Secrecy Analysis in SWIPT Systems Over Generalized-$K$ Fading Channels

Abstract

Citation Zhang L, Zhao H, Pan G, et al. Secure analysis over generalized-K channels. Sci China Inf Sci, for reviewDear editor, The secrecy outage probability (SOP) is used to estimate the secrecy outage performance when the transmitter has no state information about potential wiretap channels [1], i.e., silent eavesdropping. Most previous work, such as [2,3], has focused on the SOP defined in [1], which we call the conventional SOP in this letter, where both unreliable transmission from the transmitter to the legitimate receiver (i.e., outage) and information leakage to eavesdroppers are considered to be secrecy outage. Thus, according to the conventional SOP definition, a secrecy outage does not necessarily imply that any information has been leaked to eavesdroppers. To capture the actual information leakage, [4] proposed a new SOP definition, which we call the proposed SOP in this letter, that is exactly the information leakage probability. However, they only considered the SOP over Rayleigh fading channels, a simple small-scale channel model. In actual wireless communications scenarios, shadowing is typically involved, resulting in large-scale fading [5].The generalized-K (GK) fading model was proposed [6] to capture composite fading channels (with both small-and large-scale fading), but the exact model involves modified Bessel functions of the second kind, which usually results in Meijer's G-function or more advanced special functions appearing in the final SOP expression [7]. It is still a matter of debate as to whether the Meijer's Gfunction can be viewed as a closed-form expression.To avoid this function, [8] simplified the GK model by using a mixed Gamma distribution.Although the SOP over GK fading channels has already been investigated [2,7], the authors in [2,7] only considered the conventional SOP definition, which does not give the actual information leakage probability. Moreover, they did not investigate the asymptotic performance when the main link's signal-to-noise ratio (SNR) is sufficiently large, which gives the secrecy diversity order and array gain [3]. Others have studied the SOP's asymptotic behavior [9], but their conclusions as to its secrecy diversity order are not valid in the general case.In this letter, we adopt the SOP definition in [4] and the simplified model of [8], and derive a closed-form expression for the proposed SOP over GK fading channels. To simplify this expression and obtain additional insights, we also perform an asymptotic analysis of the main link in the high-SNR region.System Model. In the standard Wyner model [1], a source transmits confidential messages to a destination d. Meanwhile, an eavesdropper e wants to overhear this information. Here, we assume that all links undergo independent GK fading. The exact probability density function (PDF) γ t of the instantaneous SNR at t (t ∈ {d, e}) is given by [7] f γt (x) = G 2,0 0,2

A Simple Evaluation for the Secrecy Outage Probability Over Generalized-K Fading Channels

“…In this section, we use the Monte-Carlo simulation to validate the high accuracy of our proposed SOP and ASOP expressions, i.e., (6), (15) and (20).…”

“…This approximation is tight for small γ e . When γ e is too large, (15) in [17] derived based on γ e ≫ 0 can be used to derive the SOP. Therefore, an approximate and simple SOP expression with a high accuracy can be always derived for any γ e .…”

“…Lemma 1: When γ d → ∞ and γ e is finite, the ASOP for k d = m d over GK fading channels is given by (15) where v = min{k d , m d }, i.e., v is the minimum between k d and m d . It is obvious that the secrecy diversity order is min{k d , m d }.…”

“…The authors in [12] firstly investigated the typical Wyner's three-node model of [5] in physical layer security over GK fading channels, and derived the closed-form expression for the secrecy outage probability (SOP) by using the mixture Gamma distribution approximation introduced in [4]. This mixture Gamma approximation was also adopted in many works about the secure analysis over GK fading channels, such as [13]- [15]. Further, based on the mixture Gamma distribution model in [4], the authors in [16] developed a general method to analyze the SOP by using the Fox's H-function.…”

“…The secure approximation analysis in [19] for Log-normal and Log-normal-Rayleigh composite fading channels based on the work of [20] shows a strong robustness in the low variance region of the wiretap channel, where the difference calculation takes place of the integration calculation, resulting in a much faster computation for the SOP. Although the asymptotic SOP (ASOP) valid in the high SNR region of the main channel, showing the secrecy diversity order and array gain, was analyzed in [13], [15], the authors only considered a special parameter setting of GK fading, which cannot be used in the general GK fading case.…”