# Efficient MIMO Signal Predistortion for Secrecy-Enhancing
## 4 Simulation Results  
We estimate the performance simulation results of the proposed schemes over a Rayleigh fading environment in comparison to the conventional STBC and SM schemes. In the simulations, we assume that the power of the modulation symbols was normalized to one. Figure 1 shows a comparison of the signal constellation change in the QPSK modulation scheme, when PLS schemes are applied for STBC schemes. If AN or AI is used to enhance secrecy [7; 9], the amplitude of the signal varies greatly, which will lead to a high PAPR problem at the transmitter. On the other hand, due to its phase distortion characteristics, the proposed scheme maintains constant amplitude value, and it will therefore not suffer from a high PAPR problem. Figure 2 shows the BER performance comparison for various STBC schemes with QPSK modulation. Without any secrecy enhancing schemes, [PERSON] and [PERSON] are expected to achieve exactly the same BER performance. The conventional secrecy enhancing scheme with the Alamouti scheme can achieve excellent security protection by making the BER at [PERSON] so bad that it is almost impossible for [PERSON] to extract information [7]. However, this scheme involves sacrificing a power loss of 3 dB for AN to obtain high secrecy protection from [PERSON]. We also note that these AN (or AI)-aided PLS schemes involve a trade-off between the power allocated to AN (or AI) and secrecy protection. Figure 1: Signal constellation comparison at the transmitter. On the other hand, the proposed scheme maintains high secrecy protection, and it also achieves BER performance comparable to that of the conventional full-rate or full-diversity scheme without any additional power allocation. The BER performance of the proposed \(4\times 1\) scheme shows exactly the same performance as the half rate \(4\times 1\) O-STBC scheme, indicating that it achieves full diversity, even with \(R=1\). In addition, the BER performance at Eve with the proposed scheme shows that the proposed scheme does not allow any information leakage to Eve. To evaluate the performance of the SM schemes, we use the \(4\times 4\) MIMO systems with QPSK and \(16\)-QAM, respectively. Figure 3 shows the BER performance comparison with the ZF and MMSE detection schemes. As in the previous case, the conventional schemes without any secrecy enhancing capability lead to the same BER performance at Bob and Eve. The BER performance of the proposed scheme at Bob shows exactly the same performance as the conventional schemes, while the BER performance at Eve is highly deteriorated, indicating that it is almost impossible for Eve to properly extract information. Figure 2: BER performance comparison for various STBC schemes. (**a**) without PLS. (**b**) with PLS. We also investigate the influence of channel estimation error on BER performance. At this time, signals are transmitted through the channel with \(h=\sqrt{1-\rho^{2}}h+\sqrt{\rho^{2}}e\), where \(\tilde{h}\) is an estimated channel gain, \(e\) is the estimation error, and \(\rho^{2}\) is the variance of estimation error [16]. Figure 4 shows the BER performance changes for various STBC schemes according to \(\rho^{2}\). As can be seen in the figure, as \(\rho^{2}\) increases, the proposed method for rate one STBC shows worse performance than the conventional O-STBC scheme with rate \(1/2\). This is because the phase distortion cannot be perfectly nulled out at the receiver in the proposed scheme, which results in a non-orthogonal channel matrix. Nevertheless, the proposed scheme still shows better performance than the conventional QO-STBC scheme with the same rate, and it also provides high security protection. On the other hand, Figure 5 shows the proposed method for SM achieves the same performance behavior as the conventional schemes. The results confirm that the proposed methods are not particularly vulnerable to channel estimation error relative to other conventional methods. Figure 4: BER performance comparison of various STBC schemes with channel estimation error.