III. Methodology
3.2 Post-Collection Processing
Following emission collections on all ZigBee devices using both receivers, a series of post-collection processing steps were performed using MATLAB before RF-DNA fingerprint generation. Collected bursts were first put through an amplitude-based detection process, with bursts meeting specific criteria “extracted,” and those not discarded. Extracted bursts were down-converted (center frequency shifted to f= 0), and subsequently placed through a baseband filter to remove background noise. Finally AWGN was generated, like-filtered, power-scaled, and added to the bursts to achieve a desired S NR∈[0 24] dB. Each of these steps followed those from previous work [9, 30, 31], and are described specific to this research next.
3.2.1 Burst Detection.
As discussed in Section 2.2.1, collected emissions from both receivers were stored as interleaved I/Q components according to [28]:
[I0, Q0, I1, Q1, ..., INC, QNC]; (3.1)
where NC is the total number of collected samples. For easier processing in MATLAB, each I/Q pair was converted into its corresponding complex format as:
[(I0+ jQ0), (I1+ jQ1), ..., (INC + jQNC)]. (3.2)
The collected bursts were then put through an amplitude-based detection process to extract usable bursts out of the background noise. Bursts that met specific detection criteria were determined as suitable to subsequently turn into fingerprints for later Device Classification, while others were discarded. Specific requirements for detected bursts included specific leading (tL) and trailing (tT) edge thresholds, as well as minimum (TMin) and maximum (TMax) time duration, shown in Table. 3.1.
Table 3.1: Amplitude-based burst detection parameters for ZigBee transmission collec- tions.
Parameter Variable Value Leading Threshold tL -6.0 dB Trailing Threshold tT -6.0 dB Min Duration TMin 425 µsec Max Duration TMax 550 µsec
The detection process began with the instantaneous amplitude response (a[n]) being calculated according to (2.1). These values for a specific collection (multiple bursts) were then converted into dBv using:
a[n]dBv = 20 log10( a[n]
1.0 v). (3.3)
This provides a direct relation between amplitude and dB so that the largest a[n]dBv for a specific n can be found throughout the entire collection. A normalized peak value is then established such that all other bursts in the collection meeting the required tL and tT thresholds from this peak are retained for possible extraction. If a burst has met this re- quirement, it is then examined for duration requirements. Recalling that fs = 20 Msps, and∆t = 1/ fs= 0.05 µsec, a direct relation between NC samples and time duration can be established. The burst duration is then calculated according to its leading sample (nL) and trailing sample (nT) where
TMin< (NDur∗∆t) < TMax. (3.5) If threshold and duration requirements are met, a burst is retained and “extracted” for use in classification; if it does not meet the requirements it is discarded.
3.2.2 Down Conversion and Filtering.
After burst extraction was completed, the retained bursts were subsequently placed through a two-stage process where each was down-converted to baseband ( fc = 0) and filtered. Each process is outlined below:
1. MATLAB was used to down-convert each extracted burst to baseband using its own center frequency estimate derived from a gradient-based frequency estimation process [9, 30].
2. The down-converted burst was placed through a baseband filter to remove back- ground noise and minimize fluctuations in Device Classification. This was done as in [9, 30], using a 8th-order Butterworth filter having a baseband bandwidth of WBB = 1MHz. The result was a single burst, centered at fc = 0, with minimal ef- fect from noise outside of the collected IEEE 802.15.4 channel. This process was repeated for all extracted bursts, with one such burst shown in Fig.3.5 [30].
3.2.3 SNR Scaling.
Finally, to provide a desired analysis range of S NR∈[0 24] dB (S NRA) for Device Classification, AWGN was created using MATLAB and like-filtered before addition to each burst to form the collective SHR used to generate fingerprints.
The collected S NR (S NRC) is a function of both power in the collected signal (without background noise) (PC), and the power in the background noise during collection (PN). PN
Figure 3.5: Normalized PSD Response for Atmel RZUSBstick after baseband down- conversion and application of 8th-order Butterworth Filter W
BB = 1MHz [30].
was measured when none of the six devices was transmitting so that it represents a true “noise-only” power. The resulting S NRC in dB is represented as
S NRC = 10 × log10 PC
PN !
(dB) , (3.6)
which for typical ZigBee collections here ranged from S NRC ≈ 24 dB (USRP) to S NRC ≈ 30 dB (PXIe).
The total signal (sT ot) used for analysis over S NRA is the summation of the received signal with no noise (sr), background noise alone (sN), and added AWGN (sGN), and is given by
sT ot = sr+ sN + sGN . (3.7) The average power in sGN required to achieve S NRA is noted as PGN. The noise samples used to create the desired average AWGN were generated using a random sequence with a
normal distribution that was complex with zero mean. With PGN = 1, the associated scale factor (SF) required to obtain the desired analysis S NRAis given by
SF = q
10−S NRA10 × PC . (3.8)
Following the definition of S NR as the ratio of total signal (without noise) to total noise (without signal), (3.6) can be rewritten to incorporate PGN, shown as
S NRA = 10 × log10
PC PN+ PGN
!
(dB) , (3.9)
where it is noted that generally, the scaled AWGN power is far greater than the collected background noise power (PGN>>PN). This allows for (3.9) to be simplified, reducing it to
S NRA = 10 × log10 PC
PGN !
(dB) . (3.10)
Finally, the total estimated average power for PGN can be calculated following the expression for the total of any given arbitrary complex sequence as shown below
PGN = 1 NC NC X i=1 SF · nGN(i)SF · n ∗ GN(i) . (3.11)
where nGN(i) is the real power, and nGN∗ (i) is the complex conjugate or reactive power, over i=1, 2, . . . , NC total samples. As described above, this process of generating AWGN and appropriately scaling it such that Device Classification could be performed over S NRA∈[0 24] dB, was repeated and subsequently added to each extracted burst before RF-DNA fingerprint generation. Finally, it is noted that S NRAhenceforth is referred to as S NR∈[0 24] dB throughout this document.