Extended Generalized-K (EGK): A New Simple and General Model for Composite Fading Channels
Ferkan Yilmaz, Mohamed-Slim Alouini
备注：
Composite fading distribution, generalized-K distribution, probability density function, cumulative distribution function, fractional moments, level crossing rate, amount of fade duration, moments, amount of fading, average bit error probability, average capacity
In this paper, we introduce a generalized composite fading distribution (termed extended generalized-K (EGK)) to model the envelope and the power of the received signal in millimeter wave (60 GHz or above) and free-space optical channels. We obtain the first and the second-order statistics of the received signal envelope characterized by the EGK composite fading distribution. In particular, expressions for probability density function, cumulative distribution function, level crossing rate and average fade duration, and fractional moments are derived. In addition performance measures such as amount of fading, average bit error probability, outage probability, average capacity, and outage capacity are offered in closed-form. Selected numerical and computer simulation examples validate the accuracy of the presented mathematical analysis.
Most of the well-known fading distributions, if not all of them, could be encompassed by Fox's $H$-function fading. Consequently, we investigate the exact and asymptotic behavior of physical layer security (PLS) over Fox's $H$-function fading wiretap channels. In particular, closed-form expressions are derived for secrecy outage probability (SOP), probability of non-zero secrecy capacity (PNZ), and average secrecy capacity (ASC). These expressions are given in terms of either univariate or bivariate Fox's $H$-function. In order to show the comprehensive effectiveness of our derivations, three …
The performance of energy detection (ED) for independent and identically distribution (i.i.d.) signal models is analyzed over generalized composite non-linear line-of-sight (LOS) and non-line-of-sight (NLOS) shadowed fading scenarios. The novel expressions for α-\k{appa}-μ/Gamma and α-η-μ/Gamma fading channels have been derived to approximate by using the mixture gamma (MG) distribution under low instantaneous signal-to-noise (SNR) condition. On the basis of the deduced fading distributions, novel, exact and close-form detective models are derived to evaluate the sensing performance with diffe…
In this paper, we present the $α$-$η$-$\mathcal{F}$ and $α$-$κ$-$\mathcal{F}$ composite fading distributions. The two distributions generalize the two well-known composite fading distributions, namely the $η$-$μ$/inverse gamma and the $κ$-$μ$/inverse gamma distributions. For both distributions, we derive new exact closed-form expressions for the probability density function (PDF) and cumulative density function (CDF) of the instantaneous signal-to-noise ratio (SNR). Additionally, the outage probabilities (OPs) of a wireless communication system operating over the new composite fading channels …
This letter analyses the effective capacity of communications system using unified models. In order to obtain a simple closed-form mathematically tractable expression, two different unified approximate models have been used. The mixture gamma (MG) distribution which is highly accurate approximation approach has been firstly employed to represent the signal-to-noise-ratio (SNR) of fading channel. In the second approach, the mixture of Gaussian (MoG) distribution which is another unified representation approach has been utilised. A comparison between the simulated and numerical results using bot…
Energy detection is a reliable non-coherent signal processing technology of spectrum sensing of cognitive radio networks, which thanks to its low complexity, no requirement of priori received information and fast sensing ability etc. Since the excellent performance of energy detection would be actually affected by physical multipath fading, this paper is concentrating on characteristics analysis of energy detection over composite shadowed fading channels. The small-scale and line-of-sight fading distribution consists of particular examples such as Rayleigh, Hoyt, Nakagami-m and one sided Gauss…
The secrecy performance of realistic wireless multicast scenarios can be significantly deteriorated by the simultaneous occurrence of multipath and shadowing. To resolve this security threat, in this work an opportunistic relaying-based dual-hop wireless multicast framework is proposed in which the source dispatches confidential information to a bunch of receivers via intermediate relays under the wiretapping attempts of multiple eavesdroppers. Two scenarios, i.e. non-line of sight (NLOS) and line of sight (LOS) communications along with the multiplicative and LOS shadowing are considered wher…
In this study, the product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for \k{appa}-μ fading distribution and α-μ fading distribution is considered. The method of the product model of RVs has been widely applied in numerous of communications fields, such as cascaded fading channels, multiple input multiple output (MIMO) systems, radar communications and cognitive radio networks (CRs). The exact series expressions of the product of two i.n.i.d. RVs X for \k{appa}-μ variates and Y for α-μ variates are derived instead of Fox H-function to solve the problem…
In this paper, we propose a mixture Gamma shadowed (MGS) distribution as a unified composite model via representing the shadowing by an inverse Nakagami-$m$. Accordingly, the exact expression and the asymptotic behaviour at high average signal-to-noise ratio (SNR) regime of the fundamental statistics of a MGS distribution are derived first. These statistics are then applied to analyze the performance of the wireless communications systems over double shadowed $α-κ-μ$ fading via providing the outage probability (OP), the average bit error probability (ABEP), the average channel capacity (ACC), …
In this paper, we investigate the performance of energy detection-based spectrum sensing over F composite fading channels. To this end, an analytical expression for the average detection probability is firstly derived. This expression is then extended to account for collaborative spectrum sensing, square-law selection diversity reception and noise power uncertainty. The corresponding receiver operating characteristics (ROC) are analyzed for different conditions of the average signal-to-noise ratio (SNR), noise power uncertainty, time-bandwidth product, multipath fading, shadowing, number of di…
In this letter, the performance analysis of physical layer security over Fisher-Snedecor $\mathcal{F}$ fading channels is investigated. In particular, the average secrecy capacity (ASC), the secure outage probability (SOP), the lower bound of the SOP (SOP$^L$), and the strictly positive secure capacity (SPSC) are derived in exact closed-from expressions. The Fisher-Snedecor $\mathcal{F}$ fading channel is a composite of multipath/shadowed fading that are represented by the Nakagami-$m$ distribution. Moreover, it provides close results to the practical measurements than the generalised $K$ ($K_…
This paper embodies the Fox's ${\mathcal H}$-transform theory into a unifying modeling and analysis of HetNets. The proposed framework has the potential, due to the Fox's ${\mathcal H}$-functions versatility, of significantly simplifying the cumbersome analysis and representation of cellular coverage, while subsuming those previously derived for all known simple and composite fading models. The paper reveals important insights into the practice of densification in conjunction with signal-to-noise plus interference (SINR) thresholds and path-loss models.
The research presents a procedure of the closed-form average bit error rate evaluation for wireless communication systems in the presence of multipath fading. A generalization of the classical moment generating function is applied, and a connection between the Hankel-type contour-integral representation of the Marcum Q-function and Gauss Q-function is obtained and applied to the analytic derivation of the quadrature amplitude modulated signal average bit error rate in the presence of Nakagami-m fading. The correctness of the obtained solution was verified, and its computational efficiency (in …
In this paper, we analyze the performance of cognitive radio (CR) systems over different composite generalized multipath /shadowed fading scenarios. The \k{appa}-μ shadowed and Fisher-Snedecor F fading channels which are proposed as a simple and high accurate distributions in comparison with generalized-K (KG) and Nakagami-m shadowed conditions are used in this analysis. For the \k{appa}-μ shadowed, a novel simple exact closed-form analytic expression for the probability density function (PDF) and the cumulative distribution function (CDF) are introduced by assuming the fading parameters are i…
This paper develops an innovative approach to the modeling and analysis of downlink cellular networks with device-to-device (D$2$D) transmissions. The analytical embodiment of the signal-to-noise and-interference ratio (SINR) analysis in general fading channels is unified due to the H-transform theory, a taxonomy never considered before in stochastic geometry-based cellular network modeling and analysis. The proposed framework has the potential, due to versatility of the Fox's H functions, of significantly simplifying the cumbersome analysis procedure and representation of D$2$D and cellular c…
In this paper, we investigate the secrecy performance of stochastic MIMO wireless networks over small-scale $α$-$μ$ fading channels, where both the legitimate receivers and eavesdroppers are distributed with two independent homogeneous Poisson point processes (HPPPs). Specifically, accounting for the presence of non-colluding eavesdroppers, secrecy performance metrics, including the connection outage probability (COP), the probability of non-zero secrecy capacity (PNZ) and ergodic secrecy capacity, are derived regarding the $k$-th nearest/best user cases. The index for the $k$-th nearest user …
An alternative or supplementary approach named as physical layer security has been proposed to afford an extra security layer on top of the conventional cryptography technique. In this paper, an overview of secrecy performance investigations over the classic Alice-Bob-Eve wiretap fading channels is conducted. On the basis of the classic wiretap channel model, we have comprehensively listed and thereafter compared the existing works on physical layer secrecy analysis considering the small-scale, large-scale, composite, and cascaded fading channel models. Exact secrecy metrics expressions, inclu…
This paper investigates the performance of Multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) systems with randomly deployed users, where the randomly deployed NOMA users follow Poisson point process (PPP), the spatial correlation between MIMO channels are characterized by using Kronecker model, and the composite channel model is used to capture large-scale fading as well as small-scale fading. The spatial randomness of users' distribution, the spatial correlation among antennas and large-scale fading will severally impact the system performance, but they are seldom cons…
