## 3 Performance Metrics and Application Scenarios in PLS
### Secrecy Capacity Metrics  
The goal of secrecy metrics is to quantify and evaluate the security performance of a communication system or a user's privacy under the consideration of a specific adversary. The limits of PLS are characterized by the channel secrecy capacity or the more general trade-off between the maximum transmission rate and the secrecy capacity equivocation rate [66; 67; 68]. In PLS, the secrecy rate is described as the data that are transmitted via the given transmission medium per second, which are available on Bob's channel but are not decoded on the eavesdropper channel. More precisely, to assess the security performance of a system, the achievable secrecy rate and the Gaussian channel inputs have usually been considered in pioneering works [69]. Therefore, the secrecy rate can be defined as the performance difference between the capacities of the main transmission and the wiretap channel. Considering the PLS system model in Figure 1, the achievable rate of a transmission strategy is described as:  
\[R_{s}=\left[R_{B}-R_{E}\right]^{+} \tag{14}\]where the conjugate transpose \(\left[x\right]^{+}\triangleq max\left\{0,\,x\right\}\). \(R_{B}\) and \(R_{E}\) are the data transmission rates of the Bob and eavesdropper channels from the source Alice to the legitimate user and intruder, respectively. Basically, the rate of transmission \(R_{s}\) can be improved using signal processing techniques and optimization approaches, which have been proven to be the lower bounds of security channel capacity [69]. In the actual design of secure transmission systems, a non-zero rate of transmission can be achieved using some multi-antenna techniques, such as secure precoding, beamforming, adaptive resource allocation, etc. Such techniques attempt to intentionally degrade the wiretap channel while enhancing the channel quality for the intended receiver. On the other hand, the performance metrics that are sometimes referred to as the upper bounds of secrecy rate were defined by [70; 71], which play a central role in PLS in terms of secrecy capacity. More accurately, they describe the maximum transmission rate at which confidential messages can be securely delivered to the intended user while preventing the eavesdropper from decoding any important information within the communication. The secrecy capacity of a wireless transmission is an essential theoretical tool for assessing the performance of practical PLS system designs. By examining a channel's secrecy capacity and related features, information-theoretic security can provide common ground and guidance for the design of secure wireless transmission systems. To maximize performance capacity, the qualities of both legitimate and wiretap channels play a significant role in AWGN channels [72]. This can be realized by optimizing the optimal input probability distribution P(X) of mutual information [73], which can be expressed as:  
\[C_{s}=\max_{p(X)}(I(X;Y)-I(X;Z)) \tag{15}\]  
where \(I(X;Y)=H(X)-H(X/Y)\) and \(I(X;Z)=H(X)-H(X/Z)\). \(X\) represents the channel inputs that are sent by source Alice and \(Y\) and \(Z\) are the channel outputs that are received and observed by [PERSON] and the eavesdropper, respectively. It should be noted that wiretap channels are degraded; therefore, the corresponding signals of \(X,\ Y\) and \(Z\) form a Markov chain in any distribution of \(p(X)\)[70; 67]. Based on [72], the secrecy capacity of an AWGN channel is defined as the difference between the capacities of the main transmission channel and the wiretap channel, which is mathematically given as:  
\[C_{s}=C_{B}-C_{E} \tag{16}\]  
where \(C_{B}\) and \(C_{E}\) are the secrecy capacities of the legitimate and wiretap channels, respectively. In this case, it is possible to obtain a non-zero security capacity when the eavesdropper channel is downgraded relative to the Bob channel. Specifically, the intended receiver and eavesdropper channels are supposed to have variances of \({\sigma_{B}}^{2}\) and \({\sigma_{E}}^{2}\), respectively.