- Open Access
An improved ITU-R rain attenuation prediction model over terrestrial microwave links in tropical region
© Islam et al; licensee Springer. 2012
- Received: 13 February 2012
- Accepted: 7 June 2012
- Published: 7 June 2012
An improved approach of predicting rain attenuation cumulative distribution (CD) over terrestrial microwave links operating in tropical regions is presented in this article. The proposed method offers a better extrapolation approach for determining the values of rain attenuation at different exceedance probability from the measured attenuation at 0.01% of the time. The experimental data consist of measured rainfall rates and rain attenuation over six geographically spread DIGI MINI-LINKs operating at 15 GHz in Malaysia. A new set of numerical coefficients was derived for improved rain attenuation CD predictions in the Malaysian tropical climate. In order to test the applicability of the proposed extrapolation method, a validation was performed using rain rate and rain attenuation measurements from five Brazilian and seven Nigerian tropical locations. When tested against measurements, the proposed method seems to provide a significant improvement over the current extrapolation method adopted by ITU-R Recommendations P.530-14, for the prediction of rain attenuation CD over tropical regions.
- Rain Rate
- Rainfall Rate
- Rain Attenuation
- Bucket Size
- Microwave Link
Heavy traffic in the C-band has forced telecommunications service providers to migrate to higher frequency bands, which have enough band-widths to support numerous users. However, rain-induced attenuation is the major issue at frequencies above 10 GHz, more especially in tropical regions which experience heavier rainfall intensities . Rain attenuation plays significant role in the design of terrestrial and Earth-satellite radio links especially at frequencies above 10 GHz .
The major difficulty faced by engineers working on higher bands is balancing the trade-off between bandwidth availabilities and rain attenuation issues. Even though ITU-R has provided a methodological approach for predicting the rain attenuation on any terrestrial radio link, the model does not perform well in tropical climates because it is based on data collected from temperate regions [2, 3]. A number of research works have been published to emphasize the inappropriateness of ITU-R method in tropical regions [2–4]. Generally, the required inputs in most attenuation prediction models are the rainfall rate exceeded at %p of time, the effective propagation path length, and the link's operating frequency .
Da Silva Mello et al.  have reported that the extrapolation procedure of Equation (4) adopted by the current ITU-R P.530-14  is the major limitation of the prediction method. This is because the same rain attenuation will be predicted for two regions with different rainfall rate regimes but similar values of A0.01. In his efforts to correct the inappropriateness, the method of using the full rainfall rate distribution is introduced as input for predicting the rain attenuation cumulative distribution (CD).
In this article, nonlinear multiple regression and moving average techniques have been employed for fitting the measured rain attenuation at different time percentages. Based on the numerical results obtained, a more accurate prediction method has been proposed for extrapolating determining the values of attenuation at different exceedance probability %p from the measured attenuation at 0.01% of the time. The measured attenuation data have been tested against the proposed method and ITU-R predictions; and it was found that the proposed method seems to be more suitable than the ITU method for the Malaysian tropical climate.
where R%p(mm/h) is the rain rate exceeded at %p of the time, r%pis the path reduction factor at %p of the time, d(km) is the link path length. Parameters k and α depend on frequency, rain drop shape, rain temperature, and polarization; and the values of these parameters can be obtained from ITU-R P.838-3 .
2.2. ITU-R rain attenuation prediction method
Specifications of the 15 GHz link in Malaysia
Type of antenna
Frequency band (GHz)
14.80 - 15.30
Maximum transmit power (dBm)
BER Received threshold (dBm)
Antenna beam width
Dynamic range (dB)
Antenna for both transmit and receive side
In addition, 1-min rainfall rate data were collected for 4 years at both campuses of Universiti Teknologi Malaysia (UTM), Malaysia (UTM-Skudai and UTM Kuala-Lumpur campuses). The Skudai campus is located at Johor, southern part of Malaysia peninsula close to Singapore with annual average accumulation as high as 4184.3 mm. The average values of the 4-year rainfall rate measurements have been correlated with the 1-year measured attenuation data for these two locations due to seasonal variability of the rainfall pattern. Since rain rate CD varies from year to year, most especially at higher rain rates, we have assumed that 4-year CD will be fairly stable; and take care of any anomalies that might have been observed during the rain rate data collection. For instance, the average annual value of the 4-year rainfall rate data will have a lower variance and thus smaller variation.
For the remaining four sites (Alor Star, Penang, Taiping, and Temerloh), the average of 12-year rain-rate data collected from Malaysian Meteorological Station have been used in the study. These rain-rate data have 1-h integration time, so we used Chebil and Rahman's model [8, 9] for converting them to the equivalent 1-min integration time. Again, the average values of the 12-year rainfall rate measurements have been correlated with the 1-year measured attenuation data for the four sites due to seasonal variability of the rainfall pattern. Chebil and Rahman's model was based on rainfall data of 1-h integration time collected from over 70 locations in Malaysia, Indonesia, and Singapore. The conversion method has been found to be quite accurate and reliable, within reasonable limit of statistical accuracy, for the Malaysian tropical region and other tropical regions . However, the conversion method is limited to 0.001% ≤ p ≤ 1.0% of the time when rainfall rate is exceeded. Due to this constraint, the method could not offer accurate results for high rainfall rates when p ≤ 0.001%. Nevertheless, our analyses were limited to the time percentages within the validity range of the rain rate conversion method.
In the ITU-R P.530-14 model, the rainfall rate exceeded at 0.01% of the time is used for predicting the corresponding rain attenuation value. The other percentages of time, within the range of 0.001 to 5.0%, are estimated by an extrapolation approach. The ITU-R predicted value of A0.01(dB) is much smaller compared to the measured data . In this study, a modification is proposed to the extrapolation formula used in the ITU-R method, based on the results presented in Figures 1, 2, and 3.
On the other hand, the modified ITU-R model seems to closely match the measured rain attenuation for all the six links. For instance, the predictions of the proposed modified model are in good agreement with measurements in the range of 1.0≤%p≤0.001 for three links (Alor Star, Kuala Lumpur, and Temerloh). Moreover, the proposed model accurately predicts measurements for the remaining three links (Johor Bahru, Penang, and Taiping) in the range of 1.0≤%p≤0.01. The prediction errors associated with proposed model are generally less than 10%, compared to the ITU-R whose errors are close to 30%, especially at extremely high rain rates.
Characteristics of the terrestrial links in Brazil 
Path length (km)
Measurement duration (years)
As shown in Figures 6b, 7, and 8, the ITU-R method does not match with measurements for all the exceedance probability at which rain rate is exceeded. The method largely underestimates the measured values at low rain rates, while overestimating them at extremely high rain rates. On the other hand, the proposed method seems to match the measured values more accurately, with up to 80% reduction in relative RMS errors compared to ITU-R method.
Percentage errors comparison
Annual mean accumulation (mm)
Rio de Janeiro
Annual mean accumulation (mm)
This article has presented the results on rainfall rate, and rain attenuation CDs on six microwave links operating at 15 GHz in tropical Malaysia. The relationship between effective specific attenuation and ITU-R predicted one is investigated. The experimental results have clearly shown that the extrapolation approach adopted by the current ITU-R method seems to be unsuitable for predicting rain attenuation CD from the knowledge of measured rain attenuation A0.01 in Malaysia and similar tropical climates. A new set of numerical coefficients was derived for improved rain attenuation CD predictions in tropical Malaysia.
The applicability of the proposed method was validated using rain measurements from 12 tropical locations. When tested against measurements, the proposed method seems to provide a significant improvement over the current extrapolation method adopted by ITU-R Recommendations P.530-14, for the prediction of rain attenuation CD over tropical regions. The test results presented in Table 3 have also shown that the proposed approach seems to provide a better and more reliable alternative to the ITU-R method in tropical Malaysia, and probably other tropical climates, regardless of link's operating frequencies and polarizations. The new set of parameters resulted in an improvement in terms of the RMS of the relative error variable compared to the RMS obtained with the original ITU-R parameters.
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