Millimeter wave attenuation prediction using a piecewise uniform rain rate model

A piecewise uniform rain rate distribution model is introduced as a quasi-physical model of real rain along earth-space millimeter wave propagation paths. It permits calculation of the total attenuation from specific attenuation in a simple fashion. The model predications are verified by comparison with direct attenuation measurements for several frequencies, elevation angles, and locations. Also, coupled with the Rice-- Holmberg rain rate model, attenuation statistics are predicated from rainfall accumulation data.     

Slant path rain attenuation predictions for Ku and Ka band frequencies from rain cell size distribution over a tropical region in southern India

Rain cell size distribution that provides an insight into the modelling of effective slant path length and also imperative for site diversity studies are carried out for a tropical inland location, Tirupati (13.6°N, 76.3°E), India. Rain cell size distribution obtained from 5 years (2013–2015 and 2017–2018) of Parsivel disdrometer measurements is observed to follow the power law. Reduction factor that accounts for the inhomogeneity of the rain along the propagation path for the region of study is modified in terms of the rain cell size distribution of the area. Slant path rain attenuation, a major propagation impediment at Ku and Ka-band links, is then studied using the results from the regional rain characteristics by modifying the CCIR 564-4 report. The attenuation results are compared with Garcia-Lopez, Excell, Bryant, and Ramachandran models while considering the ITU-R P. 618-13 as the standard model.     

Modelling attenuation by rain in tropical regions

The data in the CCIR data banks were employed for a statistical study of the relative performance of several rain attenuation prediction procedures in temperate and tropical regions. The results show that the models worked well, in general, when used for prediction at latitudes more than 30° from the equator, but, in the equatorial region, significant prediction errors were observed for all the models. Three sources of error were discovered. The most important is the use of too few rain climate zones to span the wide range of rain conditions present in the equatorial region. The second is an inadequate procedure for taking the naturally occurring vertical variations of specific attenuation into account. Finally, for the CCIR attenuation prediction model, the use of a universal shape for the cumulative distribution of path attenuation must be called into question.     

Time series prediction of rain attenuation from rain rate measurement using synthetic storm technique for a tropical location

A comparison of measured attenuation series with the attenuation series obtained from rain rate measurement by using synthetic storm technique is made for Ku band signal at a tropical location. Validity of the model is tested for the long-term statistics in terms of the cumulative distribution of attenuation occurrence and fade duration. Applicability of the model is also shown to be valid event-wise. It has been demonstrated that the long term statistics of predicted rain attenuation are insensitive to storm translation speed. No significant differences are found when cumulative distributions of predicted attenuation values are compared for different data sampling intervals. It has been observed that there exists a good correlation between the predicted and measured values of attenuation for at least 80% of the events.     

Centimeter and millimeter wave attenuation by atmospheric gases and rainfall at a tropical station

The radiowave attenuation due to oxygen and water vapour has been computed over the frequency range 3–350 GHz making use of the mean surface air pressure, temperature and water vapour at Ile-Ife (geog. lat 7.5°N, long 4.5°E) in Southern Nigeria. It is observed that the attenuation at this tropical location is generally higher than at temperate climates. A similar analysis was performed for rainfall attenuation using rainfall intensity measurements. The results obtained with three different expressions for the rain height showed that a rain height of 3 km is a reasonable assumption for estimating earth-space rainfall attenuation at this location. It is found that for frequencies above 200 GHz, the polarization dependence of the specific attenuation due to rainfal becomes negligible. The computed attenuation is lower that that predicted using the corresponding CCIR rain climate data. The results show that whilst the contribution of oxygen and water vapour to the total atmospheric attenuation could be neglected when compared with rainfall attenuation up to about 150 GHz, the contribution becomes significant for frequencies above 190 GHz.     

Inference of raindrop size distribution from attenuation and rain rate measurements

A method to infer the raindrop size distribution from the measurements of point rain rate and rain attenuation at a frequency in centimeter or millimeter wave bands is proposed. This method is applied to the results of field propagation experiments at 81.8, 34.5, and 11.5 GHz through natural rain. It is shown that, if an appropriate frequency is employed, this method is effective as a frequency-scaling method for short terrestrial propagation paths.     

New rain rate analyses to assess rain attenuation on satellite ehf communications

This paper provides estimates of the frequency of occurrence, duration and probability of satellite EHF communication outages due to attenuation by rain. These can be used to determine optimum frequencies, power levels and the need for space diversity of terminals or other alternatives to maintain reliable communications. Ten years of 1 min rain rates at each of 12 U.S. cities were used in conjunction with an attenuation model to quantify communication outages at locations representing a variety of climatic regimes. Analyses of the 1 min rain rates and outage estimates at 10, 30 and 45 GHz for elevation angles of 10°, 30°, 50° and 70° are presented.     

Time series predictor of Ku band rain attenuation over an Earth–space path at a tropical location

A channel model is proposed to predict the time series of Ku band rain attenuation during a rain event at a tropical location. The model is based on considering the Gaussian distribution of the conditional occurrence of rain attenuation with a particular value of the attenuation occurring before. The mean (μ) and standard deviation (σ) for the distribution are modeled with the experimental data. The measured attenuation at a particular time instant is used to obtain μ and σ and to predict the attenuation after certain interval. The channel model has tested well giving the predicted attenuation that agrees with the measured value with a mean error within 15% higher than 1 dB. Validity of the model is also tested with the first‐order and second‐order statistics of attenuation occurrence, on a long‐term basis. The method can also be applied even if attenuation measurements are missing for certain period of time with increased error. Copyright © 2011 John Wiley & Sons, Ltd.     

A simple method for estimating rain attenuation distribution

This paper deals with a method for estimating rain attenuation distribution at frequencies above 10 GHz. This method depends only on point rainfall rate. Based on statistical independence among rain cells, a relation connecting cell dimension, path distance, precipitation and attenuation is established. Numerical results have shown good agreement with experimental data.     

Measurements of cloud contribution to rain millimeter wave attenuation by using a radar and radiometers

The measurement technique of cloud contribution to rain attenuation and the equipment consisted of the coherent pulse Doppler radar at wavelength λ=3.2 cm, the radiometers at λ=0.4; 0.8 and 1.35 cm and apparatus for signal recording and processing is described. The results of such measurements are given. The Doppler spectrum of the rain backscattered radar signal was used for determination of rain drop size distribution height profile then rain attenuation was calculated and cloud attenuation was determined as the difference between the total attenuation measured by using the radiometers and rain attenuation. The results of this work gave possibility to improve the known rain model of P.Misme for prediction of rain attenuation statistics for Earth-satellite links at millimeter wave.     

Variations in raindrop size distribution and specific attenuation due to rain in Nigeria

The raindrop size distributions had been measured at three locations in Nigeria - Calabar, Ile-Ife and Zaria. The data collected over a period of three years have been utilized to obtain models of drop size distributions for drizzle, shower, widespread and thunderstorm rain. The lognormal distribution provides a good fit for all the rain types at these tropical locations except drizzle, where the exponential model is adequate. The implications of the models for specific attenuation calculations for tropical rain are discussed.     

Characteristics of rain induced attenuation and phase shift at cm and mm waves using a tropical raindrop size distribution model

The tropical raindrop size distribution model developed by Ajayi and Olsen has been employed to study some characteristics of rain induced attenuation and phase shift for a tropical location for spherical, oblate spheroidal and Pruppacher-Pitter drop shapes. Parameters such as the a and b values for the power law relation between the specific attenuation and rainfall rate as well as differential attenuation and phase shift and their normalized values, were computed. A single power law between the specific phase shift and the rain rate was found to be adequate for vertical polarization, whilst a two-segment power law fitting is required for horizontal polarization between 1GHz and about 100GHz. The results were compared in many cases with those obtained with the Laws and Parsons drop size distribution, currently adopted by the CCIR for scattering applications.     

Survival probability of precipitations and rain attenuation in tropical and equatorial regions

This contribution presents a stochastic model useful for the generation of a long-term tropospheric rain attenuation time series for Earth space or a terrestrial radio link in tropical and equatorial heavy rain regions based on the well-known Cox–Ingersoll–Ross model previously employed in research in the fields of finance and economics. This model assumes typical gamma distribution for rain attenuation in heavy rain climatic regions and utilises the temporal dynamic of precipitation collected in equatorial Johor, Malaysia. Different formations of survival probability are also discussed. Furthermore, the correlation between these probabilities and the Markov process is determined, and information on the variance and autocorrelation function of rain events with respect to the particular characteristics of precipitation in this area is presented. The proposed technique proved to preserve the peculiarities of precipitation for an equatorial region and reproduce fairly good statistics of the rain attenuation correlation function that could help to improve the prediction of dynamic characteristics of rain fade events.     

Effect of raindrop size distribution and rain rate inhomogeneity on the relationship between attenuation and depolarization

In addition to attenuation, depolarization due to rain is another factor that degrades satellite propagation signals, especially in the higher frequency bands and in places that have high rates of rainfall. A formula to predict cross‐polarization as a function of attenuation has been proposed, and it is derived by a theoretical calculation using frequency, the forward scattering amplitude of raindrops, rainfall rates, the raindrop size distribution (DSD), and various other propagation parameters. In this paper, a formula for predicting cross‐polarization is derived on the basis of the assumption of a gamma‐type DSD up to 100 GHz. These results are compared with conventional exponential‐type DSDs, such as the Marshall‐and‐Palmer DSD. Moreover, for a more realistic propagation situation, we consider the effect on the aforementioned relationship of rainfall rate inhomogeneity along the propagation path. It is shown that, for practical purposes, this inhomogeneity does not have a significant effect on satellite propagation. Copyright © 2017 John Wiley & Sons, Ltd.     

Millimeter wave propagation in aridland: The effect of rain and sand storms

Reliability analysis of millimetric wave propagation in airdland is presented. Based on long term rain data and sand storm record in Riyadh, the paper estimates the outage due to individual effects. The total outage due to rain and sand is then derived under various storm conditions. It is particularly shown that rain and sand storms may have comparable effects on link reliability for typical storms. For adverse storm conditions marked by large and wet particles, rain will have less effect on system reliability compared to sand storms.     

Rain cell size statistics as a function of rain rate for attenuation modeling

Rain cell size statistics as a function of rain rate have been deduced by employing a radar data base of rain reflectivity data acquired over a three-year period at Wallops Island, VA. These cell statistics have important applications in slant path rain attenuation modeling and remote sensing of the earth's surface from space at frequencies above 10 GHz.     

雨滴谱模型对雨衰减计算的适用性分析

雨滴谱分布模型是影响红外激光在雨中传输性能的一个重要因素。尽管现有的雨滴谱模型很多,但并未形成统一的结论,具体应用中模型的选择没有依据,使得计算中模型的选择具有一定的盲目性。针对此问题,论文从Mie散射理论出发,采用理论分析与仿真分析相结合的方法,讨论了几种雨滴的谱分布特性,比较了几种典型雨滴谱模型下的光传输衰减特性,分析了雨滴尺寸分布在计算大气衰减时的差异。并通过与实测雨衰减数据进行比较,最终得到了L-P模型对大雨条件下的衰减计算较为准确,Joss模型对小雨条件下的衰减计算较为准确的结论。论文的结论对于无线光通信等应用领域中模型的合理选择具有一定的指导意义。     

Dependence of rain attenuation and cross-polarization on drop size distribution

Attenuation and cross-polarization due to precipitation are calculated for five drop size distribution functions, namely Laws-Parsons, Marshall-Palmer, Joss drizzle, Joss thunderstorm, and a renormalization of the latter. Propagation paths from the Communications Technology Satellite (CTS) and Comstar D1 synchronous satellites to Ottawa are considered. Clear weather antenna isolation effects are included in the results. We find that various drop size distributions introduce substantial deviations only in the attenuation versus rain rate curves. A proper normalization of the Joss thunderstorm model is important for attenuation. The deviations are much less in the crosspolarization versus attenuation plots, which are close together for all five drop size distributions. This is so even for the thunderstorm model at 28.56 GHz of Comstar D1, where the differential phase per unit length is decreasing at high rain rates. Unexpectedly, it is also found that for attenuation values not too large, the thunderstorm model provides less depolarization for a given attenuation as compared wth the other models.     

Modified rain attenuation model for tropical regions for Ku‐Band signals

Attenuation measurement on Ku‐ band satellite signal in a tropical site, Fiji is presented. Rain‐attenuation prediction by ITU‐R and the Crane Global models showed noticeable deviation to the measured values. Unlike the monotonic decrease predicted by these models, exceedance of rain‐rate and attenuation in Fiji and other tropical regions showed the presence of breakpoints. For Suva, the breakpoint in rain‐rate and attenuation were at 58 mm/h and 9.4 dB with exceedances of 0.009 and 0.018%, respectively. Modifications to the ITU‐R model are proposed in this paper, for adopting it in the tropics. These modifications are based on the properties that in the tropics (i) the accumulation time factor at the breakpoints is an invariant (ii) for elevation angles <60° and at high rain rates multiple rain cells intersect the slant path. The attenuation exceedance is predicted by two expressions similar to the ITU‐R model, one for rain‐rates lower than the breakpoint rain‐rate and the other above it. The modified prediction model show remarkable agreement with the measured Ku‐band attenuation in seven tropical sites. Copyright © 2006 John Wiley & Sons, Ltd.