ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus GmbHGöttingen, Germany10.5194/angeo-33-321-2015Modeling of rain attenuation and site diversity predictions for tropical regionsSemireF. A.fasemire@lautech.edu.ngMohd-MokhtarR.IsmailW.MohamadN.MandeepJ. S.School of Electrical and Electronic Eng., Universiti Sains Malaysia, Engineering Campus, 14300, Nibong Tebal, MalaysiaDept. of Electronic and Electrical Engineering, Ladoke Akintola University of Technology, P.M.B 4000, Ogbomoso, NigeriaDept. of Electrical, Electronic and System Engineering, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, MalaysiaF. A. Semire (fasemire@lautech.edu.ng)17March201533332133119March201430January201515February2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/33/321/2015/angeo-33-321-2015.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/33/321/2015/angeo-33-321-2015.pdf
Presented in this paper is an empirical model for
long-term rain attenuation prediction and statistical prediction of site
diversity gain on a slant path. Rain attenuation prediction on a slant path is
derived using data collected from tropical regions, and the formula proposed
is based on Gaussian distribution. The proposed rain attenuation model shows
a considerable reduction in prediction error in terms of standard deviation
and root-mean-square (rms) error. The site diversity prediction model is
derived as a function of site separation distance, frequency of operation,
elevation angle and baseline orientation angle. The novelty of the model is
the inclusion of low elevation angles and a high link frequency up to 70 GHz in
the model derivation. The results of comparison with Hodge, Panagopoulos and
Nagaraja empirical predictions show that the proposed model provides a
better performance for site separation distance and elevation angle. The
overall performance of the proposed site diversity model is good, and the
percentage error is within the allowable error limit approved by International Telecommunication Union – Region (ITU-R).
Meteorology and atmospheric dynamics (Climatology)Introduction
In recent years, there has been a high demand for high data rates, wide
bandwidths and high availability of satellite communication signals for multimedia
services. Due to this great demand and overcongestion of the Ku-frequency
band, satellite communication is now exploiting the Ka (20/30 GHz) band (Yeo et
al., 2011; Luini et al., 2011; Pan et al., 2008). However, microwave signals
propagating in these bands suffer from more rain attenuation in comparison
to the conventional C and Ku band. Therefore, in order to reduce the effect
of attenuation on the communication links, several rain attenuation
prediction models coupled with fade mitigation techniques have been
proposed. The fade mitigation techniques include diversity protection schemes
and power-control and adaptive-wave techniques (Castanet et al., 1998; Panagopoulos et al., 2004;
ITU-R, 1994). Among the fade mitigation techniques, site diversity has been found
to be the most efficient of all (Panagopoulos et al., 2004, 2005; ESA, 2002). The site
diversity technique is based on the concept of the inhomogeneous nature of a
rainfall event which occurs within a localized rain cell of a few kilometers
in the horizontal and vertical extent (Panagopoulos et al., 2004; Hodge, 1982; Callaghan et al., 2008).
“Site diversity system” is a general term used in describing the utilization
of two or more geographically separated Earth base stations in a satellite
communication link to minimize the effect of attenuation due to rain during a
exhaustive rainfall period. This concept is employed in such a way that if
two Earth base stations are separated by at least the average horizontal
extent of the rain cell, the cell may likely not intersect the satellite
path of both ground stations at any given time (Ippolito, 2008). The signal streams
received at each station are sent to the so-called reference station, where
they are processed with certain criteria such as switching or selection or
are combined so as to improve the signal-to-noise ratio, and a decision process is
implemented to select the less attenuated signal for use in the
communications system (Bosisio and Riva, 1998).
The impact of site diversity on communication system performance is
evaluated as a function of site diversity gain. Diversity gain is the
improvement in the system margin at a given reliability level which results
from the use of path diversity. Models for prediction of rain attenuation
and site diversity performance are categorized into two major classes: (1) regression
models based on long-term rain attenuation and site diversity
statistics (Panagopoulos et al., 2005; Hodge, 1982; ITU-R, 2009; Moupfouma, 1984; Dissanayake et al., 1997; Mandeep et al.,
2006) and (2) physical models based on the solution of wave equations for a
medium with raindrops which employs lognormal distribution of rain rate and
rain attenuation in prediction of joint probability of dual site diversity
(Bosisio and Riva, 1998; Mass, 1987; Capsoni and Matricciani, 1985; Crane and Shieh, 1989; Matricciani, 1994).
This work presents rain attenuation and site diversity prediction models
based on long-term beacon rain attenuation and both ground and satellite
radar measurements. The two proposed models are derived from tropical region
rainfall data and are easy to implement for rain attenuation prediction and
site diversity performance evaluation.
This paper is arranged as follows: Sect. 2 describes the experimental
setup and data collection, while Sect. 3 explains modeling of rain
attenuation prediction using an appropriate regression fitting analysis. The
derivation of this model is based on both radar and beacon measurements. The
radar data are used for horizontal adjustment factor derivation, while a
beacon measurement is used for vertical reduction factor formulation. The site
diversity prediction model derived in line with the Hodge prediction model is
presented in Sect. 4. The model data are derived from beacon measurement,
which serves as a reference site, and Tropical Rainfall Measuring Mission (TRMM) data for diverse sites at different
link parameters. The prediction capabilities of both models are tested
against the ITU-R 618-10 for rain attenuation prediction, and Hodge,
Panagopoulos and Nagaraja models for site diversity gain prediction are
shown in Sect. 5 (Panagopoulos, 2005; Hodge, 1982; ITU-R, 2009; Nagaraja and Otung, 2012). Finally, Sect. 6 draws some useful conclusions.
Experimental setup and data collection
Radar and beacon measurement techniques were employed in the derivation of
the improved rain attenuation model. The receiver site for beacon
measurement of signal attenuation due to rain was located at Universiti
Sains Malaysia, USM (5.17∘ N, 100.4∘ E). The Ku-band beacon receiver
received signal from the SUPERBIRD-C satellite at 144∘ at an elevation
and azimuth angle of 40.1 and 95.4∘, respectively. The
antenna dish was set at 57 m above mean sea level. The output of the
LNB (low-noise block) was connected to a data logger and interfaced with Kisyo
software. Kisyo is the software that came with the beacon equipment. It is used
for downloading and extracting signal information measured by the beacon. The
signal was sampled at 1 s intervals and data were averaged over 1 min. The data were collected for 5 years over the period of 2005 to
2009. The average data availability was over 95 %.
The radar data employed in rain attenuation modeling were collected from the
Malaysian Meteorological Department (MMD). The Malaysian radar system employs a 3-D
RAPIC system developed by the Australian Meteorological Bureau. The radar
reflectivity data are converted to rainfall rate using the Marshall–Palmer radar
reflectivity model (Marshall and Palmer, 1948). Four months of radar data from November 2008 to
February 2009 were obtain from the MMD, from which only data from the
Butterworth radar station were employed. The accuracy of the radar data as
compared with rain gauge observation and data availability for the period of
measurement were 92 and 98 %, respectively.
The modeling of site diversity gain prediction for South Asian countries was
derived from spatial rainfall measurements obtained from TRMM Precipitation Radar (PR) data. The
rain attenuation measurement was carried out at the following locations in
the South Asia region: School of Electrical and Electronic Engineering,
Universiti Sains Malaysia (USM), Institute of Technology Bandung (ITB)
Indonesia; University of the South Pacific (USP), Fiji; King Mongkut's
Institute of Technology Ladkrabang (KMITL), Thailand; and Anteneo de Manila
University (AdMU), the Philippines. A reference site for each location was set
at (5.17∘ N, 100.4∘ E), (6.5∘ S,
107.4∘ E), (18.1∘ S, 178.5∘ E),
(13.7∘ N, 100.8∘ E) and (14.7∘ N,
121.1∘ E) for USM, ITB, USP, KMITL and AdMU, respectively. The
details of site and antenna specifications are shown in Table 1.
Site and antenna specifications.
LocationUSMKMITLITBUSPAdMUEarth station location5.17∘ N13.7∘ N6.5∘ S18.1∘ S14.7∘ N100.4∘ E100.8∘ E107.4∘ E178.5∘ E121.1∘ EBeacon frequency (GHz)12.25512.7412.24712.25512.255Downlink polarizationHorizontal Antenna diameter (m)2.42.41.81.81.8Antenna receiving gain (dBi)47.948.345.445.745.7
The system availability for the beacon data employed in site diversity
modeling for the reference site was 93 % for both 2002 and 2003. The site
diversity stations were spaced at random from 1 to 50 km along a fixed
baseline orientation spanning from 0 to 90∘. The
elevation angle and frequency of operation were varied from 10 to
50∘ and 10 to 70 GHz, respectively. The corresponding diverse
stations rainfall data between 2002 and 2003 were extracted from the TRMM
website at a spatial and temporal resolution of 0.25∘ by
0.25∘ and monthly, respectively. The coarse spatial resolution was
further interpolated linearly using the MATLAB platform by varying the location
coordinate. The interpolated annual rainfall accumulation derived from the TRMM
databank at specified locations was then converted to rain rate and
consequently to rain attenuation in line with the proposed rain attenuation
model for 100 hypothetical slant paths within the range of frequency
and elevation angles shown in Table 2. The site diversity gain GDp is modeled using Eq. (1):
GDp=ASp-AJp,
where ASp and AJp are the
single-site and joint attenuation values at probability p, respectively.
AJp=minA1p,A2p,
where A1(p) and A2(p) are the instantaneous rain attenuation
values at the reference and diversity station, respectively.
Frequency and elevation angle of the diverse stations.
Freq.Elev.Freq.Elev.Freq.Elev.Freq.Elev.Freq.Elev.(GHz)(θ∘)(GHz)(θ∘)(GHz)(θ∘)(GHz)(θ∘)(GHz)(θ∘)12.2551012.2552012.2553012.2554012.25550201020202030204020505010502050305040505070107020703070407050Proposed rain attenuation model
The proposed model is derived in two phases: the horizontal and vertical
reduction factors. These factors are included so as to accommodate the
impact of the inhomogeneous nature of rainfall events on the prediction model.
The horizontal reduction factor of the model is derived based on the Goddard
concept, with an assumption that there is a virtual link along every radial
line, which can be likened to a transmission path on which a signal can be
propagated (Goddard and Thurai, 1997). The horizontal adjustment factor is deduced from
rain rate, and derived rain attenuation is extracted from Malaysian radar
rainfall data at a radar line of 7 km from the referenced site.
Regarding the vertical reduction factor, the effect of horizontal adjustment is normalized
from the 5-year slant path attenuation measurements at USM and the
derived parameter is used in linear regression fitting for deduction of the
vertical reduction factor. The regression fitting of attenuation against the
vertical reduction factor follows Gaussian distribution. The proposed
attenuation model is given as follows.
The vertical and reduction factors rV and
rh are given as
rv0.01=1.429exp-1γR0.01Ls-0.02510.01082,rh0.01=aLgb+c,
with
a=2.989exp-f-45.8323.612,b=-8128f-3.329-0.1432,c=-0.00006553f3-0.005906f2+0.08657f+0.1513,Lg=Lscosθ,Ls=HR-HSsinθ,
where f is the frequency of operation, θ is the elevation angle,
HR is the rain height and HS is the altitude of the Earth
station. The path attenuation exceeded for 0.01 % percent of the time
is
A0.01=γR0.01Lsrv0.01rh0.01.
Attenuation at other time percentage (p) ranging from 0.001 to 1 % is
ApA0.01=0.117p-0.637+0.0371logp.
The agreement of the proposed model is tested using error prediction
algorithm (ITU-R, 2009b). The procedure is as follows:
estimate the ratio Si of the predicted attenuation ASi to the measured attenuation Ami for each radio
link
Si=ASiAmi;
calculate the corresponding test variable as
Vi=lnSi,forAmi≥10dBAmi100.2lnSi,forAmi≺10dB;
repeat the procedure for each time percentage
calculate the mean μV, the standard deviation σV, and the rms value ρV of the Vi values for each time
percentage;
ρV=μV2+σV20.5.
The cumulative distribution of the measured rain attenuation is compared
with three existing prediction models. The comparison result is shown in
Fig. 1a and b. Figure 1a shows that the Garcia model (Garcia and da Silvo Mello,
2004) underestimates the measured rain attenuation values at every percentage of
time. The ITU-R model underestimates at 1 to 0.8 % and 0.08 to
0.001 % of availability time and overestimates at 0.3 to 0.01 %. The
same trend is observed in the Goddard and Thurai model. The proposed model
agrees reasonably well with measured values from low availability time up to
0.008 % time percentage. The deviation of the proposed model from the
experimental values at time percentage above 0.008 % may be due to
saturation of rainfall at a high rain rate (Mandeep and Allnutt, 2007).
(a) Comparison of measured and predicted rain attenuation
distribution. (b) Results of comparative test of models (mean).
(a) Results of comparative test of models (standard deviation). (b) Results of comparative test of models
(rms).
The results of error, standard deviation and rms error values of the
proposed and three other existing models are shown in Figs. 1b and 2a, b.
The ITU-R and Goddard and Thurai models exhibit a similar behavior. The highest mean
error is observed in the Garcia model. The proposed model shows a significant
improvement over the existing prediction models, with considerable reduction
in rms error as compared with other testing models.
Proposed site diversity model
The site diversity prediction model is derived based on rain attenuation
measurements from five countries in the South Asia region. A regression
fitting is obtained on the numerical results obtained from rain attenuation
and site diversity measurements. The dependence of diversity gain on four
major link factors (site separation distance D, common elevation angle of
slant path B,link frequency f, and orientation of the baseline between
the two Earth stations β) is modeled.
In the deduction of the model of site separation distance dependence, five sets of
data are selected for each location at different separation distances with a
frequency of operation at 12.255 GHz for USM, AdMU and USP; 12.74 GHz for
KMITL; and 12.247 GHz for ITB. The elevation angle and baseline orientation
angle are kept at 30 and 0∘, respectively. The
regression fit of diversity gain as a function of D is shown in Fig. 3.
Further regression analysis is performed to determine the set of equations
that define the two coefficients a and b. Single-site attenuation is
plotted against coefficient a and b, and the resulting regression curves
with their corresponding equations are shown in Fig. 4.
The nonlinear regression curve between diversity gain and
separation distance.
(a) Regression line of fit for coefficient a. (b) Regression line of fit for coefficient b.
(a) Nonlinear regression fit of diversity gain as a function of
frequency (USM). (b) Nonlinear regression fit of diversity gain as a function of
frequency (USP).
(a) Nonlinear regression fit of diversity gain as a function of
elevation angle (USM). (b) Nonlinear regression fit of diversity gain as a function of
elevation angle (USP).
(a) Nonlinear regression fit of diversity gain as a function of
baseline orientation angle (USM). (b) Nonlinear regression fit of diversity gain as a function of
baseline orientation angle (USP).
The dependence of frequency of operation is modeled by selecting rain attenuation measurements at different frequencies ranging from
10 to 70 GHz from the
database, while keeping separation distance, elevation angle and
baseline angle at 11 km, is 30∘ and 0∘, respectively. The
set of data selected for frequency dependence is normalized to remove its
dependence on separation distance, D. The resulted normalized Gf is
plotted against frequency of operation, and the resulting regression fit of
diversity gain as a function of frequency f along with the rms error is shown in
Fig. 5 for the USM and USP stations. Similar results are derived for the three
other stations, and the coefficient of the regression equation is shown in
Table 3.
The dependence of elevation angle is also determined by following the same
procedure as used for frequency dependence. The dependence of elevation on
the attenuation measurement is estimated by extracting values of rain
attenuation at different elevation angles from 10 to
50∘ while keeping other link parameters constant. The set of
values derived are also normalized to remove the effect of site separation
and frequency. The regression plot of elevation angle dependence follows a
nonlinear quadratic law model as shown in Fig. 6, and the constants of the
coefficient for all the five stations are shown in Table 4.
The dependence of diversity gain on the orientation of the baseline relative
to the propagation path is also examined. The regression fit obtained is
shown in Fig. 7, and the corresponding coefficient constants are shown in
Table 5.
The model expression is given as
GD,f,B,β=GDGfGBGβ,
with
GD=a1-e-bD,a=0.7755AS+0.33741+exp-9.16AS,b=0.15841+exp-0.03164AS,Gf=1.006exp-0.0015f-0.395exp-0.473f,GB=0.8991+B-0.683,Gβ=-0.0000015β+0.9877,
where D is the separation distance in kilometers, AS is the single-site
attenuation in decibels, f is the link frequency in gigaherz, B is the angle of elevation
in degrees and β is the baseline orientation angle in degrees. The
modeling procedure is in line with the Hodge prediction model, but different
expressions and coefficients are obtained for tropical regions.
Constants of regression coefficient for operating frequency
dependence.
Constants of regression coefficient for elevation angle dependence.
p1p2USM1.03×10-50.9671KMITL1.03×10-50.9671ITB-1.90×10-51.005USP-1.13×10-50.9953AdMu2.00×10-61.004Average-1.5×10-60.9877Performance evaluation of the prediction models
The agreement of the proposed model with experimental results is tested
using the concept of relative diversity gain g as described below:
g=GAs
The parameter g is less dependent on attenuation than G. The percentage error
ε is defined as
εp=100gestp-gmeap,
where gestp and gmeap
are, respectively, the predicted and measured relative gains for a given
probability (Bosisio and Riva, 1998; Matricciani, 1994).
The model is tested along with some other existing site diversity gain
prediction models like Hodge, Panagopoulos and Nagaraja. The rms error is
determined as the difference between predicted and measured gain for the 13
time percentage values from 0.001 to 1.0 %. The equation is given as
rms=∑Gpred-GmeasGmeas132.
The proposed model performance is compared with site diversity measurement
and prediction estimates provided by the Panagopoulos and Nagaraja models. The
performance of the models as a function of distance is shown in Fig. 8,
with other site parameters set at 12.255 GHz for link frequency,
30∘ for elevation angle and 0∘ for baseline orientation
angle. The results depicted in the figures show that the proposed model
performed better than the existing models, which are largely derived from
temperate regions. The site diversity gain prediction for 24.22 km at USM is
closer to the experimental measurement compared to site diversity (SD) gain at 11.82 km. The
results at KMITL and AdMu show similar trends to that of USM. Diversity gain
at USP and ITB shows a slightly high deviation from the experimental value.
However, the difference is still incomparable with the deviation recorded
for other existing models. This shows that, despite the difference in the
experimental values and the predicted one, the model's performance still makes
it preferable to other existing models. The details of the performance analysis
in terms of mean error and root mean square at 0.01 % time percentage are
given in Table 6.
(a) Cumulative distribution of diversity gain predictions at
different site separation distances (USM). (b) Cumulative distribution of diversity gain predictions at
different site separation distances (USP).
(a) Cumulative distribution of diversity gain predictions at
different frequency of operation (USM). (b) Cumulative distribution of diversity gain predictions at
different frequency of operation (USP).
(a) Cumulative distribution of diversity gain predictions at
different elevation angle (USM). (b) Cumulative distribution of diversity gain predictions at
different elevation angle (USP).
(a) Cumulative distribution of diversity gain predictions at
different baseline angle (USM). (b) Cumulative distribution of diversity gain predictions at
different baseline angle (USP).
Performance evaluation of site diversity gain prediction models at
0.01 % time percentage.
Mean error 10 km (%) rms 10 km (%) ProposedHodgePanagopoulosNagarajaProposedHodgePanagopoulosNagarajaUSM4.12-5.45-45.15-52.579.1023.0366.9774.90KMITL1.36-8.31-45.56-45.416.7429.2669.3770.14ITB0.67-10.39-47.53-53.195.2724.2868.4876.97USP-2.50-1.70-42.02-45.793.8923.9768.0578.55AdMU3.41-6.52-44.15-45.898.7226.5768.1371.52Mean error 20 km (%) rms 20 km (%) ProposedHodgePanagopoulosNagarajaProposedHodgePanagopoulosNagarajaUSM-1.49-15.75-49.21-54.282.9927.9265.7673.64KMITL-5.54-21.65-52.77-52.405.9533.1466.8767.67ITB-8.22-22.48-53.39-58.318.9232.5565.2573.09USP-5.83-19.69-52.56-59.426.7630.4166.1576.45AdMU-2.80-17.97-50.44-52.443.8330.2166.2869.80
The proposed model presents a reduced relative diversity mean error of
4.12, 1.36, 0.67, -2.50 and 3.41 % for USM, KMITL, ITB,
USP and AdMU, respectively, at 0.01 % time percentage. The rms ranges from
5 to 9.10 %. The performance degrades slowly with increasing distance.
The Hodge model has relative diversity mean errors from -1.70 to
10.39 % at 0.01 % time percentage, with a corresponding rms not more than
30 %. The Panagopoulos model presents mean error slightly above 40 % and
rms around 70 %. The Nagaraja model has a similar trend for percentage mean
error and rms of above 50 and 70 %, respectively. The details are
shown in Table 6.
The performance of the model as a function of operating frequency is shown in Fig. 9. With site parameters kept at 10 km site separation,
30∘ elevation angle and 0∘ of baseline orientation for
all the five locations, link frequency is varied between 12.255 and 20 GHz.
The cumulative distribution of site diversity gain prediction for 20 GHz
at USM is closer to the experimental measurement compared to SD gain at
12.255 GHz. The results at KMITL, ITB, USP and AdMU show similar trends
to that of USM. Diversity gain predicted by Hodge at all locations shows a
slight deviation from the experimental value. The two other models predict
very high deviation from the experimental values. The reasons for the
discrepancies can be traced back to regional differences. However, the Hodge
model prediction is closer to the measured values because some of the data used in
the derivation of its model are at Ku-band frequency.
The performance analysis in terms of mean error and root mean square for the
proposed model presents a reduced percentage relative diversity mean error
of 1.12, -1.83, -2.85, -2.04 and -0.98 % for USM, KMITL,
ITB, USP and AdMU, respectively, at 20 GHz at 0.01 % time percentage. The
rms ranges from 1.85 to 3.557 %. The Hodge model has relative
diversity mean errors from -6.54 to -9.66 % at 0.01 % time
percentage for all locations, with a corresponding rms not more than 25 %.
The Panagopoulos model presents mean error slightly above -40 % and rms
around 65 %. The Nagaraja model has similar trend for percentage mean
error and rms of above -50 and 80 %, respectively.
The performance of the model as a function of elevation angle is also
examined, with site parameters kept at 10 km site separation, 12 GHz and
0∘ of baseline orientation for all the five locations. The dish
elevation was varied between 10 and 30∘. The
cumulative distribution of site diversity gain prediction for all stations
at 10∘ is closer to the experimental measurement compared to SD
gain at an elevation angle of 30∘. The results of the cumulative
distribution function of site diversity at an elevation of 30∘ are
much closer to the Hodge prediction model for all stations. The closeness of
the Hodge model at an elevation of 30∘ is due to the database used for the
derivation of the model. The database used is composed of measurements taken at
30∘ and above. The prediction error of the Hodge model at an elevation angle of 10∘ is high. Therefore, the Hodge model cannot predict
well for site diversity gain at a low elevation angle. The two other existing
models follow the same trend of high deviations in site diversity gain from the
experimental values. Although the elevation angle used in the derivation of
the model is within the measured elevation angle range, the
thresholds of data in the models are based on the data from temperate regions.
Thus, the Panagopoulos and Nagaraja models tend to underestimate the diversity
gain in tropical regions. The details are shown in Fig. 10.
The cumulative distribution of site diversity gain prediction at both
30 and 60∘ baseline orientation angle at 10 km site
separation, 30∘ elevation angle and 12 GHz frequency are closely
related at all stations. It is observed that the Hodge model also has a similar
pattern to the measured and proposed model. It is apparent that baseline
angle has no or little correlation between baseline angle and site diversity
gain. As is evident in Fig. 11, the thresholds of both orientation
angles are almost the same. This implies that there are insignificant changes
in the cumulative distribution function of site diversity gain with respect
to increase in orientation angle. The observed trends for the other two
existing models follow the same pattern, with little or no changes in the
observed threshold as baseline angle increases. Although the Panagopoulos and
Nagaraja models follow the same trend to that of the experimental value, they
both tend to underestimate site diversity gain in the region.
The performance analysis of the proposed model presents a reduced percentage
relative diversity error of 2.05, 1.51, 0.43, -0.27 and
2.45 % for USM, KMITL, ITB, USP and AdMU, respectively, at 60∘
baseline angle at 0.01 % time percentage. The lowest and highest
percentage error is observed at ITB and AdMU, respectively. The
estimated rms is below 10 %. The Hodge model has relative diversity mean
errors between 2.29 and 11.25 % at 0.01 % time percentage for all
locations, with a corresponding rms less than 30 %. The Panagopoulos model
presents mean error slightly above -40 %, and rms is around 60 %. The
Nagaraja model has a similar trend for percentage mean error and rms of above
-50 and 70 %, respectively.
Conclusion
Two new prediction models have been proposed. The proposed model for
long-term rain attenuation prediction on a slant path is derived based on
data collected from tropical regions and the formula proposed follows a
Gaussian distribution function. The performance of the proposed model is
tested using three existing prediction models, and the results are very
encouraging. The model proposed presents a good representation of cumulative distribution
function of the measurement site as compared with other
prediction models. The model can thereby be employed in rain attenuation
prediction for tropical countries with similar rain rate patterns to that of
Malaysia.
Also, a new empirical site diversity prediction model is derived using rain
attenuation measurements and TRMM radar data from five countries in
Southeast Asia. The improvement on the model is the inclusion of low
elevation angles and a high link frequency up to 70 GHz. The performance
validation of the new prediction model is tested using three existing SD
models over different link parameters. The comparison results with Hodge,
Panagopoulos and Nagaraja empirical prediction show that the proposed model
provides a better performance for site separation distance and elevation
angle.
The overall results show that the last two models (Panagopoulos and
Nagaraja) are not suitable for prediction of site diversity gain in tropical
regions. Although the models tested by the authors proved to perform
better than the Hodge model, their performance has been found unsuitable for
tropical regions. On the side of the Hodge model, the performance is still
relatively acceptable as compared to the other two models. It can be
employed at high altitude in tropical and temperate regions. Its
applicability still needs to be tested with more in situ SD measurements for
further clarification. Above all, the performance of the proposed site
diversity model has been found to be very good, and the percentage error is
within the allowable error limit as determined in the ITU-R 618
recommendation.
Acknowledgements
The authors would like to thank Universiti Sains Malaysia, Universiti Kebangsaan Malaysia and Ladoke Akintola University of Technology for their
support. Topical Editor V. Kotroni thanks the two anonymous referees for their
help in evaluating this paper.
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