# Physical-Layer Security Analysis over M-Distributed Fading Channels
## 1 Introduction  
For future wireless communications, it can be expected that it will be necessary to support massive user connections and exponentially increasing wireless services [1]. With the explosive growth of wireless services, information privacy and security are becoming a major growing concern for users [2]. Traditionally, classical network security techniques [3] are often employed. However, these techniques do not consider the physical nature of the wireless channel. Recently, as a compelling technology for supplementing traditional network security, physical layer security (PLS) has been proposed [4]. The framework of PLS was pioneered by [PERSON], who proposed the concept of perfect secrecy over noiseless channels [5]. However, random noise is an intrinsic element of almost all wireless communication channels. Under noisy channels, [PERSON] established the wiretap channel model and proposed the concept of secrecy capacity [5]. For [PERSON]'s wiretap model, a passive eavesdropper wiretapped the transmission over the main channel. While attempting to decode the information, noconditions are imposed on the available resources for the eavesdropper. After that, [PERSON] introduced the non-degraded channels [5]. It was proved that the secure communication over additive white Gaussian noise (AWGN) channels can be achieved as long as the channel capacity of the main channel is better than that of the eavesdropping channel. By considering the impacts of channel fadings in wireless communications, recent works extended previous results to many scenarios. Under complex Gaussian fading channels, the secrecy capacity was derived in [6]. For Rayleigh fading channels, the average secrecy capacity and secrecy outage performance for frequency diverse array communications were investigated in [7]. In [8], the average secrecy outage probability (SOP) and the average secrecy outage duration of Nakagami-m fading channel were discussed. Under generalized Gamma fading channels, the theoretical expressions of the probability of strictly positive secrecy capacity (SPSC) and the SOP were derived in [9]. Moreover, for Nakagami-n (i.e., Rice) fading channel, the probability of SPSC was derived [10]. Another commonly used model is called lognormal fading, which was usually employed to characterize the shadow fading in radio frequency wireless communications (RFWC) [11], the atmosphere turbulence effects in optical wireless communications (OWC) [12], or the small-scale fading for indoor ultra wide band (UWB) communications [13]. In [14], the SOP of the correlated lognormal fading channels was discussed. For independent/correlated lognormal fading channels, the ergodic secrecy capacity (ESC) and the SOP were investigated in [15]. Moreover, in [16] and [17], the secrecy capacities were analyzed over generalized-K fading channel and \(\kappa-\mu\) fading channel, respectively. As mentioned above, the PLS for many well-known fading channels have been discussed. However, to the best of our knowledge, the PLS for a newly proposed fading model, M distribution, has not been involved in open literature. One motivation to consider the M distribution in this paper is its generality. The M distribution is a general fading model since it covers many well-known fading models as special cases, such as lognormal, Gamma, K, Gamma-Gamma, exponential, et al. [18]. In other words, the M-distributed fading model unifies many previously proposed fading models in a single one. Another motivation is that the M-distributed fading can be applied to many communication environments. Specifically, it can be used to characterize the shadow fading in RFWC, the atmosphere turbulence effects in OWC, or the small-scale fading in indoor UWB communications. As a new tractable fading model, it has been widely used to describe the statistical behavior of these wireless channels. Up to now, closed-form expressions of different performance indicators (such as bit error rate [19], outage probability [20] and capacity [21]) over M fading channels had been analyzed.