On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances

We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally, closed-form expressions of the CDF of the sum of order statistics are unavailable for many practical distributions. Moreover, the naive Monte Carlo (MC) method requires a substantial computational effort when the probability of interest is sufficiently small. In the region of small OP values, we propose instead two effective variance reduction techniques that yield a reliable estimate of the CDF with small computing cost. The first estimator, which can be viewed as an importance sampling estimator, has bounded relative error under a certain assumption that is shown to hold for most of the challenging distributions. An improvement of this estimator is then proposed for the Pareto and the Weibull cases. The second is a conditional MC estimator that achieves the bounded relative error property for the Generalized Gamma case and the logarithmic efficiency in the Log-normal case. Finally, the efficiency of these estimators is compared via various numerical experiments

Estimation of the composite fast fading and shadowing distribution using the log-moments in wireless communications

In this work, we propose a framework to obtain estimators from a variety of distributions used in composite fast fading and shadowing modeling with applications in wireless communications: the Suzuki (Rayleigh-lognormal), Nakagami-lognormal, K (Rayleigh-gamma), generalized-K (Nakagami-gamma) and alpha-mu; (generalized gamma) distributions. These estimators are derived from the method of moments of these distributions in logarithmic units, usually known as log-moments. The goodness-of-fit of these estimators to experimental distributions has been checked from a measurement campaign carried out in an urban environment. Moreover a new method to separate fast fading and shadowing based on the Rathgeber procedure is proposed. The results conclude that the best-fitting distribution to the measurements is the Nakagami-lognormal. Also, the alpha-mu; distribution provides an acceptable matching with the advantage of its simplicity.The authors would like to thank the editor and reviewers their valuable comments which have enriched the quality of this paper. We would also express our gratitude to Dr. C. S. Withers, retired research statistician from the Applied Maths Group at Industrial Research Ltd, Lower Hutt, New Zealand, for his revision of the paper and his estimable remarks. This work has been funded in part by the Spanish Ministerio de Ciencia e Innovacion (TEC-2010-20841-C04-1).Reig, J.; Rubio Arjona, 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. https://doi.org/10.1109/TWC.2013.050713.120054S3672368112

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. 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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. 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On Simple Estimators of the alpha-mu Fading Distribution

In this letter, new estimators of the alpha-mu distribution are derived based on the skewness of the logarithmic alpha-mu distribution using the moments method. This distribution has been recently proposed to model the received field strength in nonlinear propagation mediums. Therefore, simple and computationally efficient estimators are required to infer the parameters of the received signal amplitude distribution in nonlinear wireless communication propagation channels. The performance of these new estimators is compared to that obtained with the estimators calculated with the moments method of the alpha-mu distribution by solving numerically transcendental equations. These estimators are easily evaluated with simple expressions.Reig, J.; Rubio Arjona, L. (2011). On Simple Estimators of the alpha-mu Fading Distribution. IEEE Transactions on Communications. 59(12):3254-3258. doi:10.1109/TCOMM.2011.080111.090223S32543258591

Analysis and Modeling of Realistic Compound Channels in Transparent Relay Transmissions

Analytical approaches for the characterisation of the compound channels in transparent multihop relay transmissions over independent fading channels are considered in this paper. Compound channels with homogeneous links are considered first. Using Mellin transform technique, exact expressions are derived for the moments of cascaded Weibull distributions. Subsequently, two performance metrics, namely, coefficient of variation and amount of fade, are derived using the computed moments. These metrics quantify the possible variations in the channel gain and signal to noise ratio from their respective average values and can be used to characterise the achievable receiver performance. This approach is suitable for analysing more realistic compound channel models for scattering density variations of the environment, experienced in multihop relay transmissions. The performance metrics for such heterogeneous compound channels having distinct distribution in each hop are computed and compared with those having identical constituent component distributions. The moments and the coefficient of variation computed are then used to develop computationally efficient estimators for the distribution parameters and the optimal hop count. The metrics and estimators proposed are complemented with numerical and simulation results to demonstrate the impact of the accuracy of the approaches

Multi-RIS-aided Wireless Systems: Statistical Characterization and Performance Analysis

In this paper, we study the statistical characterization and modeling of distributed multi-reconfigurable intelligent surface (RIS)-aided wireless systems. Specifically, we consider a practical system model where the RISs with different geometric sizes are distributively deployed, and wireless channels associated to different RISs are assumed to be independent but not identically distributed (i.n.i.d.). We propose two purpose-oriented multi-RIS-aided schemes, namely, the exhaustive RIS-aided (ERA) and opportunistic RIS-aided (ORA) schemes. In the ERA scheme, all RISs participate in assisting the communication of a pair of transceivers, whereas in the ORA scheme, only the most appropriate RIS participates and the remaining RISs are utilized for other purposes. A mathematical framework, which relies on the method of moments, is proposed to statistically characterize the end-to-end (e2e) channels of these schemes. It is shown that either a Gamma distribution or a LogNormal distribution can be used to approximate the distribution of the magnitude of the e2e channel coefficients in both schemes. With these findings, we evaluate the performance of the two schemes in terms of outage probability (OP) and ergodic capacity (EC), where tight approximate closed-form expressions for the OP and EC are derived. Representative results show that the ERA scheme outperforms the ORA scheme in terms of OP and EC. Nevertheless, the ORA scheme gives a better energy efficiency (EE) in a specific range of the target spectral efficiency (SE). In addition, under i.n.i.d. fading channels, the reflecting element setting and location setting of RISs have a significant impact on the overall system performance of both the ERA or ORA schemes. A centralized large-RIS-aided scheme might achieve higher EC than the distributed ERA scheme when the large-RIS is located near a transmitter or a receiver, and vise-versa