*3.1. Performance Metrics*

In the non-colluding case, the eavesdropper individually overhears the communication between Alice and Bob without any centralized processing. Therefore, the SNR of multiple eavesdroppers is given by SNR*<sup>E</sup>* = max (SNR*Ei* ), where SNR*Ei* is defined in Equation (11). Whereas, in the colluding case, *NE* Eves are capable of sending the information to a central data processing unit (CDPU) and jointly process their received information as shown in Figure 1a. Thus, the SNR of multiple eavesdroppers is given by SNR*<sup>E</sup>* = <sup>∑</sup>*NE <sup>i</sup>*=<sup>1</sup> SNR*Ei* . We adopt the following metrics to evaluate the secrecy performance of the proposed system.

*Secure transmission probability* (STP): STP is defined as a complementary element of secrecy outage probability (SOP) [31]. A supremum of the secrecy transmission rate *R* is determined by the difference of the main channel capacity *CB* = *log*(1 + SNR*B*) and the wiretap channel capacity *CE* = *log*(1 + SNR*E*). If secrecy transmission rates *R* are less than this supremum *CS* = *CB* − *CE*, a secure transmission can be realized, otherwise, a secrecy outage occurs. The STP in non-colluding and colluding cases are, respectively, defined as:

$$P(C\_S > R) = \prod\_{E\_i \in \Phi} P(\frac{1 + \text{SNR}\_B}{1 + \text{SNR}\_{E\_i}} > 2^R),\tag{12}$$

$$P(\mathbb{C}\_S > R) = P(\frac{1 + \text{SNR}\_B}{1 + \sum \text{SNR}\_{E\_i}} > 2^R). \tag{13}$$

*Ergodic secrecy capacity* (ESC): ESC is defined as the average transmission rate of the confidential message, which is formulated as:

$$\overline{\mathbb{C}}\_{\mathcal{S}} = E[\mathbb{C}\_{\mathcal{S}}] = \int\_0^\infty P(\mathbb{C}\_{\mathcal{S}} > R)dR. \tag{14}$$

In practice, ECS is used to describe the fast fading channel while STP for a slow fading channel. However, the numerical value of ECS is still determined by the STP. As long as we obtain the STP, the ESC can be simply calculated by its integration.
