# Application of S-UTD-CH Model into Multiple Diffraction Scenarios

Authors: Mehmet Baris Tabakcioglu; Ahmet Cansiz
Journal: International Journal of Antennas and Propagation
 (2013)

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## Abstract

Propagation prediction models based on ray tracing in coverage estimation for digital broadcasting systems are compared. Geometrical Theory of Diffraction (GTD), Slope  Uniform Theory of Diffraction (S-UTD), and Slope UTD with Convex Hull (S-UTD-CH) models are compared for computation time and propagation path loss. S-UTD-CH model is optimum model with respect to computation time and relative path loss.


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## Body

## 1. Introduction

It is vital to calculate relative path loss of electromagnetic wave reaching to the receiver in multiple diffraction scenarios for more reliable radio broadcasting. A lot of electromagnetic wave propagation models based on ray tracing technique have been developed for a long time. Base station location is vital for efficiency of field strength on receiver and computational time. For reaching for all users, predicting the coverage field accurately and quickly is most significant. Radio propagation models run for calculating electromagnetic wave strength in radio planning tools predicting coverage and field strength on the receiver. In radio planning tools, Geometrical Theory of Diffraction (GTD), based on ray tracing technique, model is used due to less computation time [1]. In urban regions there are multiple diffractions, and due to that the height, of buildings are close to each other, buildings are in the transition region of the previous one. In that case GTD model fails to calculate the electric field strength at the receiver accurately. This model can be used in rural areas not having multiple diffractions with less computation time. To remove the continuity problem on the transition region, Slope Uniform Theory of Diffraction (S-UTD) model is proposed. This model based on adding of derivative of incoming fields [2, 3]. S-UTD model gives inaccurate prediction results and require great computation time in scenarios having diffraction larger than 10. According to accuracy of predicted field and computation time, Slope UTD with Convex Hull model is optimum model [4, 5]. In this study, GTD, S-UTD, and S-UTD-CH propagation models being used in broadcasting are compared with respect to accuracy and computation time. Moreover effects of transmitter height to relative path loss are discussed.


## 2. GTD Based Models

GTD based models have been used for a long time in terrestrial broadcasting. GTD model gives inaccurate results on predicting field strength in application of multiple diffractions. GTD model can be used in prediction in two cases. The first one is single diffraction case. The other one is that buildings are not in the transition zone of the previous buildings in multiple diffractions. Otherwise, GTD model fails to predict the field strength at the receiver. To remove the failure of GTD model in the transition zone, derivatives of the incoming fields are taken and added to total field. S-UTD model has large computation time and loses the accuracy due to more than 10 diffractions. To remove the failure of S-UTD model, S-UTD-CH model is proposed. In fact the proposed model is not new. It is only combination of two previously proposed models. This model is combination of Convex Hull [6] and S-UTD model. In this model firstly the obstacles not having contribution to total field are excluded according to Fresnel zone concept, and then Convex Hull is constructed via remaining obstacles [7]. Next, ray tracing algorithm runs for determining all ray paths ending at the receiver. Finally, S-UTD model runs for all ray paths [8]. In this model, because the obstacles having so little contributions are excluded from scenario, accuracy of predicted field is not compromised. Moreover, thanks to less obstacle computation time reduced. Remarkably, even if only one obstacle is excluded, computation time reduces to one-fifth [9]. Vogler’s model [10] is numerical model and gives ultimate accuracy in field prediction to real scenarios. S-UTD-CH model is compared with this model in real geometry and gives accurate results [4].


## 3. Comparison of GTD Based Models

In the case of multiple diffraction scenarios including less than 11 diffractions, S-UTD model is reference model with higher accuracy. To compare the model the scenario given in Figure1 is used. In this scenario, transmitting antenna height is selected as 25, 20, 15, 10, and 5 m, respectively. Operational frequency, assigned to 2100 MHz. Average height of building 10 m and buildings’ heights are randomly distributed between 10±4 m. Distance between the buildings is 20 m, and distances between the buildings are randomly distributed between 20±5 m. Finally receiving antenna height is 1,5 m.Figure 1
Scenario of comparison of GTD based models.For given scenario, are made 20 simulations, for GTD, S-UTD, and S-UTD-CH models, respectively. Firstly, transmitter antenna height is selected 25 m (highly elevated) and simulation results are given in Table1.Table 1
Comparison results of highly elevated receiver height (25 m).
GTD    (s)
S-UTD (s)
S-UTD-CH   (s)
GTD versus S-UTD                  (dB)
S-UTD-CH versus S-UTD (dB)
Elected
0,562
83,585
0,047
0,071
0,05
6
0,749
154,722
0
0,017
0,002
7
0,499
114,302
0
0,54
0,054
7
0,905
145,471
0
0
0,074
8
1,108
209,135
0,015
0,175
0,02
7
1,294
215,375
0,047
0,208
0,131
6
0,639
170,79
0
0,173
0,038
7
1,17
197,138
0
0,238
0,239
8
1,544
296,761
0
0,034
0,015
7
0,89
148,7
0
0,014
0,446
9
0,874
141,353
0
0,001
0,473
9
0,609
86,814
0,047
0,014
0,027
6
0,78
180,571
0
0,603
0,143
8
0,889
129,871
0
0,025
1,63
9
1,357
189,447
0
0,01
0,541
9
0,499
85,426
0
0,03
0,006
7
1,388
215,001
0,015
0,019
0,564
7
0,499
75,957
0
0,044
0,134
7
1,279
236,498
0
0
0,049
8
0,421
75,442
0,032
0,135
0,041
6
0,898
157,618
0,010
0,118
0,234
7,400
0,347
60,877
0,018
0,173
0,379
1,046As can be seen from Table1, leftmost three columns give computation times for GTD, S-UTD, and S-UTD-CH models. Next column gives the contribution of S-UTD model to GTD model. This contribution is caused by adding derivatives of the incoming fields. Next column gives the difference between S-UTD and S-UTD-CH models. The rightmost column shows the elected building number. These buildings are elected because there is almost no contribution to total field at the receiver. 20 simulations are made for each model. Last two rows illustrate the mean and standard deviation. Moreover it is illustrated in Table 1 that S-UTD model requires the most computation time. As diffraction number increases, computation time increases. Because of excluding not effective building, computation time of S-UTD-CH model is very lower. In spite of that S-UTD and S-UTD-CH models give almost the same results (0,234 dB), computation time of S-UTD-CH model is 0,010 s whereas computation time of S-UTD model is 157,618 s. The contribution of S-UTD model to GTD model is 0,118 dB resulting from adding of derivatives of incoming fields. Furthermore averagely 7,4 buildings are excluded from the scenario caused by not having contribution.Secondly, transmitting antenna height is selected as 20 m (elevated) with all the same parameters, and results are given in Table2.Table 2
Comparison results of elevated receiver height (20 m).
GTD    (s)
S-UTD (s)
S-UTD-CH   (s)
GTD versus S-UTD                  (dB)
S-UTD-CH versus S-UTD (dB)
Elected
1,357
262,051
0
0,038
0,585
9
1,358
213,581
0,015
0,001
0,029
7
0,577
156,048
0,016
0,061
0,33
7
1,872
346,228
0
0,003
0,424
7
0,982
177,561
0
0,022
0,821
9
0,499
143,942
0,016
0,097
0,185
7
0,78
172,506
0
0,059
0,011
7
0,983
184,596
0
0,002
0,22
8
1,529
259,507
0
0,129
1,355
9
0,826
199,728
0,016
0,072
0,07
7
1,217
212,598
0,234
0,066
0,037
5
0,531
118,982
0
0,043
0,056
7
0,702
122,336
0,046
0,863
0,173
6
2,356
391,578
0,015
0,034
0,182
7
0,577
97,938
0,046
0,033
0,181
6
0,452
68,531
0
1,848
0,278
7
0,484
80,777
0,047
0,125
0,14
6
0,437
79,576
0,016
0,109
0,036
7
1,077
266,933
0,016
1,03
0,044
7
0,78
199,182
0,046
5,376
0,014
6
0,969
187,709
0,026
0,501
0,259
7,050
0,518
86,713
0,052
1,239
0,332
1,05020 simulations are made for each model. Last two rows illustrate the mean and standard deviation. Moreover it is illustrated in Table2 that S-UTD model again has the most computation time. Because of ignoring not effective building, computation time of S-UTD-CH model is very lower. In spite of that S-UTD and S-UTD-CH models give almost the same results (0,259 dB), computation time of S-UTD-CH model is 0,026 s whereas computation time of S-UTD model is 187,709 s. The contribution of S-UTD model to GTD model is 0,501 dB resulting from adding of derivatives of incoming fields. Furthermore averagely 7,05 buildings are excluded from the scenario caused by not having contribution.Thirdly, transmitting antenna height is selected as 15 m (same) with all the same parameters, and results are given in Table3.Table 3
Comparison results of the same receiver height (15 m).
GTD    (s)
S-UTD (s)
S-UTD-CH   (s)
GTD versus S-UTD                  (dB)
S-UTD-CH versus S-UTD (dB)
Elected
1,404
289,35
0,016
0,127
0,185
7
0,811
186,062
0,266
0,081
0,028
5
0,749
92,43
0,016
0,103
0,241
7
0,39
77,938
0,032
1,992
0,23
6
1,342
303,422
0
0,248
0,171
7
0,562
82,712
0
1,887
0,015
7
2,012
443,511
0,016
0,089
0,015
7
1,185
277,152
0,031
2,239
0,166
6
1,061
297,291
0,046
0,174
0,315
6
1,342
276,153
0,046
0,037
0,28
6
1,295
259,195
0,25
0,386
0,077
5
0,686
133,319
0,062
0,074
0,119
6
1,077
216,841
0,25
0,638
0,114
5
1,887
379,598
0,031
0,597
0,039
6
1,077
240,101
0,031
1,397
0,193
6
0,998
142,85
5,881
0,31
0,072
3
2,808
514,164
0,015
0,009
0,043
8
0,5
119,527
0,219
0,017
0,005
5
0,733
188,871
0,046
0,731
0,011
6
1,014
179,776
0
0,385
0,07
7
1,147
235,013
0,363
0,576
0,119
6,050
0,574
118,359
1,302
0,714
0,097
1,09920 simulations are made for each model. Last two rows illustrate the mean and standard deviation. Moreover it is illustrated in Table3 that S-UTD model again has the most computation time. Because of ignoring not effective building, computation time of S-UTD-CH model is very lower. In spite of that S-UTD and S-UTD-CH models give almost the same results (0,119 dB), computation time of S-UTD-CH model is 0,363 s whereas computation time of S-UTD model is 235,013 s. The contribution of S-UTD model to GTD model is 0,576 dB resulting from adding of derivatives of incoming fields. Furthermore averagely 6,05 buildings are excluded from the scenario caused by not having contribution.Fourthly, transmitting antenna height is selected as 10 m (lower) with all the same parameters, and results are given in Table4.Table 4
Comparison results of highly lower receiver height (10 m).
GTD    (s)
S-UTD (s)
S-UTD-CH   (s)
GTD versus S-UTD (dB)
S-UTD-CH versus S-UTD (dB)
Elected
0,327
103,85
0,094
0,081
0,236
5
0,749
191,086
0,702
1,208
0,015
4
1,638
313,063
0,047
1,019
0,091
6
1,186
288,227
0,203
1,53
0,166
5
0,671
126,018
0,187
0,052
0,005
5
0,546
158,465
0,016
0,026
0,285
6
1,17
324,17
0,187
0,065
0,27
5
1,529
347,539
0,202
1,075
0,451
5
1,279
322,766
5,21
0,886
0,173
3
0,468
76,441
0,031
1,517
0,019
6
0,468
66,862
0
0,127
0,112
8
1,731
342,017
113,553
0,613
0,001
1
0,531
86,409
0,156
1,832
0,29
5
0,858
182,646
0,156
0,225
0,073
5
0,904
198,215
0,827
0,148
0,15
4
0,312
50,326
0,609
0,021
0,268
4
0,733
153,443
0,202
0,884
0,068
5
1,623
367,429
0,031
0,054
0,078
6
1,201
233,659
0
0,173
0,255
7
1,248
348,179
0,171
0,556
0,006
5
0,959
214,041
6,129
0,605
0,151
5,000
0,459
109,416
25,311
0,595
0,125
1,45120 simulations are made for each model. Last two rows illustrate the mean and standard deviation. Moreover it is illustrated in Table4 that S-UTD model again has the most computation time. Because of ignoring not effective building, computation time of S-UTD-CH model is very lower. In spite of that S-UTD and S-UTD-CH model gives almost the same results (0,151 dB), computation time of S-UTD-CH model is 6,129 s whereas computation time of S-UTD model is 214,041 s. The contribution of S-UTD model to GTD model is 0,605 dB resulting from adding of derivatives of incoming fields. Furthermore averagely 5 buildings excluded from the scenario caused by not having contribution.Finally, transmitting antenna height is selected as 5 m (highly lower) with all the same parameters and results are given in the Table5.Table 5
Comparison results of highly lowered receiver height (5 m).
GTD    (s)
S-UTD (s)
S-UTD-CH (s)
GTD versus S-UTD (dB)
S-UTD-CH versus S-UTD (dB)
Elected
1,155
255,202
0,203
0,04
0,192
5
0,203
37,066
0,437
0,67
0,2
4
0,764
203,223
0,015
0,143
1,134
6
0,483
112,4612
0,531
0,429
0,081
4
0,359
82,852
0,015
0,612
0,041
6
0,795
194,705
0,172
0,107
0,166
5
1,529
351,314
0,156
2,207
0,144
5
0,764
181,227
0,546
0,353
0,001
4
0,437
91,666
0,436
1,687
0,007
4
0,873
235,999
0,093
0,082
0,457
5
0,624
145,643
0,093
0,202
0,396
5
0,671
165,486
0,514
0,332
0,321
4
0,952
225,905
4,196
1,455
0,007
3
0,608
138,045
0,016
0,037
0,071
6
0,639
176,079
0,452
2,954
0,003
4
0,265
46,77
0,093
0,471
0,079
5
0,327
75,879
0,094
0,591
0,158
5
0,499
104,318
9,75
3,515
0,077
2
0,89
258,072
0,031
0,314
0,589
6
0,561
134,348
0,125
1,715
0,12
5
0,670
160,813
0,898
0,896
0,212
4,650
0,317
79,980
2,272
1,021
0,271
1,040There are made 20 simulations for each model. Last two rows illustrate the mean and standard deviation. Moreover it is illustrated in Table5, S-UTD model again has the most computation time. Because of ignoring not effective building, computation time of S-UTD-CH model is very lower. In spite of that S-UTD and S-UTD-CH models give almost the same results (0,271 dB), computation time of S-UTD-CH model is 0,898 s whereas computation time of S-UTD model is 160,813 s. The contribution of S-UTD model to GTD model is 0,896 dB resulting from adding of derivatives of incoming fields. Furthermore averagely 4,65 buildings are excluded from the scenario caused by not having contribution.


## 4. Results and Discussions

In general, GTD model is the fastest model to predict the field strength in radio propagation. If the scenario includes less than 11 buildings, S-UTD model gives the ultimate accuracy. Despite that S-UTD model gives accurate results, this model has large computation time. With decreasing eliminated building number, S-UTD and S-UTD-CH models give almost the same results. In the case of not eliminating buildings, these two models predict the relative path loss at the receiver similarly. As the difference between the building heights decreases, building heights are close to each other. Therefore S-UTD model has the most contribution to GTD model resulted from adding derivatives of the incoming fields. In the cases of elevated and highly elevated transmitting antennae, direct fields are dominant, and so contribution of derivative terms is very small and can be ignored. In these cases, GTD model can be used with higher accuracy and less computation time.  As a conclusion, S-UTD-CH model is optimum model for accuracy of predicted field and relatively less computation time in multiple diffraction scenarios.



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*Source: 285304-2013-05-30.xml*