# Efficient MIMO Signal Predistortion for Secrecy-Enhancing
## 4 Simulation Results
Figure 3: BER performance comparison for various SM schemes. To compare a security capability of PLS schemes, the secrecy capacity has usually been investigated in the previous studies [3; 9; 17]. Here we first present the equations for the secrecy capacities of the proposed and conventional PLS schemes. The secrecy capacity \(C_{s}\) can be defined as follows:  
\[C_{s}=C_{B}-C_{E}, \tag{25}\]  
where \(C_{B}\) and \(C_{E}\) are the capacities at Bob and Eve, respectively. For conventional AN (or AI)-aided schemes [7; 9], the capacity at Bob, \(C_{A,B}\) can be represented as:  
\[C_{A,B}=\log_{2}\left(1+\frac{||\mathbf{Z}_{A}\mathbf{h}||^{2}/N_{T}}{{\sigma_ {\text{b}}}^{2}}\right), \tag{26}\]  
where \({\sigma_{\text{b}}}^{2}\) represents the variance of AWGN at Bob. On the other hand, Eve suffers from the noise effect of uncanceled \(\mathbf{W}\) as well as AWGN, that is,  
\[\mathbf{y}_{\text{e}}=\underbrace{\mathbf{Z}_{A}\mathbf{g}}_{\text{Signal}}+ \underbrace{\mathbf{W}\mathbf{g}}_{\text{AN}}+\underbrace{\mathbf{n}_{\text{ e}}}_{\text{AWGN}}, \tag{27}\]  
and thus, \(\mathbf{W}\mathbf{g}\) should be treated as noise in addition to AWGN. The capacity at Eve for AN (or AI)-aided schemes, \(C_{A,E}\), can be estimated as follows:  
\[C_{A,E}=\log_{2}\left(1+\frac{||\mathbf{Z}_{A}\mathbf{g}||^{2}/N_{T}}{|| \mathbf{W}\mathbf{g}||^{2}/N_{T}+{\sigma_{\text{e}}}^{2}}\right), \tag{28}\]  
where \({\sigma_{\text{e}}}^{2}\) represents the variance of AWGN at Eve. In the case of the proposed method, the detector at Eve cannot discriminate signal components inside \(\mathbf{y}_{\text{e}}\) in (17), since the signal is distorted by unknown phase information at Alice. That is,  
\[\mathbf{y}_{\text{e}}=\underbrace{\left[g_{1}e^{-j\angle h_{1}}\mathbf{z}_{1} +\ldots+g_{N_{T}}e^{-j\angle h_{N_{T}}}\mathbf{z}_{N_{T}}\right]}_{\text{Noise to Eve}}+ \underbrace{\mathbf{n}_{\text{e}}}_{\text{AWGN}}, \tag{29}\]  
Figure 5: BER performance comparison of various SM schemes with channel estimation error. and thus there is no pure signal component inside \(\mathbf{y_{e}}\). Therefore, the capacities at Bob and Eve for the proposed method can be represented as follows:  
\[ \begin{split} C_{P,B}&=\log_{2}\left(1+\frac{\left| \mathbf{Z}_{N_{T}}^{\prime}\mathbf{h}\right|^{2}/N_{T}}{\sigma_{\mathrm{b}}{}^ {2}}\right),\\ C_{P,E}&=\log_{2}\left(1+\frac{0}{\left|\mathbf{Z}_ {N_{T}}^{\prime}\mathbf{g}\right|^{2}/N_{T}+\sigma_{\mathrm{e}}{}^{2}}\right).\end{split}  \tag{30}\]  
This eventually leads to \(C_{P,E}\) of 0, and this can be confirmed from the BER simulation results shown in Figure 2b. The result shows that BER at Eve is 0.5 regardless of signal to noise ratio (SNR) values, showing no information leakage to Eve. We evaluate the capacities of various PLS schemes by using the above derived equations, and Figure 6 presents the capacity comparisons of PLS schemes at Bob and Eve. Since the proposed method does not consume any additional power for PLS, the capacity of the proposed method at Bob accomplishes the highest, while the capacity of the proposed method at Eve is the lowest that is always zero. The capacity of the existing AN method at Bob shows about 3 dB power loss compared to the proposed method because of the power consumption for AN. On the other hand, the existing AI method barely consumes extra energy, and thus it achieves almost the same capacity as the proposed method at Bob. Nevertheless, Eve also can accomplish better capacity performance with the AI method since the energy consumed for AI is much less than that for AN. This can also be confirmed in Figure 2b, where the BER performance of the AI method is better than that of AN, at Eve. Figure 7 shows the secrecy capacity comparison of the proposed and AN (or AI)-aided PLS schemes. It reveals that the secrecy capacity of the proposed method shows the best performance due to the best and worst capacities at Bob and Eve, respectively, as shown in Figure 6. On the other hand, the conventional AN scheme should sacrifice secrecy capacity due to additional power consumption.