# Waveform Design for Space-Time Coded MIMO Systems with High Secrecy Protection +
## 4 Performance Evaluation  
This section presents the secrecy and BER performances of the proposed waveform design using LD-QO-STBC over a Rayleigh-faded MIMO channel, and compares them with the conventional schemes. In order to consider the worst-case for secrecy protection, we assume that not only [PERSON] but also [PERSON] have perfect CSI, and that they have the same signal-to-noise ratio (SNR). On the other hand, [PERSON] only shares the CSI for [PERSON]. We also assume that [PERSON] transmits information using 4-QAM through the MIMO channel without frequency selectivity. All channel gains for each transmit symbol are assumed to be independent and constant over four consecutive symbol periods. In the simulations, the aggregated power from all the transmit antennae was normalized to one.  
We first compare the secrecy capacity of the proposed scheme with the conventional schemes. It is well known that the secrecy capacity \(C_{s}\) can be expressed by [6]:  
\[\mathbf{C}_{s}=\max\left(C_{B}-C_{E},0\right), \tag{27}\]  
where \(C_{B}\) and \(C_{E}\) are the capacities achieved at Bob and Eve, respectively. Because the added AI can be canceled at Bob, \(C_{B}\) can be estimated as in the conventional MIMO systems, as follows:  
\[C_{B}=\log_{2}\det\left(\mathbf{I}+\frac{P}{\sigma_{b}^{2}}\mathbf{H}\mathbf{H}^{\rm H }\right), \tag{28}\]  
where \(P\) and \(\sigma_{b}^{2}\) are the transmit power and noise variance at Bob, resulting in \(P/\sigma_{b}^{2}\) being the SNR. On the other hand, \(C_{E}\) is estimated by accounting for the added AI, as follows [18]:  
\[C_{E}=\log_{2}\det\left(\mathbf{I}+\frac{P}{(\|\mathbf{W}\|^{2}+\sigma_{e}^{2})} \mathbf{G}\mathbf{G}^{\rm H}\right), \tag{29}\]  
where, \(\sigma_{e}^{2}\) is the noise variance at Eve.  
We estimate the secrecy performance in terms of \(C_{s}\) in (27), and Figure 3 compares the simulation results of the average secrecy capacity. For comparative purpose, we implement a number of conventional schemes: (1) the Alamouti scheme [15], (2) the LD-QO-STBC scheme [14], (3) the QO-STBC scheme with power scaling [13], (4) the Alamouti scheme with AN [10], and (5) the proposed scheme. Because we assume that [PERSON] and [PERSON] have perfect CSI of their own and the same SNR, the secrecy capacities of the conventional schemes without any AN or AI, i.e., (1), (2), and (3), are almost zero. On the other hand, the addition of AN to the Alamouti scheme contributes largely to enhancing the secrecy capacity, even though [PERSON] has the same SNR as [PERSON]. Moreover, the proposed scheme achieves the best secrecy performance amongst the various schemes.  
Next, Figure 4 compares the BER performance simulation results. With the conventional schemes, (1), (2), and (3), [PERSON] and [PERSON] will have almost the same BER performance. On the other hand, due to the highly enhanced secrecy protection in (4) the Alamouti scheme with AN, and (5) the proposed scheme, the BER performance at [PERSON] approaches to 0.5. This means that there is no information leakage to [PERSON]. However, at the expense of power usage of adding AN in scheme (4), we have to sacrifice  
Figure 3: Secrecy capacity of the proposed scheme over a Rayleigh fading channel compared to the conventional space–time block coding (STBC)-based PLS schemes.  
power loss. For example, in scheme (4) the same power is allocated to AN as to the information signal, so we can find a 3 dB power loss in the performance. On the other hand, the proposed scheme utilizes the pairwise power reallocation for AI, and thus it does not incur any power loss.