Secrecy Capacity Analysis over $\kappa-\mu$ Fading Channels: Theory and Applications

In this paper, we consider the transmission of confidential information over a κ-μ fading channel in the presence of an eavesdropper, who also observes κ-μ 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) 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 μ 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 κ and μ 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 κ and μ for the legitimate channel. The versatility of the κ-μ fading model, means that the results presented in this paper can be used to determine the probability of SPSC and SOP 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. To demonstrate the efficacy of the novel formulations proposed here, we use the derived equations to provide a useful insight into the probability of SPSC for a range of emerging applications such as cellular device-to-device, vehicle-to-vehicle and body centric fading channels using data obtained from field measurements. Index Terms Fading channels, κ−μ fading, secrecy capacity, co-channel interference, device-to-device communications, vehicular communications, body centric communications. N. Bhargav and S. L. Cotton are with the Wireless Communications Laboratory, Institute of Electronics, Communications and Information Technology, The Queen’s University of Belfast, Queen’s Road, Belfast, BT3 9DT, UK. Email: {nbhargav01, simon.cotton}@qub.ac.uk. D. E. Simmons is with the Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK. Email: [email protected]. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. 2