Modification of the ITU-R P.530-17 Rain Attenuation Prediction Model

Modification of the ITU-R P.530-17 Rain Attenuation Prediction Model

Joseph Mom

Department of Electrical and Electronics Engineering Joseph Sarwuan Tarka University,

Makurdi, Nigeria

Soo Tyokighir

Department of Electrical and Electronics Engineering Joseph Sarwuan Tarka University,

Makurdi, Nigeria

Gabriel Igwue

Department of Electrical and Electronics Engineering Joseph Sarwuan Tarka University,

Makurdi, Nigeria

Abstract Rain is the major factor that affects the propagation of signals, especially above 10 GHz frequency. To perform adequate link budget planning, the propagation impairments posed on microwave links by rain needs investigation. The ITU- R recommends a global rain attenuation prediction model for terrestrial and earth-space links, but the model is based on propagation measurement missions in temperate region hence not suitable for tropical locations. In this study, a modification to the existing ITU-R P. 530-17 rain attenuation prediction model is proposed. The modified model is implemented based on measurement data collected from four geographically spread terrestrial microwave DIGI MINI-LINKs operating at 15-18 GHz frequency. The curve fitting technique is used to modify the second constant in the ITU-R P.530-17 model to 0.743. Results suggest that for rain rates ranging from 20 mm/h to 100 mm/h, the modified ITU-R model reduced the root mean square (RMS) error value by at least 5.46%. Therefore the modified ITU-R P.530-17 model is suitable for rain attenuation prediction in tropical climates and locations characterized by heavy yearly rain.

KeywordsRain attenuation, ITU-R P.530-17, Tropical climate, Terrestrial link, RMS Error

1. INTRODUCTION

   The propagation of high-frequency waves especially in rain has become an issue for radio engineers over recent years. A microwave signal can be scattered, diffracted absorbed, or depolarized by rain. This can restrict signal propagation hence decrease the quality of service. Above 10 GHz, rain poses deleterious effects to terrestrial and satellite- to-earth communication links [1], [2], [3], [4]. In the design and planning of reliable communication systems, rain attenuation prediction studies become necessary [5]. The emergence and development of complex radio access networks have increased spectrum occupancy necessitated by the demand for higher bandwidths. It then becomes imperative to employ the advantages of higher frequencies that are capable of supporting these demands [6], [7], [8], [9]. Over the years, some rain attenuation prediction models have been developed by different researchers. Some key parameters used for most of the rain attenuation models include rainfall rate, frequency, specific attenuation, and

   elevation angle [10]. Short integration time rainfall rate is also one of the essential input parameters in rain attenuation prediction models. Some prediction models in South Korea have used the polynomial regression fitting method for the estimation of one-minute rainfall rate distribution [11], [12], [13]. The major issue with recent rain attenuation prediction models is their poor performance when used in tropical countries such as Nigeria. Considerable disparities are known to exist between the measured and predicted rain attenuation values. Research has also shown that rain structures in temperate regions differ from the ones in tropical locations. Because of this, the rain attenuation prediction model described in [14] is not sufficiently accurate hence the need for modification.

2. RESEARCH METHOD

   1. Experimental procedure

      Define The rain attenuation data were retrieved from four DiGi telecommunications stations (Abuja, Plateau, Sokoto, Edo) in Nigeria each consisting of microwave MINI-LINK having data acquisition, retrieval, and processing system. The antennas are horizontally polarized and are strategically located in-between buildings to remove interference from strong winds. The antenna is frequently sprayed with WD 40 spray to eliminate wet antenna effects. By doing this, interference from other hydrometeor sources becomes negligible. Specifications of the MINI-LINKS stations are shown in Table 1(a) while the measurement site characteristics are shown in Table 1(b). The signal monitoring device at the receiving stations alongside a computer system is used to monitor the signal strength at one- minute intervals for rainy and clear sky conditions. The path attenuation is calculated by finding the difference between the received signal level (RSL) during clear sky conditions and the RSL during rainy conditions for horizontally polarized signals at various rain rates. The equation is given as follows:

      Attenuation (dB) = RSL clear sky – RSL rainy (1)

      Table 1a. Specifications of the link

      Type of antenna	Front-fed
      Frequency band	15-18 GHz
      Polarization	Horizontal
      Max transmit power Antenna beamwidth Dynamic range (dB) Antenna size (m) Gain (dBi)	+16.0 dBm 1.9° 45 0.9 35

      City	Latitude °N	Longitude °E	Hs (m)	Path length
      Plateau	9.21	9.51	1217	3.26
      Abuja	9.07	7.39	360	1.5
      Edo Sokoto	6.63 13.00	5.93 5.24	150 265	4.19 1.22

      City	Latitude °N	Longitude °E	Hs (m)	Path length
      Plateau	9.21	9.51	1217	3.26
      Abuja	9.07	7.39	360	1.5
      Edo Sokoto	6.63 13.00	5.93 5.24	150 265	4.19 1.22

      Table 1b. Measurement site characteristics

   2. Weather monitoring station

      The rain rate data has been obtained from a locally built rain gauge with a 0.7 mm bucket size. A small 12 watt and 6- volt solar panel are used to ensure continuous data collection and processing. The average of the 10-year rain rate data obtained from the Nigerian Meteorological Agency (NiMet) was used for the four sites (Abuja, Plateau, Sokoto, and Edo). The Chebil model [17] was used to convert the 3-hr rain data integration time to 1-min integration time as recommended by the ITU. Figure 1a shows the map of Nigeria containing regions of interest while Figure 1b shows the graph of attenuation vs. rainfall for the selected stations.

   3. Site details

      October.

      October.

      According to the ITU-R rainfall climatic zoning, Nigeria falls in the region 'K' with an average annual rain accumulation exceeding 2000 mm in the south, 3000 mm in the south-eastern part and below 1500 mm in most parts of the North. The Nigerian climate is considered tropical and is characterized by wet and dry seasons. The wet season occurs due to northeast trade winds from November to March while the dry season occurs due to southeast trade winds from April to

      Fig 1a. Map of Nigeria showing selected stations

      Fig 1b. Probability plots: Rain ratevs. rain attenuation

   4. Modified ITU-R P.530-17 rain attenuation model

      The concept of the proposed ITU-R model remains the same as the existing one. The modified ITU-R model is proposed based on the curve fitting technique with the goal of reducing the prediction error of the existing model. The root mean square error obtained from the existing ITU-R model exceeds 10% [15] hence, the need for reduction. The modified ITU-R model is based on measured data from a tropical location. The measured values from the MINILINKs are used to obtain the coefficients for the new model. The rain rate for 99.99 % availability is one of the variables utilized by the modified model. The percentage of time for the range 0.001 to 1 is used to determine the coefficient of the newly modified model. The curve-fitting function in the Microsoft Excel suite is used to determine the coefficients of the modified model while the solver function was used to solve the non-linear equation of the ITU-R model using the sum of square residuals method to best fit the measured data. Hence, the coefficient that best fits the existing ITU-R model is obtained based on measured data. The measured rain attenuation value and percentage of time for a range of 0.001

      % to 1 % are used as input data to determine the coefficients. The new coefficients obtained from the curve fitting function are significantly fit with measured data obtained from tropical climate. The second coefficient for the existing ITU-R model for prediction of attenuation for other percentages of time p is 0.6082. However, to fit the data in a tropical climate, the coefficient has been replaced with 0.743. By implementing the modified model, the percentage error and RMS error can be significantly reduced. The modified model is shown step by step from equations (2) to (6) as follows:

      We calculate the attenuation for p percentage of time as:

      (2)

      Where:

      And:

      (3)

      Where: k and are obtained using Recommendation ITU-R P.838-3 and point rainfall rate with one minute integration time (R0.01) is obtained using the method described in [17]. The distance factor r is obtained as follows:

      And p is the percentage probability for an average year. While A0.01 is the rain attenuation exceeded at 0.01% given as:

      (dB) (4)

      Where: R is the specific attenuation given as:

      (5)

      is the effective pat length given as follows:

      (km) (6)

      Where:

      d and r are the link distance and path reduction factor respectively

   5. Budalal model

      The model described in [16] is based on the measured attenuation of smaller than 1 km terrestrial link and frequency of 26/38 GHz. Due to inconsistencies found on the ITU-R P.530-17 Model for link lengths below 1 km, a modification to the distance factor denoted (Ify) proposed by the ITU-R was implemented as follows:

      (7)

      Where: f = frequency, d = link length, R0.01 = rainfall rate for 99.99% availability.

      Hence to improve the performance of the ITU-R P.530-17 model for short-range terrestrial link communications, the parameter Ify proposed in equation (7) is recommended. The attenuation for 0.01% of time is then given as:

      dB (8)

      Where specific attenuation kR0.01 is obtained from the procedure in Equation (5) and d is the link length.

   6. ITU-R P.530-17 model

      The model described in [14] is based on a distance factor denoted r which relies on the point rain rate (R0.01), frequency, link length, and power-law relationship coefficients of the specific attenuation are given as follows:

      (9)

      (10)

      Where: f, and d are the frequency and actual path length respectively. With given as 1.1825 from [18]. The attenuation for 0.01 % of time is given as:

      dB (11)

      Where: deff is the effective path length given as:

      (km) (12)

      is obtained from Equation (5).

      Attenuation for other percentages of time p for the range 0.001% to 1% is given by the following power law:

      (13)

      Where:

      (14)

      (15)

      (16)

   7. Abdulrahman model

   The model proposed by Abdulrahman [19] is based on the differential approach. According to the model, attenuation is given as follows:

   (17)

   p

   p

   Where: kR% is the specific attenuation for p percentage of time obtained from ITU-R recommendations. d is the link distance and deff is the effective path length through rain.

3. RESULTS AND DISCUSSION

   In this section, the results from the performance of the four

   (4) models described in section two are presented and discussed. The percentage of time considered ranges between

   0.001 % to 1 %.

   Fig. 1a Rain attenuation @ 100 mm/h

   Fig.1d Rain attenuation @ 40 mm/h

   Fig. 1b Rain attenuation @ 80 mm/h

   The results from Figures 2(a) and 2(b) show that for 0.001% unavailability, the modified ITU-R model overestimates attenuation due to rain by 5.613 dB and 5.4179 dB respectively. All models underestimated attenuation for 0.01% of time as attenuation ranged from 9.2587 dB to 32.628 dB across all models. From Figures 2(c), 2(d) and 2(e), all models underestimate attenuation for 0.001% to 1% unavailability for reference rain rates of 60 mm/h, 40 mm/h and 20 mm/h respectively. Figures 2(a) suggest that for 1% of time, all three models predict attenuation with similarity although an underestimation value of 4.12 dB was realized for the Modified ITU-R and ITU-R model. The Budalal model however underestimated attenuation by 4.299 dB.

   Fig.1c Rain attenuation @ 60 mm/h

   Fig.1e Rain attenuation @ 20 mm/h

   An underestimation of attenuation by 21.761 dB and 24.718 dB was recorded for the ITU-R and Budalal model respectively at 0.001% of time. The modified ITU-R model however overestimated attenuation by 5.417 dB. Figure 2(b) further suggests attenuation ranging from 2.8178 dB to 4.615 dB for a system design of 8.77 hours a year across all models. An attenuation of 0.8017 dB going up to 0.9627 dB across all three models is estimated for a system design with 99% link availability. From Figure 2(c), all three models suggest that for a system design of 5.26 minutes of outage in a year, attenuation values ranging from 10.6293 dB to 33.3658 dB is expected. This comes with an underestimation value of at least 24.1967 dB. For time availabilities of 0.01% to 1% attenuation ranged from 0.5789 dB to 6.653 dB across all models. It was also observed from Figure 2(d) that the attenuation due to rainfall recorded a maximum value of 21.9838 dB for 99.999% availability and a minimum value of 6.7175 dB at 99.999% availability based on the modified ITU-R and Budalal models respectively. The ITU-R model however predicted attenuation of 8.6636 dB for a system design of 5.26 minutes of outage in a year. For 0.01% unavailability, the modified ITU-R and ITU-R model performed better than the Budalal model as both models underestimated attenuation by 8.851 dB. The Budalal model however underestimated attenuation by 9.836 dB. For 0.1% to 1% of time, all three models predicted attenuation due to rain ranging from 0.3658 dB to 2.2621 dB. Figure 2(e) shows that for 0.001% of time the modified ITU-R model predicted

   attenuation of 10.7686 dB which was the maximum attenuation predicted across all models. The ITU-R and Budalal model however predicted attenuation of 4.2438 dB and 3.0655 dB respectively. An attenuation of 0.16695 dB to 2.1473 dB across all models was realized for 0.01% to 1% of time.

   Table 2. Percent error for rain rate (R) = 20 mm/h

   % of time	% error ITU-R model	% error Modified ITU-R model	% error Budalal model
   0.001	-68.63	-20.40	-77.34
   0.01	-71.03	-71.03	-79.07
   0.1	-61.68	-47.73	-72.32
   1	-87.12	-87.12	-90.69

   The accuracy of the modified ITU-R rain attenuation prediction model is tested by the root mean square value (RMS) and the percentage error measurement [20], [21], [22],

   [23], [24], [25], [26]. The percentage error and the root mean square error are adopted to determine the measured error between the existing ITU-R model, Budalal model, and modified ITU-R model. The percentage error can be calculated by the following equation:

   (18)

   Where:: Apredicted is the rain attenuation predicted and Ameasured is the rain attenuation measured at a given percentage of time. The root mean square (RMS) value can be estimated by using the mean error µe and standard deviation e. It is given as follows:

   (19)

   Table 3. Percent error for rain rate (R) = 40 mm/h

   % of time	% error ITU-R model	% error Modified ITU-R model	% error Budalal model
   0.001	-69.47	-22.53	-76.32
   0.01	-66.87	-66.87	-74.31
   0.1	-48.10	-29.22	-59.76
   1	-79.00	-79.00	-83.71

   The comparison of the root-mean-square values for percentage of time ranging from 0.001% to 1% unavailability is shown in Table 2 to Table 6. Comparison is made between the Budalal model, modified ITU-R model, and the existing ITU-R model. From Table 2, the percentage error value of the existing ITU-R model for 0.001% of time is -68.6313%. This resulting percentage error value is slightly higher and is not preferable for tropical climates. However, from the calculations, the percentage error of the modified ITU-R model for 0.001% of time is -20.4031%. Hence, it can be

   shown that the modified ITU-R model significantly reduced the percentage error. For 99.99% link availability, both the ITU-R and modified ITU-R models estimated similar percentage errors of -71.0336%. The Budalal model however estimates a higher percentage error of -79.0765%. Results further suggest that for 0.1% unavailability, the maximum percentage error realized was -72.32% while the minimum percentage error was -47.7332%. For 99% link availability, the minimum percentage error was -87.1235% while the maximum percentage error obtained was -90.6988% across all models.

   Table 4. Percent error for rain rate (R) = 60 mm/h

   % of time	% error ITU-R model	% error Modified ITU-R model	% error Budalal model
   0.001	-62.24	-4.19	-69.47
   0.01	-65.89	-65.89	-72.43
   0.1	-56.02	-40.02	-64.45
   1	-81.50	-81.50	-85.45

   From Table 3, it is shown the ITU-R model and modified ITU-R model's performance for a system design of 99.99% and 99% availability was the same. The percentage error of – 66.8789% and -79.0009 was realized for 0.01% and 1% of time respectively. However, the Budalal model estimated a higher percentage error for time availabilities of 99 to 99.999% with percentage error ranging from -76.3285% to – 83.7181%. Table 4, Table 5, and Tables 6 show that both the ITU-R and modified ITU-R model account for similar percentage errors for 99.99% availability for rain rates of 60 mm/h, 80 mm/h, and 100 mm/h respectively, while the modified ITU-R performed best for 99.999% availability when compared to the other two models as shown in Table 5.

   Table 5. Percent error for rain rate (R) = 80 mm/h

   % of time	% error ITU-R model	% error Modified ITU-R model	% error Budalal model
   0.001	-55.17	13.73	-62.67
   0.01	-64.07	-64.07	-70.08
   0.1	-65.35	-52.73	-71.14
   1	-78.02	-78.02	-81.70

   Table 6. Percentage error for rain rate (R) = 100 mm/h

   % of time	% error ITU-R model	% error Modified ITU-R model	% error Budalal model
   0.001	-65.21	11.04	-62.70
   0.01	-72.58	-65.51	-70.61
   0.1	-80.94	-66.83	-79.27
   1	-81.94	-77.28	-80.64

   Table 7. Root Mean Square value for selected models

   	% error ITU-R model	% error Modified ITU-R model	% error Budalal model
   20	72.91	63.58	80.23
   40	67.12	56.66	74.21
   60	67.29	58.62	82.69
   80	66.32	60.86	71.83
   100	75.50	64.26	73.78

   RMS values obtained from Table 7 suggest that the RMS of the existing ITU model was 75.504 for rain rate value 100 mm/h. The resulting RMS value has been reduced by the modified ITU-R model to 64.2617. Results further suggest that for rain rates ranging 20 to 100 mm/h, the modified ITU- R model reduced the RMS error value by at least 5.46135%.

4. CONCLUSION

In this study, a modification to the existing ITU-R P.530-17 rain attenuation prediction technique has been developed. Based on the results, it can be concluded that the modified ITU-R P.530-17 rain attenuation model has significantly improved the prediction error of the existing ITU-R model. The new model is now suited for tropical locations and has been modified based on measured data and characteristics of rain in a tropical climate. The modified model can be implemented in different frequency bands and elevation angles for the prediction of attenuation due to rain. The new model can aid network engineers in the planning of fade mitigation techniques such as power control and site diversity.

ACKNOWLEDGMENT

The authors wish to thank the Nigerian Multilink's Telecommunications Center (NMTC) for making their facilities available for this research.

REFERENCES

1. Z. Yun, and M. Iskander, "Ray tracing for radio propagation modeling: Principles and applications", IEEE Access, vol. 3, pp. 10891100. 2015.

2. X. Yin, C. Ling, and M. Kim, "Experimental multipath-cluster characteristics of 28-GHz propagation channel", IEEE Access, vol. 3, pp. 3138 3150. 2015.

3. X. Yin, Y. Ji, H. Yan, "Measurement-based characterization of 15 GHz propagation channels in a laboratory environment", IEEE Access, vol. 5, pp. 14281438. 2017.

4. J. Aviles, and A. Kouki, "Exploiting site-specific propagation characteristics in directional search at 28 GHz," IEEE Access, vol. 4, pp. 3894-3906, 2016.

5. J. Mandeep, N. Yann, and S. Hassan, "Case study of the rain attenuation at Ka-band", Journal of electromagnetic waves and applications, vol. 22, pp. 1517-1527. 2008.

6. M. Samad, F. Diba, and D. Choi, "A survey of rain attenuation prediction model for terrestrial links: Current research challenges and state of the art", Sensors, pp. 1-7. 2021.

7. S. Sujan, and D. Choi, "Rain attenuation study over 18 GHz Terrestrial Microwave link in South Korea", International Journal of Antennas and Propagation. pp. 1-7. 2019.

8. R. Xue, H. Yu, and Q. Cheng, "Adaptive coded modulation based on continuous phase modulation for inter-satellite links of global navigation satellite systems", IEEE Access, vol. 6, pp. 2065220662. 2018.

9. S. Sujan, I. Nadeem, J. Ghimire, S. Kim, H. Yu, and D. Choi, "Seasonal and diurnal variations of rain attenuation measured with the Koreasat 6 at 20.73 GHz", Proceedings of the International Conference on ICT convergence, pp. 1-18. 2017.

10. L. Mello, and M. Pontes, "Unified method for the prediction of rain attenuation in satellite and terrestrial links", Journal of microwave optoelectronics and electromagnetic applications, vol. 11, pp. 1-14. 2012.

11. S. Sujan, J. Park, and D. Choi, "Rain rate modeling of 1-min from various integration times in South Korea", Springer plus, vol. 5, no. 1, pp. 433. 2016.

12. S. Sujan, P. Jung-Jin, S. Kim, J. Kim, H. Jung, and D. Choi, "1-Minute rain rate derivation from various integration times in South Korea. 1st International Conference on Next Generation Computing, pp. 1-9. 2016.

13. S. Sujan, and D. Choi, "Proposed one-minute rain rate conversion method for microwave applications in Korea", Journal of information and communication convergence engineering, vol. 14, no. 3, pp. 153- 162. 2016.

14. ITU-R Recommendations, "Prediction Methods Required for the Design of Terrestrial Line-of-Sight Systems", Document ITU-R P.530- 17, 2017.

15. J. Mandeep, O. Hui, M. Abdullah, M. Islam, M. Ismail, W. Suparta, P. Menon, and H. Abdullah, "Modified ITU-R rain attenuation model for equatorial climate", IEEE International Conference on Space Science and Communication, pp. 89-92. 2011.

16. A. Budalal, M. Islam, K. Abdullah, T. Rahman. "Modification of distance factor in rain attenuation prediction for short-range millimeter- wave links", Bulletin of electrical engineering and informatics, vol. 16, no. 9, pp. 1027-1031. 2020.

17. J. Chebil, J. T. Rahman, "Development of 1 min rain rate contour maps for microwave applications in Malaysia Peninsula", Electronics Letters, vol. 35, pp. 1712-1774.

18. Recommendation ITU-R. P.838-3 Series, "Specific attenuation model for rain for use in prediction methods", Recommendation ITU-R P. 8383, pp. 18. 2005.

19. A. Abdulrahman, T. Rahman, S. Rahim, M. Rafiqul, M. Abdulrahman, "Rain attenuation predictions on terrestrial radio links: differential equations approach", Transactions on emerging telecommunications technologies, vol. 23, pp. 293-301. 2012.

20. S. Begum, I. Otung, "Rain cell size distribution inferred from radar data ", Radio Sci, vol. 44, no. 2, pp. 1-7. 2009.

21. G. Brussaard, "Rain induced polarization & raindrop canting",

    Electronic Letters, vol .10, no. 20, pp. 411-412. 1974.

22. N. Blaunstein, S. Yehuda, "Satellite communication networks",

    Networks beyond 4G", vol. 10 pp. 211-240. 2020.

23. R. Crane, "Prediction of attenuation by rain", IEEE transactions on communication, vol. 28, pp.1717-1733. 1980.

24. R. Crane, "A two-component rain model for prediction of attenuation",

    Radio Science, vol. 17, pp. 1371-1387. 1982.

25. L. Ippolito, "Propagation effects modeling and prediction. Wiley and Blackwell, vol. 7, pp. 138-204. 2017

26. S. Ishii, "Rain attenuation in the microwave band. Wireless engineering & tech, vol.7, no. 2, pp. 59-66. 2016.

BIOGRAPHIES OF AUTHORS

Joseph Mom received his BEng in Electrical and Electronics Engineering from Joseph Sarwuan Tarka University, Makurdi, Nigeria in 2004, he also received his MEng and Ph.D. Degree in Electronics Engineering from the University of Nigeria, Nsukka in 2009 and 2015 respectively. He is currently an associate Professor in the Department of Electrical and Electronics Engineering, Joseph Sarwuan Tarka University, Makurdi. He has published many articles in reputable journals and conference proceedings. He is a registered Engineer with the Council for the Regulation of Engineering in Nigeria (COREN) and also a member of the IEEE and ACM.

Soo Tyokighir holds BEng and MEng degree in Electrical and Electronics Engineering from the Joseph Sarwuan Tarka University, Makurdi in 2013 and 2019. He is currently a Ph.D. student and research assistant at Joseph Sarwuan Tarka University, Makurdi. He is a member of the Space & Satellite Professionals International, USA (SSPI), IEEE, Nigerian Society of Engineers (NSE) and COREN. His research interests are in engineering physics, radio communication and RF technologies.

Gabriel Igwue holds a B.Sc from the University of Lagos in 1973; M.Sc from the Massachusetts Institute of Technology, USA and a Ph.D from the North Caroline State University, USA, all in Electrical Engineering in 1975 and 1982 respectively. Professor Igwue has taught Electrical Engineering courses at both polytechnic and University for over thirty years. He has held many management positions in the public and private sectors. He is a COREN registered Engineer and a member of the Nigerian Society of Engineers (NSE). He has written several books in Electrical Engineering including Circuit Theory; Electrical Engineering Materials; Mathematical Methods for Engineers; Principles of Communications and Basic Circuit Theory and Industrial Electronics for physicists. He is married with children.