Average level crossing rate and average fade duration of low-ordermaximal ratio diversity with unbalanced channels

The average level crossing rate and average fade duration of a maximal ratio diversity combiner, operating on independent, unequal power Rayleigh fading branches in isotropic scattering, are derived in closed-form for dual-branch diversity, and as definite integrals for threefold and fourfold diversity     

Average level crossing rate and average outage duration of generalized selection combining

The paper presents an analytical methodology for the evaluation of the average level crossing rate and the average outage duration of generalized selection combining. More specifically, it presents a general approach when this scheme is employed over independent, but not necessarily identically distributed, fading channels. The general approach is then specialized to independent identically distributed Rayleigh fading paths. Selected numerical examples and plots are also provided and discussed.     

Level crossing rate and average fade duration of MRC and EGC diversity in Ricean fading

The average level crossing rate and average fade duration of the output signal of a maximal ratio combiner (MRC) and equal gain combiner (EGC), operating on independent Ricean fading input branch signals, are derived. Exact, closed-form results are obtained for MRC diversity, while precise expressions for EGC diversity are presented with an infinite series method. The results are valid for an arbitrary number of independent, identically distributed diversity branches, isotropic scattering, and a specular component perpendicular to the line of motion of the mobile.     

Level crossing rate and average fade duration for pure selection and threshold selection diversity‐combining systems

Exact and closed‐form expressions for the level crossing rate and average fade duration are presented for the M‐branch Pure Selection Combining and for the two‐branch Threshold Selection Combining schemes, assuming independent branches in a Rayleigh environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The plots presented here are also compared with those of the general solution recently published for the Equal Gain and Maximal Ratio Combining and an agreeable coherence is found. Copyright © 2001 John Wiley & Sons, Ltd.     

Level crossing rate and average fade duration of the select-and-hold policy of selection diversity combining in a Rayleigh fading channel

The select-and-hold policy (SAH) is a general form of selection diversity combining (SDC). In this letter, we provide closed-form expressions for average level crossing rate and average fade duration for Nth-order SAH-SDC. The diversity branches are assumed to be independent and identical Rayleigh fading channels. A useful guideline for choice of the holding time is also obtained.     

Level crossing rate and average fade duration of the double nakagami-m random process and application in MIMO keyhole fading channels

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

Mobile speed estimation based on average fade slope duration

Based on the zero crossing rate of the slope (first derivative) of the underlying fading process, a mobile speed-estimation scheme, constructed by counting the average number of sampling steps in a positive-going (and/or negative-going) fade envelope slope, is proposed. The proposed speed-estimation approach requires neither knowledge of the average fade power nor a variable temporal observation window. The computational complexity and the required memory storage are negligibly small. Simulation results show that the proposed speed estimator yields good estimation accuracy, with relatively small estimation error.     

Analysis of 11 GHz slant path fade duration and fade slope

The letter presents results of an analysis of fade slope and fade duration data collected at 11 GHz within the framework of the OTS propagation experiments in Europe. Evidence is given of the fact that on a statistical basis, fade slope and fade duration are related. This could possibly be used in uplink power control systems.     

On the average outage rate and average outage duration of wireless communication systems with multiple cochannel interferers

This paper studies the average outage rate [or average level crossing rate (LCR)] and average outage duration (AOD) of wireless communication systems subject to cochannel interference. In particular, it presents closed-form expressions for the LCR and AOD when a minimum desired signal power requirement is specified for satisfactory reception. The results are quite general and account for systems operating over independent identically distributed Rician and/or Nakagami fading environments. When applicable, these new expressions are compared to those previously reported in the literature dealing with the LCR and AOD of 1) interference-limited systems when both the desired and interfering signals are subject to Rayleigh type of fading and 2) power-limited systems operating over Rician or Nakagami fading channels. Corresponding numerical examples that illustrate applications of the results are also provided and discussed. These results show that specifying a certain minimum desired signal power requirement induces a floor on the AOD. They also show that the AOD is essentially affected by the the maximum Doppler frequencies (or equivalently the speed) of the desired users.     

一种联合链路持续时间与平均速率的中继选择方法

针对中继系统中节点快速移动时采用传统中继选择方法造成系统可传输数据量较低的问题,提出一种联合链路持续时间与平均速率的中继选择方法.该方法首先分析了系统采用两跳传输及协作传输两种模式下的链路持续时间,分别给出了节点速度及相互之间距离满足不同条件时的链路持续时间表达式,然后计算两种模式下的链路平均可达速率,最后基于所提出的准则完成中继选择.仿真结果表明,与传统的中继选择方法相比,该方法可以使系统获得更多的数据传输,同时具有较低的中断概率.     

On the rain attenuation dynamics: spatial‐temporal analysis of rainfall rate and fade duration statistics

Knowledge about the dynamic characteristics of rain attenuation is of utmost importance for many applications in terrestrial and satellite communication systems operating at frequencies above 10 GHz. Long‐term rain rate statistics and rain rate duration statistics are usually available from meteorological data. In this paper, a spatial–temporal analysis is employed in order to evaluate the rain attenuation power spectrum of a terrestrial/satellite path. The predicted power spectrum is compared with experimental data. Based on the spectral analysis of rainfall rate a method for converting rain rate duration statistics to link fade duration statistics is also proposed. Fade duration statistics are presented for terrestrial and satellite links and compared with available experimental data. The agreement between the predicted results and the experimental data has been found to be quite encouraging. Finally, numerical results are presented for various climatic zones, elevation angles and frequencies. Some very useful conclusions concerning the dynamic properties of rain attenuation for a microwave path are deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Level-crossing rate and average duration of fades of deterministicsimulation models for Rice fading channels

The concept of Rice's sum of sinusoids is often applied to the design of deterministic simulation models for Rice fading channels. This paper investigates in detail the level-crossing rate (LCR), average duration of fades (ADF), and cumulative distribution function (CDF) of such classes of simulation models. Exact and simple approximative formulas are deduced for these statistical quantities. Several numerical results for the derived expressions are presented by using different procedures for the design of the parameters of the deterministic simulation model. Moreover, comparisons with the corresponding simulation results-obtained by evaluating the deterministic simulation models output data-are also given     

On the average crossing rates in selection diversity

This letter presents new results on the average crossing rate of the combined signal of a selection diversity in Rayleigh fading channels. Exact closed-form expressions are derived for the inphase zero crossing rate, inphase rate of maxima, phase zero crossing rate, and the instantaneous frequency zero crossing rate of the output of the selection combiner. The utility of the new theoretical formulas, validated by Monte Carlo simulations, are briefly discussed as well     

Generalized Nakagami-m phase crossing rate

This paper provides simple, exact, new closed-form expressions for the generalized phase crossing rate of Nakagami-m fading channels. Sample numerical results obtained by simulation are presented that validate the formulations developed here. A special case of this formulation is the Rayleigh case, whose result agrees with that obtained elsewhere in the literature. In passing, several new closed-form results concerning the statistics of the envelope, its in-phase and quadrature components, phase, and their time derivatives are obtained.     

Three‐year fade and inter‐fade duration statistics from the Q‐band Alphasat propagation experiment in Madrid

Propagation campaigns are carried out at different frequencies and geographical areas to characterize the slant‐path propagation channel. One of the objectives of the Alphasat Propagation Experiment is to evaluate the performance of satellite links that operate in the Q/V band. Since March 2014, the copolar level of the Alphasat Q‐band beacon signal has been measured at Universidad Politécnica de Madrid, Spain. The fade dynamics—fade and inter‐fade durations—results for three complete years (March 2014 to February 2017) of measurements are presented in this paper. Moreover, the experimental setup and receiver characteristics are described in detail. The collected data (with a mean availability of 97%) can be used to evaluate the atmospheric propagation impairments with a very good degree of accuracy. The probability of occurrence and the fraction of time of fade duration for an average‐year have been compared with the ITU‐R and CRC models with moderate agreement. For this reason, a modeling effort has been made leading to the conclusion that there is room for improvement in the models.     

Simulation of average fading duration using deterministic method

Measurements and modelling of average fading duration (AFD) for a mobile channel with line-of-sight (LOS) component at VHF frequencies (69.75 MHz) show that the deterministic method can be used to simulate the AFD of a mobile channel, and that a mobile channel with a LOS component can be modelled using Loo's model. To obtain an accurate simulated AFD, an appropriate sample interval should be used in the simulation     

Rain-rate duration statistics over a five-year period: a tool forassessing slant path fade durations

A rain gauge network of 10 tipping bucket rain gauges on the Mid-Atlantic coast of the United States has been in continuous operation since June 1, 1986. Rain-rate distributions and estimated slant path fade distributions at 20 and 30 GHz covering the first five-year period have been derived from the gauge network measurements and published data of Goldhirsh, Krichevsky and Gebo (see ibid., vol.40, no.11, p.1408, 1992). In this article, we present rain-rate time duration statistics. The conversion of rain-rate duration statistics derived from in situ measurements to slant path fade duration statistics is complicated because of the vertical and lateral inhomogeneity of the rain. A benchmark set of fade duration statistics at 20 and 30 GHz for a vertical path is derived from the rain-rate duration statistics employing Crane's (1980) global model. These results may be used by investigators for comparison with and/or conversion to slant path fade duration statistics. Such statistics are important for better assessing optimal coding procedures over defined bandwidths     

Average outage duration of multihop communication systems with regenerative relays

Closed-form expressions for the average outage duration (AOD) of multihop regenerative communication systems over generalized fading channels are presented. Both noise-limited and interference-limited systems are studied. To show the usefulness of the presented expressions, some specific fading scenarios are considered. In addition, some numerical examples of interest comparing direct versus relayed transmission and studying the effect of increasing the number of hops and/or cochannel interferers are plotted and discussed.