# On Improving 5G Internet of Radio Light Security Based on LED Fingerprint Identification Method
## 2 LED Fingerprint Verification Mechanism
### Implementation of Features for Extraction and Identification  
As described above, the signal transmitted by a device will pass through an optical wireless channel and be captured at the receiver. The power spectrum of this received signal will be fitted with its theoretical function to extract the feature vector as its fingerprint. The theoretical power spectrum function at the receiver \(p_{Rx}(j\omega)\) is derived as follows:  
\[P_{Rx}(j\omega)=H_{LED}*H_{channel}*G_{PD}*G_{circuit}*P_{input}(j\omega) \tag{7}\]  
\[\omega=[2\pi f_{1},\ 2\pi f_{2},\ 2\pi f_{3},\ldots,2\pi f_{n}] \tag{8}\]  
\[H_{LED}(j\omega)=\frac{\eta r_{d}Z_{in}}{\left((j\omega r_{d}C+1)(R_{s}+Z_{in}+ j\omega L)+r_{d}\right)^{2}} \tag{9}\]  
\[H_{channel}=\frac{Adet(m+1)cos^{m}(\phi)}{2\pi D^{2}} \tag{10}\]  
where \(H_{LED}\) is the power transfer function of the LED. It can be derived from the proposed LED equivalent circuit model. \(H_{channel}\) is the power-loss function of the wireless optical channel [17]. \(G_{PD}\) and \(G_{circuit}\) are the power gain of the photodiode and the VLC front  
Figure 2: LED Fingerprint Extraction and Identification Mechanism.  
end circuits, respectively. In this paper, the lights from the transmitter are considered to propagate only through line-of-sight (LOS), the non-line-of-sight (NLOS) propagation of lights is ignored. Based on the theoretical power spectrum function \(P_{Rx}\) and the practical measurement \(P_{rx}\), optimization can be employed to fit the feature vector \(\lambda\) as defined by (11):  
\[\min_{\lambda}\sum_{\omega=2\pi f_{n}}^{2\pi f_{n}}[P_{Rx}(j\omega)-P_{rx}(j \omega)] \tag{11}\]  
Afterwards, all the feature vectors of devices from 1 to \(n\) will be extracted by the proposed method. The extraction result will be put into a model to train an identification classifier. Here, a multi-SVM classifier [31] is introduced as an example to solve the identification problem of M devices. We supposed that there are \(N\) training samples: \(\{\lambda_{1},LED_{1}\},\ldots,\{\lambda_{N},LED_{N}\}\). Here, \(\lambda_{i}\) is the extracted fingerprint and \(LED_{i}\) is the label that represents the feature vectors extracted from each LED. Subsequently, a one-against-all approach constructs M binary SVM classifiers, each of which separates one LED fingerprint from all the rest. Mathematically, \(i\)th SVM solves Equation (12) to yield the decision function (13):  
\[\left\{\begin{array}{c}\arg\min L\Big{(}\omega,\xi_{j}^{i}\Big{)}=\frac{1}{2 }\|\omega_{i}\|^{2}+C\sum\limits_{l=1}^{N}\xi_{j}^{i}\\ y_{j}\big{(}\omega_{i}^{T}\phi\big{(}\lambda_{j}\big{)}+b_{i}\big{)}\geq 1- \xi_{j}^{i},\ \xi_{j}^{i}\geq 0\end{array}\right. \tag{12}\]  
\[f_{i}(\lambda)=\omega_{i}^{T}\phi(\lambda_{j})+b_{i} \tag{13}\]  
where \(\xi_{j}^{i}\) denotes slack variables that are related to the soft margin, and \(C\) is the tuning parameter used to balance the margin and the training error. \(\phi(\lambda_{j})\) is the nonlinear mapping of \(\lambda_{j}\). It maps the \(\lambda_{j}\) to a much higher dimensional space in which the optimal hyperplane is found. During the classification phase, an unidentified feature vector \(\lambda\) is classified as \(LED_{k}\) which decision function produces the largest value (14).  
\[f_{i}(\lambda)=\omega_{i}^{T}\phi k=\underset{i=1,\ldots,M}{\text{arg max}}\ f_{i}(\lambda)=\underset{i=1,\ldots,M}{\text{max}}\ \omega_{i}^{T}\phi(\lambda)+b_{i}\big{(}\lambda_{j}\big{)}+b_{i} \tag{14}\]