Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters

[EN] In this paper, a generation procedure of two correlated Nakagami-m random variables for arbitrary fading parameters values (not necessary identical) is described. For the generation of two correlated Nakagami-m samples, the proposed method uses the generalized Rice distribution, which appears in the conditional distribution of two correlated Nakagami-m variables. This procedure can be applied to simulate diversity systems such as selection combiners, equal-gain combiners, and maximal-ratio combiners as well as multiple-input multipleoutput (MIMO) receiver systems, in Nakagami-m channels.Contract/grant sponsor: Generalitat Valenciana; contract/grant number: GV04B/357.Reig, J.; Martínez Amoraga, MÁ.; Rubio Arjona, L. (2007). Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters. Wireless Communications and Mobile Computing. 7(4):531-537. https://doi.org/10.1002/wcm.386S5315377

On the Bivariate Nakagami-Lognormal Distribution and Its Correlation Properties

The bivariate Nakagami-lognormal distribution used to model the composite fast fading and shadowing has been examined exhaustively. In particular, we have derived the joint probability density function, the cross-moments, and the correlation coefficient in power terms. Also, two procedures to generate two correlated Nakagami-lognormal random variables are described. These procedures can be used to evaluate the robustness of the sample correlation coefficient distribution in both macro- and microdiversity scenarios. It is shown that the bias and the standard deviation of this sample correlation coefficient are substantially high for large shadowing standard deviations found in wireless communication measurements, even if the number of observations is considerable.This work was supported by the Spanish Ministerio de Ciencia e Innovacion TEC-2010-20841-C04-1.Reig, J.; Rubio Arjona, L.; Rodrigo Peñarrocha, VM. (2014). On the Bivariate Nakagami-Lognormal Distribution and Its Correlation Properties. International Journal of Antennas and Propagation. 2014:1-8. https://doi.org/10.1155/2014/328732S182014Rubio, L., Reig, J., & Cardona, N. (2007). Evaluation of Nakagami fading behaviour based on measurements in urban scenarios. AEU - International Journal of Electronics and Communications, 61(2), 135-138. doi:10.1016/j.aeue.2006.03.004Suzuki, H. (1977). A Statistical Model for Urban Radio Propogation. IEEE Transactions on Communications, 25(7), 673-680. doi:10.1109/tcom.1977.1093888Abu-Dayya, A. A., & Beaulieu, N. C. (1994). Micro- and macrodiversity NCFSK (DPSK) on shadowed Nakagami-fading channels. IEEE Transactions on Communications, 42(9), 2693-2702. doi:10.1109/26.317410Tjhung, T. T., & Chai, C. C. (1999). Fade statistics in Nakagami-lognormal channels. IEEE Transactions on Communications, 47(12), 1769-1772. doi:10.1109/26.809692Shankar, P. M. (2004). Error Rates in Generalized Shadowed Fading Channels. Wireless Personal Communications, 28(3), 233-238. doi:10.1023/b:wire.0000032253.68423.86Atapattu, S., Tellambura, C., & Jiang, H. (2011). A Mixture Gamma Distribution to Model the SNR of Wireless Channels. IEEE Transactions on Wireless Communications, 10(12), 4193-4203. doi:10.1109/twc.2011.111210.102115Reig, J., & Rubio, L. (2013). Estimation of the Composite Fast Fading and Shadowing Distribution Using the Log-Moments in Wireless Communications. IEEE Transactions on Wireless Communications, 12(8), 3672-3681. doi:10.1109/twc.2013.050713.120054Mukherjee, S., & Avidor, D. (2003). Effect of microdiversity and correlated macrodiversity on outages in a cellular system. IEEE Transactions on Wireless Communications, 2(1), 50-58. doi:10.1109/twc.2002.806363Zhang, R., Wei, J., Michelson, D. G., & Leung, V. C. M. (2012). Outage Probability of MRC Diversity over Correlated Shadowed Fading Channels. IEEE Wireless Communications Letters, 1(5), 516-519. doi:10.1109/wcl.2012.072012.120452Rui, Z., Jibo, W., & Leung, V. C. M. (2013). Outage probability of composite microscopic and macroscopic diversity over correlated shadowed fading channels. China Communications, 10(11), 129-142. doi:10.1109/cc.2013.6674217Abdel-Hafez, M., & Safak, M. (1999). Performance analysis of digital cellular radio systems in Nakagami fading and correlated shadowing environment. IEEE Transactions on Vehicular Technology, 48(5), 1381-1391. doi:10.1109/25.790511Shankar, P. M. (2009). Macrodiversity and Microdiversity in Correlated Shadowed Fading Channels. IEEE Transactions on Vehicular Technology, 58(2), 727-732. doi:10.1109/tvt.2008.926622MOSTAFA, M. D., & MAHMOUD, M. W. (1964). On the problem of estimation for the bivariate lognormal distribution. Biometrika, 51(3-4), 522-527. doi:10.1093/biomet/51.3-4.522Reig, J., Rubio, L., & Cardona, N. (2002). Bivariate Nakagami-m distribution with arbitrary fading parameters. Electronics Letters, 38(25), 1715. doi:10.1049/el:20021124Tan, C. C., & Beaulieu, N. C. (1997). Infinite series representations of the bivariate Rayleigh and Nakagami-m distributions. IEEE Transactions on Communications, 45(10), 1159-1161. doi:10.1109/26.634675Lien, D., & Balakrishnan, N. (2006). Moments and properties of multiplicatively constrained bivariate lognormal distribution with applications to futures hedging. Journal of Statistical Planning and Inference, 136(4), 1349-1359. doi:10.1016/j.jspi.2004.10.004Sørensen, T. B. (1999). Slow fading cross-correlation against azimuth separation of base stations. Electronics Letters, 35(2), 127. doi:10.1049/el:19990085Reig, J., Martinez-Amoraga, M. A., & Rubio, L. (2007). Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters. Wireless Communications and Mobile Computing, 7(4), 531-537. doi:10.1002/wcm.386Lai, C. D., Rayner, J. C. W., & Hutchinson, T. P. (1999). Robustness of the sample correlation - the bivariate lognormal case. Journal of Applied Mathematics and Decision Sciences, 3(1), 7-19. doi:10.1155/s117391269900001

On the connection between noncircularly-symmetric and noncentral fading models: univariate and multivariate analysis

This thesis provides new statistical connections between noncircularly-symmetric central and circularly-symmetric noncentral underlying complex Gaussian models. This is particularly interesting since it facilitates the analysis of noncircularly-symmetric models, which are often underused despite their practical interest, since their analysis is more challenging. Although these statistical connections have a wide range of applications in different areas of univariate and multivariate analysis, this thesis is framed in the context of wireless communications, to jointly analyze noncentral and noncircularly-symmetric fading models. We provide an unified framework for the five classical univariate fading models, i.e. the one-sided Gaussian, Rayleigh, Nakagami-m, Nakagami-q and Rician, and their most popular generalizations, i.e the Rician shadowed, η-µ, κ-µ and κ-µ shadowed. Moreover, we present new simple results regarding the ergodic capacity of single-input single-output systems subject to κ-µ shadowed, κ-µ and η-µ fadings. With applications to multiple-input multiple-output communications, we are interested in matrices of the form W=XX^H (or W=X^HX), where X is a complex Gaussian matrix with unequal variance in the real and imaginary parts of its entries, i.e., X belongs to the noncircularly-symmetric Gaussian subclass. By establishing a novel connection with the well-known complex Wishart ensemble, we facilitate the statistical analysis of W and give new insights on the effects of such asymmetric variance profile

Characterisation and Modelling of Indoor and Short-Range MIMO Communications

Over the last decade, we have witnessed the rapid evolution of Multiple-Input Multiple-Output (MIMO) systems which promise to break the frontiers of conventional architectures and deliver high throughput by employing more than one element at the transmitter (Tx) and receiver (Rx) in order to exploit the spatial domain. This is achieved by transmitting simultaneous data streams from different elements which impinge on the Rx with ideally unique spatial signatures as a result of the propagation paths’ interactions with the surrounding environment. This thesis is oriented to the statistical characterisation and modelling of MIMO systems and particularly of indoor and short-range channels which lend themselves a plethora of modern applications, such as wireless local networks (WLANs), peer-to-peer and vehicular communications. The contributions of the thesis are detailed below. Firstly, an indoor channel model is proposed which decorrelates the full spatial correlation matrix of a 5.2 GHzmeasuredMIMO channel and thereafter assigns the Nakagami-m distribution on the resulting uncorrelated eigenmodes. The choice of the flexible Nakagami-m density was found to better fit the measured data compared to the commonly used Rayleigh and Ricean distributions. In fact, the proposed scheme captures the spatial variations of the measured channel reasonably well and systematically outperforms two known analytical models in terms of information theory and link-level performance. The second contribution introduces an array processing scheme, namely the three-dimensional (3D) frequency domain Space Alternating Generalised Expectation Maximisation (FD-SAGE) algorithm for jointly extracting the dominant paths’ parameters. The scheme exhibits a satisfactory robustness in a synthetic environment even for closely separated sources and is applicable to any array geometry as long as its manifold is known. The algorithm is further applied to the same set of raw data so that different global spatial parameters of interest are determined; these are the multipath clustering, azimuth spreads and inter-dependency of the spatial domains. The third contribution covers the case of short-range communications which have nowadays emerged as a hot topic in the area of wireless networks. The main focus is on dual-branch MIMO Ricean systems for which a design methodology to achieve maximum capacities in the presence of Line-of-Sight (LoS) components is proposed. Moreover, a statistical eigenanalysis of these configurations is performed and novel closed-formulae for the marginal eigenvalue and condition number statistics are derived. These formulae are further used to develop an adaptive detector (AD) whose aim is to reduce the feasibility cost and complexity of Maximum Likelihood (ML)-based MIMO receivers. Finally, a tractable novel upper bound on the ergodic capacity of the above mentioned MIMO systems is presented which relies on a fundamental power constraint. The bound is sufficiently tight and applicable for arbitrary rank of the mean channel matrix, Signal-to-Noise ratio (SNR) and takes the effects of spatial correlation at both ends into account. More importantly, it includes previously reported capacity bounds as special cases

Measurement techniques enhancements for MIMO 4G mobile communication systems. extension of mode stirred reverberation chambers (MSRCs) emulation capabilities

[ENG] Mobile communications have experienced a brutal raise over the past 15 years. What started as a voice communication system (GSM or 2G) has finished yet as a data communication system of any kind, which in some cases has come to replace the conventional cabled data access infrastructure. This change in the use given to mobile devices necessarily entails a change in the underlying technology, which should be capable to provide the transmission speeds that these new applications require. This has emerged in recent years an increasing interest in multiple antenna techniques, usually referred as multiple-input multiple-output (MIMO) techniques, as they increase the spectral efficiency (and thus the transmission rate for a given bandwidth) of wireless systems. In this thesis, some of the factors limiting the ideal advantages of these multiantenna techniques are studied, in order to quantify the differences between the ideal behavior of 4G devices and behavior that users will experience in actual use conditions. The effect that the user has on the final performance of the devices is one of the main limitations that these devices are in daily use. Mobile phones are used almost all the time in the vicinity of the user, causing a decrease in the richness of the multipath electromagnetic environment (and thus a reduction of the MIMO benefits). As a result of this reduction, the number of signal paths that reach the user is also reduced. In this thesis both factors (user influence and influence of the number of signal paths) will be studied both for passive devices (antenna prototypes) and active devices (commercial phones). The second part of this thesis consist on the study of how to transfer some of these factors reducing the isotropicity of the environment, to one of the most promising measurement techniques, as it is the mode-stirred reverberation chamber (MSRC). This technique emulates naturally an isotropic rich multipath environment with the signal strength following a Rayleigh distribution. However, in this thesis two new techniques are proposed that allow the emulation of less isotropic environments without altering the basic operating principle of the MSRC. [SPA] Las comunicaciones móviles han experimentado un aumento brutal en los últimos 15 años. Lo que comenzó como un sistema de comunicación de voz (GSM o 2G) ha terminado todavía como un sistema de comunicación de datos de cualquier tipo, que en algunos casos ha llegado a sustituir la infraestructura de cableado convencional de acceso a datos. Este cambio en el uso que se da a los dispositivos móviles implica necesariamente un cambio en la tecnología subyacente, que debe ser capaz de proporcionar las velocidades de transmisión que estas nuevas aplicaciones requieren. Esto se ha convertido en los últimos años un creciente interés en las técnicas de múltiples antenas, normalmente se conoce como técnicas de múltiple entrada y múltiple salida (MIMO), ya que aumentan la eficiencia espectral (y por lo tanto la velocidad de transmisión para un ancho de banda dado) de los sistemas inalámbricos. En esta tesis, algunos de los factores que limitan las ventajas ideales de estas técnicas de múltiples antenas son estudiados, con el fin de cuantificar las diferencias entre el comportamiento ideal de dispositivos 4G y comportamiento que los usuarios experimentarán en condiciones reales de uso. El efecto que el usuario tiene sobre el rendimiento final de los dispositivos es una de las principales limitaciones que estos dispositivos son de uso diario. Los teléfonos móviles se utilizan en casi todo el tiempo en la proximidad del usuario, causando una disminución en la riqueza del entorno electromagnético trayectos múltiples (y por tanto una reducción de los beneficios MIMO). Como resultado de esta reducción, el número de trayectorias de señal que llegan al usuario también se reduce. En esta tesis ambos factores (la influencia del usuario y la influencia del número de caminos de señal) se estudió tanto para dispositivos pasivos (prototipos de antenas) y los dispositivos activos (los teléfonos comerciales). La segunda parte de esta tesis consisten en el estudio de cómo transferir algunos de estos factores que reducen la isotropicity del medio ambiente, a una de las técnicas de medición más prometedores, como es la cámara de agitación de modos (MSRC). Esta técnica emula naturalmente un entorno isotrópico multipath rico con la intensidad de la señal después de una distribución de Rayleigh. Sin embargo, en esta tesis, dos nuevas técnicas que se proponen permitir la emulación de entornos isotrópicos menos sin alterar el principio de funcionamiento básico del MSRC.Universidad Politécnica de Cartagen

Applications of Meijer's factorization theorems in performance analyses of all-optical multi-hop FSO systems

The use of bivariate Fox H-functions (BFHFs) in performance analyses of wireless communication systems has gained considerable attention in past few decades. However, the non-existence of robust built-in routines for evaluating such functions in standard computing systems poses numerous challenges in numerical experiments and simulations. Motivated by the apparent need to circumvent these difficulties in performance analyses of cooperative wireless communications, this work presents an alternative method for obtaining the exact, approximate and asymptotic BFHF-free cumulative distribution function (CDF) of the end-to-end (e2e) signal-to-noise ratio (SNR) of multi-hop amplify-and-forward (AF) relaying wireless communication systems. As an illustration, the e2e performance analysis of an all-optical dual-hop free-space optical (FSO) transmission system over Gamma-Gamma turbulence in the presence of pointing errors is revisited. Specifically, new mathematical formulae for the statistical characteristics of the e2e SNR for systems with AF fixed-gain relaying as well as channel-state-information(CSI)-assisted using heterodyne detection (HD) or intensity modulation with direct detection (IM/DD) are derived in terms of mathematically malleable and uniformly convergent infinite series of weighted Meijer G-functions. The usefulness of the derived CDFs is illustrated through derivation of traditional system performance metrics. The accuracy of the derived analytical formulae is verified via Monte Carlo simulations in MATLAB®. Finally, based on results observed in this paper, useful expansions of common BFHFs in terms of easily computable univariate hypergeometric functions are proposed