Abstract
In this paper, the physical layer security over the M-distributed fading channel is investigated. Initially, an exact expression of secrecy outage probability (SOP) is derived, which has an integral term. To get a closed-form expression, a lower bound of SOP is obtained. After that, the exact expression for the probability of strictly positive secrecy capacity (SPSC) is derived, which is in closed-form. Finally, an exact expression of ergodic secrecy capacity (ESC) is derived, which has two integral terms. To reduce its computational complexity, a closed-from expression for the lower bound of ESC is obtained. As special cases of M-distributed fading channels, the secure performance of the K, exponential, and Gamma-Gamma fading channels are also derived, respectively. Numerical results show that all theoretical results match well with Monte-Carlo simulation results. Specifically, when the average signal-to-noise ratio of main channel is larger than 40 dB, the relative errors for the lower bound of SOP, the probability of SPSC, and the lower bound of ESC are less than 1.936%, 6.753%, and 1.845%, respectively. This indicates that the derived theoretical expressions can be directly used to evaluate system performance without time-consuming simulations. Moreover, the derived results regarding parameters that influence the secrecy performance will enable system designers to quickly determine the optimal available parameter choices when facing different security risks.
Highlights
For future wireless communications, it can be expected that it will be necessary to support massive user connections and exponentially increasing wireless services [1]
For the M-distributed fading channels (i.e., Hn ∼ M(αn, β n, ρn, Ωn, ξ n, φ1,n, φ2,n ), a closed-form expression for the lower bound of secrecy outage probability (SOP) can be derived as
For the M-distributed fading channels (i.e., Hn ∼ M(αn, β n, ρn, Ωn, ξ n, φ1,n, φ2,n ), a closed-form expression for the lower bound of the ergodic secrecy capacity (ESC) is given by
Summary
It can be expected that it will be necessary to support massive user connections and exponentially increasing wireless services [1]. Under generalized Gamma fading channels, the theoretical expressions of the probability of strictly positive secrecy capacity (SPSC) and the SOP were derived in [9]. 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). Under the M-distributed fading channel, the exact expression of the SOP is first derived. The closed-form expression for the probability of the SPSC over the M-distributed fading channel is derived. N ( a, b ) denotes a Gaussian distribution with mean a and variance b. f X ( x ) and FX ( x ) denote the probability density function (PDF) and the cumulative distribution function (CDF) of a random variance X. { x }+ denotes max{ x, 0}
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