Secrecy Capacity Analysis over $κ-μ$ Fading Channels: Theory and Applications

In this paper, we consider the transmission of confidential information over a $\kappa$-$\mu$ fading channel in the presence of an eavesdropper, who also observes $\kappa$-$\mu$ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and the lower bound of secure outage probability (SOP$^L$) for channel coefficients that are positive, real, independent and non-identically distributed ($i.n.i.d.$). We also provide a closed-form expression for the probability of SPSC when the $\mu$ parameter is assumed to only take positive integer values. We then apply the derived results to assess the secrecy performance of the system in terms of the average signal-to-noise ratio (SNR) as a function of the $\kappa$ and $\mu$ fading parameters. We observed that for fixed values of the eavesdropper's average SNR, increases in the average SNR of the main channel produce a higher probability of SPSC and a lower secure outage probability (SOP). It was also found that when the main channel experiences a higher average SNR than the eavesdropper's channel, the probability of SPSC improved while the SOP was found to decrease with increasing values of $\kappa$ and $\mu$ for the legitimate channel. The versatility of the $\kappa$-$\mu$ fading model, means that the results presented in this paper can be used to determine the probability of SPSC and SOP$^L$ for a large number of other fading scenarios such as Rayleigh, Rice (Nakagami-$n$), Nakagami-$m$, One-Sided Gaussian and mixtures of these common fading models. Additionally, due to the duality of the analysis of secrecy capacity and co-channel interference, the results presented here will also have immediate applicability in the analysis of outage probability in wireless systems affected by co-channel interference and background noise.