could be considered for active DNA fingerprinting. Demo tions here are based on collections made in [19], with W being the device Direct connecting wire and W being the device HART Signal connecting wire. It was e ically determined that this wire pair consistently yielded discernable device respons consistent fingerprint features across all eight experimental devices.
To reduce computational complexity and improve device discrimination rela results reported in [19], additional pre-fingerprint generation processing was intro here. For each collected device response, the sequential pre-fingerprint generatio cessing included (a) BandPass (BP) filtering at the as-collected center frequency o 425 MHz using a 16th-order Butterworth filter having a passband of WBP = 50 MH Down-Conversion (D/C) to near-BaseBand (BB) using a frequency of fD/C = 375 MH post-D/C BP filtering at a center frequency of fCtr = 50 MHz using a 16th-order Butter filter having a passband of WBP = 50 MHz, and (d) sample decimation by a factor o Thus, each of the as-received WirelessHART responses at a sample rate of fS = 1 (1,115,000 samples per pulse) were converted to an fS = 200 MSps rate (230,000 sa per pulse) prior to fingerprint generation.
The impact of pre-fingerprint generation processing for a representative lessHART response is shown in Figure 2. This processing was performed for colle from each of the NDev = 8 WirelessHART adapters (D1, D2, …, D8) listed in Table  hough the Siemens AW210 [25] and Pepperl+Fuchs Bullet [26] device labels make pear that the devices are from two different manufacturers, it was determined tha Experimental setup similar to that used in [19] for collecting WirelessHART DUT responses used for active DNA fingerprint generation.
To reduce computational complexity and improve device discrimination relative to results reported in [19], additional pre-fingerprint generation processing was introduced here. For each collected device response, the sequential pre-fingerprint generation processing included (a) BandPass (BP) filtering at the as-collected center frequency of f Col = 425 MHz using a 16th-order Butterworth filter having a passband of W BP = 50 MHz, (b) Down-Conversion (D/C) to near-BaseBand (BB) using a frequency of f D/C = 375 MHz, (c) post-D/C BP filtering at a center frequency of f Ctr = 50 MHz using a 16th-order Butterworth filter having a passband of W BP = 50 MHz, and (d) sample decimation by a factor of five. Thus, each of the as-received WirelessHART responses at a sample rate of f S = 1 GSps (1,115,000 samples per pulse) were converted to an f S = 200 MSps rate (230,000 samples per pulse) prior to fingerprint generation.
The impact of pre-fingerprint generation processing for a representative WirelessHART response is shown in Figure 2. This processing was performed for collections from each of the N Dev = 8 WirelessHART adapters (D1, D2, . . . , D8) listed in Table 1. Although the Siemens AW210 [25] and Pepperl+Fuchs Bullet [26] device labels make it appear that the devices are from two different manufacturers, it was determined that these devices are actually from the same manufacturer and were distributed under two different labels with dissimilar serial number sequencing-this difference is a result of company ownership transition to Pepperl+Fuchs. Thus, the discrimination conditions being considered represent the most challenging, like-model intra-manufacturer conditions using identical hardware devices that vary by serial number. Table 1 shows that the devices were received with two different versions of operating firmware-the firmware version number is available when the devices are connected to the gateway. In an attempt to remove firmware as an experimental variable, the manufacturer was contacted about having the D1 and D3 devices reprogrammed with the version 200 firmware. Researchers were told that this was not a customer support option and thus firmware remained as an uncontrolled experimental variable. As supported by results presented here in Section 3 and previous related work [4,14,19] using these same devices, there is no correlation between firmware version and device discriminability.   Table 1 shows that the devices were received with two different versions of ope firmware-the firmware version number is available when the devices are connec the gateway. In an attempt to remove firmware as an experimental variable, the ma turer was contacted about having the D1 and D3 devices reprogrammed with the v 200 firmware. Researchers were told that this was not a customer support option an firmware remained as an uncontrolled experimental variable. As supported by r presented here in Section 3 and previous related work [4,14,19] using these same d there is no correlation between firmware version and device discriminability.

1D Time Domain DNA (TdDna) Fingerprint Generation
The time domain DNA (TdDna) fingerprint generation process used he evolved over time and has been predominantly used in wireless passive DNA finge ing applications [4,[13][14][15]18]. Selected process details are presented here for complet and the reader is referred to [4] for more details. Statistical fingerprint features are lated from instantaneous responses of the down-converted, bandpass filtered, near

1D Time Domain DNA (TdDna) Fingerprint Generation
The time domain DNA (TdDna) fingerprint generation process used here has evolved over time and has been predominantly used in wireless passive DNA fingerprinting applications [4,[13][14][15]18]. Selected process details are presented here for completeness, and the reader is referred to [4] for more details. Statistical fingerprint features are calculated from instantaneous responses of the down-converted, bandpass filtered, near-baseband pulses such as illustrated in Figure 3. Denoting the real-valued sample sequence as {s Out (n)}, the fingerprinted responses include instantaneous (1) magnitude calculated as M(n) = |s Out (n)}|, (2)

2D Gabor Transform DNA (GtDna) Fingerprint Generation
Consideration of Gabor transform features is motivated by related historical [12,13,[31][32][33] that considered detection, characterization and exploitation of transien nonlinear effects in time varying signals. These effects are manifest in the Gabor tran space as localized signal energy distributions that vary as a function of frequency N5222B source inherently produces an SFM pulse having a non-uniform amplitud sponse across time. As evident in Figure 3, this variation is generally preserved i device output response although altered by the SFM-to-DUT interaction. Empirical ysis showed that response amplitude transitions at all step boundaries correspond instantaneous phase transients that randomly varied at each boundary on a puls pulse basis for all devices. Thus, device responses here possess transient characte consistent with those considered in [12,13,31,32], and the Gabor transform was deem be a reasonable first choice for 2D DNA fingerprint generation.
The mk th Gabor transform coefficient for sampled signal s(n) is given by [12,13,   A Region Of Interest (ROI) within {s Out (n)} is selected and the corresponding instantaneous {M(n)}, {Θ(n)} and {Φ(n)} response sequences are divided into N Rgn subregions for statistical feature calculation. This is illustrated in Figure 3, which shows the {M(n)} magnitude response for the representative pulse shown in Figure 2. Considering the calculation of three statistics (variance, skewness and kurtosis [30]) using samples within each of the N Rgn = 12 indicated subregions, and across all samples within entire ROI as well, the time domain fingerprints include a total of N FD,TD = (12+ 1) × 3 × 3 = 117 features when accounting for the three instantaneous {M(n)}, {Θ(n)} and {Φ(n)} response sequences.

2D Gabor Transform DNA (GtDna) Fingerprint Generation
Consideration of Gabor transform features is motivated by related historical work [12,13,[31][32][33] that considered detection, characterization and exploitation of transient and nonlinear effects in time varying signals. These effects are manifest in the Gabor transform space as localized signal energy distributions that vary as a function of frequency. The N5222B source inherently produces an SFM pulse having a non-uniform amplitude response across time. As evident in Figure 3, this variation is generally preserved in the device output response although altered by the SFM-to-DUT interaction. Empirical analysis showed that response amplitude transitions at all step boundaries corresponded to instantaneous phase transients that randomly varied at each boundary on a pulse-by-pulse basis for all devices. Thus, device responses here possess transient characteristics consistent with those considered in [12,13,31,32], and the Gabor transform was deemed to be a reasonable first choice for 2D DNA fingerprint generation.
The mk th Gabor transform coefficient for sampled signal s(n) is given by [12,13,31,33] where W(n) is a given synthesis window of width W τ , * denotes complex conjugate, m = 1, 2, . . . , M T , where M T is the total number of time index shifts, k = 0, 1, . . . , M F -1, where M F is the total number of frequency index shifts, and N ∆ is the number of samples shifted between transformations. Additional parameter constraints for the Gabor transform given by (1) include M F ≥ N ∆ and mod(M T × N ∆ , M F ) = 0. Consistent with [12,13,31], an energy normalized Hamming window was used for W(n).
The utility of Gabor transformation for highlighting transients and localizing energy concentration is evident by comparing the conventional spectrogram response in Figure 4 with the Gabor transform response in Figure 5. These responses are shown using the same color bar scale (dB) and were generated using the representative SFM response used for Figure 3. The Gabor transform response was generated using a window width of W τ = 1 × 10 −3 , N ∆ = 460, M T = 500, and M F = 500 for a resultant (M T × N ∆ )/M F = 460. As implemented here, the transformation for M F = 500 > N ∆ = 460 represents oversampling conditions, which are generally desirable when processing noisy data [31,33].
The utility of Gabor transformation for highlighting transients and localizing concentration is evident by comparing the conventional spectrogram response in 4 with the Gabor transform response in Figure 5. These responses are shown u same color bar scale (dB) and were generated using the representative SFM respon for Figure 3. The Gabor transform response was generated using a window width 1 × 10 -3 , NΔ = 460, M T = 500, and M F = 500 for a resultant (M T × NΔ)/M F = 460. As imple here, the transformation for M F = 500 > NΔ = 460 represents oversampling condition are generally desirable when processing noisy data [31,33]. Relative to the spectrogram response, it is evident in Figure 5 that the highes of Gabor localization occurs around 3-of-9 frequency step regions (k = 55, 82, 10 moderate degree of localization occurs around extreme frequency step regions 136). The Gabor localization effects are also evident by comparing low energy t quency regions where the Gabor response exhibits a more distinct structure.   Relative to the spectrogram response, it is evident in Figure 5 that the highes of Gabor localization occurs around 3-of-9 frequency step regions (k = 55, 82, 10 moderate degree of localization occurs around extreme frequency step regions 136). The Gabor localization effects are also evident by comparing low energy t quency regions where the Gabor response exhibits a more distinct structure.   Relative to the spectrogram response, it is evident in Figure 5 that the highest degree of Gabor localization occurs around 3-of-9 frequency step regions (k = 55, 82, 109) and a moderate degree of localization occurs around extreme frequency step regions (k = 28, 136). The Gabor localization effects are also evident by comparing low energy time-frequency regions where the Gabor response exhibits a more distinct structure. Representative examples of this include the response regions bounded within (1) k ∈ {20, 21, . . . , 58} and m ∈ {175, 176, . . . , 500}, and (2) k ∈ {70, 71, . . . , 116} and m ∈ {1, 2, . . . , 175}.
The Gabor transform features are generated from a given 2D Gabor transform response, e.g., the normalized magnitude response such as shown in Figure 5. As shown in Figure 6, a fingerprinting ROI is identified and divided into N Tim × N Frq 2D subregions (patches), where N Tim and N Frq are the number of time dimension and frequency dimension indices defining each patch. Fingerprint generation indexing is set such that the ROI is uniformly divided into N TimBlcks and N FrqBlcks along the time and frequency dimensions. Figure 6 shows the overlay of ROI patches used here for generating demonstration results.

Sensors 2022, 22, x FOR PEER REVIEW
The Gabor transform features are generated from a given 2D Gabor transf sponse, e.g., the normalized magnitude response such as shown in Figure 5. As s Figure 6, a fingerprinting ROI is identified and divided into NTim × NFrq 2D sub (patches), where NTim and NFrq are the number of time dimension and frequency sion indices defining each patch. Fingerprint generation indexing is set such that is uniformly divided into NTimBlcks and NFrqBlcks along the time and frequency dim Figure 6 shows the overlay of ROI patches used here for generating demonstration The ROI overlay in Figure 6 was generated using NTimBlcks = 8 and NFrqBlcks = 9 total number of NTim = 55 and NFrq = 12 indices defining the block time-frequency Thus, there are a total of NPtch = 8 × 9 = 72 total time-frequency patches with eac containing a total of 55 × 12 = 660 elements. Fingerprint statistics (variance, skewn kurtosis statistics [30]) were calculated using elements within each of the NPtch = 72 and across all ROI elements as well, such that the resultant Gabor transform DNA prints included a total of NFD-GT = (72 + 1) × 3 = 219 statistical features.

Multiple Discriminant Analysis (MDA)
The MDA-based discrimination methodology used here was primarily adopt related work in [4] that exploited passive DNA features and work in [19] that e passive DNA features. Both of these earlier works considered the same NDev = lessHART adapters shown in Table 1 and used here for demonstration. The fund differences (processing, objectives, etc.) between active and passive DNA finger preclude direct comparison of results presented here with those presented in [4 providing a motivational basis for the active DNA fingerprinting work undertak care is taken in making comparisons of results in [19] with those provided here addressed further in Section 3 results. However, the MDA processing is fundam the same and limited details for the device discrimination process are presented The ROI overlay in Figure 6 was generated using N TimBlcks = 8 and N FrqBlcks = 9, with a total number of N Tim = 55 and N Frq = 12 indices defining the block time-frequency extent. Thus, there are a total of N Ptch = 8 × 9 = 72 total time-frequency patches with each patch containing a total of 55 × 12 = 660 elements. Fingerprint statistics (variance, skewness, and kurtosis statistics [30]) were calculated using elements within each of the N Ptch = 72 patches, and across all ROI elements as well, such that the resultant Gabor transform DNA fingerprints included a total of N FD-GT = (72 + 1) × 3 = 219 statistical features.

Multiple Discriminant Analysis (MDA)
The MDA-based discrimination methodology used here was primarily adopted from related work in [4] that exploited passive DNA features and work in [19] that exploited passive DNA features. Both of these earlier works considered the same N Dev = 8 Wire-lessHART adapters shown in Table 1 and used here for demonstration. The fundamental differences (processing, objectives, etc.) between active and passive DNA fingerprinting preclude direct comparison of results presented here with those presented in [4]. While providing a motivational basis for the active DNA fingerprinting work undertaken here, care is taken in making comparisons of results in [19] with those provided here-this is addressed further in Section 3 results. However, the MDA processing is fundamentally the same and limited details for the device discrimination process are presented here for completeness. The reader is referred to [4] for a more detailed description and development of MDA-based device classification and device ID verification.
The N Dev = 8 WirelessHART devices in Table 1 were used to perform discrimination assessments for the N Mdl = 56 (8-choose-5) model conditions shown in Table 2. As indicated, each model included N Cls = 5 classes with each class represented by one of the designated Authentic (A) devices. The remaining three held-out devices were introduced as Counterfeit (C) devices for each of the modeled devices. As adopted from [4], the trained MDA model elements are denoted by (W, is the input fingerprint standard deviation normalization factor (dimension 1 × N Feat ), (4) µ n is the projected training class means (dimension 1 × N CLS − 1), and (5) Σ n is the training class covariance matrix (dimension N Cls − 1 × N Cls − 1). Table 2. Device assignments for the N Mdl = 56 models the N Dev = 8 adapters serving in the indicated Authentic (A) or Counterfeit (C) roles.

Model ID
ances are presented in a %C versus Model ID format to enable comparison -an overall cross-model average %C is calculated and presented as well. so presented for average per-device performance in a %C versus Device ID ble comparison across devices-an overall cross-device average %C is calresented as well. These results are obtained by considering diagonal confutries (correct estimates) for a given device in all models where that device n authentic role. Thus, the per-device %C averages are based on diagonal es in 35-of-56 models. or the looks-how-much like device ID verification (counterfeit detection) proerated using the same NMdl = 56 MDA models used for device classification. evice ID verification assessments for a given model are denoted by D U : D thentic), where D U is one of three non-modeled counterfeit devices and D modeled authentic devices. Considering model M54 in Table 2 as an exama total of 3 × 5 = 15 D U : D counterfeit assessments performed for all i∈{1, 2, , 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were a total of 15x56 = l counterfeit detection assessments completed for estimating %CDR. counterfeit ID verification assessments and %CDR estimation are based ccept/reject declaration process. The accept/reject decisions are made on a -fingerprint basis using the following: ng a Unk = [( Unk − )⨀ − ] fingerprint projection for each of the NTst finfrom the counterfeit D U device; ng the test statistic Z Unk , associated with the claimed authentic D device h of the counterfeit Unk projections; ng a Z Unk , ⁝ ⪋ V threshold comparison, where t V is the device-de-ID verification for the claimed authentic device D and the ⪋ inequality is set as (a) greater than (>) for a higher-is-better match statistic (e.g., MVN ty), or (b) less than (<) for a lower-is-better match statistic (e.g., Euclidean ); binary accept/reject declaration based on threshold criteria with (a) an ace positive) being an undesirable outcome-counterfeit not detected, and (b) rue negative) being a desirable outcome-counterfeit detected; ng %CDR = [(NTst − NRej)/NTst] × 100 as an estimate of counterfeit detectability, Rej is the total number of binary reject decisions. evice classification, counterfeit device ID verification results are presented s. The first is a per-model %CDR versus Model ID format. In this case, the e is based on averaging binary reject decisions for three different counterfeit D1, D2 and D5 in M54) being compared against all five authentic devices D6, D7, D8 in M54)-the per-model %CDR averages are based on a total of terfeit ID verification assessments. The second presentation format includes DR versus Device ID. In this case, the presented %CDR average is based on ct decisions for a given device when serving as a counterfeit in 21-of-56 D1 in M36-M56) and being compared against all other devices-the peraverages are based on a total of 21 × 5 = 105 counterfeit ID verification as-del performances are presented in a %C versus Model ID format to enable comparison oss models-an overall cross-model average %C is calculated and presented as well. sults are also presented for average per-device performance in a %C versus Device ID mat to enable comparison across devices-an overall cross-device average %C is calated and presented as well. These results are obtained by considering diagonal confun matrix entries (correct estimates) for a given device in all models where that device erving in an authentic role. Thus, the per-device %C averages are based on diagonal r-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterfeit detection) pros were generated using the same NMdl = 56 MDA models used for device classification. unterfeit device ID verification assessments for a given model are denoted by D U : D unterfeit:authentic), where D U is one of three non-modeled counterfeit devices and D ach of the modeled authentic devices. Considering model M54 in Table 2 as an exam-, there are a total of 3 × 5 = 15 D U : D counterfeit assessments performed for all i∈{1, 2, and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were a total of 15x56 = individual counterfeit detection assessments completed for estimating %CDR. The D U : D counterfeit ID verification assessments and %CDR estimation are based a binary accept/reject declaration process. The accept/reject decisions are made on a gerprint-by-fingerprint basis using the following: Generating a Unk = [( Unk − )⨀ − ] fingerprint projection for each of the NTst fingerprints from the counterfeit D U device; Calculating the test statistic Z Unk , associated with the claimed authentic D device using each of the counterfeit Unk projections; Performing a Z Unk , ⁝ ⪋ V threshold comparison, where t V is the device-dependent ID verification for the claimed authentic device D and the ⪋ inequality condition is set as (a) greater than (>) for a higher-is-better match statistic (e.g., MVN probability), or (b) less than (<) for a lower-is-better match statistic (e.g., Euclidean Distance); Making a binary accept/reject declaration based on threshold criteria with (a) an accept (false positive) being an undesirable outcome-counterfeit not detected, and (b) a reject (true negative) being a desirable outcome-counterfeit detected; Calculating %CDR = [(NTst − NRej)/NTst] × 100 as an estimate of counterfeit detectability, where NRej is the total number of binary reject decisions.
As with device classification, counterfeit device ID verification results are presented two formats. The first is a per-model %CDR versus Model ID format. In this case, the DR average is based on averaging binary reject decisions for three different counterfeit vices (e.g., D1, D2 and D5 in M54) being compared against all five authentic devices ., D3, D4, D6, D7, D8 in M54)-the per-model %CDR averages are based on a total of 5 = 15 counterfeit ID verification assessments. The second presentation format includes r-device %CDR versus Device ID. In this case, the presented %CDR average is based on raging reject decisions for a given device when serving as a counterfeit in 21-of-56 dels (e.g., D1 in M36-M56) and being compared against all other devices-the pervice %CDR averages are based on a total of 21 × 5 = 105 counterfeit ID verification assments.
model performances are presented in a %C versus Model ID format to enable comparison across models-an overall cross-model average %C is calculated and presented as well.
Results are also presented for average per-device performance in a %C versus Device ID format to enable comparison across devices-an overall cross-device average %C is calculated and presented as well. These results are obtained by considering diagonal confusion matrix entries (correct estimates) for a given device in all models where that device is serving in an authentic role. Thus, the per-device %C averages are based on diagonal per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterfeit detection) process were generated using the same NMdl = 56 MDA models used for device classification. Counterfeit device ID verification assessments for a given model are denoted by D U : D (counterfeit:authentic), where D U is one of three non-modeled counterfeit devices and D is each of the modeled authentic devices. Considering model M54 in Table 2 as an example, there are a total of 3 × 5 = 15 D U : D counterfeit assessments performed for all i∈{1, 2, 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were a total of 15x56 = 840 individual counterfeit detection assessments completed for estimating %CDR.
The D U : D counterfeit ID verification assessments and %CDR estimation are based on a binary accept/reject declaration process. The accept/reject decisions are made on a fingerprint-by-fingerprint basis using the following: • Generating a Unk = [( Unk − )⨀ − ] fingerprint projection for each of the NTst fingerprints from the counterfeit D U device; • Calculating the test statistic Z Unk , associated with the claimed authentic D device using each of the counterfeit Unk projections; • Performing a Z Unk , ⁝ ⪋ V threshold comparison, where t V is the device-dependent ID verification for the claimed authentic device D and the ⪋ inequality condition is set as (a) greater than (>) for a higher-is-better match statistic (e.g., MVN probability), or (b) less than (<) for a lower-is-better match statistic (e.g., Euclidean Distance);

•
Making a binary accept/reject declaration based on threshold criteria with (a) an accept (false positive) being an undesirable outcome-counterfeit not detected, and (b) a reject (true negative) being a desirable outcome-counterfeit detected; • Calculating %CDR = [(NTst − NRej)/NTst] × 100 as an estimate of counterfeit detectability, where NRej is the total number of binary reject decisions.
As with device classification, counterfeit device ID verification results are presented in two formats. The first is a per-model %CDR versus Model ID format. In this case, the %CDR average is based on averaging binary reject decisions for three different counterfeit devices (e.g., D1, D2 and D5 in M54) being compared against all five authentic devices (e.g., D3, D4, D6, D7, D8 in M54)-the per-model %CDR averages are based on a total of 3 × 5 = 15 counterfeit ID verification assessments. The second presentation format includes per-device %CDR versus Device ID. In this case, the presented %CDR average is based on averaging reject decisions for a given device when serving as a counterfeit in 21-of-56 models (e.g., D1 in M36-M56) and being compared against all other devices-the perdevice %CDR averages are based on a total of 21 × 5 = 105 counterfeit ID verification assessments.
model performances are presented in a %C versus Model ID format to enable comparison across models-an overall cross-model average %C is calculated and presented as well. Results are also presented for average per-device performance in a %C versus Device ID format to enable comparison across devices-an overall cross-device average %C is calculated and presented as well. These results are obtained by considering diagonal confusion matrix entries (correct estimates) for a given device in all models where that device is serving in an authentic role. Thus, the per-device %C averages are based on diagonal per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterfeit detection) process were generated using the same NMdl = 56 MDA models used for device classification. Counterfeit device ID verification assessments for a given model are denoted by D U : D (counterfeit:authentic), where D U is one of three non-modeled counterfeit devices and D is each of the modeled authentic devices. Considering model M54 in Table 2 as an example, there are a total of 3 × 5 = 15 D U : D counterfeit assessments performed for all i∈{1, 2, 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were a total of 15x56 = 840 individual counterfeit detection assessments completed for estimating %CDR.
The D U : D counterfeit ID verification assessments and %CDR estimation are based on a binary accept/reject declaration process. The accept/reject decisions are made on a fingerprint-by-fingerprint basis using the following: • Generating a Unk = [( Unk − )⨀ − ] fingerprint projection for each of the NTst fingerprints from the counterfeit D U device; • Calculating the test statistic Z Unk , associated with the claimed authentic D device using each of the counterfeit Unk projections; • Performing a Z Unk , ⁝ ⪋ V threshold comparison, where t V is the device-dependent ID verification for the claimed authentic device D and the ⪋ inequality condition is set as (a) greater than (>) for a higher-is-better match statistic (e.g., MVN probability), or (b) less than (<) for a lower-is-better match statistic (e.g., Euclidean Distance);

•
Making a binary accept/reject declaration based on threshold criteria with (a) an accept (false positive) being an undesirable outcome-counterfeit not detected, and (b) a reject (true negative) being a desirable outcome-counterfeit detected; • Calculating %CDR = [(NTst − NRej)/NTst] × 100 as an estimate of counterfeit detectability, where NRej is the total number of binary reject decisions.
As with device classification, counterfeit device ID verification results are presented in two formats. The first is a per-model %CDR versus Model ID format. In this case, the %CDR average is based on averaging binary reject decisions for three different counterfeit devices (e.g., D1, D2 and D5 in M54) being compared against all five authentic devices (e.g., D3, D4, D6, D7, D8 in M54)-the per-model %CDR averages are based on a total of 3 × 5 = 15 counterfeit ID verification assessments. The second presentation format includes per-device %CDR versus Device ID. In this case, the presented %CDR average is based on averaging reject decisions for a given device when serving as a counterfeit in 21-of-56 models (e.g., D1 in M36-M56) and being compared against all other devices-the perdevice %CDR averages are based on a total of 21 × 5 = 105 counterfeit ID verification assessments.
model performances are presented in a %C versus Model ID format to enable comp across models-an overall cross-model average %C is calculated and presented a Results are also presented for average per-device performance in a %C versus Dev format to enable comparison across devices-an overall cross-device average %C culated and presented as well. These results are obtained by considering diagonal sion matrix entries (correct estimates) for a given device in all models where that is serving in an authentic role. Thus, the per-device %C averages are based on di per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterfeit detectio cess were generated using the same NMdl = 56 MDA models used for device classifi Counterfeit device ID verification assessments for a given model are denoted by (counterfeit:authentic), where D U is one of three non-modeled counterfeit devices a is each of the modeled authentic devices. Considering model M54 in Table 2 as an ple, there are a total of 3 × 5 = 15 D U : D counterfeit assessments performed for all 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were a total of 1 840 individual counterfeit detection assessments completed for estimating %CDR.
The D U : D counterfeit ID verification assessments and %CDR estimation are on a binary accept/reject declaration process. The accept/reject decisions are mad fingerprint-by-fingerprint basis using the following: • Generating a Unk = [( Unk − )⨀ − ] fingerprint projection for each of the N gerprints from the counterfeit D U device; • Calculating the test statistic Z Unk , associated with the claimed authentic D using each of the counterfeit Unk projections; • Performing a Z Unk , ⁝ ⪋ V threshold comparison, where t V is the dev pendent ID verification for the claimed authentic device D and the ⪋ ine condition is set as (a) greater than (>) for a higher-is-better match statistic (e.g. probability), or (b) less than (<) for a lower-is-better match statistic (e.g., Euc Distance);

•
Making a binary accept/reject declaration based on threshold criteria with (a) cept (false positive) being an undesirable outcome-counterfeit not detected, a a reject (true negative) being a desirable outcome-counterfeit detected; • Calculating %CDR = [(NTst − NRej)/NTst] × 100 as an estimate of counterfeit detect where NRej is the total number of binary reject decisions.
As with device classification, counterfeit device ID verification results are pre in two formats. The first is a per-model %CDR versus Model ID format. In this ca %CDR average is based on averaging binary reject decisions for three different coun devices (e.g., D1, D2 and D5 in M54) being compared against all five authentic d (e.g., D3, D4, D6, D7, D8 in M54)-the per-model %CDR averages are based on a 3 × 5 = 15 counterfeit ID verification assessments. The second presentation format in per-device %CDR versus Device ID. In this case, the presented %CDR average is ba averaging reject decisions for a given device when serving as a counterfeit in 2 models (e.g., D1 in M36-M56) and being compared against all other devices-th device %CDR averages are based on a total of 21 × 5 = 105 counterfeit ID verificat sessments.
model performances are presented in a %C versus Model ID format to e across models-an overall cross-model average %C is calculated and p Results are also presented for average per-device performance in a %C format to enable comparison across devices-an overall cross-device a culated and presented as well. These results are obtained by considerin sion matrix entries (correct estimates) for a given device in all models is serving in an authentic role. Thus, the per-device %C averages are b per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterf cess were generated using the same NMdl = 56 MDA models used for de Counterfeit device ID verification assessments for a given model are d (counterfeit:authentic), where D U is one of three non-modeled counterfe is each of the modeled authentic devices. Considering model M54 in Ta ple, there are a total of 3 × 5 = 15 D U : D counterfeit assessments perform 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were 840 individual counterfeit detection assessments completed for estimati The D U : D counterfeit ID verification assessments and %CDR est on a binary accept/reject declaration process. The accept/reject decisio fingerprint-by-fingerprint basis using the following: As with device classification, counterfeit device ID verification res in two formats. The first is a per-model %CDR versus Model ID forma %CDR average is based on averaging binary reject decisions for three di devices (e.g., D1, D2 and D5 in M54) being compared against all five (e.g., D3, D4, D6, D7, D8 in M54)-the per-model %CDR averages are b 3 × 5 = 15 counterfeit ID verification assessments. The second presentatio per-device %CDR versus Device ID. In this case, the presented %CDR av averaging reject decisions for a given device when serving as a coun models (e.g., D1 in M36-M56) and being compared against all other device %CDR averages are based on a total of 21 × 5 = 105 counterfeit sessments.
model performances are presented in a %C versus Model ID across models-an overall cross-model average %C is calcu Results are also presented for average per-device performan format to enable comparison across devices-an overall cro culated and presented as well. These results are obtained by sion matrix entries (correct estimates) for a given device in a is serving in an authentic role. Thus, the per-device %C ave per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification cess were generated using the same NMdl = 56 MDA models u Counterfeit device ID verification assessments for a given m (counterfeit:authentic), where D U is one of three non-modele is each of the modeled authentic devices. Considering mode ple, there are a total of 3 × 5 = 15 D U : D counterfeit assessme 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models 840 individual counterfeit detection assessments completed The D U : D counterfeit ID verification assessments and on a binary accept/reject declaration process. The accept/re fingerprint-by-fingerprint basis using the following: As with device classification, counterfeit device ID veri in two formats. The first is a per-model %CDR versus Mode %CDR average is based on averaging binary reject decisions devices (e.g., D1, D2 and D5 in M54) being compared again (e.g., D3, D4, D6, D7, D8 in M54)-the per-model %CDR ave 3 × 5 = 15 counterfeit ID verification assessments. The second per-device %CDR versus Device ID. In this case, the presente averaging reject decisions for a given device when serving models (e.g., D1 in M36-M56) and being compared agains device %CDR averages are based on a total of 21 × 5 = 105 c sessments.
model performances are presented in a %C versus across models-an overall cross-model average % Results are also presented for average per-device format to enable comparison across devices-an culated and presented as well. These results are o sion matrix entries (correct estimates) for a given is serving in an authentic role. Thus, the per-dev per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID cess were generated using the same NMdl = 56 MD Counterfeit device ID verification assessments fo (counterfeit:authentic), where D U is one of three n is each of the modeled authentic devices. Conside ple, there are a total of 3 × 5 = 15 D U : D counterfe 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 840 individual counterfeit detection assessments The D U : D counterfeit ID verification assess on a binary accept/reject declaration process. Th fingerprint-by-fingerprint basis using the followin As with device classification, counterfeit dev in two formats. The first is a per-model %CDR v %CDR average is based on averaging binary rejec devices (e.g., D1, D2 and D5 in M54) being com (e.g., D3, D4, D6, D7, D8 in M54)-the per-model 3 × 5 = 15 counterfeit ID verification assessments. T per-device %CDR versus Device ID. In this case, t averaging reject decisions for a given device wh models (e.g., D1 in M36-M56) and being compa device %CDR averages are based on a total of 21 sessments. model performances are presented in a across models-an overall cross-mode Results are also presented for average format to enable comparison across d culated and presented as well. These r sion matrix entries (correct estimates) is serving in an authentic role. Thus, t per-class entries in 35-of-56 models.
Results for the looks-how-much like cess were generated using the same N Counterfeit device ID verification asse As with device classification, cou in two formats. The first is a per-mod %CDR average is based on averaging b devices (e.g., D1, D2 and D5 in M54) (e.g., D3, D4, D6, D7, D8 in M54)-the 3 × 5 = 15 counterfeit ID verification ass per-device %CDR versus Device ID. In averaging reject decisions for a given models (e.g., D1 in M36-M56) and be device %CDR averages are based on a sessments.

Device Discrimination
The trained MDA models were used for both Device Classification and Device ID Verification assessments. Given a trained (W, µ F , σ F , µ n , Σ n ) MDA model, a fingerprint from an unknown device, denoted as F Unk (dimension 1xN Feat ), is projected into the MDA decision [4]. The resultant p Unk is used with a given measure of similarity to generate a test statistic (Z Unk ) that is used for making device classification and device ID verification decision. Test statistic Z Unk is a real number that is used to estimate (1) which of the N Cls modeled devices the unknown F Unk most closely represents-the fundamental device classification process, and (2) how much the unknown F Unk looks like fingerprints from 1-of-N Cls specified devices-the fundamental device ID verification process used for estimating %CDR. Consistent with results in [4,19], the Z Unk test statistics used here were generated from distance-based Euclidean and probability-based Multi-Variate Normal (MVN) measures of similarity. The reader is referred to [4] for a detailed description of test statistic Z Unk generation and its use in making classification and ID verification decisions.
Results for the looks-most-like device classification process are summarized in a confusion matrix format [34]. A representative confusion matrix is shown in Table 3 for MDA classifier testing of an N Cls = 5 model using N Tst = 565 unknown testing fingerprints per class. The average cross-class percent correct classification (%C) is calculated as the sum of diagonal elements divided by the total number of estimates represented in the matrix (N Tst × N Cls ). The Table 3 Table 3 shows that a majority of the classification error is attributable to mutual "confusion" between Class 2 (D2) and Class 5 (D5). The classification estimates in Table 3 effectively represent Monte Carlo trials and 95% Confidence Interval (CI 95% ) analysis [35] is used throughout the paper when making comparisons and drawing conclusions. The ±CI 95% intervals for per-class %C Cls are presented in Table 3 by way of example and are based on N Tst = 565 Monte Carlo trials.
MDA-based confusion matrix results such as presented in Table 3 were generated for all N Mdl = 56 MDA models in Table 2. The presentation of a large number of resultant confusion matrices is avoided in the interest of brevity. As an alternative, the average permodel performances are presented in a %C versus Model ID format to enable comparison across models-an overall cross-model average %C is calculated and presented as well.
Results are also presented for average per-device performance in a %C versus Device ID format to enable comparison across devices-an overall cross-device average %C is calculated and presented as well. These results are obtained by considering diagonal confusion matrix entries (correct estimates) for a given device in all models where that device is serving in an authentic role. Thus, the per-device %C averages are based on diagonal per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterfeit detection) process were generated using the same N Mdl = 56 MDA models used for device classification. Counterfeit device ID verification assessments for a given model are denoted by D U i : D k (counterfeit:authentic), where D U i is one of three non-modeled counterfeit devices and D k is each of the modeled authentic devices. Considering model M54 in Table 2 as an example, there are a total of 3 × 5 = 15 D U i : D k counterfeit assessments performed for all i∈{1, 2, 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all N Mdl = 56 models, there were a total of 15 × 56 = 840 individual counterfeit detection assessments completed for estimating %CDR.
The D U i : D k counterfeit ID verification assessments and %CDR estimation are based on a binary accept/reject declaration process. The accept/reject decisions are made on a fingerprint-by-fingerprint basis using the following:  Table 3 shows that a majority of the classification error is attributable to mutual "confusion" between Class 2 (D2) and Class 5 (D5). The classification estimates in Table 3 effectively represent Monte Carlo trials and 95% Confidence Interval (CI95%) analysis [35] is used throughout the paper when making comparisons and drawing conclusions. The ±CI95% intervals for per-class %CCls are presented in Table 3 by way of example and are based on NTst = 565 Monte Carlo trials.
MDA-based confusion matrix results such as presented in Table 3 were generated for all NMdl = 56 MDA models in Table 2. The presentation of a large number of resultant confusion matrices is avoided in the interest of brevity. As an alternative, the average permodel performances are presented in a %C versus Model ID format to enable comparison across models-an overall cross-model average %C is calculated and presented as well.
Results are also presented for average per-device performance in a %C versus Device ID format to enable comparison across devices-an overall cross-device average %C is calculated and presented as well. These results are obtained by considering diagonal confusion matrix entries (correct estimates) for a given device in all models where that device is serving in an authentic role. Thus, the per-device %C averages are based on diagonal per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification (counterfeit detection) process were generated using the same NMdl = 56 MDA models used for device classification. Counterfeit device ID verification assessments for a given model are denoted by D U : D (counterfeit:authentic), where D U is one of three non-modeled counterfeit devices and D is each of the modeled authentic devices. Considering model M54 in Table 2 as an example, there are a total of 3 × 5 = 15 D U : D counterfeit assessments performed for all i∈{1, 2, 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models, there were a total of 15x56 = 840 individual counterfeit detection assessments completed for estimating %CDR.
The D U : D counterfeit ID verification assessments and %CDR estimation are based on a binary accept/reject declaration process. The accept/reject decisions are made on a fingerprint-by-fingerprint basis using the following: Performing a Z Unk , ⁝ ⪋ V threshold comparison, where t V is the device-dependent ID verification for the claimed authentic device D and the ⪋ inequality condition is set as (a) greater than (>) for a higher-is-better match statistic (e.g., MVN probability), or (b) less than (<) for a lower-is-better match statistic (e.g., Euclidean Distance);   Table 3 shows that a majority of the classification error is fusion" between Class 2 (D2) and Class 5 (D5). The classific fectively represent Monte Carlo trials and 95% Confidence In used throughout the paper when making comparisons an ±CI95% intervals for per-class %CCls are presented in Table 3 based on NTst = 565 Monte Carlo trials.
MDA-based confusion matrix results such as presented all NMdl = 56 MDA models in Table 2. The presentation of confusion matrices is avoided in the interest of brevity. As an model performances are presented in a %C versus Model ID across models-an overall cross-model average %C is calcu Results are also presented for average per-device performanc format to enable comparison across devices-an overall cro culated and presented as well. These results are obtained by sion matrix entries (correct estimates) for a given device in a is serving in an authentic role. Thus, the per-device %C ave per-class entries in 35-of-56 models.
Results for the looks-how-much like device ID verification cess were generated using the same NMdl = 56 MDA models u Counterfeit device ID verification assessments for a given m (counterfeit:authentic), where D U is one of three non-modele is each of the modeled authentic devices. Considering mode ple, there are a total of 3 × 5 = 15 D U : D counterfeit assessme 5} and all k∈{3, 4, 6, 7, 8}. Accounting for all NMdl = 56 models 840 individual counterfeit detection assessments completed The D U : D counterfeit ID verification assessments and on a binary accept/reject declaration process. The accept/re fingerprint-by-fingerprint basis using the following: inequality condition is set as (a) greater than (>) for a higher-is-better match statistic (e.g., MVN probability), or (b) less than (<) for a lower-is-better match statistic (e.g., Euclidean Distance);

•
Making a binary accept/reject declaration based on threshold criteria with (a) an accept (false positive) being an undesirable outcome-counterfeit not detected, and (b) a reject (true negative) being a desirable outcome-counterfeit detected; • Calculating %CDR = [(N Tst − N Rej )/N Tst ] × 100 as an estimate of counterfeit detectability, where N Rej is the total number of binary reject decisions.
As with device classification, counterfeit device ID verification results are presented in two formats. The first is a per-model %CDR versus Model ID format. In this case, the %CDR average is based on averaging binary reject decisions for three different counterfeit devices (e.g., D1, D2 and D5 in M54) being compared against all five authentic devices (e.g., D3, D4, D6, D7, D8 in M54)-the per-model %CDR averages are based on a total of 3 × 5 = 15 counterfeit ID verification assessments. The second presentation format includes per-device %CDR versus Device ID. In this case, the presented %CDR average is based on averaging reject decisions for a given device when serving as a counterfeit in 21-of-56 models (e.g., D1 in M36-M56) and being compared against all other devices-the per-device %CDR averages are based on a total of 21 × 5 = 105 counterfeit ID verification assessments.

Dimensional Reduction Analysis (DRA)
Processing efficiency improvement can be obtained using fingerprints having a reduced number of DRA selected (N DRA ) features. The DRA features are selected as a proper subset of the Full-Dimensional (FD) feature set containing N FD features with a goal of minimizing the impact (degradation) in classifier %C performance. DRA feature selection was performed here using classification results of (1) an Artificial Neural Network (ANN) based Learning Vector Quantization (LVQ) process adopted from [12], and (2) ensemble based Random Forest (RndF) process adopted from [14]. While there are certainly other feature selection methods that could be considered, the FD-vs-DRA classification results in Section 3 show that both methods are sufficiently robust for demonstration purposes. Unlike MDA classification, these classifiers provide a direct indication of feature relevance (importance) on the final classification decision.
Relative to MDA, there are increased computation costs with implementing ANN-based and ensemble-based classifiers. Thus, their envisioned use is limited to pre-deployment training and feature selection, with a goal of identifying DRA subsets of sufficiently relevant features that can be used with the more computationally efficient MDA-based discrimination processes described in Section 2.4. The DRA subsets are referred to herein as RndF-selected and LVQ-selected subsets and include a total of N DRA < N FD features. The total percentage of DRA reduction is calculated as [(N FD − N DRA )/N FD )/] × 100.
The DRA feature selection process is illustrated in the stem plots provided in Figures 7 and 8. These plots show post-classification RndF and LVQ relevance metrics for the N FD = 219 full-dimensional feature set at SNR = −20 dB. The SNR conditions are noted given that feature relevance and DRA selection are generally SNR dependent, with a greater number of features becoming increasingly relevant as SNR decreases. The post-classification N DRA = 43 selected features are denoted by blue asterisk ( * ) markers and the remaining least relevant 176-of-219 features are denoted by the red dot (•) markers. The 43-of-219 selection represents an approximate 80% reduction.
The top plots in Figures 7 and 8 show the sorted (highest-to-lowest relevance) rankordered features with a majority of the N FD = 219 total features having zero to near-zero relevance and contributing minimally to the final classification decision. The bottom plot in each figure shows the unsorted feature relevance and the actual fingerprint feature indices for the most relevant features. The green triangle ( ) markers in each of the bottom plots denote 18 common features identified by both the RndF and LVQ classifiers. ordered features with a majority of the NFD = 219 total features having zero to nea relevance and contributing minimally to the final classification decision. The bottom in each figure shows the unsorted feature relevance and the actual fingerprint featu dices for the most relevant features. The green triangle (▽) markers in each of the b plots denote 18 common features identified by both the RndF and LVQ classifiers.  The common features in Figures 7 and 8 were used as an additional jointly se feature set containing NJoint = 18 features, i.e., the joint set was the intersection NDRA,RndF = 43 RndF-selected and NDRA,LVQ = 43 LVQ-selected feature sets. The imp DRA on classification is determined by rerunning the classifiers and comparing t sultant %CDRA using the NDRA selected subsets with the original %CFD perform Though not the main emphasis of this section, it is interesting to note that the NDRAjointly selected feature set identified in Figures 7 and 8 yielded statistically equi %CFD and %CDRA performance of %C ≈ 91% for both the RndF and LVQ classifiersa 92% reduction in the required number of features with no sacrifice in %C perform What remains to be shown in the Results section is how the MDA classifier performs the reduced dimensional NDRA,RndF and NDRA,LVQ selected feature sets.
For final discussion on DRA feature selection, it is insightful to consider whe jointly selected RndF features in Figure 7 and LVQ features in Figure 8 were gen For final discussion on DRA feature selection, it is insightful to consider where the jointly selected RndF features in Figure 7 and LVQ features in Figure 8 were generated from within the Gabor transform domain. This is illustrated in Figure 9, which shows (1) the Gabor transform response and overlaid ROI patches in Figure 6, and (2) numerical values in specific patches to indicate the number of jointly selected features generated from elements within those patches-the vertical side note indicates that 2-of-18 features were generated using all ROI elements. As indicated, all but one of the N Joint = 18 features were generated along diagonal patches where the Gabor transform produced the maximum element-to-element energy concentration changes.

Device Discrimination Results
Performance of MDA models representing all NCls = 8 devices is first consid Section 3.1. These results are provided to (1) highlight benefits for transitioning f time domain to 2D Gabor transform fingerprint features, and (2) demonstrate th tiveness of RndF and LVQ DRA feature selection for reducing the number of fing features while maintaining acceptable discrimination performance. The benefits of bor-based fingerprints and DRA feature selection are carried over into multi-m sessments in Section 3.2. These results include NCls = 5 device multi-model classi and counterfeit ID verification for the NMdl = 56 models in Table 2.

1D vs. 2D Classification Performance
The first step toward characterizing discrimination performance and process ciency improvement included generating the full-dimensional (FD) TdDna baseli sification results for comparing with GtDna classification results. The TdDna basel generated using NFD,TD = 117 TdDna features generated per Section 2.2 and the M discrimination process in Section 2.4 for the NCls = 8 WirelessHART devices. The b TdDna FD (117) results are presented in Figure 10 and exhibit the typical trend performance for variation in SNR. This includes a range of %C ≈ 100% at higher S resenting collected response conditions and %C ≈ 1/NCls ≈ 12.5% at the lowest SNR senting random guessing. The one off-diagonal feature in Figure 9 (patch centered at m ≈ 50 and k ≈ 65) corresponds to fingerprint feature index number 10 in Figures 7 and 8 and has near-zero relevance for either the RndF or LVQ classifier. A cursory analysis of device discrimination performance with fingerprint feature number 10 removed from the jointly selected N Joint = 18 feature set proved to be inconsequential, i.e., there was no statistically significant change in either device classification or device ID verification performance.

Device Discrimination Results
Performance of MDA models representing all N Cls = 8 devices is first considered in Section 3.1. These results are provided to (1) highlight benefits for transitioning from 1D time domain to 2D Gabor transform fingerprint features, and (2) demonstrate the effectiveness of RndF and LVQ DRA feature selection for reducing the number of fingerprint features while maintaining acceptable discrimination performance. The benefits of 2D Gabor-based fingerprints and DRA feature selection are carried over into multi-model assessments in Section 3.2. These results include N Cls = 5 device multi-model classification and counterfeit ID verification for the N Mdl = 56 models in Table 2.

1D vs. 2D Classification Performance
The first step toward characterizing discrimination performance and processing efficiency improvement included generating the full-dimensional (FD) TdDna baseline classification results for comparing with GtDna classification results. The TdDna baseline was generated using N FD,TD = 117 TdDna features generated per Section 2.2 and the MDA/ML discrimination process in Section 2.4 for the N Cls = 8 WirelessHART devices. The baseline TdDna FD (117) results are presented in Figure 10 and exhibit the typical trends in %C performance for variation in SNR. This includes a range of %C ≈ 100% at higher SNR representing collected response conditions and %C ≈ 1/N Cls ≈ 12.5% at the lowest SNR representing random guessing.

Multi-Model Discrimination
The benefits of 2D GtDna fingerprinting highlighted in Section 3.1 for the N device models were likewise observed for all NMdl = 56 models in Table 2. That is, s cally equivalent discrimination was achieved using the NFD-GT = 219 and NDRA-GT = ture sets. Thus, representative results for SNR = −20 dB conditions are presented an vide the basis for detailed discussion of multi-model classification and counterfeit ification performance. As noted in Section 2.5, both per-model and per-device %C fication and %CDR counterfeit ID verification performances are presented.
The per-device and per-model %C classification performances using the NFD-G feature set are shown in Figures 11 and 12, respectively. These include overlaid res both ED (■) and MVN (•) measures of similarity. The corresponding per-device an model %C performances for the NDRA-GT = 18 feature set are shown in Figures 13 a respectively. Comparison of Figure 11 through Figure 14 shows that (1) the ind per-device and per-model results for MVN are statistically equivalent to, or bette ED results for a majority of the individual assessments, with (2) the corresponding device and cross-model averages (dashed lines) indicating that MVN provides marginally better performance (0.66% < %CΔ = %CMVN − %CED < 1.28%). The better versus ED performance here is consistent with findings in [4,19]. The overlaid GtDna comparison results in Figure 10 were generated using the same device SFM responses. Note that each plotted data point in this figure includes the CI 95% intervals, and all intervals effectively span the vertical extent of the data markers. These results were generated using N FD-GT = 219 full-dimensional and N DRA ∈ {18, 43, 117} dimensionally reduced feature sets selected using both the RndF and LVQ relevance rankordering process detailed in Section 2.6. The additional "Joint" N DRA = 18 feature set was generated as the intersection of RndF and LVQ selected feature sets. Collectively considering all plotted data points in Figure 10 and their corresponding CI 95% intervals, GtDna fingerprinting is superior for all but one of the SNR conditions. The one exception occurs under the highest SNR = −6 dB condition, where TdDna and GtDna performances are statistically equivalent for all fingerprint sets considered. Most notably, GtDna DRA performance is statistically equivalent to GtDna FD performance for all DRA subsets under SNR ≥ −20 dB conditions. Benefits for using the N DRA = 18 feature set include (1) a GtDna vs. TdDna performance gain of %C ∆ = %C GT − %C TD ≈ 51%, and (2) an approximate 92% reduction in the number of required GtDna features (18 vs. 291) with no trade-off penalty incurred in average cross-class %C performance.

Multi-Model Discrimination
The benefits of 2D GtDna fingerprinting highlighted in Section 3.1 for the N Cls = 8 device models were likewise observed for all N Mdl = 56 models in Table 2. That is, statistically equivalent discrimination was achieved using the N FD-GT = 219 and N DRA-GT = 18 feature sets. Thus, representative results for SNR = −20 dB conditions are presented and provide the basis for detailed discussion of multi-model classification and counterfeit ID verification performance. As noted in Section 2.5, both per-model and per-device %C classification and %CDR counterfeit ID verification performances are presented.
The per-device and per-model %C classification performances using the N FD-GT = 219 feature set are shown in Figures 11 and 12, respectively. These include overlaid results for both ED ( ) and MVN (•) measures of similarity. The corresponding per-device and permodel %C performances for the N DRA-GT = 18 feature set are shown in Figures 13 and 14, respectively. Comparison of Figure 11 through Figure 14 shows that (1) the individual per-device and per-model results for MVN are statistically equivalent to, or better than, ED results for a majority of the individual assessments, with (2) the corresponding cross-device and cross-model averages (dashed lines) indicating that MVN provides overall marginally better performance (0.66% < %C ∆ = %C MVN − %C ED < 1.28%). The better MVN versus ED performance here is consistent with findings in [4,19].   The N Mdl = 56 MDA models used for classification results in Figure 11 through Figure 14 were next used for counterfeit device ID verification assessments. The per-device and per-model performances for the N FD-GT = 219 feature set are shown in Figures 15 and 16, respectively, with overlaid results for both the ED ( ) and MVN (•) measures. The corresponding per-device and per-model counterfeit ID verification performances for the N DRA-GT = 18 feature set are shown in Figures 17 and 18, respectively. These results collectively embody performance of 56 × 5 × 3 = 840 individual counterfeit device ID verification assessments. In comparing Figure 15 through Figure 18 results, it is evident that (1) the per-device and per-model MVN results are statistically equivalent to, or better than, ED results for a majority of the individual assessments, (2) the cross-device and cross-model %CDR averages (dashed lines) show that the MVN measure is once again marginally superior (%CDR ∆ = %CDR MVN − %CDR ED ≈ 1.6%), and (3) the per-device performance for the more efficient N DRA-GT = 18 feature set includes 87.0% < %CDR < 99.7% and an overall cross-device average of %CDR ≈ 91.4%. This represents a 92% reduction in the required number of fingerprint features with no trade-off penalty incurred in average %CDR performance. Figure 11. Per-device MDA classification performance for the NMdl = 56 models in Table 2. are for the full-dimensional NFD-GT = 219 feature set generated under SNR = −20 dB condition ED (■) and MVN (•) measures of similarity.     The NMdl = 56 MDA models used for classification results in Figure 11 through 14 were next used for counterfeit device ID verification assessments. The per-devi per-model performances for the NFD-GT = 219 feature set are shown in Figure 15 and 16, respectively, with overlaid results for both the ED (■) and MVN (•) measure corresponding per-device and per-model counterfeit ID verification performances NDRA-GT = 18 feature set are shown in Figures 17 and 18, respectively. These results tively embody performance of 56 × 5 × 3 = 840 individual counterfeit device ID verif assessments. In comparing Figure 15 through Figure 18 results, it is evident that per-device and per-model MVN results are statistically equivalent to, or better th results for a majority of the individual assessments, (2) the cross-device and cross-%CDR averages (dashed lines) show that the MVN measure is once again margina perior (%CDRΔ = %CDRMVN − %CDRED ≈ 1.6%), and (3) the per-device performance more efficient NDRA-GT = 18 feature set includes 87.0% < %CDR < 99.7% and an overall

Summary
This work was motivated by the need for providing reliable communications i IIoT and IR 4.0 systems that are becoming increasingly reliant on automation. lessHART communications is one of the key technologies for achieving desired au tion objectives and its operational integrity must be ensured. This is addressed using ulated responses from eight commercial WirelessHART adapters and active 2D D Native Attribute (2D-DNA) fingerprinting. The 2D-DNA fingerprints are generated Gabor transformed responses and used to train 56 Multiple Discriminant Analysis (M models. Each 5-class model represents five authentic network devices and the three modeled devices are introduced as counterfeits to complete 5 × 3 × 56 = 840 indiv authentic (modeled) versus counterfeit (non-modeled) ID verification assessments.

Summary
This work was motivated by the need for providing reliable communications in IoT/IIoT and IR 4.0 systems that are becoming increasingly reliant on automation. Wire-lessHART communications is one of the key technologies for achieving desired automation objectives and its operational integrity must be ensured. This is addressed using stimulated responses from eight commercial WirelessHART adapters and active 2D Distinct Native Attribute (2D-DNA) fingerprinting. The 2D-DNA fingerprints are generated from Gabor transformed responses and used to train 56 Multiple Discriminant Analysis (MDA) models. Each 5-class model represents five authentic network devices and the three non-modeled devices are introduced as counterfeits to complete 5 × 3 × 56 = 840 individual authentic (modeled) versus counterfeit (non-modeled) ID verification assessments.
Counterfeit Detection Rate (%CDR) is estimated using an MDA-based ID verification process and is the primary metric for characterizing counterfeit detectability. ID verification is performed for the 840 authentic:counterfeit assessments using binary accept/reject threshold testing. The desired outcome is a reject decision (true negative) when a counterfeit device is presented for ID verification. Relative to motivational work in [19], the statistical significance of estimated %CDR is increased here given (1) a factor-of-2 increase in the number of MDA models considered (56 vs. 28), and (2) a factor-of-2.5 increase in the number of counterfeit detection assessments performed (840 vs. 336). Processing efficiency improvement is also achieved using Dimensional Reduction Analysis (DRA) to perform feature down-selection with Random Forest (RndF) [14] and Learning Vector Quantization (LVQ) [12] classifiers. The jointly selected DRA feature set contains only 18-of-291 fulldimensional features (an approximate 92% reduction) and is an important step toward achieving computational efficiency objectives.
The %CDR estimates are based on fingerprint-by-fingerprint ID verification assessments with the best case per-device %CDR of 87.6% < %CDR FD < 99.9% in Figure 15 obtained using the probability-based MVN measure of similarity. Considering all eight devices, this corresponds to average cross-device %CDR FD ≈ 92.5% for the full-dimensional fingerprints. This performance was echoed by the N Joint = 18 DRA performance in Figure 17 that includes per-device 87.0% < %CDR DRA < 99.7% and average cross-device %CDR DRA ≈ 91.4% using only 18-of-291 features. This represents a marginal sacrifice in %CDR performance (%CDR FD − %CDR DRA ≈ 1.1%) with considerable reduction in the number of required fingerprint features (18 vs. 291) and a corresponding boost in computational efficiency.

Conclusions
The %CDR > 90% here under small-scale network constraints are believed to be sufficient for motivating supply chain participants (manufacturers, distributors, customers) to consider using active 2D-DNA fingerprint features to certify field kits containing "matched" devices. The certification process could include generation of digital 2D-DNA credentials (e.g., model parameters, device fingerprint features, etc.) for certified package contents that are passed point-to-point as the package traverses the supply chain. The envisioned kit-based protection would require access to active 2D-DNA processing capability (stimulus generator, response collector, fingerprint generator, classifier) at each ID verification check point. The required processing would ideally be hosted in a relatively low cost, small form factor unit such as a Software Defined Radio (SDR) hosting an analog source generator and sufficient Field Programmable Gate Array (FPGA) processing capability to perform required post-collection fingerprint generation and discrimination.
Obtaining computational efficiency amidst limited resource constraints is a common challenge when bringing an experimental method to fruition for operational deployment. Of particular relevance to enhancing the experimental-to-operational transition potential of active 2D-DNA fingerprinting is that the %CDR > 90% here was achieved using 92% fewer fingerprint features (18-of-291) relative to what was used in prior motivational work [19]-this effectively reduces the required fingerprint generation, storage, transfer, and computation requirements. Processing improvements such as this are important, and work continues to further enhance computational efficiency. As a next step, work is underway to address digitization requirements for SDR-FPGA implementation. This specifically includes considering 2D surface quantization that must occur prior to fingerprint generation and the effect of bit depth on device discrimination.