Fade Duration Research Articles

Second Order Statistics of -Fisher-Snedecor Distribution and Their Application to Burst Error Rate Analysis of Multi-Hop Communications

An advantage of using the composite fading models (CFMs) is their ability to concurrently address the impact of multi-path and shadowing phenomena on the system performance in wireless communications. A Fisher-Snedecor (FS) F CFM has been recently proposed as an experimentally verified and tractable fading model that can be efficiently applied for 5G and beyond 5G wireless communication systems. This paper provides second-order (s-order) performance analysis of the product of N independent but not identically distributed (i.n.i.d) FS F random variables (RVs). In particular, accurate and closed-form approximations for level crossing rate (LCR) and average fade duration (AFD) of the product of N i.n.i.d FS F ( N-FS F) RVs are successfully derived by exploiting a general property of a Laplace approximation method for evaluation of the N-folded integral-form LCR expression. Based on the obtained s-order statistical results, the burst error rate and maximum symbol rate of the N-FS F distribution are addressed and thoroughly examined. The numerical results of the considered performance measures are discussed in relation to the N-FS F multi-path and shadowing severity parameters. Moreover, the impact of the number of hops ( N) of the N-FS F CFM on the s-order metrics, the burst error rate and maximum symbol rate are numerically evaluated and investigated. The derived s-order statistical results can be used to address the cooperative relay-assisted (RA) communications for vehicular systems. Monte-Carlo (M-C) simulations for the addressed statistical measures are developed in order to confirm the provided theoretical results.

RAIN FADE ANALYSIS AND LINK BUDGET PLANNING FOR 14.8-15.3 GHz TERRESTRIAL MICROWAVE LINKS OPERATING IN PENINSULA MALAYSIA

Most of the reported works on fade duration analyses were mainly based on the ITU-R method. Other related works were based on experimental radio links (less than 1 km path length) rather than actual operational radio links. However, empirical evidences have shown that ITU-R method is not excellently accurate for analyzing the link budgets of terrestrial microwave links operating in tropical and equatorial climates, hence the motivation for this study. The measured rain rate and attenuation on seven, geographically spread, terrestrial microwave links in tropical Malaysia are analysed in this article. The rain attenuation data were collected from 7 DIGI MINI-LINKs operating at Ku-band (14.8 – 15.3 GHz) with 99.95 % availability. The results were used to determine rain fade depth corresponding to a particular rain event on each of the links. The experimental results (attenuation, path reduction and receive signal level) were also compared with the ITU-R predictions. The fades predicted by ITU-R method are comparable to those obtained experimentally; however there is noticeable discrepancy between the experimental and ITU-R path reduction. The rain fade depth increases both with increasing path length and rain rate. More so, the RSLs predicted by the ITU-R method are higher compared to those of experimental values especially at extremely high rain rates, which is due to underestimation of the measured attenuation by the former. Therefore, the fade margins based on the ITU-R predictions come with low accuracy. This study is a useful tool for link budget design and planning of terrestrial radio links operating in Peninsula Malaysia and similar tropical equatorial climates.

Statistical analysis of the influence of peoplemovement and antenna radiation pattern onsmall-scale fading

This paper presents a statistical analysis of small-scale fading on static propagation environment due to the movement of people between antennas. We also analyze the influence of the antenna radiation pattern on narrowband-channel statistics. For this, we use signal samples received by omnidirectional and directional microstrip antenna. We evaluate the adherence of measured data to classical distributions (Rayleigh, Rice, Nakagami, and Weibull) with three hypothesis tests: Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling. Measurements are performed with low-cost equipment and using software-defined radio apparatus. In order to evaluate the effect of temporal variation of the signal due to the movement of people, we calculate two second-order statistics: the level crossing rate and the average fade duration. Our results endorse the fact that the scatters' movement also contributes to Doppler effect, and emphasize the importance of hypothesis tests on distribution fitting to measured data.

LCR and AFD of the Products of Nakagami-m and Nakagami-m Squared Random Variables: Application to Wireless Communications Through Relays

The paper considers level crossing rate (LCR) and average fade duration (AFD) of the product of independent and identically distributed (i.i.d) Nakagami-m (NM) and double NM squared (also known as gamma-gamma) random variables (RVs). The derived statistics are then directly applied to the radio-frequency (RF) - free space optical (FSO), dual-hop (DH), amplify-and-forward (AF) relaying system over non turbulent-induced-fading channels (nTIFCs) and turbulent-induced-fading channels (TIFCs). The obtained results for LCR and AFD of DH-AF, RF-FSO system over TIFCs and nTIFCs are numerically evaluated and graphically presented for various system model parameters.

Performance Analysis of RIS-Assisted FSO Communications over Fisher–Snedecor F Turbulence Channels

The Fisher–Snedecor (F-S) F distribution has recently been introduced as a tractable turbulence-induced (TI) fading model that fits well with the experimental data. This paper provides a performance evaluation of a free-space optical (FSO) re-configurable intelligent surface (RIS)-assisted communications (ACs) link over the F-S F TI fading channels, assuming the intensity modulation–direct detection (IM–DD) technique. In particular, novel and closed-form (C-F) analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) in terms of Gaussian hyper-geometric functions are efficiently derived. Capitalizing on the obtained results, novel C-F analytical expressions for the moment generating function (MMGF), outage probability (OP), average bit error rate (BER) and ergodic channel capacity (Cγ) of the FSO RIS-ACs system over the F-S F TI fading channels are provided and numerically evaluated under the various TI fading severity conditions. Furthermore, the second-order (S-O) statistical expressions for the level crossing rate (LCR) and average fade duration (AFD) are obtained and thoroughly examined for various FSO RIS-ACs system model parameters.

Characterization of rain fade dynamics for Ku band satellite communication systems in a tropical location

Rain fade has always been regarded as the main obstacle to the terrestrial and satellite communication links operating at higher frequencies, particularly in the tropics. The dynamic features of rain fade such as duration and slope of fade are important parameters for system engineers to design and plan attenuation techniques for high reliability Ku-band services and other higher frequency bands. Twenty - four (24) consecutive months (January 2017 – December 2018) received signal strength data at 12.245 GHz (Ku-band) from EUTELSAT-W4 (geostationary at 36°E) is collected concurrently with rain intensity data at The Federal University of Technology, Akure (7.17°N, 5.18°E) Nigeria. Measured fade duration is compared with ITU-R P. 1623 model and the Cheffena-Amaya prediction model. The results show that the ITU-R model is close to the data measured, while the Cheffena-Amaya model overestimates the measurement for all timeframes taken into account. A modification of the ITU-R fade duration model is suggested according to the data measured. The proposed modified ITU-R prediction model is a recommended model to be adopted for Nigeria climate. These results can be used in the planning and design of fade mitigation techniques to overcome the effects of intense rain on terrestrial-satellite microwave links operating in the Ku-band in tropical regions.

Characteristics of rain fade slopes on microwave communication in Mowe, Nigeria

In this paper, the rain fade characteristics at Ka-band (30 GHz) in Mowe (Lat 6.80° N, Lon 3.40° E) Nigeria have been presented. The analysis includes both the first- and second-order statistics of rain rate and rain attenuation, and fade duration and fade slope, respectively. Both parameters are useful for planning the point-to-point microwave link for various communication feeder networks. The estimated fade duration and the fade slope were compared with the ITU-R P.837-5 model. The results of this study would be valuable for improving rain fade mitigation techniques in Nigeria.

атухание низкочастотных электромагнитных волн в нижней ионосфере земли под влиянием сильного локального возмущения в атмосфере.

The value and duration of attenuation of low frequency waves (1...10 kHz) in the presence of a strong local disturbance of the atmosphere have been estimated. Sources of significant local disturbances of the atmosphere are, for example, precipitation of energetic particles of radiation belts; electromagnetic pulses of lightning discharges; radiation of powerful low-frequency ground-based transmitters; invasion of large meteors. Strong local disturbances lead to an increase of ionization (concentration of free electrons) of the environment by several orders of magnitude in the region of space whose characteristic dimensions are comparable to the length of the wave (tens and hundreds of kilometers). As such a disturbance, we use the previously developed macroscopic model of an instantaneous, point release of a relatively large amount of energy in the atmosphere below the ionosphere. This model makes it possible to estimate the features of the propagation of low-frequency waves through the disturbed layer of the lower ionosphere by changing only two initial parameters: the disturbance energy and its initial height. It is shown that the attenuation value is almost independent of frequency and geo- and heliophysical conditions. For initial heights up to 50 km, the fading duration does not exceed ~ 2 min. With an increase of the initial altitude, the attenuation in the lower ionosphere becomes extremely large. However, for heights of 50 ... 70 km (depending on the value of energy), the horizontal size of the disturbance decreases significantly, which leads to a decrease in the fading time to tens of seconds for initial heights of more than 80 km.

Outage statistics of double gamma–gamma random process and its application to cooperative optical wireless communication relay systems

AbstractThis article investigates outage statistics of double gamma–gamma random variable (RV) modeled as the product of two independent and identically distributed gamma–gamma RVs. The outage closed‐form statistics in terms of the first‐order statistical measures (probability density function and cumulative distribution function) and the second‐order statistical measures (level crossing rate and average fade duration) by Laplace approximation integral (LAI) and exponential LAI are derived. The statistical results are directly related to the performance evaluation of dual‐hop as well as cooperative dual‐hop optical wireless communications over moderate to strong turbulence‐induced fading channels.

Average Contiguous Duration—A Novel Metric for Characterizing Wireless Fading Channels

We define the average contiguous duration (ACD) of the received fading signal as the average time duration during which the signal envelope contiguously remains within a bounded amplitude interval. Also, the multi-interval ACD or L-ACD function is defined as the set of ACD values for L non-overlapping amplitude-intervals whose union spans the received envelope's amplitude range. We derive closed-form expressions of the ACD for Rayleigh, Rice, and Nakagami- m fading signals, which are widely analyzed in the literature. The derived expressions hold practical significance for several signal processing applications such as non-uniform quantization of channel samples for secret key generation (SKG) in physical layer security (PLS) techniques. The well-known channel fading metric of average fade duration (AFD) is shown as a special case of the proposed ACD metric and the proposed theoretical analysis is validated by simulations.

Investigating Ionospheric Scintillation Effects on Multifrequency GPS Signals

Over the last 15 years, the satellite constellation of the global positioning system (GPS) has been modernized for more precise applications, with the introduction of the L2C and L5 signals. However, among other effects, they are susceptible to severe ionospheric effects, particularly in the equatorial and low-latitude regions. Equatorial plasma bubbles, resulting from the combination of the ionospheric electrodynamics with plasma instability mechanisms and thermospheric coupling, may generate irregularity structures with scale sizes ranging from hundreds of kilometers to a few meters (or less). Ionospheric irregularities may cause deep amplitude fades and phase shifts to transionospheric signals. That is, they are responsible for amplitude and phase scintillation, which degrade receiver operations and may cause failures and unavailability to positioning and navigation services under extreme conditions. The objective of the present work is to analyze ionospheric scintillation effects on the L2C and L5 GPS signals, to compare their vulnerabilities with those of the L1 signal. The data used in this analysis were collected between November 2014 and March 2015, during the maximum solar activity of cycle 24 (a period of great scintillation incidence), by scintillation monitors deployed at four different sites in the Brazilian territory: Fortaleza, Presidente Prudente, Sao Jose dos Campos, and Porto Alegre. Intensity fades will be analyzed, considering different thresholds, to reveal their empirical probability distributions of scintillation occurrence, average fading occurrences and durations. The results will show that greater probabilities of strong scintillation occurrences are present in the modernized signals, reaching up to five times more events in the L5 signal in comparison with those in the legacy L1 signal. It will be shown that the L5 average fade duration is distinctly longer than the corresponding ones for the other frequencies, considering the same site, threshold, and L1 amplitude scintillation level. The results will also show that the average fade duration decreases according to the average ratio 0.6 s/3 dB within the threshold range from − 6 to − 15 dB, considering the same amplitude scintillation level and location.

Analysis of rain fade characteristics from experimental satellite measurements at Ka/Q bands for a temperate location Vigo, Spain

Rain is one of the most dominant factors for satellite communication systems link performance at frequencies above 10 GHz, increasing rapidly at higher frequencies. The prediction of time dynamics of the rain attenuation is required to improve the efficiency of various fade mitigation techniques (FMTs) to reduce signal fading. Fade duration and fade slope statistics are used to describe the dynamic behavior of attenuation experienced by radio communication links. The present study is based on experimental measurements from a Ka band (KaSAT) and Q band (AlphaSAT) beacon receiver at the frequencies 19. 7 GHz and 39. 4 GHz respectively. In this paper, annual and monthly variation of rain attenuation statistics for a temperate location Vigo, Spain is presented. Monthly variation of rain attenuation statistics is much larger than the yearly variation for the present location. This paper also analyzes the fade duration and fade slope statistics for both the bands. The conditional probability density function (PDF) of fade slope shows general symmetry between positive and negative slope values for both Ka and Q bands. All the measured statistics (1st order and 2nd order) are compared with the existing ITU-R and COST-205 models. Predictions of rain attenuation by both the models are close to the measured data. For fade duration statistics, as attenuation threshold increases, performance of both ITU-R and COST-205 models improves for Ka band. For Q band, COST model performs better compared to ITU-R model. Measured probability density function of fade slope fits with the ITU-R model more closely for Q band compared to Ka band.

Validation of Synthetic Storm Technique for Rain Attenuation Prediction Over High-Rainfall Tropical Region

Validation of synthetic storm technique (SST) has been done for prediction of attenuation due to rain over a hilly, high-rainfall, tropical location, Shillong (25°N, 91°E), India. In this letter, considering one year of rain attenuation and rain rate data shows that SST predicted attenuation overestimates while comparing the available experimental result. Storm speed has been found to have no significant effect on the attenuation prediction by SST. Second-order rain attenuation prediction, i.e., prediction of fade slope, has also been studied. Fade slope is found to have been overestimated by SST for all categories of rain events at 20.2- and 30.3-GHz frequency. Exceedance plot of fade duration by SST shows an overestimation for higher frequency and underestimation for lower frequency.

Second order experimental statistics of rain attenuation at Ka band in a tropical location

Abstract Some second order rain attenuation statistics such as fade duration and fade slope are investigated on the basis of experimental measurements of received signals using the GSAT-14 satellite beacon signal at 20.2 GHz for three years (2014–2016) over the tropical location Ahmedabad (23.02 0E, 72.510N), India with an Elevation angle of 630. Existing models of fade duration are compared with experimental data in this study and exponent of power law model of fade duration at Ka band is further explored. A new model for fade duration for Ka band for tropical locations is proposed where the constant of exponent of attenuation in the power law is found to be 0.143 instead of 0.055 used in ITU-R. Other relevant parameters for implementation of fade mitigation technique to prevent the link outage like cumulative distribution of signal fade rate, maximum and minimum fade rise and fade fall are also studied. Fade slope asymmetry over tropical region is also investigated. Keeping in view of exploiting the commercial launch of Ka band in Indian region there is an urgent need for validation of the existing models of fade slope (specially looking into fade symmetry) and fade duration. It will help the SATCOM (Satellite Communication) link designer to improve closed loop fade mitigation technique to minimize the possible link failure/link outage over the tropical region.

Fade Duration Measurements and Modeling in Terrestrial Radio Links for the Millimeter-Wave Frequencies of 38, 75, and 85 GHz [Measurements Corner

Due to the need for very high data rates in 5G, terrestrial radio links at millimeter-wave frequencies (particularly in the E band) are of paramount importance for use in the network front-/backhauling. An accurate estimation of the probability of occurrence of fade duration may help operators in the assessment of radio link time outages. Furthermore, experimental data for relatively long periods of time are needed for the development of a fade duration model.

Level Crossing Rate and Average Fade Duration of Satellite-to-UAV FSO Channels

This paper investigates the second-order statistics of the level crossing rate (LCR) and average fade duration (AFD) for the optical wireless channels between a satellite and a vehicle. Specifically, the novel expressions of LCR and AFD for the low earth orbit (LEO) satellite-to-unmanned aerial vehicles (UAVs) laser links are derived in the presence of the generalized misalignments caused by the satellite vibration together with the UAV hovering, which is modeled by a four-parameter Beckmann distribution, and the atmospheric turbulence conditions. The analysis can also be applied to other kinds of vehicles, which, in fact, require simpler channel models. Several numerical examples are presented to quantitatively demonstrate the impact of both atmospheric turbulence and pointing errors on the LCR and AFD. The Monte Carlo simulations are performed to validate the correctness of the theoretical derivations.

On Second-Order Statistics of the Composite Channel Models for UAV-to-Ground Communications With UAV Selection

Unmanned-aerial-vehicles (UAVs) are intended to be a vital part of beyond 5G (B5G) and 6G communication networks. UAV-to-ground communications in urban and populated areas are usually exposed to highly variable propagation conditions that can be often characterized by composite fading channels. This paper provides mathematical framework for the performance evaluation of UAV-to-ground communications over double-scattered single-shadowed (DS-SS), and double scattered double shadowed (DS-DS) fading channels. To analyse in details we provide probability density function (PDF), cumulative distribution function (CDF), average fade duration (AFD) and level crossing rate (LCR) of the product of double Nakagami-m (DN) and single inverse Gamma (SIG) random processes (RPs), as well as the product of DN and double inverse Gamma (DIG) RPs. Furthermore, the derived integral-form formulas for the second order (SO) statistical measures are approximated by Laplace integration (LI) and exponential LI in order to provide closed-form expressions. The impact of DS-SS and DS-DS fading types on the SO statistics of UAV-to-ground propagation scenario are thoroughly examined. Moreover, the impact of different values of DS-SS and DS-DS fading severities on the SO statistics are also taken into investigation. Lastly, the proposed UAV-to-ground model is extended to include the SO performance analysis of L-number of UAVs. All the analytical results for the SO statistics are confirmed by Monte-Carlo simulations.

Experimental Channel Statistics of Drone-to-Ground Retro-Reflected FSO Links With Fine-Tracking Systems

The utilization of drones as flying base stations (BSs) in the sixth-generation (6G) cellular networks has attracted much attention recently. In this context, free-space optical (FSO) systems could be deployed to provide high-capacity fronthaul/backhaul links between drones and ground BSs. Particularly, a drone-to-ground FSO communication link can be established by equipping the drone with a modulating retro-reflector (MRR) to modulate the incoming optical beam and reflect the modulated beam back along the same path. This helps to alleviate stringent pointing requirements from the drone while satisfying the limited size, weight, and power (SWaP) consumption requirements. Nevertheless, the underlying physical channel effects of this aerial retro-reflected FSO system have never been experimentally explored in the literature. In this paper, we report, for the first time, the experimental channel statistics of a drone-to-ground retro-reflected FSO link, offering practical insights into the angle-of-arrival (AoA) fluctuations at the receiver, the channel coherence time, the probability of fade, the level crossing rate, the average fade duration, and the time-frequency channel characteristics. Our results are expected to serve as practical sources of reference for the theoretical performance analyses and engineering designs of drone-based retro-reflected FSO systems.

Average Contiguous Duration (ACD)-Based Quantization for Secret Key Generation in Generalized Gamma Fading Channels

The wireless channel-based Secret Key Generation (SKG) algorithms aim at securing the wireless link against unauthorized eavesdropping by exploiting the channel’s randomness for generating matching secret keys at the legitimate nodes for message encryption/decryption. To counter differences in hardware and noise conditions at the legitimate nodes, which can lead to key mismatch, the SKG algorithms typically include the intermediate steps of sampling, quantization, information reconciliation, and privacy amplification. These steps collectively aim to improve the performance trade-offs between Key Generation Rate (KGR), Key Agreement Probability (KAP), and Secret Key Randomness (SKR) properties. This paper derives a closed-form expression for the Average Contiguous Duration (ACD) of Generalized Gamma (GG) fading wireless channels. The ACD is a recently introduced novel quantifier for characterizing the second-order statistics of fading channels, which includes Average Fade Duration (AFD) as its special case. The proposed GG fading ACD expression is shown to include, as its special cases, the ACD for commonly observed fading distributions such as Gamma, Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> , and Rayleigh. By exploiting the derived GG ACD expression, a multi-level quantization scheme for SKG is proposed that determines suitable quantization intervals for identical likelihood of an equal number of consecutive channel samples falling in each quantization interval. A comprehensive comparative analysis of the proposed ACD-based quantization for SKG is conducted in relation to conventional Uniform Quantization (UQ) and Cumulative Distribution Function (CDF)-based Non-Uniform Quantization (NUQ) schemes. The presented numerical results confirm the superior performance trade-off between KGR and KAP offered by the proposed ACD-based quantization in relation to that offered by UQ and CDF-based NUQ.

A Symbolic Encapsulation Point as Tool for 5G Wideband Channel Cross-Layer Modeling.

Considering that networks based on New Radio (NR) technology are oriented to provide services of desired quality (QoS), it becomes questionable how to model and predict targeted QoS values, especially if the physical channel is dynamically changing. In order to overcome mobility issues, we aim to support the evaluation of second-order statistics of signal, namely level-crossing rate (LCR) and average fade duration (AFD) that is missing in general channel 5G models. Presenting results from our symbolic encapsulation point 5G (SEP5G) additional tool, we fill this gap and motivate further extensions on current general channel 5G. As a matter of contribution, we clearly propose: (i) anadditional tool for encapsulating different mobile 5G modeling approaches; (ii) extended, wideband, LCR, and AFD evaluation for optimal radio resource allocation modeling; and (iii) lower computational complexity and simulation time regarding analytical expression simulations in related scenario-specific 5G channel models. Using our deterministic channel model for selected scenarios and comparing it with stochastic models, we show steps towards higherlevel finite state Markov chain (FSMC) modeling, where mentioned QoS parameters become more feasible, placing symbolic encapsulation at the center of cross-layer design. Furthermore, we generate values within a specified 5G passband, indicating how it can be used for provisioningoptimal radio resource allocation.