The aim of this paper is threefold: 1) we introduce a unified statistical characterization for the instantaneous power of a plethora of Gaussian-based fading models; 2) we propose a general framework for the power sum of either independent and identically distributed (i.i.d.) or independent and non-identically distributed (i.non-i.d.) fading distributions; and 3) we provide a unified performance assessment of wireless communications systems in the presence of small-scale fading channels. To accomplish these three goals, we first show that the instantaneous power of a broad Gaussian class of fading models is governed by a mixture of gamma (MG) distribution. Later, we propose novel, tractable, and efficient solutions for the exact sum statistics of i.i.d. and i.non-i.d. MG variates. Lastly, we show that two key performance indicators—namely, the average bit-error rate and the outage probability—of a maximal-ratio combining (MRC) diversity receiver subject to a wide variety of Gaussian-based fading channels can be expressed, in a unified fashion, as a weighted sum of the performance indicators of a single-branch wireless system subject to independent Nakagami-m fading channels. Extensive numerical simulations reveal the outstanding improvement in computational efficiency and mathematical tractability of our derived expressions when compared with state-of-the-art solutions.

Two generalizations of the fluctuating two-ray (FTR) fading model have recently appeared in the literature. In particular, in these FTR-based models, the specular components of the complex baseband signal are modulated by the square root of either (i) the product (Cascade FTR) or (ii) the ratio of products (Ratio-Product FTR) of Gamma random variables (RVs). Leveraging the applicability of the sum of RVs in performance analysis of communications systems, this paper explores the sum statistics of these two newly introduced FTR-based RVs. More precisely, we obtain novel exact formulations for the probability density function (PDF), the cumulative distribution function (CDF), and the raw moments of the sum of independent and identically distributed (i.i.d.) squared FTR-based RVs. Moreover, we carry out a truncation error analysis for the derived PDFs and CDFs. Finally, we obtain in an exact and asymptotic manner essential performance metrics such as outage probability (OP) and symbol error probability (SEP) for a maximal-ratio combining (MRC) receiver.

In the context of synthetic aperture radar (SAR) systems, the Gamma distribution stands out as a strong contender for clutter modeling. The cell-averaging constant false alarm rate (CA-CFAR) detector has frequently been employed as a well-balanced detection technique, ensuring a blend of high performance and comparatively low complexity. In this study, we evaluate, in an exact manner, the CA-CFAR detector’s performance in an SAR system, assuming the presence of correlated Gamma-distributed clutter. To this aim, we derive novel exact expressions for the probability of detection (PD) and the probability of false alarm (PFA), simplifying their runtime evaluations without depending on specific mathematical software. The independent and identically distributed (IID) and independent not identically distributed (INID) cases are also analyzed. In particular, for the IID case, our derived PD and PFA expressions are given in closed form. Our analytical findings are validated through Monte Carlo simulations.

The execution of large deep neural networks (DNN) at mobile edge devices requires considerable consumption of critical resources, such as energy, while imposing demands on hardware capabilities. In approaches based on edge computing the execution of the models is offloaded to a compute-capable device positioned at the edge of 5G infrastructures. The main issue of the latter class of approaches is the need to transport information-rich signals over wireless links with limited and time-varying capacity. The recent split computing paradigm attempts to resolve this impasse by distributing the execution of DNN models across the layers of the systems to reduce the amount of data to be transmitted while imposing minimal computing load on mobile devices. In this context, we propose a novel split computing approach based on slimmable ensemble encoders. The key advantage of our design is the ability to adapt computational load and transmitted data size in real-time with minimal overhead and time. This is in contrast with existing approaches, where the same adaptation requires costly context switching and model loading. Moreover, our model outperforms existing solutions in terms of compression efficacy and execution time, especially in the context of weak mobile devices. We present a comprehensive comparison with the most advanced split computing solutions, as well as an experimental evaluation on GPU-less devices.

Sea clutter has been a long-standing issue in old and modern radars. Under this context, the K-distribution has emerged as a promising clutter model to accurately mimic sea signal variations in a large variety of radar systems. To guarantee an adequate radar performance in the presence of sea clutter, the family of constant false-alarm rate (CFAR) detectors has been commonly used. In particular, due to its adequate balance between performance and implementation, the cell-averaging CFAR (CA-CFAR) detector has been considered an attractive detection mechanism to enhance radar performance over various clutter environments. In this work, we assess radar performance considering a CA-CFAR detector operating over K-distributed sea clutter with fully correlated texture. More precisely, we derive novel closed-form expressions for the probability of detection ( $P_{\text {D}}$ ) and the probability of false alarm ( $P_{\text {FA}}$ ) that can be readily evaluated using any mathematical software. Monte-Carlo (MC) simulations corroborate our analytical findings.

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.

In the past few years, mobile deep-learning deployment progressed by leaps and bounds, but solutions still struggle to accommodate its severe and fluctuating operational restrictions, which include bandwidth, latency, computation, and energy. In this work, we help to bridge that gap, introducing the first configurable solution for collaborative object detection that manages the triple communication-computation-accuracy trade-off with a single set of weights. Our solution shows state-of-the-art results on COCO–2017, adding only a minor penalty on the base EfficientDet-D2 architecture.

Modern radar systems use square-law detectors to search and track fluctuating targets embedded in Weibull-distributed ground clutter. However, the theoretical performance analysis of square-law detectors in the presence of Weibull clutter leads to cumbersome mathematical formulations. Some studies have circumvented this problem by using approximations or mathematical artifacts to simplify calculations. In this work, we derive aclosed-formandexactexpression for the probability of detection (PD) of a square-law detector in the presence of exponential targets and Weibull-distributed ground clutter, given in terms of the Fox H-function. Unlike previous studies, no approximations nor simplifying assumptions are made throughout our analysis. Furthermore, we derive a fast convergent series for the referred PD by exploiting the orthogonal selection of poles in Cauchy’s residue theorem. In passing, we also obtain closed-form solutions and series representations for the probability density function and the cumulative distribution function of the sum statistics that govern the output of a square-law detector. Numerical results and Monte Carlo simulations corroborate the validity of our expressions.

Multi-connectivity (MC) is regarded as one of the key features that meet the requirements of ultra-reliable low-latency communications for 5th generation networks, as it provides multiple diversity branches. Recently, we evaluated the decoding reliability of various MC setups and different combining algorithms by analyzing the resulting outage probabilities. In this work, we are interested in how much the performance is affected by correlated fading. Specifically, we analyze the outage probability of MC systems with joint decoding reception operating over correlated quasi-static Rayleigh and Nakagami-m fading channels. Our main contributions are as follows: (i) deriving the exact outage probability in integral form and the asymptotic outage probability at high signal-to-noise ratio (SNR) in closed form; (ii) deriving the correlation loss, which quantifies the extra SNR required under correlated fading as compared with the independent scenario; and (iii) evaluating frame-error rates of quasi-cyclic low-density parity-check codes by Monte-Carlo simulations. Our results show that the correlation loss is marginal for a low to moderate level of correlation, whereas the diversity gain is not affected by correlation whatsoever. Furthermore, we find that the correlation loss is independent of the degrees of freedom encapsulated by the Nakagami-m fading parameter.

Wireless communications are affected by several aspects of the multipath fading channel, including clustering, nonlinearity, correlation, scattered waves, and specular components. These aspects have been incorporated into many existing probabilistic fading models. The more aspects are covered, the more complicated is the resulting model. In many cases, the model or the associated system performance or both cannot be obtained in a closed form. As a result, little insight is gained into how each aspect of fading ultimately impacts key metrics such as symbol error rate and outage probability. In this work, we provide a novel asymptotic analysis at high signal-to-noise ratio that yields simple, general, and unified closed-form expressions for the diversity and coding gains of the symbol error rate and outage probability. We cover generalized fading scenarios and all the referred fading aspects. Our results give a handy, yet thorough, characterization of the system performance as impacted by multiple physical aspects of the multipath fading phenomenon. We provide further insights to reveal that all the addressed fading aspects affect the coding gain, whereas only the clustering and nonlinearity affect the diversity gain.

We propose a unified approach to approximate the probability density function and the cumulative distribution function of a sum of independent channel envelopes following generalized, and possibly mixed, fading models. In the proposed approach, the approximate sum distribution can be chosen out of a broad class of statistical models. More fundamentally, given any chosen model, the parameters of the approximate sum distribution are calibrated by matching its asymptotic behavior around zero to that of the exact sum. In a subsidiary fashion, one or more moments of the exact and approximate sums are also matched to one another if the approximate distribution has three or more parameters to be adjusted, respectively. As illustrated through many numerical examples, our approach outperforms existing ones that are solely based on moment matching, by yielding statistical approximations that are remarkably accurate at medium to high signal-to-noise ratio - a paramount operational regime for communications systems. Our results find applicability in several wireless applications where fading sums arise, and can be readily extended to accommodate sums of fading (power) gains and, in a broader context, generic sums of non-negative random variables.

Multi-connectivity (MC) is regarded as one of the key features that meet the requirements of ultra-reliable low-latency communications for 5th generation networks, as it provides multiple diversity branches. Recently, we evaluated the decoding reliability of various MC setups and different combining algorithms by analyzing the resulting outage probabilities. In this work, we are interested in how much the performance is affected by correlated fading. Specifically, we analyze the outage probability of MC systems with joint decoding reception operating over correlated quasi-static Rayleigh fading channels. Our main contributions are as follows: (i) deriving the exact outage probability in integral form and the asymptotic outage probability at high signal-to-noise ratio (SNR) in closed form; (ii) deriving the correlation loss, which quantifies the extra SNR required under correlated fading as compared with the independent scenario; and (iii) evaluating frame-error rates of quasi-cyclic low-density parity-check codes by Monte-Carlo simulations. Our results show that the correlation loss is marginal for a low to moderate level of correlation, whereas the diversity gain is not affected by correlation whatsoever.

We capitalize on the Wasserstein distance to obtain two information-theoretic bounds on the generalization error of learning algorithms. First, we specialize the Wasserstein distance into total variation, by using the discrete metric. In this case we derive a generalization bound and, from a strong data-processing inequality, show how to narrow the bound by adding Gaussian noise to the output hypothesis. Second, we consider the Wasserstein distance under a generic metric. In this case we derive a generalization bound by exploiting the geometric nature of the Kantorovich-Rubinstein duality theorem. We illustrate the use of these bounds with examples. Our bounds can handle certain cases in which existing bounds via mutual information fail.

This letter presents a novel and exact formulation for the probability of detection of a cell-averaging, constant false-alarm rate (CFAR) radar system operating in a homogeneous Weibull clutter environment. We consider a realistic scenario with both target returns and clutter residues within the cell under test by the radar processing. In passing, we derive novel closed-form expressions for the probability density function and the cumulative distribution function of the sum of an exponentially fluctuating target embedded in Weibull clutter. The derived exact expressions are given in terms of both: 1) bivariate Fox H-function, for which we provide a portable and efficient MATHEMATICA code and 2) easily computable series representations. The validity of all expressions is confirmed via Monte Carlo simulation. The derived results are compared with the idealized Neyman-Pearson detector so as to quantify the CFAR losses, and they indicate that even a small change in the shape parameter of the clutter distribution can significantly affect the radar detection performance.

Multi-connectivity (MCo) is considered to be a key strategy for enabling reliable transmissions and enhanced data rates in fifth-generation mobile networks, as it provides multiple links from source to destination. In this paper, we quantify the communication performance of MCo in terms of outage probability and throughput. For doing so, we establish a simple, yet accurate analytical framework at high signal-to-noise ratio (SNR), in which the number of links, the spectral efficiency, the path loss, and the SNR are incorporated, giving new insights into the potentials of MCo as compared with the single-connectivity (SCo). These are our main contributions: 1) finding the exact coding gain of the outage probability for parallel block-fading channels; 2) quantifying the performance improvement of MCo over SCo in terms of SNR gain; and 3) comparing optimal and suboptimal combining algorithms for MCo at the receiver side, namely joint decoding, selection combining, and maximal-ratio combining, also in terms of SNR gain. In addition, we apply our analytical framework to real field channel measurements and thereby illustrate the potential of MCo to achieve high reliability and high data rates in real cellular networks.

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.

The so-called chief executive officer problem suggests that the source message can be recovered at the destination by merging a set of corrupted replicas forwarded by multiple relays, as long as these replicas are sufficiently correlated with the original message. In this paper, we build on Slepian-Wolf's correlated source coding theorem to design a simple, yet efficient power allocation scheme for a multirelay system, in which the direct link is unavailable to convey information. In such a system, the replicas forwarded by the relays are allowed to contain intra-link errors due to previous unreliable hops, and the destination is supposed to retrieve the source message by jointly decoding all received replicas. Importantly, the proposed power allocation is asymptotically optimal at high signal-to-noise ratio.

In this paper, an adaptive scheme for amplify-and-forward relaying networks is proposed, which selects a certain transmission mode for each communication process. Depending on the instantaneous channel conditions, one of the following modes is selected: direct transmission with no cooperation, cooperative transmission with half-duplex relaying and maximal-ratio combining at the destination, or cooperative transmission with full-duplex relaying and maximal-ratio combining at the destination. A three-node network is considered, containing a single-antenna source, a two-antenna relay that is able to implement full-duplex communication, and a single-antenna destination. Energy normalization per block is assumed, so that in those modes using cooperation, the system’s transmission power is shared between source and relay. The performance analysis is provided in terms of outage probability and energy efficiency. We derive a tight approximate expression in closed form for the outage probability and an approximate expression in integral form for the mean energy consumption. The results show that our scheme outperforms all of transmission modes separately in terms of outage probability, while being more energy efficient than the cooperative transmission modes. In addition, the asymptotic analysis proves that the proposed scheme achieves full diversity order equal to 2, thus outperforming those schemes with direct transmission or full-duplex cooperation only.

Although transmit-antenna selection (TAS) is an alternative low-cost strategy to capture the advantages of multi-antenna systems, its application may require a large amount of feedback transmissions. Owing to this fact and in order to reduce such requirement, herein we analyze the outage performance of two distributed TAS (DAS) schemes. One scheme employs maximal-ratio combining (DAS/MRC) at the destination, whereas the other employs selection combining (DAS/SC). We consider a dual-hop fixed-gain amplify-and-forward relaying network, equipped with multi-antenna source/relay nodes and a single-antenna destination. A lower bound expression is derived for the outage probability of each investigated scheme. Importantly, the derived bounds prove to be very tight approximations to the exact outage performance. Also, capitalizing on a strikingly interesting property of Stirling numbers of the second kind, we provide closed-form asymptotic expressions for the obtained bounds. Our results show that the diversity order of the proposed distributed schemes is identical to that of their optimal centralized counterparts, namely Nt+ min(Nrr, Nrt), with Nt, Nrr, and Nrtdenoting the number of transmit antennas at the source, the number of receive antennas at the relay, and the number of transmit antennas at the relay, respectively. In addition, as the relay approaches the destination, the outage performance of the proposed schemes approaches the optimal one.

We propose an adaptive transmission scheme for cognitive decode-and-forward relaying networks, whereby, before each communication process, one out of three transmission modes is dynamically selected in order to maximize the instantaneous capacity of the system, namely, half-duplex (HD) relaying, full-duplex (FD) relaying, or direct transmission with no cooperation. The following key issues, relevant to underlay spectrum sharing and cooperative relaying, are considered: 1) the overall transmit power at the secondary network is constrained by both the maximum tolerable interference at the primary receiver and the maximum transmit power available at the secondary nodes; 2) under FD operation, the secondary relay is subject to residual self-interference, which is modeled as a fading channel; and 3) the signals coming from the secondary source and relay are handled at the secondary destination via maximal-ratio combining, in the HD relaying mode, and via a joint-decoding technique, in the FD relaying mode. We derive an exact analytical expression for the outage probability of the proposed scheme. Then, an approximate closed-form expression is proposed, and a corresponding asymptotic expression is derived. Monte Carlo simulations are run to validate the accuracy of the presented mathematical analysis and to showcase the tightness of the proposed approximation.

This letter investigates the outage probability of a variable-gain amplify-and-forward full-duplex relaying network in which not only the relaying link but also the direct link is used to convey information, thus improving the system reliability. We consider a basic three-node relaying system composed of a source, a destination, and a two-antenna relay—one antenna for transmission, one antenna for reception. Also, we consider that the full-duplex relay undergoes some residual self interference, modeled as a fading channel, and that maximal-ratio combining is employed at the destination to merge the signals from the source and relay. We derive an exact integral-form expression for the outage probability and validate this via Monte Carlo simulation. In addition, we propose a highly-accurate closed-form approximation to the outage probability, as well as a simple asymptotic expression at high signal-to-noise ratio. The use of the direct link is shown to overcome the zero diversity order inherent to full-duplex relaying.

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 design and analyze two distributed suboptimal schemes for transmit-antenna selection and link selection in a dual-hop, fixed-gain, amplify-and-forward relaying system, composed by one multi-antenna source, one single-antenna destination, and one single-antenna relay. The proposed schemes share the same antenna-selection policy, but differ from each other in the way the direct or relaying link is selected for communication. In a first scheme, the link is selected after transmission, at the destination; in a second scheme, it is selected before transmission, at the source. A great advantage of the proposed schemes over the optimal centralized solution is their low and constant delay/feedback overhead, regardless of the number of transmit antennas. In addition, the second scheme brings an improved spectral efficiency, once it saves one time slot when selecting the direct link. We derive analytical lower and upper bounds for the outage probability of the first scheme, in single-fold integral form, and exact closed-form expressions for the outage probability and mean spectral efficiency of the second scheme. We also perform an asymptotic analysis, showing that the first scheme achieves full diversity order, whereas the second scheme achieves full diversity order minus one, as a penalty for its improved spectral efficiency.

We analyze the outage performance of two spectrally efficient schemes for exploiting multiuser diversity in cognitive relaying networks. We consider a secondary network composed by one source node communicating with the best one out of $L$ available destinations, selected according to the channel quality of the direct links. If the transmission through the selected direct link drops below a given threshold, then a half-duplex decode-and-forward relaying transmission is invoked. At this stage, two schemes are considered. In the first scheme, the previously selected secondary destination employs maximal-ratio combining to handle the signals received from the secondary source and relay. In the second scheme, maximal-ratio combining is employed as well, but at a possibly different secondary destination, selected so as to maximize the signal-to-noise ratio at the combiner output. In both schemes, we consider an underlay spectrum-sharing mechanism. We derive exact analytical expressions for the outage probability of the proposed schemes and validate them by Monte Carlo simulations. An asymptotic analysis reveals that the proposed schemes can achieve full diversity order, equal to $L+1$. Importantly, we show that, at high signal-to-noise ratio, the mean spectral efficiency of the proposed schemes approximates that one attained by direct transmission.

This paper investigates the outage performance of a spectrally efficient scheme for multiuser cognitive relaying networks under spectrum sharing constraints. In the proposed setup, we consider a secondary network composed by one source node communicating with the best one out of L available destinations, selected according to the channel quality of the direct links. If the selected direct link drops below a given threshold, a half-duplex decode-and-forward relaying transmission strategy is invoked, and then the selected secondary destination employs a maximal-ratio combining technique to combine the received signals from the secondary source and relay. In our analysis, the overall transmit power at the secondary network is considered to be limited by the maximum tolerable interference power at the primary user receiver, as well as by the maximum transmit power available at the secondary nodes. A closed-form expression for the outage probability is obtained and validated by Monte Carlo simulations. Moreover, an asymptotic analysis is carried out and reveals that the achievable diversity order equals L+1.

A distributed and spectrally efficient link selection scheme for multiuser multirelay cooperative networks with transmit beamforming is proposed and analyzed in terms of outage probability and mean spectral efficiency. More specifically, we consider a network composed by a base station equipped with M antennas which is communicating with one out of L single-antenna mobile stations under the aid of one out of N single-antenna, variable-gain amplify-and-forward relay stations. Either the direct link or the dual-hop relaying link is selected for each communication process by following a distributed link selection scheme. Single-integral expressions for upper and lower bounds of the outage probability and mean spectral efficiency are obtained and validated by Monte Carlo simulations. Furthermore, closed-form expressions derived from the asymptotic analysis of the outage probability reveal that the proposed system achieves full diversity order, which is equal to ML+N. Importantly, it is shown that the mean spectral efficiency is always higher than half of that one attained by direct transmission.

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.

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).

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.

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.

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.

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.