Modeling and Analysis of Wireless Channels via the Mixture of Gaussian Distribution

Considerable efforts have been devoted to statistical modeling and the characterization of channels in a range of statistical models for fading channels. In this paper, we consider a unified approach to model wireless channels by the mixture of Gaussian (MoG) distribution. Simulations provided have shown the new probability density function to accurately characterize multipath fading as well as composite fading channels. We utilize the well known expectation-maximization algorithm to estimate the parameters of the MoG model and further utilize the Kullback-Leibler divergence and the mean square error criteria to demonstrate that our model provides both high accuracy and low computational complexity, in comparison with existing results. Additionally, we provide closed form expressions for several performance metrics used in wireless communication systems, including the moment generating function, the raw moments, the amount of fading, the outage probability, the average channel capacity, and the probability of energy detection for cognitive radio. Numerical Analysis and Monte-Carlo simulations are presented to corroborate the analytical results and to provide detailed performance comparisons with the other models in the literature.Comment: This paper is submitted to IEEE Trans. Veh. Tech. (Edited: V2)

A Generalized Non-Linear Composite Fading Model

This work is devoted to the formulation and derivation of the $\alpha{-}\kappa{-}\mu{/}$gamma distribution which corresponds to a physical fading model. The proposed distribution is composite and is constituted by the $\alpha{-}\kappa{-}\mu$ non-linear generalized multipath model and the gamma shadowing model. It also constitute the basis for deriving the $\alpha{-}\kappa{-}\mu$ \textit{Extreme}${/}$gamma model which accounts for non-linear severe multipath and shadowing effects and also includes the more widely known $\alpha{-}\mu$ and $\kappa{-}\mu$ models which includes as special cases the Rice, Weibull, Nakagami-$m$ and Rayleigh distributions. The derived models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects. This is achieved thanks to the remarkable flexibility of their named parameters which have been shown to render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is also evident by the fact that they include as special cases the widely known composite fading models such as the recently reported $\kappa{-}\mu{/}$gamma model and the novel $\alpha{-}\mu{/}$gamma model. Novel analytic expressions are derived for the corresponding probability density function of these distributions which are expressed in a convenient algebraic form and can be efficiently utilized in the derivation of numerous vital measures in investigations related to the analytic performance evaluation of digital communications over composite multipath${/}$shadowing fading channels.Comment: 16 page

A Unified Fading Model Using Infinitely Divisible Distributions

This paper proposes to unify fading distributions by modeling the magnitude-squared of the instantaneous channel gain as an infinitely divisible random variable. A random variable is said to be infinitely divisible, if it can be written as a sum of $n \geq 1$ independent and identically distributed random variables, for each $n$. Infinitely divisible random variables have many interesting mathematical properties, which can be applied in the performance analysis of wireless systems. It is shown that the proposed unification subsumes several unifications of fading distributions previously proposed in the wireless communications literature. In fact, almost every distribution used to model multipath, shadowing and composite multipath/shadowing is shown to be included in the class of infinitely divisible random variables.Comment: 28 pages, 4 figure

Ergodic Capacity of Composite Fading Channels in Cognitive Radios with the Product of κ\kappa-μ\mu and α\alpha-μ\mu Variates

In this study, the product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for \k{appa}-{\mu} fading distribution and {\alpha}-{\mu} 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}-{\mu} variates and Y for {\alpha}-{\mu} variates are derived instead of Fox H-function to solve the problem that Fox H-function in the RVs product could not be implemented in popular mathematical software packages as Mathematica and Maple. Novel Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) of proposed models are deduced to present the series expressions of product and generalized composite multipath shadowing models. Furthermore, novel exact expressions of the ergodic channel capacity (ECC) are obtained under optimal rate adaptation with constant transmit power (ORA). At last, these analytical results are confirmed with monte-carlo simulations to evaluate spectrum efficiency over generalized composite shadowing fading scenarios in CRs

Security Performance Analysis of Physical Layer over Fisher-Snedecor F\mathcal{F} Fading Channels

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 $K$ ($K_G$) fading channels. To validate our analysis, the numerical results are affirmed by the Monte Carlo simulations.Comment: 4 pages, 5 figure

Performance Analysis of Energy Detection over Mixture Gamma based Fading Channels with Diversity Reception

The present paper is devoted to the evaluation of energy detection based spectrum sensing over different multipath fading and shadowing conditions. This is realized by means of a unified and versatile approach that is based on the particularly flexible mixture gamma distribution. To this end, novel analytic expressions are firstly derived for the probability of detection over MG fading channels for the conventional single-channel communication scenario. These expressions are subsequently employed in deriving closed-form expressions for the case of square-law combining and square-law selection diversity methods. The validity of the offered expressions is verified through comparisons with results from respective computer simulations. Furthermore, they are employed in analyzing the performance of energy detection over multipath fading, shadowing and composite fading conditions, which provides useful insighs on the performance and design of future cognitive radio based communication systems.Comment: To appear in the IEEE WiMob 2015 conference proceeding

Unified Analysis of Cooperative Spectrum Sensing over Composite and Generalized Fading Channels

In this paper, we investigate the performance of cooperative spectrum sensing (CSS) with multiple antenna nodes over composite and generalized fading channels. We model the probability density function (PDF) of the signal-to-noise ratio (SNR) using the mixture gamma (MG) distribution. We then derive a generalized closed-form expression for the probability of energy detection, which can be used efficiently for generalized multipath as well as composite (multipath and shadowing) fading channels. The composite effect of fading and shadowing scenarios in CSS is mitigated by applying an optimal fusion rule that minimizes the total error rate (TER), where the optimal number of nodes is derived under the Bayesian criterion, assuming erroneous feedback channels. For imperfect feedback channels, we demonstrate the existence of a TER floor as the number of antennas of the CR nodes increases. Accordingly, we derive the optimal rule for the number of antennas that minimizes the TER. Numerical and Monte-Carlo simulations are presented to corroborate the analytical results and to provide illustrative performance comparisons between different composite fading channels.Comment: Submitted to IEEE Trans. Veh. Tech

On the Ergodic Capacity of Underlay Cognitive Dual-Hop AF Relayed Systems under Non-Identical Generalized-K Fading Channels

The ergodic capacity of underlay cognitive (secondary) dual-hop relaying systems is analytically investigated. Specifically, the amplify-and-forward transmission protocol is considered, while the received signals undergo multipath fading and shadowing with non-identical statistics. To efficiently describe this composite type of fading, the well-known generalized-$K$ fading model is used. New analytical expressions and quite accurate closed-form approximations regarding the ergodic capacity of the end-to-end communication are obtained, in terms of finite sum series of the Meijer's-$G$ function. The analytical results are verified with the aid of computer simulations, while useful insights are revealed.Comment: 11 pages, 2 figures, 1 tabl

Entropy and Channel Capacity under Optimum Power and Rate Adaptation over Generalized Fading Conditions

Accurate fading characterization and channel capacity determination are of paramount importance in both conventional and emerging communication systems. The present work addresses the nonlinearity of the propagation medium and its effects on the channel capacity. Such fading conditions are first characterized using information theoretic measures, namely, Shannon entropy, cross entropy and relative entropy. The corresponding effects on the channel capacity with and without power adaptation are then analyzed. Closed-form expressions are derived and validated through comparisons with respective results from computer simulations. It is shown that the effects of fading nonlinearities are significantly larger than those of fading parameters such as the scattered-wave power ratio, and the correlation coefficient between the in-phase and quadrature components in each cluster of multipath components.Comment: Latest/Priprint versio

Sensing of Unknown Signals over Weibull Fading Conditions

Energy detection is a widely used method of spectrum sensing in cognitive radio and Radio Detection And Ranging (RADAR) systems. This paper is devoted to the analytical evaluation of the performance of an energy detector over Weibull fading channels. This is a flexible fading model that has been shown capable of providing accurate characterization of multipath fading in, e.g., typical cellular radio frequency range of 800${/}$900 MHz. A novel analytic expression for the corresponding average probability of detection is derived in a simple algebraic representation which renders it convenient to handle both analytically and numerically. As expected, the performance of the detector is highly dependent upon the severity of fading as even small variation of the fading parameters affect significantly the value of the average probability of detection. This appears to be particularly the case in severe fading conditions. The offered results are useful in evaluating the effect of multipath fading in energy detection-based cognitive radio communication systems and therefore they can be used in quantifying the associated trade-offs between sensing performance and energy efficiency in cognitive radio networks.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1505.0333