Co-channel interference and background noise in κ - μ fading channels

In this letter, we derive novel analytical and closed form expressions for the outage probability, when the signal-of- interest (SoI) and the interferer experience kappa-mu fading in the presence of Gaussian noise. Most importantly, these expressions hold true for independent and non-identically distributed kappa-mu variates, without parameter constraints. We also find the asymptotic behaviour when the average signal to noise ratio of the SoI is significantly larger than that of the interferer. It is worth highlighting that our new solutions are very general owing to the flexibility of the kappa-mu fading model21512151218CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ304248/2014-2This work was supported by the U.K. Engineering and Physical Sciences Research Council under Grant Reference EP/L026074/1 and by CNPq under Grant Reference 304248/2014-2

Log-moment estimators of the Nakagami-lognormal distribution

[EN] In this paper, estimators of the Nakagami-lognormal (NL) distribution based on the method of log-moments have been derived and thoroughly analyzed. Unlike maximum likelihood (ML) estimators, the log-moment estimators of the NL distribution are obtained using straightforward equations with a unique solution. Also, their performance has been evaluated using the sample mean, confidence regions and normalized mean square error (NMSE). The NL distribution has been extensively used to model composite small-scale fading and shadowing in wireless communication channels. This distribution is of interest in scenarios where the small-scale fading and the shadowing processes cannot be easily separated such as the vehicular environment.This work has been funded in part by the Programa de Estancias de Movilidad de Profesores e Investigadores en Centros Extranjeros de Ensenanza Superior e Investigacion of the Ministerio de Educacion, Cultura y Deporte, Spain, PR2015-00151 and by the Ministerio de Economia, Industria y Competitividad of the Spanish Government under the national project TEC2017-86779-C2-2-R, through the Agencia Estatal de Investigacion (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER).Reig, J.; Brennan, C.; Rodrigo Peñarrocha, VM.; Rubio Arjona, L. (2019). Log-moment estimators of the Nakagami-lognormal distribution. EURASIP Journal on Wireless Communications and Networking. 1-10. https://doi.org/10.1186/s13638-018-1328-6S110J. M. Ho, G. L. Stüber, in Co-channel interference of microcellular systems on shadowed Nakagami fading channels. Proc. IEEE 43rd Vehicular Technology Conference, 1993 (VTC 93) (IEEESecaucus, 1993), pp. 568–571.A. A. Abu-Dayya, N. C. Beaulieu, Micro- and macrodiversity NCFSK (DPSK) on shadowed Nakagami-fading channels. IEEE Trans. Commun.42(9), 2693–2702 (1994).X. Wang, W. Wang, Z. Bu, Fade statistics for selection diversity in Nakagami-lognormal fading channels. Electron. Lett.42(18), 1046–1047 (2006).D. T. Nguyen, Q. T. Nguyen, S. C. Lam, Analysis and simulation of MRC diversity reception in correlated composite Nakagami-lognormal fading channels. REV J. Electron. Commun.4(1–2), 44–51 (2014).P. Xu, X. Zhou, D. Hu, in Performance evaluations of adaptive modulation over composite Nakagami-lognormal fading channels. 2009 15th Asia-Pacific Conference on Communications (IEEEShanghai, 2009), pp. 467–470.G. C. Alexandropoulos, A. Conti, P. T. Mathiopoulos, in Adaptive M-QAM systems with diversity in correlated Nakagami-m fading and shadowing. IEEE Global Telecommunications Conference (GLOBECOM 2010) (IEEEMiami, 2010), pp. 1–5.Ö. Bulakci, A. B. Saleh, J. Hämäläinen, S. Redana, Performance analysis of relay site planning over composite fading/shadowing channels with cochannel interference. IEEE Trans. Veh. Technol.62(4), 1692–1706 (2013).W. Cheng, Y. Huang, On the performance of adaptive SC/MRC cooperative systems over composite fading channels. Chin. J. Electron.25(3), 533–540 (2016).M. G. Kibria, G. P. Villardi, W. Liao, K. Nguyen, K. Ishizu, F. Kojima, Outage analysis of offloading in heterogeneous networks: Composite fading channels. IEEE Trans. Veh. Technol.66(10), 8990–9004 (2017).K. Cho, J. Lee, C. G. Kang, Stochastic geometry-based coverage and rate analysis under Nakagami & log-normal composite fading channel for downlink cellular networks. IEEE Commun. Lett.21(6), 1437–1440 (2017).R. Singh, M. Rawat, Closed-form distribution and analysis of a combined Nakagami-lognormal shadowing and unshadowing fading channel. J Telecommun. Inf. Technol.4:, 81–87 (2016).J. Reig, L. Rubio, Estimation of the composite fast fading and shadowing distribution using the log-moments in wireless communications. IEEE Trans. Wireless. Commun.12(8), 3672–3681 (2013).S. Atapattu, C. Tellambura, H. Jiang, A mixture gamma distribution to model the SNR of wireless channels. IEEE Trans. Wireless Commun.10(12), 4193–4203 (2011).Q. Wang, H. Lin, P. Kam, Tight bounds and invertible average error probability expressions over composite fading channels. J. Commun. Netw.18(2), 182–189 (2016).J. M. Holtzmann, On using perturbation analysis to do sensitivity analysis: derivatives versus differences. IEEE Trans. Autom. Control. 37(2), 243–247 (1992).H. Suzuki, A statistical model for urban radio propagation. IEEE Trans. Commun.25(7), 673–680 (1977).M. D. Yacoub, The α- μ distribution: a physical fading model for the Stacy distribution. IEEE Trans. Veh. Technol.56(1), 122–124 (2007).P. M. Shankar, Error rates in generalized shadowed fading channels. Wirel. Pers. Commun.28(3), 233–238 (2004).J. -M. Nicolas, Introduction aux statistiques de deuxième espèce: applications des logs-moments et des logs-cumulants à l’analyse des lois d’images radar. Traitement du Signal. 19(3), 139–167 (2002). Translation to English by S. N. Anfinsen.C. Withers, S. Nadarajah, A generalized Suzuki distribution. Wirel. Pers. Commun.62(4), 807–830 (2012).M. Abramowitz, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, 9th edn. (Dover, New York, NY, 1972).M. K. Simon, M. S. Alouini, Digital Communication over Fading Channels, 2nd edn. (Wiley, Hoboken, NY, 2005).Z. Sun, J. Du, in Proc. 10th International Conference, ICIC 2014, ed. by D. -S. Huang, V. Bevilacqua, and P. Premaratne. Log-cumulant parameter estimator of log-normal distribution. Intelligent computing theory (SpringerNew York, NY, 2014), pp. 668–674.S. Zhang, J. M. Jin, Computation of Special Functions (Wiley, New York, 1996).G. Casella, R. L. Berger, Statistical Inference (Duxbury Thomson Learning, Pacific Grove, CA, 2002).C. Kleiber, S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences (Wiley, Hoboken, NJ, 2003).L. Devroye, Non-uniform Random Variate Generation (Springer, New York,1986).A. Abdi, M. Kaveh, Performance comparison of three different estimators for the Nakagami m parameter using Monte Carlo simulation. IEEE Commun. Lett.4(4), 119–121 (2000).L. Rubio, J. Reig, N. Cardona, Evaluation of Nakagami fading behaviour based on measurements in urban scenarios. Int. J. Electron. Commun. (AEÜ). 61(2), 135–138 (2007)

Error vector magnitude analysis of fading SIMO channels relying on MRC reception

We analytically characterize the data-aided Error Vector Magnitude (EVM) performance of a Single Input Multiple Output (SIMO) communication system relying on Maximal Ratio Combining (MRC) having either independent or correlated branches that are non-identically distributed. In particular, exact closed form expressions are derived for the EVM in -? fading and -? shadowed fading channels and these expressions are validated by simulations. The derived expressions are expressed in terms of Lauricella’s function of the fourth kind F(N) D (.), which can be easily computed. Furthermore, we have simplified the derived expressions for various special cases such as independent and identically distributed branches, Rayleigh fading, Nakagamim fading and -? fading. Additionally, a parametric study of the EVM performance of the wireless system is presented

Special Functions: Fractional Calculus and the Pathway for Entropy

Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010). The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis, utilizing Boltzmann entropy, and standard deviation analysis was undertaken with Super-Kamiokande solar neutrino data. This analysis revealed a non-Gaussian signal with harmonic content. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the Super-Kamiokande data deviate considerably from the value of ½, which indicates that the statistics of the underlying phenomenon is anomalous. Here experiment may provide guidance about the generalization of theory of Boltzmann statistical mechanics. Arguments in the so-called Boltzmann-Planck-Einstein discussion related to Planck's discovery of the black-body radiation law are recapitulated mathematically and statistically and emphasize from this discussion is pursued that a meaningful implementation of the complex ‘entropy-probability-dynamics’ may offer two ways for explaining the results of diffusion entropy analysis and standard deviation analysis. One way is to consider an anomalous diffusion process that needs to use the fractional space-time diffusion equation (Gorenflo and Mainardi) and the other way is to consider a generalized Boltzmann entropy by assuming a power law probability density function. Here new mathematical framework, invented by sheer thought, may provide guidance for the generalization of Boltzmann statistical mechanics. In this book Boltzmann entropy, generalized by Tsallis and Mathai, is considered. The second one contains a varying parameter that is used to construct an entropic pathway covering generalized type-1 beta, type-2 beta, and gamma families of densities. Similarly, pathways for respective distributions and differential equations can be developed. Mathai's entropy is optimized under various conditions reproducing the well-known Boltzmann distribution, Raleigh distribution, and other distributions used in physics. Properties of the entropy measure for the generalized entropy are examined. In this process the role of special functions of mathematical physics, particularly the H-function, is highlighted