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We introduce a new class of fading channels, built as the superposition of two fluctuating specular components with random phases, plus a clustering of scattered waves: the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel. The MFTR model emerges as a natural generalization of both the fluctuating two-ray (FTR) and the $\kappa$-$\mu$ shadowed fading models through a more general yet equally mathematically tractable model. This generalization enables the presence of additional multipath clusters in the purely ray-based FTR model, and the convenience of the new underlying fading channel model is discussed in depth. Then, we derive all the chief probability functions of the MFTR model (e.g., probability density function (PDF), cumulative density function (CDF), and moment generation function) in closed-form, having {a mathematical complexity similar to} other fading models in the state-of-the-art. We also provide two additional analytical formulations for the PDF and the CDF: (i) in terms of a continuous mixture of $\kappa$-$\mu$ shadowed distributions, and (ii) as an infinite discrete mixture of Gamma distributions. Such expressions enable to conduct performance analysis under MFTR fading by directly leveraging readily available results for the $\kappa$-$\mu$ shadowed or Nakagami-$m$ cases, respectively. The performance of wireless communications systems undergoing MFTR fading is exemplified in terms of a classical benchmarking metric like the outage probability, both in exact and asymptotic forms, and the amount of fading., Comment: This work was submitted to the IEEE for publication on May 31, 2022. Copyright may be transferred without notice, after which this version may no longer be accessible

We introduce and characterize the independent fluctuating two-ray (IFTR) fading model, a class of fading models consisting of two specular components which fluctuate independently, plus a diffuse component modeled as a complex Gaussian random variable. The IFTR model complements the popular fluctuating two-ray (FTR) model, on which the specular components are fully correlated and fluctuate jointly. The chief probability functions of the received SNR in IFTR fading, including the PDF, CDF and MGF, are expressed in closed-form, having a functional form similar to other state-of-the-art fading models. Then, the IFTR model is empirically validated using multiple channels measured in rather diverse scenarios, including line of sight (LOS) millimeter-wave, land mobile satellite (LMS) and underwater acoustic communication (UAC), showing a better fit than the original FTR model and other models previously used in these environments. Additionally, the performance of wireless communication systems operating under IFTR fading is evaluated in closed-form in two scenarios: (i) exact and asymptotic bit error rate for a family of coherent modulations; and (ii) exact and asymptotic outage probability., Comment: 11 pages, 8 figures. arXiv admin note: text overlap with arXiv:1611.05063

The recently proposed Fluctuating Two-Ray (FTR) model is gaining momentum as a reference fading model in scenarios where two dominant specular waves are present. Despite the numerous research works devoted to the performance analysis under FTR fading, little attention has been paid to effectively understanding the interplay between the fading model parameters and the fading severity. According to a new scale defined in this work, which measures the hyper-Rayleigh character of a fading channel in terms of the Amount of Fading, the outage probability and the average capacity, we see that the FTR fading model exhibits a full hyper-Rayleigh behavior. However, the Two-Wave with Diffuse Power fading model from which the former is derived has only strong hyper-Rayleigh behavior, which constitutes an interesting new insight. We also identify that the random fluctuations in the dominant specular waves are ultimately responsible for the full hyper-Rayleigh behavior of this class of fading channels., 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 accesible

This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the original CGQF. Since the mean squared error between both is given in a simple closed-form formulation, the auxiliary RV can be particularized to achieve the required accuracy. The technique is valid for both definite and indefinite CGQFs and yields simple expressions of the probability density function (PDF) and the cumulative distribution function (CDF) that involve only elementary functions. This overcomes a major limitation of previous approaches, in which the complexity of the resulting PDF and CDF prevents from using them for subsequent calculations. To illustrate this end, the proposed method is applied to maximal ratio combining systems over correlated Rician channels, for which the outage probability and the average bit error rate are derived.

We present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed $\kappa$-$\mu$ shadowed random variables. Simple closed-form expressions for the probability density function, cumulative distribution function and moment-generating function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami-$m$ random variables. This model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. We leverage these results to analyze performance measures of interest in the contexts of wireless powered and backscatter communications, where both forward and reverse links are inherently of LOS nature, as well as in device-to-device communications subject to composite fading. In these contexts, the model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics., Comment: 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

We here introduce an extension and natural generalization of both the \kappa-\mu$\,$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, \kappa-\mu, \eta-\mu, \eta-\kappa, Beckmann, Rician shadowed and the \kappa-\mu$\,$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., 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 accesible

We introduce the Fluctuating Two-Ray (FTR) fading model, a new statistical channel model that consists of two fluctuating specular components with random phases plus a diffuse component. The FTR model arises as the natural generalization of the two-wave with diffuse power (TWDP) fading model; this generalization allows its two specular components to exhibit a random amplitude fluctuation. Unlike the TWDP model, all the chief probability functions of the FTR fading model (PDF, CDF and MGF) are expressed in closed-form, having a functional form similar to other state-of-the-art fading models. We also provide approximate closed-form expressions for the PDF and CDF in terms of a finite number of elementary functions, which allow for a simple evaluation of these statistics to an arbitrary level of precision. We show that the FTR fading model provides a much better fit than Rician fading for recent small-scale fading measurements in 28 GHz outdoor millimeter-wave channels. Finally, the performance of wireless communication systems over FTR fading is evaluated in terms of the bit error rate and the outage capacity, and the interplay between the FTR fading model parameters and the system performance is discussed. Monte Carlo simulations have been carried out in order to validate the obtained theoretical expressions., 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 accesible

Emerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will include the necessity to operate over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models adopted in the literature to develop network models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider $\kappa$-$\mu$ shadowed fading, which contains as special cases, the majority of the linear fading models proposed in the open literature, including Rayleigh, Rician, Nakagami-m, Nakagami-q, One-sided Gaussian, $\kappa$-$\mu$, $\eta$-$\mu$, and Rician shadowed to name but a few. In particular, we apply an orthogonal expansion to represent the $\kappa$-$\mu$ shadowed fading distribution as a simplified series expression. Then using the series expressions with stochastic geometry, we propose an analytic framework to evaluate the average of an arbitrary function of the SINR over $\kappa$-$\mu$ shadowed fading channels. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, bit error probability and outage probability of a $K$-tier HetNet with $K$ classes of BSs, differing in terms of the transmit power, BS density, shadowing characteristics and small-scale fading. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities.

We show that the popular and general {\kappa}-{\mu} shad- owed fading model with integer fading parameters {\mu} and m can be represented as a mixture of squared Nakagami (or Gamma) distributions. Thus, its PDF and CDF can be expressed in closed-form in terms of a finite number of elementary functions (powers and exponentials). The main implications arising from such connection are then discussed, which can be summarized as: (1) the performance evaluation of communication systems operating in {\kappa}-{\mu} shadowed fading becomes as simple as if a Nakagami fading channel was assumed; (2) the {\kappa}-{\mu} shadowed distribution can be used to approximate the {\kappa}-{\mu} distribution us- ing a closed-form representation in terms of elementary functions, by choosing a sufficiently large value of m; and (3) restricting the parameters {\mu} and m to take integer values has limited impact in practice when fitting the {\kappa}-{\mu} shadowed fading model to field measurements. As an application example, the average channel capacity of communication systems operating under {\kappa}-{\mu} shadowed fading is obtained in closed-form., Comment: 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

This paper shows that the recently proposed $\kappa$-$\mu$ shadowed fading model includes, besides the $\kappa$-$\mu$ model, the $\eta$-$\mu$ fading model as a particular case. This has important relevance in practice, as it allows for the unification of these popular fading distributions through a more general, yet equally tractable, model. The convenience of new underlying physical models is discussed. Then, we derive simple and novel closed-form expressions for the asymptotic ergodic capacity in $\kappa$-$\mu$ shadowed fading channels, which illustrate the effects of the different fading parameters on the system performance. By exploiting the unification here unveiled, the asymptotic capacity expressions for the $\kappa$-$\mu$ and $\eta$-$\mu$ fading models are also obtained in closed-form as special cases., Comment: 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

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart (CW) matrix ${\bf{W}}(t)$ as it varies along a certain dimension $t$. We characterize the second-order joint cdf of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ($N_T$) and receive ($N_R$) antennas is similar. However, as $N_T$ is increased while keeping $N_R$ fixed, we see how the best and worst channels tend to have a similar rate of change., Comment: 15 pages, 9 figures and 1 table. This work has been accepted for publication at IEEE Trans. Inf. Theory. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org

An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to original ones in compact matrix format., Comment: 5 pages, 3 talbes and 1 figure

The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of arbitrarily correlated gamma variables in terms of certain Lauricella functions.

This paper focuses on the analysis of average Gaussian error probabilities in certain fading channels, i.e. we are interested in E[Q((p {\gamma})^(1/2))] where Q(.) is the Gaussian Q-function, p is a positive real number and {\gamma} is a nonnegative random variable. We present a unified analysis of the average Gaussian error probability, derive a compact expression in terms of the Lauricella FD^(n) function that is applicable to a broad class of fading channels, and discuss the relation of this expression and expressions of this type recently appeared in literature. As an intermediate step in our derivations, we also obtain a compact expression for the outage probability of the same class of fading channels. Finally, we show how this unified analysis allows us to obtain novel performance analytical results.

In this paper exact closed-form expressions are derived for the outage probability (OP) in scenarios where both the signal of interest (SOI) and the interfering signals experience {\eta}-{\mu} fading and the background noise can be neglected. With the only assumption that the {\mu} parameter is a positive integer number for the interfering signals, the derived expressions are given in elementary terms for maximal ratio combining (MRC) with independent branches. The analysis is also valid when the {\mu} parameters of the pre-combining SOI power envelopes are positive integer or half-integer numbers and the SOI is formed at the receiver from spatially correlated MRC., Comment: 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