# Realizing Efficient Security and Privacy in IoT Networks
## 4 System Model
### Optimization of Swift Privacy Rate in a MIMOME  
Considering a network scenario where multiple eavesdroppers operate, the first assumption in realizing a swift privacy rate will be that [PERSON] has full knowledge of her covariance matrix of noise and interference \(\left(\mathbf{M}_{E}\right)\) just as she has full knowledge of all her entire CSI (as earlier stated); then, she can make use of the optimal receiving antenna and her achievable rate would be derived as  
\[R_{TE}=\log\left|\mathbf{M}_{E}+a\mathbf{A}_{1}\mathbf{Z}_{r}\mathbf{A}_{1}^{G} \right|-\log\left|\mathbf{M}_{E}\right| \tag{25}\]  
where  
\[\mathbf{M}_{E}=\mathbf{I}+\frac{aPm}{A_{Tx}-r}\mathbf{A}_{2}\mathbf{A}_{2}^{G }+\frac{eP_{B}}{A_{Rx}}\mathbf{B}\mathbf{B}^{G} \tag{26}\]  
Then, the swift realizable privacy rate would be expressed as  
\[P_{R}=\left(R_{TR}-R_{TE}\right)^{+} \tag{27}\]  
However, for a multiple-input multiple-output multiple-antenna eavesdropping (MIMOME) system, assuming there is a constraint on the number of [PERSON]'s antenna \(\left(A_{E}\right)\), one major issue of the system will be on how can to optimize the parameters of the transmission in such a way that [PERSON]'s interference in the transmission is made difficult. This becomes our focus in this subsection. In this MIMOME system, if there is great increase in of \(\left(A_{E}\right)\), the artificial noise does not have a significant impact on the rate of transmission between \(T_{x}\) and Eve \(\left(R_{TE}\right)\). Therefore, the assumption in this subsection is that there is a constraint on [PERSON]'s maximum number of antennas; therefore, for the reason of optimization, a worst case is assumed, and thus this maximum number of antennas is considered as \(\left(A_{E}\right)\). To achieve this optimization, \(T_{x}\) and \(R_{x}\) cannot utilize the swift CSI at Eve, so as earlier mentioned, \(P_{R}\) is inappropriate for this optimization. From some previous research [6; 13; 18], it is observed that Eve's symptotic rate is a decent approximation to the tangible rate; thus, we adopted this fact in order to achieve optimization. Suppose that the we make no assumption on the realizable random parameter \(\left(r\right)\) and assuming that \(\mathbf{z}_{r}\) is a vector encompassing the transverse elements of \(\mathbf{Z}_{r}\), and \(\left(A_{E}\right)\) is discretely huge. Then, by rewriting (26), we obtained  
\[ \begin{array}{l}R_{TE}=\log\left|\mathbf{I}+\frac{aPm}{A_{Tx}-r}\mathbf{A}_{ 2}\mathbf{A}_{2}^{G}+\frac{eP_{B}}{A_{Rx}}\mathbf{B}\mathbf{B}^{G}+a\mathbf{A} _{1}\mathbf{z}_{r}\mathbf{A}_{1}^{G}\right|\\ -\log\left|\mathbf{I}+\frac{aPm}{A_{Tx}-r}\mathbf{A}_{2}\mathbf{A}_{2}^{G}+ \frac{eP_{B}}{A_{Rx}}\mathbf{B}\mathbf{B}^{G}\right|\\ =\log\left|\mathbf{I}+\mathbf{K}_{3}\bar{\Theta}_{3}\mathbf{K}_{3}^{G}\right|- \log\left|\mathbf{I}+\mathbf{K}_{4}\bar{\Theta}_{4}\mathbf{K}_{4}^{G}\right|,\end{array}  \tag{28}\]  
as \(K_{3}\) and \(K_{4}\) are expanded as \(K_{3}=\frac{1}{\sqrt{A_{E}}}\left[\mathbf{A}_{1},\mathbf{A}_{2}\mathbf{A}_{3} \right],\) and \(K_{4}=\frac{1}{\sqrt{A_{E}}}\left[\mathbf{A}_{2},\mathbf{B}\right].\) where  
\[\bar{\Theta}_{3}=A_{E}\text{trans}\left(\left[a_{r}^{P},\frac{aP_{m}}{A_{Tx}-r }1A_{Tx}-r,\frac{bP_{B}}{A_{Rx}}1A_{Rx}\right]\right), \tag{29}\]  
\[\bar{\Theta}_{4}=A_{E}\text{trans}\left(\left[\frac{aP_{m}}{A_{Tx}-r}1A_{Tx}-r,\frac{bP_{B}}{A_{Rx}}1A_{Rx}\right]\right), \tag{30}\]  
Deriving from the approximation of \(R_{TE}\), an objective function which entails the approximation of \(P_{R}\) is proposed. Note that the proposed objective function does not depend on the CSI of [PERSON]; however, it considers the approximate swift rate of [PERSON]. Likewise, as it is assumed that the transmitter and receiverhas full knowledge of the null space \((\mathbf{G})\), the receivers exact rate is applied but not in its asymptotic form. The objective function is expressed as follows,  
\[