## 7 Secrecy Capacity Analysis  
The ergodic capacity analysed in Section 6 represents the maximum theoretical achievable data rate over a wireless channel, which is an important aspect to achieve efficient data transmission and optimise the system performance. However, in practical scenarios, the communication security is also extremely relevant, and therefore, analysing the secrecy capacity becomes equally important. The secrecy capacity or secrecy rate is a concept primarily used in information theory and communication systems to quantify the amount of secrecy or confidentiality achieved when transmitting digital information over a communication channel, particularly in the presence of potential eavesdroppers. The secrecy capacity represents the maximum theoretical achievable data rate at which information can be transmitted reliably over a wireless channel while maintaining the confidentiality of communication against attackers (commonly referred to as eavesdroppers). The secrecy capacity is essentially a measure of the amount of information that can be transmitted securely over a communication channel and can, therefore, be employed to characterise the level of security of a communication system from a physical-layer point of view. The secrecy capacity is a critical metric in assessing the security and confidentiality of communication systems. A high secrecy rate indicates that a significant amount of information can be transmitted securely, reducing the risk of sensitive data being compromised by unauthorised parties. By considering both the ergodic and secrecy capacities, a robust communication system design can be accomplished. The analysis presented for the ergodic capacity in Section 6 is here complemented by analysing the secrecy capacity. The instantaneous secrecy capacity of a wiretap channel [38] is defined as the difference between the instantaneous channel capacity for the legitimate receiver (i.e., the intended recipient) and the instantaneous channel capacity for the eavesdropper (i.e., the potential attacker). Mathematically, it is defined as \(C_{s}(\gamma_{m},\gamma_{e})=C_{m}-C_{e}\) if \(C_{m}>C_{e}\) and zero otherwise, where \(\gamma_{m}\) and \(\gamma_{e}\) represent the instantaneous SNR of the main and eavesdropper links, respectively, and their instantaneous capacities are given by \(C_{m}=W\log_{2}(1+\gamma_{m})\) and \(C_{e}=W\log_{2}(1+\gamma_{e})\), respectively. Note that the eavesdropper needs to use the same configuration as the main link in order to attempt to successfully decode its information. If the main link transmits over a bandwidth \(B\) using CA with \(N\) CCs, then the eavesdropper must do exactly the same. As a result, the bandwidth penalty parameter \(\alpha\) will be the same for both links as will the net bandwidth available for data transmission, hence the presence of the same bandwidth \(W\) in the expressions of both \(C_{m}\) and \(C_{e}\). The characteristics of the communication channel, such as bandwidth, noise, and fading effects, influence both the legitimate receiver's channel capacity and the eavesdropper's channel capacity. As a result, the instantaneous secrecy capacity will fluctuate randomly. In this context, a meaningful metric for the secrecy capacity is its average value, which can be calculated by averaging the instantaneous secrecy capacity over the fading statistics of the main and eavesdropper links.