Modeling and Analysis of Wireless Channels via the Mixture of Gaussian Distribution (original) (raw)
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Advances in Statistical Channel Modeling for Wireless Communications
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The complex electromagnetic propagation phenomena involved in modern wireless communications are taken into account by appropriate channel modeling. Statistical channel models are a powerful tool for communication engineers since they are able to capture the fundamental behavior of the wireless channel with reasonably simple mathematical formulation. New communication scenarios and services demand novel statistical channel models or extensions of those used in the field of wireless communications.
Evaluation of a Gaussian Mixture Model-based Channel Estimator using Measurement Data
arXiv (Cornell University), 2022
In this work, we use real-world data in order to evaluate and validate a machine learning (ML)-based algorithm for physical layer functionalities. Specifically, we apply a recently introduced Gaussian mixture model (GMM)-based algorithm in order to estimate uplink channels stemming from a measurement campaign. For this estimator, there is an initial (offline) training phase, where a GMM is fitted onto given channel (training) data. Thereafter, the fitted GMM is used for (online) channel estimation. Our experiments suggest that the GMM estimator learns the intrinsic characteristics of a given base station's whole radio propagation environment. Essentially, this ambient information is captured due to universal approximation properties of the initially fitted GMM. For a large enough number of GMM components, the GMM estimator was shown to approximate the (unknown) mean squared error (MSE)-optimal channel estimator arbitrarily well. In our experiments, the GMM estimator shows significant performance gains compared to approaches that are not able to capture the ambient information. To validate the claim that ambient information is learnt, we generate synthetic channel data using a state-of-the-art channel simulator and train the GMM estimator once on these and once on the real data, and we apply the estimator once to the synthetic and once to the real data. We then observe how providing suitable ambient information in the training phase beneficially impacts the later channel estimation performance. Index Terms-Gaussian mixture models, measurement data, machine learning, channel estimation, ambient information The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the program of "Souverän. Digital. Vernetzt.". Joint project 6G-life, project identification number: 16KISK002 ©This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.
IEEE Transactions on Wireless Communications, 2010
In wireless channels, multipath fading and shadowing occur simultaneously leading to the phenomenon referred to as composite fading. The use of the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing has led to the generalized-model for composite fading. However, further derivations using the generalized-PDF are quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-PDF by a Gamma PDF using the moment matching method is explored. Subsequently, an adjustable form of the expressions obtained by matching the first two positive moments, to overcome the arising numerical and/or analytical limitations of higher order moment matching, is proposed. The optimal values of the adjustment factor for different integer and non-integer values of the multipath fading and shadowing parameters are given. Moreover, the approach introduced in this paper can be used to well-approximate the distribution of the sum of independent generalized-random variables by a Gamma distribution; the need for such results arises in various emerging distributed communication technologies and systems such as coordinated multipoint transmission and reception schemes including distributed antenna systems and cooperative relay networks.
Nast Nakagami: A Novel Stochastic Model for Cascaded Fading Channels
IEEE Transactions on Wireless Communications, 2007
A generic and novel distribution, referred to as Nakagami, constructed as the product of N statistically independent, but not necessarily identically distributed, Nakagami-m random variables (RVs), is introduced and analyzed. The proposed distribution turns out to be a very convenient tool for modelling cascaded Nakagami-m fading channels and analyzing the performance of digital communications systems operating over such channels. The moments-generating, probability density, cumulative distribution, and moments functions of the N *Nakagami distribution are developed in closed form using the Meijer's G -function. Using these formulas, generic closed-form expressions for the outage probability, amount of fading, and average error probabilities for several binary and multilevel modulation signals of digital communication systems operating over the N *Nakagami fading and the additive white Gaussian noise channel are presented. Complementary numerical and computer simulation performance evaluation results verify the correctness of the proposed formulation. The suitability of the N *Nakagami fading distribution to approximate the lognormal distribution is also being investigated. Using Kolmogorov--Smirnov tests, the rate of convergence of the central limit theorem as pertaining to the multiplication of Nakagami-m RVs is quantified.
New analytical models and probability density functions for fading in wireless communications
IEEE Transactions on Communications, 2002
This paper presents new envelope probability density functions (pdfs) that describe small-scale, local area fading experienced by narrow-band wireless receivers. The paper also develops novel pdfs that describe the local area fading of two specular multipath components in the presence of other diffusely propagating waves. These pdfs are studied in the context of classical fading pdfs such as the Rayleigh, Rician, and other distributions.
IEEE Transactions on Wireless Communications, 2000
In wireless channels, multipath fading and shadowing occur simultaneously leading to the phenomenon referred to as composite fading. The use of the Nakagami probability density function (PDF) to model multipath fading and the Gamma PDF to model shadowing has led to the generalized-model for composite fading. However, further derivations using the generalized-PDF are quite involved due to the computational and analytical difficulties associated with the arising special functions. In this paper, the approximation of the generalized-PDF by a Gamma PDF using the moment matching method is explored. Subsequently, an adjustable form of the expressions obtained by matching the first two positive moments, to overcome the arising numerical and/or analytical limitations of higher order moment matching, is proposed. The optimal values of the adjustment factor for different integer and non-integer values of the multipath fading and shadowing parameters are given.
2017 IEEE 85th Vehicular Technology Conference (VTC Spring)
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Generalized MGF of Beckmann Fading With Applications to Wireless Communications Performance Analysis
IEEE Transactions on Communications, 2017
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 inphase 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.
Gaussian Mixture based Context-Aware Short-Term Characterization of Wireless Channels
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5G wireless communication technologies aim at simultaneously achieving energy efficiency and spectral efficiency. 5G also demands high communication reliability. In this context, fine-grained temporal characterization of wireless channel can be used to enhance both. To this end, we propose a novel context-aware characterization of the temporally-varying wireless channel. Our characterization of temporal variation of the channel is based on the method of finite mixture of Gaussian distributions. However, unlike the classical Gaussian mixture model, the proposed characterization does not use an iterative algorithm for its parameter estimation; it depends on the current channel state and its statistics. Based on this characterization we estimate the quantity of data that can be transferred over the channel in a time interval without knowing the actual channel state in that duration. We propose an application context dependent upper bound on the time interval over which this estimation can be made. Our numerical results demonstrate that the present channel state plays a crucial role. When the proposed characterization is used in the context of channel adaptive communication, energy efficiency obtained is as high as 3.15 times over its nearest approach. A nontrivial trade-off between energy efficiency and precision of the proposed characterization is also investigated.
Gaussian class multivariate Weibull distributions: theory and applications in fading channels
IEEE Transactions on Information Theory, 2005
Ascertaining on the suitability of the Weibull distribution to model fading channels, a theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed. Novel analytical expressions for the joint probability density function (pdf), moment-generating function (mgf), and cumulative distribution function (cdf) are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers. Two specific distributions with arbitrary number of correlated variates are considered and studied: with exponential and with constant correlation where their pdfs are introduced. Both cases assume equal average fading powers, but not necessarily identical fading parameters. For the multivariate Weibull distribution with exponential correlation, useful corresponding formulas, as for the bivariate case, are derived. The presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection, equal-gain, and maximal-ratio combining (MRC) techniques operating over correlated Weibull fading channels. For these diversity receivers, several useful performance criteria such as the moments of the output signal-to-noise ratio (SNR) (including average output SNR and amount of fading) and outage probability are analytically derived. Moreover, the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach. The proposed mathematical analysis is complemented by various evaluation results, showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance.