## 3 Performance Metrics and Application Scenarios in PLS
### Secrecy Outage Probability (SOP)  
A secure transmission system may be affected by imperfect CSI and wireless fading channels. Therefore, an appropriate secrecy metric needs to be adopted from the perspective of system design and signal processing approaches, which is referred to as secrecy outage probability (SOP). The SOP mainly focuses on the difference between the error probability rates of the legitimate user and the eavesdropper in order to achieve a practical security performance. More precisely, it describes the probability that a detailed evaluation of the secrecy rate for a specific secure transmission system is not achievable. This metric specifically investigates the information security and reliability of data transmission. Despite the importance of the conventional rate outage probability in characterizing and evaluating the achievable secrecy performance of fading channels, the SOP has three main weaknesses [76]: (1) the SOP cannot provide any insights into the capability of an eavesdropper to correctly identify secret messages; (2) the SOP cannot investigate the amount of sensitive data that have been revealed to unintended users when a secrecy outage event occurs; (3) the SOP cannot be related to the requirements of the quality of service (QoS) for different application scenarios. Analogous to the traditional rate outage probability, the SOP is used to estimate the probability that the instantaneous secrecy capacity \(C_{s}\) is below than the actual secrecy rate \(R_{s}^{0}\)[77; 78; 79; 80]. The SOP of this definition is expressed as:  
\[P_{out}\left(R_{s}\right)=P_{r}\Big{\{}C_{s}<R_{s}^{0}\Big{\}} \tag{18}\]  
More specifically, the outage secrecy incidents \(\left\{C_{s}<R_{s}^{0}\right\}\) in (18) indicate that the rate of transmission cannot be executed by the main transmission channels and that the secure communication would not be achieved. In this case, secure transmission would only be achieved when the main transmission channel has a greater SNR than the wiretap channel. On the other hand, the authors in [81] studied the SOPs and outage secrecy rates of quasi-static flat fading channels. They showed that secure transmission can be ensured even when the average SNR of the main transmission channel is less than the eavesdropper channel. Furthermore, their results demonstrated that the instantaneous secrecy performance of fading channel features would be greater than the secrecy performance of a non-fading channel with the same average SNR. Basically, the instantaneous rate capacity is different for the different realizations of fading channel scenarios. More precisely, the average secrecy capacity is equal to the maximum instantaneous secrecy capacity for fading channels. In order to maximize the secrecy performance of secure transmission strategies, the transmission power is optimally allocated based on the statistical distribution of Bob'schannel and the instantaneous realization of the eavesdropper channel. Mathematically, this can be defined as:  
\[max\{C_{B}-E[C_{E}]\};\ s.t.\ 0\leq\varnothing\leq 1 \tag{19}\]  
where \(\varnothing\) represents the ratio of power distribution across the main transmission channel and \(E[C_{E}]\) is the expected capacity of the eavesdropper channel. The average secrecy capacity (\(\overline{C_{s}}\)) can be expressed as:  
\[\overline{C_{s}}=\overline{C_{B}-E[C_{E}]} \tag{20}\]  
To be more specific, the \(\overline{C_{s}}\) can be maximized through the allocation of power based on the assumptions on the knowledge of CSI at the source node [82]. Therefore, the \(\overline{C_{s}}\) may be different when a source Alice has different knowledge about the CSI of the legitimate channels. More generally, it has been shown that the CSI of a legitimate channel is more important than the CSI of an Eve channel. An Alice can decide to send confidential information when the condition of the legitimate channel is strong enough and when the CSI is available at the transmitter. In this case, the CSI of the wiretap channel may not be important for secrecy capacity.