Fade Duration Research Articles

Second-Order Statistics for the Envelope of α - κ - μ Fading Channels

Exact closed-form expressions for the level crossing rate (LCR) and the average duration of fades (ADF) of α - κ - μ fading channels are presented. Confirmation of the derived analytical formulations is attained by reducing the general results to some widely known cases (Nakagami-m, Rice, and Weibull). Extra validation is performed by comparison with measurement data and by means of a sample of numerical results obtained by the Monte Carlo simulation.

Outage probability in Nakagami channels using fade duration distribution approximate results

The minimum duration outage concept allows an improved analysis of the outage probability and it has been reported, up to now, only for Log-normal shadowing and Rayleigh fading using asymptotic results of the level crossing theory. Capitalizing on some approximate results for the Fade Duration Distribution, FDD, in this letter we show the analysis of the minimum duration outage for the general case of Nakagami fading. We also show how some elements of the physical layer of the system can be used to determine the minimum duration outage interval ?min.

Analytical second‐order statistics of maximal‐ratio diversity over spatially correlated nakagami fading channels

To evaluate the performance of antenna diversity with maximal‐ratio combining (MRC) over spatially correlated Nakagami fading channels, the average level crossing rate (LCR) and the average fade duration (AFD) of the signal envelope are derived. To characterize the dependence among antenna branches, both the exponential and equal correlation models are considered. Numerical results of the average LCR and AFD are presented for various channel parameters and different numbers of branches.

Assessment of rain fade mitigation techniques in the EHF band on a Syracuse 3 20/44-GHz low elevation link

An Earth-to-satellite propagation experiment in the EHF band has been carried out within the framework of the Syracuse 3 program, which is a new generation French military SATCOM system. The originality of this experiment resides in the link's frequencies (20 GHz downlink and 44 GHz uplink) and its low elevation angle (17°). The first part of the article presents a statistical analysis of attenuation data providing the long-term statistics, frequency scaling ratios and fade durations. These results are compared to standard ITU models. The second part of the article is dedicated to the short-term forecasting of rain fade, useful for the implementation of Fade Mitigation Techniques (FMT). Firstly, the downlink attenuation is predicted based on a non-linear ARIMA-GARCH model. The prediction result is then separated into several physical components (gases, clouds and rain) that are scaled to the uplink frequency using specific frequency scaling factors. The performance of the model is assessed based on Syracuse 3 20/44-GHz data collected during a period of 1 year.

An Extended Generalized Rice Model for Wireless Communications

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The multipath component arriving at the mobile receiver cannot explicitly be of homogeneous nature due to nonuniform scattering caused by objects with irregular surfaces having various scattering properties. Another reason, which may contribute to this inhomogeneity, is the nonlinearity of the propagation medium. In this paper, a new general statistical small-scale model for wireless channels, which is affected by nonfrequency-selective fading, is proposed to describe the received signal level by taking into account the aforementioned effects. The advantageous physical interpretation of the model is introduced, and solutions for the probability density functions (PDFs) of the envelope and the phase as well as the cumulative distribution function (CDF) of the envelope are derived. In addition, the second-order statistics have been studied, and solutions for the level-crossing rate (LCR) and the average duration of fades (ADF) are obtained. The usefulness of the model is demonstrated by providing the best fit, compared with widely known models, to certain measurement data corresponding to a variety of real-world channel conditions. Furthermore, its validation is confirmed by simulation. Consequently, the extended generalized Rice model is applicable in wireless channels subjected to various conditions, and it can be preferable because of its outperformance. </para>

Characterisation of narrowband communication channels on the human body at 2.45 GHz

A number of propagation measurements of belt-to-head and belt-to-wrist channels have been performed with inverted F-antennas, planar inverted F-antennas (PIFAs), monopole, loop and dipole antennas, and propagation models were derived. It is found that the channel can be separated into short-term and long-term fading components. The short-term fading can generally be modelled with a Rician distribution, whereas in many cases, long-term fading is lognormal, the best distribution is dependent on the channel, antenna type and orientation. Variation of channel parameters with time is studied and an alternative approach to modelling long-term fading deterministically is suggested. Power spectral densities, autocorrelation functions, fade probabilities, level crossing rates and average fade durations are also investigated.

Three-dimensional multipath shape factors for spatial modeling of wireless channels

This paper develops a generalized theory of multipath shape factors used to study the small-scale fading statistics in three-dimensional non-omnidirectional multipath channels. Previous results for horizontal propagation channels are special cases of the present framework when the multipath angular power density (APD) and the travel direction of the mobile unit are confined to a plane. The three-dimensional multipath shape factors are derived in terms of the first three degrees of unnormalized spherical harmonics of the APD. Based on the so derived shape factors, analytical expressions for the level crossing rate, average fade duration and approximate envelope correlation are derived for a Rayleigh fading three-dimensional channel.

An Extended Loo Model with Inhomogeneous Scattering and its Statistical Properties

In this paper, an analytical model for a land mobile satellite channel is introduced that takes into consideration the Generalized Rice model for characterizing the small scale (fast) fading. The proposed model is enriched by the property of non-homogeneous scattering allowing higher flexibility and a more comprehensive description of the channel. In addition, a lognormal process affects the line of sight component, in order to characterize the large scale (slow) fading due to the shadowing effect caused by physical obstacles such as trees and small buildings. The main statistical properties of the model are investigated. Exact solutions for the power spectral density, the probability density function of the envelope and phase, and the cumulative distribution function of the envelope are derived. Approximate solutions for the level crossing rate and the average duration of fades are obtained. The validation of the model is confirmed by simulation and demonstrated by providing the best fit to certain measurement data corresponding to conditions of light and heavy shadowing. As a conclusion, the extended Loo model is applicable in realistic land mobile satellite channels subjected to various conditions and can be preferable because of its outperformance.

The Weibull–Lognormal Fading Channel: Analysis, Simulation, and Validation

In frequency-nonselective fading channels, the partial waves arriving at the mobile receiver cannot explicitly be of homogeneous nature due to nonuniform scattering caused by objects of specific reflective nature. Moreover, shadowing influences the received signal level by causing slow variations to its local mean. In this paper, we investigate a mixture stochastic process accounting for both inhomogeneous scattering and shadow fading by multiplying a Weibull process with a lognormal process. The first process models the possible scattering nonuniformities of the channel, whereas the second process accounts for the slow-term variations of the local mean due to shadowing. An exact solution for the composite probability density function (pdf) will be given, together with approximate solutions for the second-order statistics, i.e., the level crossing rate (LCR) and the average duration of fades (ADF). The approximate solutions come from the assumption of a slowly time-varying lognormal process compared with the Weibull process, the validity of which will be tested via an efficient deterministic simulation scheme that implements the analytical model on a digital computer. Finally, a curve fitting of the LCR to real-world data drawn from channel measurements will demonstrate the flexibility and usefulness of the proposed model.

Collision and Fade Localization within Packets for Wireless LANs

In this paper, we derive an algorithm for estimating the location of events which cause burst errors, such as packet collisions and multipath fades in wireless packets. Effective localization algorithms have a range of applications, and could lead to network performance improvements through techniques such as error control coding and cross-layer design between the physical and medium access control layers. Given that a collision or fade occurs in a packet, the algorithm finds the maximum-likelihood estimate of the start time and duration of the collision or fade. Due to the computational complexity of this optimal estimate, we also derive an efficient sub-optimal algorithm which decouples the estimation of the collision or fade duration from the estimation of its starting position within the packet of interest. Both algorithms are able to isolate collision locations within the packet when the signal-to-noise ratio is high enough for the link to operate at a BER of ~10?6 in the absence of collision. An extension to M-QAM demonstrates similar effectiveness for constellation sizes up to 128.

Capacity fades analysis of MIMO Rician channels in mobile ad hoc networks

Multiple-input multiple-output (MIMO) mobile ad hoc networks have been receiving increased attention in both commercial and military applications. Just as in cellular networks, MIMO technologies can benefit ad hoc networks by providing the diversity and capacity advantages as well as the spatial degree of freedom in designing the media access control (MAC) protocol. However, one fundamental issue of MIMO mobile ad hoc networks is how to accurately model the impact of spatial/temporal channel correlation in the mobile-to-mobile communications environment. In such a channel, line-of-sight (LOS) components and different scattering environments will affect both ergodic capacity and average capacity fading duration of the MIMO system. In this paper, based on the double-ring scattering model with LOS components we suggest a sum-of-sinusoids MIMO mobile-to-mobile channel simulation method, which can characterize the spatial/temporal channel correlation and Rician fading effect. Our numerical results show the ergodicity of our proposed channel model, correctness of the analytical channel correlation, effect of spatial correlation on channel capacity, impact of the number of antennas and scatterers on capacity, capacity distribution, and level crossing rate (LCR) and average fading duration (AFD) of MIMO Rician channel capacity. We also show the impacts of Rician factor K on channel capacity, probability density function (PDF), LCR, and AFD.

End-to-end performance of dual-hop semi-blind relaying systems with partial relay selection

The end-to-end performance of dual-hop cooperative links using semi-blind (fixed gain) relays and partial relay selection is investigated. The selection scheme considers that the source monitors the connectivity among the nodes (relays) of the first hop only. This scheme is interesting in practical ad-hoc and sensor networks. In our analysis, compact closed-form expressions are obtained for the outage probability, probability density function, moment generating functions, and generalized moments of the end-to-end signal-to-noise ratio(SNR), from which other relevant statistics that well-describe the distribution of the end-to-end SNR, such as mean, variance, kurtosis, skewness, and amount of fading, can also be deduced. Furthermore, the dynamic behavior of the end-to-end envelope is investigated, and the corresponding level crossing rate and average fade duration are obtained in an exact manner. Also, tight lower and upper bounds for these second-order statistics are presented in closed-form. Numerical results illustrating the system's performance in terms of the above metrics are provided, and the influence of the relay selection on performance is analyzed and discussed. For instance, it is shown that the power imbalance between the hops may have positive or negative effects on the overall system performance irrespective of the number of selected relays.

New performance results for multiuser optimum combining in the presence of rician fading

This paper analyzes the performance of multiuser optimum combining systems. We consider the practical scenario where the desired user undergoes Rician fading, and the received signals are corrupted by Rayleigh-faded interference and noise. We derive new closed-form expressions for the symbol error rate, ergodic capacity, level crossing rate, and average fade duration. These results are given as either accurate approximations or asymptotic (eg. high signal-to-noise ratio (SNR)) expressions, and are based on new closed-form statistical properties which we derive for the signal-to-interference noise ratio (SINR). Specifically, we derive exact first order expansions and accurate gamma approximations for the SINR distribution, as well as simplified exact expressions for the moments. We also present closed-form expressions for key performance parameters such as the diversity order and array gain, wideband slope, and high SNR power offset, and analyze the impact of the Rician K-factor, which is shown in all cases to yield a performance improvement.

Characterization of time variation on 1.9 GHz fixed wireless channels in suburban macrocell environments

We observed temporal fading on 1.9 GHz fixed wireless channels during short-term measurements at 107 different locations in a suburban macrocell environment characterized by flat terrain and heavy foliage in order to determine how the rate of fading varies with average wind speed and distance. For each location, we estimated: (1) the Ricean K-factor using a moment-based estimator and (2) an equivalent Doppler frequency which is related to the maximum Doppler frequency by a factor that depends upon the shape of the Doppler spectrum. We did so by fitting the measured level crossing rate (LCR) and average fade duration (AFD) distributions to expressions normally justified for mobile wireless links using a method recently proposed by Feick, Valenzuela and Ahumada (2007). As has been observed at other sites, the Ricean K-factor decreased with both average wind speed and distance. However, we found that the equivalent Doppler frequency was effectively uncorrelated with wind speed and noticeably increased with distance. Similar measurements at other sites will be required to determine the extent to which these trends are affected by foliage density and tower height.

MRCS -- selecting maximal ratio combined signals: a practical hybrid diversity combining scheme

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.

On the second order statistics of the multihop rayleigh fading channel

Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called NRayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.

Statistical Modeling and Analysis of Mobile-to-Mobile Fading Channels in Cooperative Networks Under Line-of-Sight Conditions

Recently, mobile-to-mobile (M2M) cooperative network technology has gained considerable attention for its promise of enhanced system performance with increased mobility support. As this is a new research field, little is known about the statistical properties of M2M fading channels in cooperative networks. So far, M2M fading channels have mainly been modeled under the assumption of non-line-of-sight (NLOS) conditions. In this paper, we propose a new model for M2M fading channels in amplify-and-forward relay links, where it is assumed that a line-of-sight (LOS) component exists in the direct link between the source mobile station and the destination mobile station. Analytical expressions will be derived for the main statistical quantities of the channel envelope, such as the mean value, variance, probability density function (PDF), level-crossing rate (LCR), and average duration of fades (ADF) as well as the channel phase. Our results show that the statistical properties of the proposed M2M channel are quite different from those of double Rayleigh and double Rice channels. In addition, a high-performance channel simulator will be presented for the new M2M channel model. The developed channel simulator is used to confirm the correctness of all obtained theoretical results by simulations.

Channel Characterization for Single- and Multiple-Antenna Wearable Systems Used for Indoor Body-to-Body Communications

In this paper, an analysis of radio channel characteristics for single- and multiple-antenna bodyworn systems for use in body-to-body communications is presented. The work was based on an extensive measurement campaign conducted at 2.45 GHz representative of an indoor sweep and search scenario for fire and rescue personnel. Using maximum-likelihood estimation in conjunction with the Akaike information criterion (AIC), five candidate probability distributions were investigated and from these the kappa- mu distribution was found to best describe small-scale fading observed in the body-to-body channels. Additional channel parameters such as autocorrelation and the cross-correlation coefficient between fading signal envelopes were also analyzed. Low cross correlation and small differences in mean signal levels between potential dual-branch diversity receivers suggested that the prospect of successfully implementing diversity in this type application is extremely good. Moreover, using selection combination, maximal ratio, and equal gain combining, up to 8.69-dB diversity gain can be made available when four spatially separated antennas are used at the receiver. Additional improvements in the combined envelopes through lower level crossing rates and fade durations at low signal levels were also observed.

Simulation of rain fade on arbitrary microwave link networks by the downscaling and interpolation of rain radar data

To predict the Quality of Service at a node in heterogeneous networks of line‐of‐sight, terrestrial, microwave links requires knowledge of the spatial and temporal statistics of rain over scales of a few meters to tens or hundreds of kilometers, and over temporal periods as short as 1 s. Meteorological radar databases provide rain rate maps over areas with a spatial resolution as fine as a few hundred meters and a sampling period of 2 to 15 min. Such two‐dimensional, rain rate map time series would have wide application in the simulation of rain scatter and attenuation of arbitrary millimeter‐wave radio networks, if the sampling period were considerably shorter, i.e., of the order of 10 s or less, and the integration volumes smaller. This paper investigates a stochastic‐numerical method to interpolate and downscale rain rate field time series to shorter sampling periods and smaller spatial integration areas, while conserving the measured and expected statistics. A series of radar derived rain maps, with a 10 min sample period, are interpolated to 10 s. The statistics of the interpolated‐downscaled data are compared to fine‐scale rain data, i.e., 10 s rain gauge data and radar data with a 300‐m resolution. The interpolated rain map time series is used to predict the fade duration statistics of a microwave link, and these are compared to a published and ITU‐R model.

On the second order statistics of generalized gamma process

The second order statistics, such as the level crossing rate and the average fade duration of a generalized Gamma distribution are derived in this paper. Joint distribution of the process and its derivative and the marginal distribution of the derivative is developed. It is shown that apart from the Nakagami case the velocity of the process is dependent on the value of the process. The results are applied to derive some characteristics of error flow in channels with dual mobility, generalized Gamma fading and basic modulations.