# Realizing Efficient Security and Privacy in IoT Networks
## 4 System Model  
In this section, the system model is described. There are similarities in the model to what was given in [8]. For the set-up, a three-node-based wireless transmission is illustrated in Figure 2.  
In the set-up, all three nodes are attached to a single transmitting antenna. The intention of the transmitter (Source) is to broadcast some private information to the receiver (Destination) while [PERSON] (a passive eavesdropper) attempts to gain access to the sensitive private information. We assume that each link channel entails several \(M\) orthogonal subcarriers and each subcarrier fading is flat. Tackling eavesdropping attacks in this set-up entails that artificial noise is broadcasted by \(R_{x}\) with the same frequency and in the same channel, which reduces [PERSON]'s reception quality. Considering that this jamming attack operates at the same frequency and time in which information is transmitted from \(T_{x}\) to \(R_{x}\); thus, it is  
Figure 2: A single-antenna three-node wireless transmission with a full-duplex destination.  
assumed that \(R_{x}\) has full-duplex aptitude. It is well known that there is no perfect full-duplex system, therefore \(R_{x}\) always manifests some level of residual self-interference.  
Considering \(y_{s}(x)\in{}^{\text{Mx1}}\) is the signal vector independent and identically distributed (i.i.d) zero mean cyphers and unit variance that the \(T_{x}\) will be transmitting while \(y_{d}(x)\in{}^{\text{Mx1}}\) is assumed to be the jamming noise vector of i.i.d. zero mean cyphers and unit variance the transmitter (\(T_{x}\)) will be transmitting. Thus, the signal vectors \(R_{x}\) and Eve received can be individually described,  
\[z_{d}(x)=\mathbf{g}_{sd}*\sqrt{\mathbf{p}_{s}}*y_{s}(x)+\sqrt{\delta}\mathbf{g} _{dd}*\sqrt{\mathbf{p}_{d}}*y_{d}(x)+\mathbf{m}_{d}(x), \tag{8}\]  
\[z_{e}(x)=\mathbf{g}_{se}*\sqrt{\mathbf{p}_{s}}*y_{s}(x)+\mathbf{g}_{de}*\sqrt{ \mathbf{p}_{d}}*y_{d}(x)+\mathbf{m}_{e}(x), \tag{9}\]  
where \({}^{\text{Mx1}}\) comprises the vector, \(\mathbf{g}_{sd},\mathbf{g}_{se},\mathbf{g}_{de}\), and \(\mathbf{g}_{dd}\) are explicitly described in Figure 2, and \(\mathbf{p}_{s}\) and \(\mathbf{p}_{d}\) vectors, respectively, represent the power of transmission between the \(T_{x}\) and \(R_{x}\). \(\mathbf{m}_{d}(x)\in{}^{\text{Mx1}}\) and \(\mathbf{m}_{e}(x)\in{}^{\text{Mx1}}\) are considered as the mean of independent white Gaussian noise of zero and unit variance, respectively. The multiplication and square root are used as element-wise operators, and \(\delta\) represents the attenuation factor of self-interference.  
Denoting the superscript \((m)\) as a vector \(m\)th element, we formulate the respective signal-to-noise-ratios (SNRs) of the \(m\)th subcarrier at \(R_{x}\) and Eve as  
\[\gamma_{d}^{(m)}=\frac{A_{m}y_{m}}{1+B_{m}z_{m}}\text{and}\gamma_{e}^{(m)}= \frac{C_{m}y_{m}}{1+D_{m}z_{m}}, \tag{10}\]  
where \(A_{m}=\left|\mathbf{g}_{sd}^{(n)}\right|^{2}\), \(B_{m}=\delta\left|\mathbf{g}_{dd}^{(n)}\right|^{2}\), \(C_{m}=\left|\mathbf{g}_{se}^{(n)}\right|^{2}\), \(D_{m}=\left|\mathbf{g}_{de}^{(n)}\right|^{2}\), \(y_{m}=\mathbf{p}_{s}^{(m)}\) and \(z_{m}=\mathbf{p}_{d}^{(m)}\). Recall that as stated earlier, [PERSON]'s CSI (\(C_{m}\) and \(D_{m}\forall m\)) is only supposed to be recognizable by legitimate users in this Section.  
Thus, the privacy capacity of this model is defined as  
\[S_{c}(y,z)=\frac{1}{M}\sum_{m=1}^{M}\max\left\{0,\Delta S_{m}(y_{m},z_{m})\right\}, \tag{11}\]  
where  
\[\Delta S_{m}(y_{m},z_{m})=\log\left(1+\gamma_{d}^{(m)}\right)-\log\left(1+ \gamma_{e}^{(m)}\right). \tag{12}\]