Generalized MGF of Beckmann Fading with Applications to Wireless Communications Performance Analysis

The Beckmann distribution is a general multipath fading model for the received radio signal in the presence of a large number of scatterers, which can thence be modeled as a complex Gaussian random variable where both the in-phase and quadrature components have arbitrary mean and variance. However, the complicated nature of this distribution has prevented its widespread use and relatively few analytical results have been reported for this otherwise useful fading model. In this paper, we derive a closed-form expression for the generalized moment-generating function (MGF) of the signal-to-noise ratio (SNR) of Beckmann fading, which permits to circumvent the inherent analytical complexity of this model. This is a new and useful result, as it is key for evaluating several important performance metrics of different wireless communication systems and also permits to readily compute the moments of the output SNR. Thus, we obtain simple exact expressions for the energy detection performance in Beckmann fading channels, both in terms of the receiver operating characteristic (ROC) curve and of the area under ROC curve. We also analyze the outage probability in interference limited systems affected by Beckmann fading, as well as the outage probability of secrecy capacity in wiretap Beckmann fading channels. Monte Carlo simulations have been performed to validate the derived expressions.Universidad de Málaga. Campus de Excelencia Internacional. Andalucía Tech

Analysis of energy detection of unknown signals under Beckmann fading channels

(c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The Beckmann fading is a general multipath fading model which includes Rice, Hoyt and Rayleigh fading as particular cases. However, the generality of the Beckmann fading also implies a significant increased mathematical complexity. Thus, relatively few analytical results have been reported for this otherwise useful fading model. The performance of energy detection for multi-branch receivers operating under Beckmann fading is here studied, and the inherent analytical complexity is here circumvented by the derivation of a closed-form expression for the generalized moment generating function (MGF) of the received signal-to-noise ratio (SNR), which is a new and useful result, as it is key for evaluating the receiver operating characteristics. The impact of fading severity on the probability of missed detection is shown to be less critical as the SNR decreases. Monte Carlo simulations have been carried out in order to validate the obtained theoretical expressions.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Proyecto MINECO-FEDER TEC2013-42711-R y TEC2013-44442-P. Junta de Andalucía P11-TIC-7109

On the Calculation of the Incomplete MGF with Applications to Wireless Communications

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI: 10.1109/TCOMM.2016.2626440The incomplete moment generating function (IMGF) has paramount relevance in communication theory, since it appears in a plethora of scenarios when analyzing the performance of communication systems. We here present a general method for calculating the IMGF of any arbitrary fading distribution. Then, we provide exact closed-form expressions for the IMGF of the very general κ-μ shadowed fading model, which includes the popular κ-μ, η-μ, Rician shadowed, and other classical models as particular cases. We illustrate the practical applicability of this result by analyzing several scenarios of interest in wireless communications: 1) physical layer security in the presence of an eavesdropper; 2) outage probability analysis with interference and background noise; 3) channel capacity with side information at the transmitter and the receiver; and 4) average bit-error rate with adaptive modulation, when the fading on the desired link can be modeled by any of the aforementioned distributions.Universidad de Málaga. Campus de Execelencia Internacional. Andalucía Tech

Composite Fading Models based on Inverse Gamma Shadowing: Theory and Validation

We introduce a general approach to characterize composite fading models based on inverse gamma (IG) shadowing. We first determine to what extent the IG distribution is an adequate choice for modeling shadow fading, by means of a comprehensive test with field measurements and other distributions conventionally used for this purpose. Then, we prove that the probability density function and cumulative distribution function of any IG-based composite fading model are directly expressed in terms of a Laplace-domain statistic of the underlying fast fading model and, in some relevant cases, as a mixture of wellknown state-of-the-art distributions. Also, exact and asymptotic expressions for the outage probability are provided, which are valid for any choice of baseline fading distribution. Finally, we exemplify our approach by presenting several application examples for IG-based composite fading models, for which their statistical characterization is directly obtained in a simple form.Comment: This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

On the Utility of the Inverse Gamma Distribution in Modeling Composite Fading Channels

We introduce a general approach to characterize composite fading models based on inverse gamma (IG) shadowing. We first determine to what extent the IG distribution is an adequate choice for modeling shadow fading, by means of a comprehensive test with field measurements and other distributions conventionally used for this purpose. Then, we prove that the probability density function and cumulative density function of any IG-based composite fading model are directly expressed in terms of a Laplace-domain statistic of the underlying fast fading model, and in some relevant cases, as a mixture of well-known state-of-the-art distributions. We exemplify our approach by presenting a composite IG/two-wave with diffuse power fading model, for which its statistical characterization is directly attained in a simple form.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A New Framework for the Performance Analysis of Wireless Communications under Hoyt (Nakagami-q) Fading

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI:10.1109/TIT.2017.2655342We present a novel relationship between the distribution of circular and non-circular complex Gaussian random variables. Specifically, we show that the distribution of the squared norm of a non-circular complex Gaussian random variable, usually referred to as the squared Hoyt distribution, can be constructed from a conditional exponential distribution. From this fundamental connection we introduce a new approach, the Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-q) fading in a very simple way. We illustrate that many performance metrics for Hoyt fading can be calculated by leveraging well-known results for Rayleigh fading and only performing a finite-range integral. We use this technique to obtain novel results for some information and communication-theoretic metrics in Hoyt fading channels.Universidad de Málaga. Campus de Execelencia Internacional. Andalucía Tech

An Extension of the κ -μ Shadowed Fading Model: Statistical Characterization and Applications.

Política de acceso abierto tomada de: https://v2.sherpa.ac.uk/id/publication/3582We here introduce an extension and natural generalization of both the κ-μ shadowed and the classical Beckmann fading models: the Fluctuating Beckmann (FB) fading model. This new model considers the clustering of multipath waves on which the line-of-sight (LoS) components randomly fluctuate, together with the effect of in-phase/quadrature power imbalance in the LoS and non-LoS components. Thus, it unifies a variety of important fading distributions as the one-sided Gaussian, Rayleigh, Nakagami-m, Rician, κ-μ, η-μ, η-κ, Beckmann, Rician shadowed, and the κ-μ shadowed distribution. The chief probability functions of the FB fading model, namely probability density function, cumulative distribution function, and moment generating function are derived. The second-order statistics such as the level crossing rate and the average fade duration are also analyzed. These results can be used to derive some performance metrics of interest of wireless communication systems operating over FB fading channels.Consejería de Economía, Innovación, Ciencia y Empleo of the Junta de Andalucía Spanish Government European Fund for Regional Development FEDER ( Grant Numbers: P2011-TIC-7109, P2011-TIC-8238 and TEC2014-57901-R

Analysis of Gaussian Quadratic Forms with Application to Statistical Channel Modeling

Finalmente, en el contexto de modelado de canal, la metodología de análisis de variables propuesta permite obtener dos nuevas generalizaciones del conocido modelo de desvanecimiento kappa-mu shadowed. Estas dos nuevas distribuciones, nombradas Beckmann fluctuante y kappa-mu shadowed correlado, incluyen como casos particulares a la gran mayoría de distribuciones de desvanecimientos usadas en la literatura, abarcando desde los modelos clásicos de Rayleigh y Rice hasta otros más generales y complejos como el Beckmann y el kappa-mu. Para ambas distribuciones, se presenta su caracterización estadística de primer orden, i.e., función generadora de momentos (MGF), PDF y CDF; así como los estadísticos de segundo orden del modelo Beckmann fluctuante. Fecha de lectura de Tesis Doctoral: 24 Enero 2020En esta tesis se presenta una nueva aproximación a la distribución de de formas cuadráticas gaussianas (FCGs) no centrales tanto en variables reales como complejas. Para ello, se propone un nuevo método de análisis de variables aleatorias que, en lugar de centrarse en el estudio de la variable en cuestión, se basa en la caracterización estadística de una secuencia de variables aleatorias auxiliares convenientemente definida. Como consecuencia, las expresiones obtenidas, con independencia del grado de precisión adquirido, siempre representan una distribución válida, siendo ésta su principal ventaja. Aplicando este método, se obtienen simples expresiones recursivas para la función densidad de probabilidad (PDF) y la función de distribución (CDF) de las FCGs reales definidas positivas. En el caso de las formas complejas, esta nueva forma de análisis conduce a aproximaciones para los estadísticos de primer orden en términos de funciones elementales (exponenciales y potencias), siendo más convenientes para cálculos posteriores que otras soluciones disponibles en la literatura. La tratabilidad matemática se ejemplifica mediante el análisis de sistemas de combinación por razón máxima (MRC) sobre canales Rice correlados, proporcionando aproximaciones cerradas para la probabilidad de outage y la probabilidad de error de bit

The Lomax Distribution for Wireless Channel Modeling: Theory and Applications

We investigate the application of the Lomax distribution for wireless fading modeling purposes. By a proper redefinition of its scale parameter, we present closed-form expressions for its main statistics: probability density function, cumulative distribution function, raw moments and Laplace-domain statistics. Then, relevant performance indicators are derived, including the amount of fading, channel capacity, outage probability and error rate. Other applications include diversity reception using selection combining, as well as composite fading modeling. The Lomax distribution is compared to the relevant case of Rayleigh fading, and to other benchmark distributions of similar complexity used in the literature.Junta de Andalucía under Grant EMERGIA20-00297European Social and Regional Funds and Junta de Andalucía under Grant UMA20-FEDERJA-002MCIN/AEI/10.13039/501100011033 under Grant PID2020-118139RB-I00Universidad de Málaga and TELMA Research Institut

Physical Layer Security of Large Reflecting Surface Aided Communications with Phase Errors

The physical layer security (PLS) performance of a wireless communication link through a large reflecting surface (LRS) with phase errors is analyzed. Leveraging recent results that express the \ac{LRS}-based composite channel as an equivalent scalar fading channel, we show that the eavesdropper's link is Rayleigh distributed and independent of the legitimate link. The different scaling laws of the legitimate and eavesdroppers signal-to-noise ratios with the number of reflecting elements, and the reasonably good performance even in the case of coarse phase quantization, show the great potential of LRS-aided communications to enhance PLS in practical wireless set-ups.Comment: This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accessibl