This paper introduces two comprehensive composite fading models: the α-FMixture and the α-GMixture. These models unify a broad spectrum of previously reported composite fading distributions and enable the systematic construction of hundreds of new ones. Their first-order statistics (namely, probability density function (PDF), cumulative distribution function (CDF), moment-generating function, and higher-order moments) are derived in compact, tractable forms that, for specific cases, yield singularity-free expressions improving upon existing state-of-the-art solutions. By consolidating a wide range of multiplicative shadow (MS) and LOS shadow (LOSS) fading families into a single parameterized framework, they provide a unified analytical basis for obtaining the key statistics of numerous composite fading scenarios. Serving asplug-and-playbase models, they enable direct evaluation of metrics such as outage probability (OP) and average symbol error rate (ASER) for both established and new composite fading models without rederiving channel statistics. Their unified structure and flexible parameterization also support systematic analysis of fading and shadowing in emerging scenarios, providing practical and extensible tools for next-generation wireless channel characterization.

This paper presents a general framework for deriving the statistics of RIS-based communication systems under diverse fading conditions. Specifically, the probability density function (PDF) and higher-order moments are derived considering direct and RIS-assisted links from the source to the destination. Recognizing the analytical challenges of these derivations in the context of RIS-assisted systems, we employ a more practical yet tractable and notably accurate α-μ approximation, which offers a simple and closed-form solution, producing results virtually indistinguishable from those obtained through simulations for various realistic communication scenarios of interest. This approach is a valuable tool for evaluating system performance metrics such as outage probability and average symbol error rate since such an approximation significantly outperforms the one derived from the widely employed central limit theorem, even when dealing with a reasonably large number of elements. We subsequently apply this general framework to investigate the achievable RIS performance in different realistic fading environments, including α-μ, κ-μ, and Extended η-μ, both individually and combined. Specifically, we derive reasonably simple and functional closed-form asymptotic expressions, in terms of well-known special functions, for each case study, contributing to a deeper understanding of how each fading parameter affects the system’s performance regarding coding gain and diversity gain. In particular, we demonstrate that the diversity order is directly determined by the number of reflecting elements, the density of multipath clusters, and the degree of non-linearity in the propagation medium, with higher values of these parameters leading to clear improvements in performance. The offered results enable the development of valuable insights on RIS-based communications, which will be useful in future system designs and deployments.

This paper presentssharpinequalities for the level crossing rate of a stochastic process composed of the product of independent stochastic processes. The inequalities, which are simple to state, enlighten the contribution of each process individually. Additionally, we derive an exact formulation when the conditioned pointwise derivative of each process follows a Gaussian distribution. As application examples, the results are exercised in different scenarios using the$\alpha\text{-}\mu $and$\kappa\text{-}\mu$fading models, which encompass several other well-known models such as Semi-Gaussian, Rayleigh, Rice, Nakagami-m, and Weibull. We provide unprecedented closed-form formulations for the level crossing rate bounds of the product of these widely-known fading processes. Notably, there are no closed forms for the level crossing rate of these products. Therefore, our bounds supply a benchmark for this metric, with one of them serving as an excellent approximation of the exact metric.

Reconfigurable Intelligent Surfaces (RISs) are considered a key candidate technology for next-generation 6G wireless systems, promising to extend network coverage, enhance spectral efficiency, and effectively mitigate interference. RISs will achieve this by controlling the propagation environment, enabled by carefully altering the reflective properties of their elements. In this context, this work presents a general framework for deriving the exact probability density function (PDF) and higher-order moments of the signal-to-ratio (SNR) in a RIS system, considering the direct transmission and RIS-assisted links from source to destination. Recognizing the analytical challenges associated with obtaining exact statistics for RIS-assisted systems, which persist in both common and more generalized fading models, the proposed contribution is realized with the aid of the suitable α-µ fading model. To that end, we derive accurate approximations for the κ-µ and the extended η-µ distributions, which constitute effective and versatile multipath fading models. Based on this, the achieved results are virtually indistinguishable from those obtained through simulations for various environmental settings. This renders the proposed framework a valuable tool for evaluating the performance of RIS systems, particularly in terms of the corresponding average symbol error rate (ASER). Tractable closed-form asymptotic expressions are also derived and utilized to provide a deeper understanding of the system’s behavior.

In this paper, we explore the calibration of a machine learning (ML)-based outage predictor aimed at optimizing resource allocation to minimize outages in communication systems. We model the wireless channel using an auto-correlated time series with samples distributed in accordance with a Rayleigh fading process. Our novel contribution concerns proposing histogram-based reliability plots that employ logarithmic binning to assess its impact on the model calibration compared to the traditional linear binning technique. We train our ML model using an outage loss function (OLF) tailored to this system and the well-known binary cross entropy (BCE). Additionally, we analyze the effect of different model parameters on the calibration performance of this outage predictor. Our findings demonstrate that logarithmic binning reveals nuanced calibration traits ignored by linear binning, particularly at lower confidence levels. This finding is crucial for wireless systems for which understanding behavior at very low probabilities is essential. Additionally, we observe that our ML model trained with OLF becomes more overconfident as the classification threshold increases and in scenarios characterized with rare events, namely outages. This observation serves as a tool for improving the calibration properties of OLF.

Inspired by the theory of natural evolution, Differential Evolution (DE) functions constitute an optimization tool in the field of evolutionary algorithms. Here, we propose employing DE to estimate physically acceptable fading parameters in device-to-device (D2D) communication channels. We examine four real-world D2D propagation channel measurements obtained under various conditions: indoor, outdoor, line-of-sight (LOS), and non-LOS. Four popular fading models,$\kappa-\mu, \eta-\mu, \kappa-\mu$/inverse gamma, and$\eta-\mu$/inverse gamma are used to characterize these links. Two fitness functions, Kullback-Leibler divergence (KLD) and mean squared error (MSE), are utilized for evaluation. We also compare the DE with another evolutionary algorithm, namely the genetic algorithm (GA). Notably, our results demonstrate that while both algorithms deliver excellent estimation performances, DE emerges as significantly faster and more robust compared to GA. Regarding fitness performances, the algorithm, when paired with KLD, outperforms the pairing with MSE, as assessed through the minimization of the Akaike information criterion.

In this article, a novel ultrahigh-frequency (UHF) radio frequency identification (RFID) passive tag with a current sensor is presented. The device can be used to detect electrical current flowing through the power cord of the surveyed equipment, allowing for its switched on state to be established and, for instance, its energy consumption to be computed. The identification of the tag by the system makes it possible, among other things, to individually monitor the energy consumed by the target equipment, both in domestic and industrial environments. The solution presented here is ideally placed to be used in the Internet of Things (IoT) context.

The sum of random variables (RVs) appears extensively in wireless communications, at large, both conventional and advanced, and has been subject of longstanding research. The statistical characterization of the referred sum is crucial to determine the performance of such communications systems. Although efforts have been undertaken to unveil these sum statistics, e.g., probability density function (PDF) and cumulative distribution function (CDF), no general efficient nor manageable solutions capable of evaluating the exact sum PDF and CDF are available to date. The only formulations are given in terms of either the multi-fold Brennan’s integral or the multivariate Fox$H$-function. Unfortunately, these methods are only feasible up to a certain number of RVs, meaning that when the number of RVs in the sum increases, the computation of the sum PDF and CDF is subject to stability problems, convergence issues, or inaccurate results. In this paper, we derive new, simple, exact formulations for the PDF and CDF of the sum of$L$independent and identically distributed$\alpha $-$\mu $RVs. Unlike the available solutions, the computational complexity of our analytical expressions is independent of the number of summands. Capitalizing on our unprecedented findings, we analyze, in exact and asymptotic manners, the performance of$L$-branch pre-detection equal-gain combining and maximal-ratio combining receivers over$\alpha $-$\mu $fading environments. The coding and diversity gains of the system for both receivers are analyzed and quantified. Moreover, numerical simulations show that the computation time reduces drastically when using our expressions, which are arguably the most efficient and manageable formulations derived so far.

The modeling of wireless communications channels is often broken down into two distinct states, defined according to the optical viewpoints of the transmitter (TX) and receiver (RX) antennas, namely line-of-sight (LoS) and non-LoS (NLoS). Movement by the TX, RX, both and/or objects in the surrounding environment means that channel conditions may transition between LoS and NLoS leading to a third state of signal propagation, namely quasi-LoS (QLoS). Unfortunately, this state is largely ignored in the analysis of signal propagation in wireless channels. We therefore propose a new statistical framework that unifies signal propagation for LoS, NLoS, and QLoS channel conditions, leading to the creation of the Three State Model (TSM). The TSM has a strong physical motivation, whereby the signal propagation mechanisms underlying each state are considered to be similar to those responsible for Rician fading. However, in the TSM, the dominant signal component, if present, can be subject to shadowing. To support the use of the TSM, we develop novel formulations for the probability density functions of the in-phase and quadrature components of the complex received signal as well of the received signal envelope. The offered results are corroborated with results from respective computer simulations, whilst it is shown that the proposed model is more versatile than existing conventional models.

This article proposes an extension to the η-μ fading model by including a parameter that quantifies the clustering imbalance between in-phase and quadrature components. The inclusion of such a parameter renders the model enormously flexible, extending its reach of application in a wider range of scenarios. Despite the inclusion of an additional parameter, the equations obtained remain as mathematically tractable as those for the original η-μ model. Several new closed-form expressions for important statistics are then obtained, including: (i) probability density functions for both envelope and phase; (ii) cumulative distribution functions for both envelope and phase; (iii) arbitrary moments for the envelope; (iv) moment generating function for the envelope; (v) average bit error rate for coherent binary systems; (v) level crossing rate, average fading duration, and phase crossing rate; and (vi) several other joint distributions encompassing envelope, phase, and their respective time derivatives. It is noteworthy that many of the closed-form formulations presented here are not available even for the simple η-μ model.

In this work we investigate the capacity of multilayer relaying networks operating over multipath fading channels under a non-coherent wideband regime and physically degraded broadcast stages. First, based on hyper-graph models and network equivalence techniques, we derive an upper bound on the network capacity. Then, by considering a peaky, frequency-shift keying signaling scheme, we establish a set of point-to-point achievable rates for each communication link in the network. Finally, by capitalizing on this set of rates we devise an achievable transmission scheme for the entire network via network coding. Remarkably, it turns out that this achievable rate for the network coincides with its upper bound capacity. In other words, these results give ultimately the capacity of the investigated network.

In this paper, the error performance of binary and quaternary phase-shift keying signals with imperfect carrier phase recovery is investigated assuming a flat slow α-μ fading channel and the presence of thermal noise. The phase noise is considered to be Tikhonov and Gaussian distributed. More specifically, an analytical expression for the exact average bit error rate is obtained, as well as its corresponding asymptotic expression for large signal-to-noise ratio (SNR) values. The derived expressions are valid for arbitrary values of the fading parameters, namely α and μ, and they are validated through Monte Carlo simulations. Several important conclusions concerning the system performance as a function of the channel parameters, namely, non-linearity, clustering, and loop SNR, are drawn.

In this paper, we introduce a new fading model which is capable of characterizing both the shadowing of the dominant component and composite shadowing which may exist in wireless channels. More precisely, this new model assumes a κ-μ envelope where the dominant component is fluctuated by a Nakagami-m random variable (RV) which is preceded (or succeeded) by a secondary round of shadowing brought about by an inverse Nakagami-m RV. We conveniently refer to this as the double shadowed κ-μ fading model. In this context, novel closed-form and analytical expressions are developed for a range of channel related statistics, such as the probability density function, cumulative distribution function, and moments. All of the derived expressions have been validated through Monte-Carlo simulations and reduction to a number of well-known special cases. It is worth highlighting that the proposed fading model offers remarkable flexibility as it includes the κ-μ, η-μ, Rician shadowed, double shadowed Rician, κ-μ shadowed, κ-μ/inverse gamma and η-μ/inverse gamma distributions as special cases.

A thorough millimeter-wave measurement campaign is carried out in an indoor environment with an aim at characterizing the short-term fading channel behavior. The measurements are conducted in a variety of scenarios, with frequencies ranging from 55 GHz to 65 GHz, in lineof-sight and non-line-of-sight conditions, and combinations of horizontal and vertical polarizations at both transmitter and receiver. A number of fading models are tested, namely Rayleigh, Rice, Nakagami-m, α-μ, κ-μ, η-μ, and α-η-κ-μ. The statistics under analysis are those characterizing the fading amplitude and the frequency selectivity. In particular, the probability density and cumulative distribution functions for the former and level crossing rate per bandwidth unit for the latter are the respective first- and second-order statistics used. To this end, from the experimental data, the parameters of the models are estimated and the corresponding theoretical curves are plotted and compared with the empirical ones. Whereas the required theoretical formulations of the first-order statistics of these models are already well known, those of the second-order statistics as well as these fitting process in such a band shown here are unprecedented in the literature.

Two new methods of radial velocity estimation for distributed targets in arc-scanning synthetic aperture radar (ArcSAR) systems, namely, the maximum-likelihood estimator (MLE) and the suboptimal method based on the least squares estimation (LSE), are proposed, derived, and analyzed. To this end, we establish that n scatterers of the distributed target are uniformly dispersed within the radar resolution cell of dimensions a × b and they move randomly at different velocities. Furthermore, the effect of the antenna pattern is considered to characterize the amplitude of the scattered signal. Thus, from the coherent integration of the scatters at each pulse repetition interval in radar scanning, m data sequences are obtained as samples of the composite signal, which follows a multivariate normal distribution. From this, the covariance matrix, upon which the methods are based, is derived. Simulations have been carried out to compare the new methods with existing methods, namely, phase, energy, and correlation, as a function of the signalto-noise ratio. Finally, the results show that the MLE and LSE methods outperform the conventional methods, providing a gain of more than 10 dB.

This paper presents exact, novel formulations for the probability density function and cumulative distribution function for the product of two independent and non-identically distributed α-μ, κ-μ, and η-μ variates. The expressions are given in terms of both 1) generalized Fox H-function and 2) easily computable series expansions. The formulations derived can be directly used to explore the performance of a number of wireless communication processes, including multihop systems, cascaded channels, radar communications, multiple-input multiple-output links, and others. Due to the high flexibility of the above-mentioned distributions, the results presented here comprise a substantial number of useful product distributions. As application examples, performance metrics for the cascaded fading channel are derived. The validity of the expressions is confirmed via Monte Carlo simulation. It is noteworthy that, because any composite multipath-shadowing fading model is obtained as a particular case of the product of two fading variables, the results given here provide a plethora of composite multipath-shadowing fading scenarios.

In this paper, we perform a systematic investigation of the statistics associated with the product of two independent and non-identically distributed κ-μ random variables. More specifically, we develop novel analytical formulations for many of the fundamental statistics of interest, namely, the probability density function, cumulative distribution function, and moment-generating function. Using these new results, closedform expressions are obtained for the higher order moments, amount of fading and channel quality estimation index, while analytical formulations are obtained for the outage probability, average channel capacity, average symbol error probability, and average bit error probability. These general expressions can be reduced to a number of fading scenarios, such as the double Rayleigh, double Rice, double Nakagami-m, κ-μ/Nakagami-m, and Rice/Nakagami-m, which all occur as special cases. Additionally, as a byproduct of the work performed here, formulations for the κ-μ/κ-μ composite fading model can also be deduced. To illustrate the efficacy of the novel expressions proposed here, we provide useful insights into the outage probability of a dualhop system used in body area networks, and demonstrate the suitability of the κ-μ/κ-μ composite fading for characterizing shadowed fading in device-to-device channels.

In this paper, we initially consider the product of two independent and non-identically distributed κ-μ variates, and obtain its probability density function (PDF) in novel analytical form. Following from this, the PDF for the κ-μ/κ-μ composite fading model is then deduced. Monte-Carlo simulations are performed to verify the derived results. It is worth highlighting that both sets of expressions can be reduced to a number of double and composite fading scenarios such as the double Rice, double Nakagami-m, κ-μ/Nakagami-m, and Rice/Nakagami-m. Finally, we illustrate the usefulness of the obtained formulations by characterizing the shadowed fading encountered in body area networks, device-to-device and vehicle-to-vehicle communication channels. To this end, it is shown that the κ-μ/κ-μ composite fading model provides an excellent fit to the measurement data.

In this paper, we obtain novel analytical formulations for the outage probability (OP) in scenarios with α-μ or κ-μ faded signals of interest (SoI), and κ-μ or α-μ faded co-channel interference (CCI). Both single and multiple interfering scenarios have been considered, and exact formulations are provided when the SoI experiences α-μ fading and the CCI experiences κ-μ fading. When the SoI is subject to κ-μ fading and the CCI is subject to α-μ fading, exact and highly accurate approximate OP expressions have been derived for the single and multiple interfering cases, respectively. We also analyze the asymptotic behavior of the OP when the average signal-to-noise-ratio (SNR) of the SoI is significantly larger or smaller than that of the interferers. Monte-Carlo simulations are performed to verify the derived results. It is worth highlighting that these general expressions are important as they unify the CCI for a number of previously disjoint fading scenarios.

In this paper, general, easy to compute, exact expressions for the probability density function, cumulative distribution function and average value of the ratio of independent non-identically distributed κ-μ random variables, with arbitrary parameters, are derived. As an application example, capacity analysis of spectrum sharing systems undergoing κ-μ fading is provided. Specifically, expressions for the outage capacity with peak interference power constraint, the delay-limited capacity, and the ergodic capacity with average interference power constraint are derived. Numerical results are shown in order to investigate the effect of the fading parameters on the system capacity.

The aim of this paper is to propose a simple and efficient algorithm to generate white samples for the envelope of the α-η-κ-μ fading model. To this end, capitalizing on results available in the literature, the random number generator is implemented via the acceptance-rejection approach. The goodness-of-fit is objectively measured via the Kolmogorov-Smirnov test. We also address the performance of a digital communications system over the α-η-κ-μ fading channel in terms of the average bit error rate showing the impact of the fading parameters as an application for the random sequence generator. Theoretical and simulation results are contrasted, validating the accuracy of the generator.

The performance of any multiuser wireless communications system is strongly affected by interference. Consequently, the design of such systems must comply with some outage probability criteria. Although interference occurs in a mutual entangled basis, with wireless devices interfering with each other, outage is commonly considered on an individual per-device basis. This approach, however, is a simplified solution to a more intricate multidimensional and system-wide problem, in which several mutually interfering devices may be experiencing an outage simultaneously. The true outage probability across several devices is given by a set of mutual entangled boundary conditions to be fulfilled. This paper presents useful novel formulations for outage probability in multiuser wireless settings, here named mutual outage probability (MOP), for the interference-limited environment. Several scenarios are envisaged, in which some signals are in outage, whereas others are not and still for some others these conditions are irrelevant, all at the same time. We introduce a general framework for calculating the MOP, and present closed-form formulas for the Rayleigh case. Finally, we illustrate the practical use of these formulations in a call admission control application.

A comprehensive study on the κ-μ phase statistics is conducted. A substantial number of new formulas, exact and approximate, closed form, and integral form, are presented. In particular, a tight close-form approximation for the phase probability density function is found that yields results almost indistinguishable from the exact integral formulation. Most strikingly, the approximate formulation comprises the exact Nakagami-m phase as well as the exact Von Mises (Tikhonov) densities. Joint statistics involving combinations of the envelope, phase, and their time derivatives are derived in an exact manner. The exact phase crossing rate is then obtained in an integral form. A closed-form approximation is proposed that yields very good results as compared to the exact formulation. A Monte Carlo simulation plot is used to validate the formula of the exact phase crossing rate. The formulations presented here drastically facilitate the use of the phase statistics of the κ-μ fading model.

In this article, the product of three arbitrary, independent and non-identically distributed α-μ random variables is considered. Exact, reasonably simple, closed-form expressions for the probability density and the cumulative distribution functions, as well as the moments of the resulting distribution, are derived. These results find application, for instance, in radar communications, MIMO links, multi-hop systems, and cascaded communications in general. Since the α-μ model includes a number of very important fading environments, the analysis presented here constitutes an useful model to characterize wireless fading channels. As an application of the results, the amount of fading and the outage probability for the corresponding cascaded channel are calculated. It is noteworthy that the resulting formulations compute instantaneously.

This paper derives a general analytical expression for the correlation coefficient of signals received by two identical spaced antennas in a radar system used to detect meteorological phenomena such as rain and clouds. Such a correlation coefficient is found as a function of the relevant physical parameters, namely, distance between antennas (baseline distance), signal bandwidth, and antenna directivity. One of the antennas transmits the signal and receives its echoes from the scatterers, characterizing a monostatic radar, whereas the other antenna only receives these echoes, characterizing a bistatic radar. Our approach can be easily extended to nonidentical antennas.

We propose a new Nakagami phase-envelope fading channel simulator that (i) allows for arbitrary real values of fading parameter, (ii) exactly matches the Nakagami first-order statistics, (iii) and closely matches the second-order statistics classically assigned to Nakagami fading. The proposed simulator is based on a cascade of two existing simulators—the random-mixture simulator and the rank-matching simulator. It combines the strenghts of these two simulators, outperforming them both.

This paper investigates the throughput performance of IEEE 802.11 Distributed Coordination Function (DCF) at the Medium Access Control (MAC) layer with Hoyt, Rice and Nakagami-m fading environments. The approach considered includes the signal capture model with incoherent addition of interfering signals and uniform attenuation for all terminals (or perfect power control). For the Hoyt and Rice fading channels, the results presented also cover the case of coherent addition of interfering signals. Furthermore, for the Nakagami-m fading channel, the case of unequal average power levels is also studied. For the sake of comparison, results for the carrier sense multiple access with collision avoidance (CSMA/CA) are also presented. The formulations derived here are exact and unprecedented in the literature. Some of these formulations are given in infinite series form whereas several of them are presented in closed-form expressions. For the series-based ones, only a few terms are required in order to achieve high accuracy results.

This paper investigates the outage performance of dual-hop decode-and-forward (DF) cooperative spectrum sharing systems in the presence of multiple primary user (PU) receivers and multiple secondary user (SU) destinations. Our analysis allows for a general Nakagami-m fading environment where distinct fading parameters as well as unequal average fading powers between the interference and relaying links are assumed. Focusing on the cooperation process among the SU nodes and making use of the underlay cognitive approach, an exact closed-form expression for the outage probability is derived. Our analysis employs an opportunistic scheduling algorithm for selecting one out of L SU destinations available. Additional interference constraints are also considered due to the presence of multiple PU receivers. The effects of fading severity, SU relay placement, and number of PU receivers, and SU destinations on the end-to-end system performance are examined through some representative numerical plots. Monte Carlo simulation results are presented to corroborate the proposed analysis.

Results of measurement campaigns carried out aiming at the development of a tool for design, deployment, and analysis of RFID systems are shown. Particularly, in this paper, the radio path loss from an RFID reader towards the test tag and back to the reader is characterized at the 915 MHz band. The path loss is estimated based on the received signal strength measured at the reader, for different reader-tag separation distances and different antenna tag heights. Several propagation scenarios have been considered, including outdoor and indoor environments for which an extensive number of typical real manufacturing plants have been chosen. The field data are then compared to a proposed novel, improved version of the classical 2-ray path loss model, adjusted to also include the non-omnidirectional antenna radiation patterns at the reader and tag sides. To the best of the authors' knowledge, the scope and reach of the measurements as well as the proposed path loss model are new.

The purpose of this paper is to derive a general analytical expression for the correlation coefficient of signals received by two different antennas as a function of the distance between them (baseline distance), the signal bandwidth, and the antenna beamwidth. The two antennas are supposed to be part of a radar system for detecting meteorological phenomena such as rain and clouds. One of the antennas transmits the radar signal and receives the echoes; the other antenna only receives the echoes. The good functioning of such a radar system depends on the correlation between the two antenna signals. The exact analytical framework derived here has been recently used in practice to assist in the design of a meteorological radar system for Orbisat Indústria e Aerolevantamento S.A. (a branch of Embraer Defense and Security).

This paper investigates the outage performance of dual-hop amplify-and-forward (AF) two-way relaying systems with multiple co-channel interferers at the AF relay and two noisy end-sources. Assuming a Nakagami-m fading environment, a highly precise, easy-to-compute closed-form approximate expression for the outage probability is derived. Our analysis allows for general operating scenarios with distinct Nakagami-m fading parameters and unequal average fading powers between the hops. Monte Carlo simulation results are presented to corroborate the tightness of the proposed approximations.

New, exact expressions for the probability density and distribution functions of a bivariate Hoyt (Nakagami-q) process with arbitrary correlation pattern in a nonstationary environment are derived, a solution to a longstanding unsolved problem. More specifically, the following are obtained: joint probability density function, joint cumulative distribution function, power and envelope correlation coefficients, and some statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability and probability density function. The exact expressions are given in infinite series form, but are mathematically tractable, easy to evaluate, and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment. The power correlation coefficient is found in an exact, simple, closed-form formula, whereas the envelope one, also exact, is more mathematically elaborate. Approximate, simple closed-form expressions for the joint distribution are also obtained that yield (i) excellent results for small to medium correlation coefficients and (ii) reasonable ones for high correlation coefficient.

This paper investigates the throughput performance of carrier sense multiple access (CSMA) in η-μ fading channels. The approach considered includes the signal capture model with incoherent addition of interfering signals. The case of uniform attenuation for all terminals (or perfect power control) is studied. Analytical and numerical results are presented.

A number of realistic wireless applications can be found for which the propagated signal may experience extreme fading conditions. In particular, a recent work has reported on an experiment conducted within an enclosed environment where it has been shown that the fading conditions are indeed harsh, drastically departing from those predicted by traditional fading models. This paper investigates the κ-μ Extreme fading distribution, a member of the κ-μ fading model and obtained from it when its parameters reach their extreme values (κ → ∞ and μ → 0) for a fixed amount of fading. Field data reported elsewhere and collected in enclosed environment, along with other fading data collected by the authors' team, are used to compare the curve fit performance of the κ-μ Extreme model and the recently proposed Two-Ray distribution. The results show that the κ-μ Extreme distribution is flexible and suitable to model these scenarios. The performance of this new model is then explored in the three basic combining techniques, namely selection, maximum ratio, and equal gain, and a number of exact, closed-form formulas are obtained. Interestingly, it is shown that in extreme fading conditions, the selection combiner may outperform the equal gain combiner.

This paper derives an exact, easily computable series-type formulation for the multivariate α-µ joint cumulative distribution function. Then, based on useful and practical assumptions, alternative, new, simpler formulations for the α-µ multivariate joint density function and its corresponding distribution function are provided. The formulations are still general and yet very simple, assuming arbitrary parameters and arbitrary correlation among the marginal α-µ variates. As an application example, the outage probability of the selection combining scheme is obtained, again in an exact manner. The results show that only a few number of terms of the series is sufficient to provide an excellent agreement between approximate and exact results.

This paper derives an exact closed-form expression for the phase-envelope joint distribution of the κ-μ fading environment, a general fading model that includes the Rice and the Nakagami-m models as special cases. The derived joint statistics are obtained so that compatibility with both Rice as well as Nakagami-m cases are kept. Monte Carlo simulation plots are presented that are in accordance with the formulations developed here. As a consequence of the derivation of the required PDF, an interesting solution to a very general probability problem is proposed, namely, given the PDF of the modulus of a variate, find the PDF of the variate. Additionally, several new integral relations of the modified Bessel function are given.

A very general fading scenario is considered for which exact, closed-form formulas for the correlation coefficient of the instantaneous power at the output of a Maximal Ratio Combining receiver is derived. The model includes the main fading environments as very particular cases. It is valid for both identically and non-identically distributed multipath clusters, and for both stationary and nonstationary environments. Most interestingly, the model allows for an uncountable number of combinations of novel fading scenarios. A further generalization is achieved with the angle as well as the time of arrival of the waves permitted to vary throughout the multipath clusters, as opposed to known models for which these parameters are fixed. Several particular examples illustrate the applicability of the general formulations.

An infinite series formulation for the multivariate α-μ joint probability density function with arbitrary correlation matrix and non-identically distributed variates is derived. The expression is exact and general and includes all of the results previously published in the literature concerning the distributions comprised by the α-μ distribution. The general expression is then particularized to an indeed very simple, approximate closed-form solution. In addition, a multivariate joint cumulative distribution function is obtained, again in simple, closed-form manner. As an application example, the exact and approximate performances of the selection combining scheme given in terms of the outage probability is shown. Approximate and exact results are very close to each other for small as well as medium values of correlation.

Indoor and outdoor field trial measurements are used to validate the autocorrelation function derived in an exact manner for the α-μ fading signal. In addition, accurate closedform approximations for both autocorrelation function and to the power spectrum of the α-μ envelope are obtained and also validated. Comparisons are performed and an excellent fit to the field measurements is found in both isotropic and anisotropic environments.

New, exact expressions for the bivariate Nakagami-q (Hoyt) processes with arbitrary correlation in a nonstationary environment are derived. More specifically, the following are obtained: joint probability density function, joint cumulative distribution function, power correlation coefficient, and some statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability and probability density function. The expressions are mathematically tractable and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment.

New, exact expressions for the bivariate Hoyt (Nakagami-q) processes in a nonstationary environment are derived. More specifically, the following are obtained: joint probability density function and joint cumulative distribution function. In addition the outage probability for the Maximal- Ratio and Equal-Gain Combining techniques in a correlated Hoyt channel are obtained. The expressions are mathematically tractable and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment.

Accurate closed-form approximations to the sum of independent identically distributed eta-mu and kappa-mu random variables are provided. The proposed approximations turn out to be simple, precise, and useful for obtaining important performance metrics of communications systems where sums of variates arise. In particular, average bit error rate and level crossing rate of multibranch equal-gain combining receivers are attained to illustrate the applicability of the approximations. Some sample examples show that the intricate exact solution and the simple approximate expressions yield results that are almost indistinguishable from each other.

The aim of this Letter is twofold: to propose a simulator for both the phase and the envelope of Nakagami fading channels with arbitrary parameters and to derive precise closed-form approximations to the correlation functions of the Nakagami envelope, phase, and quadrature components.

We derive important second-order statistics-joint distribution of the envelope and its time derivative, second-order distribution, autocorrelation, level crossing rate, and average fade duration-of an existing Nakagami fading simulator, and show that these statistics but the autocorrelation differ considerably from the well-established statistics of the classical simulator.

This paper presents and investigates a general diversity combining scheme, here named MRCS, in which maximal-ratio combined signals are chosen on a selection combining basis. This combining method has a simple implementation and a tractable analytical formulation that can be directly applied to situations in which site selection exists. A general analysis of the probability distribution (reliability), level crossing rate, and average fade duration at the output of the combiner is provided, along with examples for a Nakagami-m fading environment. The main result of the present work, however, is the derivation of an exact, easy-to-evaluate closed-form expression for the mean signal-to-noise ratio at the output of the combiner. Such an expression is applicable for conditions in which the product of the number of maximal-ratio combining branches and the Nakagami-m parameter is an integer and it generalizes a result presented elsewhere in the literature. The formulations derived here find a direct applicability in the dimensioning of practical wireless networks.

General exact expressions for the average level crossing rate (LCR) of multibranch selection (SC), equal-gain (EGC), and maximal-ratio (MRC) combiners operating over non-identical correlated Weibull fading channels are provided. They are given in terms of finite-range multifold integrals. Our exact formulations generalize those obtained recently in the literature for the dual-branch case. The exact solution requirements are then loosened to allow for simpler accurate approximate expressions. They appear in a fairly simple closed-form fashion, for the SC, and still as multiple integrals, for the EGC and MRC, but with much simpler integrands, which drastically reduces the calculation time. Sample numerical results are discussed by specializing the general expressions to a space-diversity system using three collinear horizontally spaced omnidirectional antennas at the mobile station.

This paper presents a useful, novel formulation for the outage probability in interference-limited communication systems, here namedJointOutageProbability(JOP). Given a set of SIR restrictions for mutually interfering signals, the JOP corresponds to the probability that at least one of the restrictions is not satisfied. A general exact solution for the joint outage probability is derived, along with a necessary and sufficient condition for a non-null JOP. Furthermore, a closed- form expression for the joint outage probability in a non- identically distributed Rayleigh scenario with independent signals is obtained. The results presented here can be directly applied in a wide range of practical scenarios.

In this paper, a new infinite series representation for the multivariate alpha-mu joint probability density function is derived allowing for an arbitrary correlation matrix and non-identically distributed variates. The formulation is general and exact and comprises all of the other joint densities that arise from alpha-mu distribution published in the literature.

This paper derives an exact closed-form expression for the phase-envelope joint distribution of the κ-μ fading environment, a general fading model that includes the Rice and the Nakagami-m models as special cases. The derived joint statistics are obtained so that compatibility with both Rice as well as Nakagami-m cases are kept. Monte Carlo simulations are used to validade the formulations.

Accurate closed-form approximations to the sum of independent identically distributed eta-mu and kappa-mu random variables are provided. The proposed approximations turn out to be simple, precise and find applicability in obtaining important performance metrics of communications systems where sums of variates arise. In particular, outage probability and average bit error rate of some modulation schemes of multibranch equal-gain combining receivers are attained to illustrate the usefulness of the approximations. In passing, based on the fading models of the corresponding fading scenarios, exact expressions for these metrics for multibranch maximal-ratio combining receivers are attained that present the same functional form of the corresponding expressions for a single branch.

Sums of fading envelopes arise in several wireless communications applications, such as equal-gain combining, outage probability, signal detection, etc. In this paper, based on the intricate task of evaluating the exact statistics of such sums, accurate approximations for the outage probability of equal-gain receivers subject to arbitrary independent cochannel interferers are proposed. In our analysis, an M-branch_N-interferer system subject to an alpha-mu fading scenario is considered. The results are obtained in terms of a singlefold integral, which replaces the M times N nested integrals required in the exact solution. The accuracy of our formulation is checked by comparing it with Monte Carlo simulation results. It is shown that approximate and simulated curves are practically indistinguishable from each other.

In this paper, a new infinite series representation for the multivariate alpha-mu joint probability density function is derived allowing for an arbitrary correlation matrix and non-identically distributed variates. The formulation is general and exact and comprises all of the other joint densities that arise from alpha-mu distribution published in the literature.

In this paper, exact expressions for the level crossing rate (LCR) and average fade duration (AFD) for two-branch selection, equal-gain and maximal-ratio combining systems in a Hoyt fading environment are presented. The expressions apply to unbalanced, non-identical, correlated diversity channels and have been validated by specializing the general results to some particular cases whose solutions are known. In passing, the joint bidimensional envelope-phase Hoyt distribution with arbitrary fading parameters is obtained.

In this work, a number of new closed-form expressions for the eta-mu fading channels involving the joint statistics of the envelope, phase, and their time derivatives are obtained. Level crossing rate (LCR), average fade duration (AFD), and phase crossing rate (PCR) are also derived. The expressions are thoroughly validated by reducing them to some particular known cases and, more generally, by means of Monte Carlo simulation. We then provide alternative (i) singlefold integral exact formulations and (ii) highly-accurate approximations to the level-crossing statistics of multibranch maximal-ratio combining (MRC) and equal-gain combining (EGC) systems, respectively, operating over independent Hoyt fading channels, for which the exact solutions appear in the literature in multifold integral forms.

Sums of fading envelopes occur in several wireless communications applications, such as equal-gain combining, signal detection, outage probability, intersymbol interference, etc. The exact evaluation of the sum statistics is known to be very intricate. One of the purposes of this Letter is to provide highly accurate closed-form approximations to the probability density function and cumulative distribution function of the sum of independent identically distributed (i.i.d.) alpha-mu (generalized gamma) variates. Based on and as an extension of such an approach, simple precise approximations for the performance metrics of equal-gain combining and maximal-ratio combining receivers operating on i.i.d. alpha-mu fading channels are proposed. Samples examples are given to illustrate that, for practical purposes, exact and approximate solutions are indistinguishable from each other.

New, exact expressions concerning the bivariate Nakagami-m processes with arbitrary correlation and fading parameters are derived. More specifically, the following are obtained in the present work: joint moment generating function; joint probability density function; joint cumulative distribution function; power correlation coefficient; and several statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability, probability density function, and mean SNR. The expressions make use of the well known generalized Laguerre polynomials. They are mathematically tractable and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment. We maintain, however, that a relation among the correlation coefficients of the corresponding Gaussian components must be kept so that convergence is attained.

The tradeoff between maximizing the number of transmissions and reducing total interference is the main problem about dimensioning wireless multihop networks. In this paper, we derive an analytical solution for the calculation of outage probability in a wireless multihop network. The outage probability is the probability of a transmission between two nodes may not be established because there is no available channels along a specific route or the signal-to-interference ratio is below a specified threshold. The proposed solution is compared with simulations, and an excellent agreement is attained.

The tradeoff between maximizing the number of transmissions and reducing total interference is the main problem about dimensioning wireless multihop networks. The estimation of how many transmissions the network can support ensuring a quality of service for its users is a difficult task due to two central aspects: the wireless medium and the multihop nature of transmissions. In this paper, we derive an analytical solution for the calculation of outage probability in a wireless multihop network that considers both aspects jointly. The outage probability is defined as the probability of a transmission between two nodes is not established because no available channels along a specific route or the signal-to-interference ratio is below a specified threshold. The proposed solution is compared with simulations, and an excellent agreement is attained.

This paper derives a simple and closed-form expression for the phase-envelope joint distribution of the η-μ distribution, a general fading model that includes the Hoyt and the Nakagami-m models as special cases. In the same way, the marginal distribution of the phase is also obtained. These analytical expressions reduce in an exact manner to those of the particular cases comprised by the η-μ distribution. Some plots illustrate the behavior of the phase for several fading conditions.

This paper derives exact expressions for the level crossing rate and average fade duration of multibranch pure-selection, equal-gain, and maximal-ratio combiners operating over independent non-identical α-μ (also called generalized Γ or Stacy) fading channels. The derived expressions are in closed form for pure-selection combining and in integral form for equal-gain and maximal-ratio combining. For the two latter schemes, accurate closed-form approximations are then provided. The analytical results are validated by reducing the general expressions to known particular cases and, more generally, by means of simulation. Numerical examples are also given to illustrate the high accuracy of the proposed closed-form approximations.

General exact expressions for the level crossing rate and average fade duration of dual-branch selection, equal-gain, and maximal-ratio combiners operating over non-identical correlated Ricean channels are derived. Sample numerical results are discussed by specializing the general expressions to a space-diversity system with horizontally spaced omnidirectional antennas at the mobile station. When the antennas are perpendicular to the direction of the vehicle motion, the average fade duration is loosely dependent on the antenna spacing and on the Ricean factor, being almost identical to that of the independent fading condition. When the antennas are parallel to the direction of the vehicle motion, the level crossing rate can be reduced below the value obtainable for independent fading signals. In this case, if a line-of-sight component exists, a further improvement in the average fade duration over the independent condition may be also achieved.

This paper specializes and parameterizes the general result presented elsewhere in the literature in order to propose, fully characterize, and investigate the symmetrical n-k distribution. It yields estimators for the involved parameters and uses field measurements to validate the distribution. The symmetrical n-k distribution includes, as special cases, important distributions such as Rayleigh, Rice, Hoyt, Nakagami-q, and one-sided Gaussian. The fact that the symmetrical n-k distribution has one more parameter than the well-known distributions renders it more flexible. Of course, in situations in which those distributions included in it give good results a better fitting is given by the symmetrical n-k distribution. In addition, in many other situations in which these distributions give poor results a good fitting may be found through the symmetrical n-k distribution. More specifically, its non-monomodal feature finds applications in several circumstances, examples of which are given in this paper.

This paper presents a general fading distribution - the /spl alpha/-/spl mu/ distribution - that includes the Nakagami-m and the Weibull as special cases. One-Sided Gaussian, Rayleigh, and Negative Exponential distributions are also special cases of the /spl alpha/-/spl mu/ Distribution.

This paper presents a general fading distribution-the /spl kappa/-/spl mu/ distribution-that includes the Rice and the Nakagami-m distributions as special cases. Therefore the one-sided Gaussian and the Rayleigh distributions also constitute special cases and the lognormal distribution may be well-approximated by the /spl kappa/-/spl mu/ distribution. Preliminary results show that the /spl kappa/-/spl mu/ distribution provides a very good fitting to experimental data.

This paper presents a study on interference in microcellular networks with reuse patterns based on a square grid. The performance of the system is assessed by means of the carrier-to-interference (C/I) ratio for a series of situations such as: the worst case condition, mobiles randomly positioned and channel activity according to a given traffic intensity. General formulas are presented for all possible reuse patterns, and graphical results are presented for systems with clusters of 5, 8, 9, 10 and 13 microcells. The results show an outstanding improvement in performance when compared to those for the worst case condition presented in previous works of the same authors.

This paper presents a simple and exact method that can be used to evaluate the frequency reuse efficiency within CDMA networks that are closer to the real networks. In this method, any traffic distribution can be used and the cells may be positioned anywhere with respect to each other, therefore, not necessarily at the well-known hexagonal grid. This later feature allows for overlaps and gaps between cells.

This paper proposes novel reuse patterns for microcellular network based on a square grid. An initial carrier-to-interference ratio assessment for these patterns considers the mobiles positioned at the worst case condition and the system operating at a full load. Among the possible reuse patterns (1, 2, 4, 5, 8, 9, 10, 13, ... microcells per cluster) the performance analysis investigates systems with clusters of 5, 8, 9, and 10 microcells. The results show a substantial difference in performance for the up and downlinks, with the former performing less satisfactorily than the latter and with this difference diminishing as the size of the cluster increases. Both the 10- and the 9-microcell clusters exhibit an outstanding performance and, if appropriately explored, a remarkable trade-off between capacity and interference may be encountered in the 5-microcell cluster.