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.

In this paper, we present the results of a set of channel measurements conducted within the 6 GHz band used in IEEE 802.11be based wireless local area networks (WLANs). A range of indoor and outdoor client to access point (AP) communication scenarios were considered for both line-of-sight (LOS) and non-LOS (NLOS) channel conditions. We have investigated the path loss, large-scale, and small-scale fading across 256 frequency points between 6.425 and 6.445 GHz. To model the large-scale fading we have utilized the lognormal and gamma distributions, while for the small-scale fading this was the Rayleigh, Rician, and Nakagami-m distributions. The information loss incurred when encoding the empirical distributions with the aforementioned theoretical ones was determined using the resistor-average distance (RAD). It was found that the gamma distribution provided a better fit to the large-scale fading, while the Rician and Nakagami-m distributions observed the lowest RAD values for the small-scale fading. To ascertain the temporal stability of the considered channels, the coherence time was inferred using an analysis of the autocorrelation. Our results indicate that the coherence time for the large-scale fading was typically longer than for small-scale fading.

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.

We present a simulation framework for evaluating the performance of cooperative reconfigurable intelligent surface (RIS) based systems, which may ultimately deploy an arbitrary number of RISs to overcome adverse propagation-related effects, such as cascaded fading. The physical model underlying the proposed framework considers the (optional) presence of a dominant signal path between the source and RIS, and then between each subsequent stage of the communication link to the destination. Accompanying the dominant signal component is a non-isotropic scattered signal contribution, which accounts for angular selectivity within the cascaded RIS stages between the source and destination. The simulation of the time-correlated scattered signal, reflected by the illuminated reflective elements, is achieved using autoregressive modelling. As a by-product of our analysis, significant insights are drawn which enable us to characterize the amplitude and phase properties of the received signal, and the associated complex autocorrelation functions (ACFs) for the product of multiple Rician channels. For both single and cooperative RIS systems, the outage probability (OP), and important second-order statistics, such as the level crossing rate (LCR) and average outage duration (AOD), are analyzed for a variety of system configurations, accounting for practical limitations, such as phase errors. It is shown that by using multiple RISs cooperatively, the AOD is reduced at a lower signal-to-noise-ratio (SNR) compared to single RIS-assisted transmission under the same operating conditions. Lastly, increased channel variations (i.e., higher maximum Doppler frequencies) are shown to decrease the AOD in the case of absent phase errors; yet, this improvement is not observed when phase errors are present.

This contribution proposes a simulation framework for quantifying the performance of employed reconfigurable intelligent surface (RIS) based systems to overcome adverse propagation-related effects. The physical model underlying the proposed framework considers the presence of a dominant signal path between the source and RIS, and then between RIS and the destination. The simulation of the time-correlated scattered signal reflected by the illuminated reflective elements is achieved using autoregressive (AR) modeling. As a by-product of our analysis, significant insights are developed which allow for the characterization of the amplitude and phase properties of the received signal, and the associated complex autocorrelation function (ACF) for the product of two Rician channels. Capitalizing on this, we derive the corresponding first and second order statistics, which lead to the development of useful theoretical and practical insights.

The$\kappa $-$\mu $/ inverse gamma and$\eta $-$\mu $/ inverse gamma composite fading models are presented and extensively investigated in this paper. We derive closed-form expressions for the fundamental statistics of the$\kappa $-$\mu $/ inverse gamma composite fading model, such as the probability density function (PDF), cumulative distribution function (CDF). Additionally, we solve the associated integral that is commonly used to obtain the moment generating function (MGF) of statistical distributions to provide an MGF-type function which is valid for performance analysis over the specified parameter space. Analytic expressions for the PDF, higher order moments and AF are also derived for the$\eta $-$\mu $/ inverse gamma composite fading model, while infinite series expressions are obtained for the corresponding CDF and MGF-type function. The suitability of the new models for characterizing composite fading channels is demonstrated through a series of extensive field measurements for wearable, cellular, and vehicular communications. For all of the measurements, two propagation geometry problems with special relevance to the two new composite fading models, namely the line-of-sight (LOS) and non-LOS (NLOS) channel conditions, are considered. It is found that both the$\kappa $-$\mu $/ inverse gamma and$\eta $-$\mu $/ inverse gamma composite fading models provide an excellent fit to fading conditions encountered in the field. The goodness-of-fit of these two composite fading models is also evaluated and compared using the resistor-average distance. As a result, it is shown that the$\kappa $-$\mu $/ inverse gamma composite fading model provides a better fit compared to the$\eta $-$\mu $/ inverse gamma composite fading model when strong dominant signal components exist. On the contrary, the$\eta $-$\mu $/ inverse gamma composite fading model outperforms the$\kappa $-$\mu $/ inverse gamma composite fading model when there is no strong dominant signal component and/or the parameter$\eta $is not equal to unity, indicating that the scattered wave power of the in-phase and quadrature components of each cluster of multipath are not identical.

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.

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, we consider the transmission of confidential information over an α-μ and a κ-μ fading channel in the presence of an eavesdropper who experiences κ-μ and α-μ fading, respectively. In particular, we derive novel analytical expressions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound on secrecy outage probability (SOPL) for independent and non-identically distributed (i.n.i.d.) channel coefficients. These results have been validated through simulations and reduction to known special cases. These new, very general formulations, are important as they bring together previously non-unified secrecy capacity and secrecy outage probabilities (SOP) such as those involving α-μ, Nakagami-m, Rayleigh, OneSided Gaussian, Weibull, Negative Exponential with κ-μ and Rice. Additionally, due to the duality of analysis of secrecy capacity and co-channel interference (CCI), the results presented here will also have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise for the aforementioned fading scenarios.

In this paper, we characterize the simultaneous channel response of narrowband on-body and body-to-body channels at 2.48 GHz using the κ-μ fading model. The measurements considered three nodes, two of these were located on the front-chest and front-central-waist of an adult male, and the third node was located on the front-central-waist of an adult female. Multiple human mobility scenarios were considered for three different environments namely an anechoic chamber, reverberation chamber and laboratory environment. For all of the measured channels, the κ-μ probability density function (pdf) provided an excellent fit to the empirical distribution of the measured short-term fading. In addition, the channel measurements also demonstrated the channel reciprocity property for each of the on-body and body-to-body links, and scenarios considered here. Finally, we also show that the sample period of the measurement system developed for this study was well within the coherence time of the channel.

In this paper, we consider the transmission of confidential information over a κ-μ fading channel in the presence of an eavesdropper who also experiences κ-μ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound of secure outage probability (SOPL) for independent and non-identically distributed channel coefficients without parameter constraints. We also provide a closed-form expression for the probability of SPSC when the μ parameter is assumed to take positive integer values. Monte-Carlo simulations are performed to verify the derived results. The versatility of the κ-μ fading model means that the results presented in this paper can be used to determine the probability of SPSC and SOPL for a large number of other fading scenarios, such as Rayleigh, Rice (Nakagamin), Nakagami-m, One-Sided Gaussian, and mixtures of these common fading models. In addition, due to the duality of the analysis of secrecy capacity and co-channel interference (CCI), the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise (BN). To demonstrate the efficacy of the novel formulations proposed here, we use the derived equations to provide a useful insight into the probability of SPSC and SOPL for a range of emerging wireless applications, such as cellular device-to-device, peer-to-peer, vehicle-to-vehicle, and body centric communications using data obtained from real channel measurements.

We describe a novel technique that can be used to allow two parties to exchange a secret key over an orthogonal frequency division multiplexing (OFDM) channel with perfect secrecy, provided subcarriers are subject to independent fading and a malicious attacker is passively eavesdropping. Our approach is shown to be robust against the eavesdropper's channel being correlated with that of the legitimate users, and also active attacks in which the eavesdropper injects fraudulent messages into the system. For the active attack, we show that when the eavesdropper injects fraudulent messages into the system, they will also inadvertently allow the legitimate users to calculate a lower bound on the secrecy capacity of the channel. This allows them to establish whether secrecy has been achieved. A consequence of our approach is that the degrees of freedom within the channel are halved.