# Secrecy Enhancing Scheme for Spatial Modulation Using Antenna Selection and Artificial Noise
## 5 Simulation and Numerical Results  
This section presents the secrecy performance comparisons in terms of the secrecy rate. The ergodic secrecy rate, derived in (32), was numerically simulated by using several parameters including \(N_{a}\), \(N_{t}\), modulation order \(M\), and SNR values. In the simulations, the power of the modulation symbol was normalized to one, and the power of the complex AWGN at both Bob and Eve was assumed to be \(\sigma^{2}\), while the SNR was \(1/\sigma^{2}\). We first compared the secrecy performance of the proposed scheme according to the antenna selection method. Figure 3 shows the comparison of the secrecy performance when [PERSON] chooses \(\mathbf{T}_{k}\) by using the optimum selection method described in Section 3.3 and the random selection method, when \(\rho^{2}=0.01\). It was assumed that \(N_{a}=6\) and \(N_{t}=4\), and different APM schemes with \(M=2\), \(M=4\), and \(M=8\) were employed. As shown in Figure 3, compared to the random selection scheme, the proposed optimum antenna selection scheme with \(\mathbf{T}_{k}\) was able to achieve a better secrecy rate. Because the secrecy capacity of fading channels had a ceiling as the transmit SNR increased [17], \(\bar{R}_{s}\) of the proposed scheme increased with the increasing SNR until the SNR approached about 30 dB. Furthermore, it is easy to see that a higher modulation order \(M\) yielded a higher secrecy rate. Next, we compared the secrecy rate of the proposed scheme with the conventional scheme in [9], by applying the same effective data rate, \(r_{e}=n_{t}+\ell\). Figures 4 and 5 show the comparison of \(\bar{R}_{s}\) when \(r_{e}\) were four and five, respectively. When \(r_{e}=4\) in Figure 4, we considered the scenario that [PERSON] employed the 8-PSK modulation, and \(N_{a}\) and \(N_{t}\) were set to three and two, respectively, in the proposed scheme. On the other hand, in the conventional scheme, [PERSON] employed QPSK modulation, and the symbol was transmitted by one of four transmit antennas, i.e., \(N_{t}=4\). When \(r_{e}=5\) in Figure 5, \(N_{a}\) and \(N_{t}\) of the proposed scheme were set to be six and 4, respectively, and the 8-PSK modulation symbol was transmitted. On the other hand, \(N_{t}\) of the conventional scheme was set to be eight, and QPSK symbol was transmitted. As shown in Figures 4 and 5, we observe that the proposed scheme can achieve better secrecy performance than the conventional scheme in [9] when the perfect CSI was given, i.e., \(\rho^{2}=0\). Furthermore, the proposed scheme with channel estimation error of \(\rho^{2}=0.01\) produced a better performance compared to the conventional scheme with perfect CSI. Figure 3: The secrecy rate, \(R_{s}\), of the proposed scheme according to the selection methods of \(T_{k}\) when \(N_{a}=6\) and \(N_{t}=4\). Figure 6 demonstrates the performance of the secrecy rate of the proposed scheme versus SNR with different numbers of transmit antennas \(N_{a}\) and \(N_{t}\), when \(\rho^{2}\) was equal to 0.01. We applied the QPSK modulation. We assumed that Alice was equipped with \(N_{a}=3\), 5, 6, 7, 10, 12, and 15 transmit antennas and utilized \(N_{t}=2\), 4, and 8 effective transmit antennas to send information. As shown in Figure 6, with the increase in the number of transmit antennas \(N_{t}\), the secrecy rate was remarkably improved. When we set \(N_{t}\) to be a fixed value, the more antennas \(N_{a}\) Alice had, the higher the secrecy rate was. Simulation results also showed that the secrecy rate was growing rapidly under the low SNR. As the SNR increased, the secrecy rate tended to approach a saturation point. Because in the case of the low SNR, most of the transmit power was used to transmit the information symbols, more transmit power was used to transmit the AN in order to improve the secrecy rate as the SNR increased. Figure 4: Comparison of \(\bar{R}_{s}\) when \(r_{e}=4\) bits. Figure 5: Comparison of \(\bar{R}_{s}\) when \(r_{e}=5\) bits.