Application of propagation models to compute wireless radio coverage maps to realistic terrain data

DUBLIN CITY UNIVERSITY SCHOOL OF ELECTRONIC ENGINEERING APPLICATION OF PROPAGATION MODELS TO COMPUTE WIRELESS RADIO COVERAGE MAPS TO REALISTIC TERRAIN DATA Trinh Xuan Dung August 2009 MASTER OF ENGINEERING IN TELECOMMUNICATIONS Supervised by: Dr Conor Brennan Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Acknowledgements I would like to give my special thanks to my supervisor Dr Conor Brennan for his guidance, enthusiasm and commitment to this project To Prof Charles McCorkell, I say thanks for his help during the time I have been in Dublin Thank finally to my family, Ngoc Dung, and friends who give me encouragement, inspiration to finish this project Declaration I hereby declare that, except where otherwise indicated, this document is entirely my own work and has not been submitted in whole or in part to any other university Signed: Student: Trinh Xuan Dung Date: Page ii Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan ABSTRACT Integral Equation (IE) method is a deterministic method to compute the UHF terrain pathloss This method has an extremely huge computation load In this project, we attempt to implement Fast Far Field Approximation (FAFFA) This is a fast solution for IE method We then evaluate the efficiency of this method in the terms of accuracy and calculation time For comparison purpose, Hata-Okumura with Knife Edge Diffraction Extension Method (Hata-Okumura with Extension in short) is used as reference method Finally, we attempt to implement the FAFFA on real map (2 dimension map) Student: Trinh Xuan Dung Page iii Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Table of Contents Acknowledgements ii Declaration ii ABSTRACT iii TABLE OF FIGURES vi TABLE OF TABLES viii CHAPTER 1: INTRODUCTION CHAPTER 2: TECHNICAL BACKGROUND 2.1 Basic Propagation Model 2.2.1 Radio Wave Propagation 2.2.2 Free space Propagation Model 2.2.3 Hata-Okumura Model 2.2 Diffraction Theory 2.2.1 Diffraction basics 2.2.2 Single Knife Edge Diffraction 11 2.2.3 Multiple knife edges diffraction 12 2.3 Deterministic Method 15 2.3.1 Integral Equation 15 2.3.2 Fast Far Field Approximation (FAFFA) 20 CHAPTER 3: IMPLEMENTATION 23 3.1 Dimension Implementation 23 3.1.1 Epstein Peterson Diffraction 23 3.1.2 Integral Equation Method 28 3.1.3 Fast Far Field Approximation 30 3.2 Dimension Implementation 32 3.2.1 Find path Algorithm 32 3.2.2 Path Linearization 35 3.2.3 Improvement of FAFFA in the 2D computation 37 Student: Trinh Xuan Dung Page iv Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan CHAPTER 4: RESULTS 38 4.1 Dimension MAP 38 4.1.1 FAFFA and Integral Equation method 38 4.1.2 FAFFA and Hata-Okumura with Epstein Peterson KED Extension 40 4.2 Dimension MAP 42 CHAPTER 5: CONCLUSION AND FURTHER WORK 44 5.1 Conclusion 44 5.2 Further Work 44 REPERENCES 45 APPENDIX 46 A1 CD Structure 46 A2 More results over rural terrain 47 Student: Trinh Xuan Dung Page v Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan TABLE OF FIGURES Figure 1-1: Graphical Interface of coverage map computation softwares Figure 2-1: Small scale and Large scale propagation model Figure 2-2: Path-loss against distance using free space propagation model Figure 2-3: Empirical model: the dots are the measurements Figure 2-4: Simple straight-ahead model Figure 2-5: A shape of a radio shadow Figure 2-6: Huygens’ wavelets filling a radio shadow Figure 2-7: Vector addition of contributions from a wavefront Figure 2-8: Cornu spiral Figure 2-9: Cornu Spiral in case an obstruction exists 10 Figure 2-10: Fresnel-Kirchoff knife-edge diffraction curve 10 Figure 2-11: Knife edge diffraction parameter 11 Figure 2-12: F(v) vs J(v) 12 Figure 2-13: Epstein Peterson Construction 13 Figure 2-14: Epstein Peterson Construction 14 Figure 2-15: Bullington Construction 14 Figure 2-16: Geometry of the transmission from a source to a receiver 15 Figure 2-17: Piecewise function 18 Figure 2-18: Forward scattering and backward scattering 19 Figure 2-19: Illustration idea of FAFFA Algorithm 20 Figure 2-20: FAFFA Algorithm 22 Figure 3-1: Different types of potential obstructions 24 Figure 3-2: All potential obstructions between the transmitter and receiver 24 Figure 3-3: Obstructions of the path (a) Fake Obstruction (b) Real Obstruction 25 Figure 3-4: Detection of real or fake obstruction 25 Figure 3-5: Usage of “long jump” to increase the speed of algorithm 26 Figure 3-6: Real Obstructions 26 Student: Trinh Xuan Dung Page vi Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Figure 3-7: Knife edge diffraction parameter 27 Figure 3-8: Total obstruction loss of Hjorring, Danmark 27 Figure 3-9: Real map and interpolated map 28 Figure 3-10: Points grouping 30 Figure 3-11: Demonstration of Tij calculation 31 Figure 3-12: Illustration of computing scattered field from far field points 31 Figure 3-13: Illustration of find path algorithm (a) step (b) step 32 Figure 3-14: Result of find path algorithm 33 Figure 3-15: Division of map into corner 34 Figure 3-16: Result of the find path algorithm when it applies to real map 34 Figure 3-17: Non-linearity of the path- side view 35 Figure 3-18: Non-linearity of the path- top view 35 Figure 3-19: Linearization of the path 36 Figure 3-20: Result of linearization 36 Figure 3-21: Fast Implementation of FAFFA on 2D Map 37 Figure 4-1: Comparison of IE Method and FAFFA Method 38 Figure 4-2: Comparison of FAFFA Method, Hata Okumura with Epstein Peterson KED Extension 40 Figure 4-3: Comparison of FAFFA Method, Hata Okumura with Epstein Peterson KED Extension 41 Figure 4-4: Fast Implementation of FAFFA on Dimension Map 42 Figure 4-5: Result of Fast Implementation of FAFFA on 2D Map 42 Figure 4-6: A suggestion to reduce error of “enhanced method” 43 Figure 4-7: Another suggestion to reduce error of “enhanced method” 43 Student: Trinh Xuan Dung Page vii Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan TABLE OF TABLES Table 4-1: Comparison of different methods Scenario: Hjorring, Denmark 39 Table 4-2: Comparison of different methods Scenario: Hadsund, Denmark 39 Student: Trinh Xuan Dung Page viii Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan CHAPTER 1: INTRODUCTION The past few years have witnessed a dramatically growth in the wireless industry, both in terms of mobile technology and numbers of subscribers Mobile networks have been being more important in the human life A disadvantage of wireless networks is that the mobile station needs to be in the coverage area to communicate to the network The coverage area of a base station is the geographic area where the base station can communicate If a mobile station is out the coverage area, he cannot communicate with the network Therefore, calculation of coverage map is essential in designing a mobile network If the received power at a mobile station is below a certain threshold, that subscriber cannot communicate with the network Hence, we must know the received power of all points in the map to compute the coverage map The problem of coverage map calculation turns into problem of received field computation Propagation models are developed to compute the received field at a certain distance from the transmitter Each of propagation models can only be applied in a particular scenario: - Rural area: Propagation of electromagnetic waves in areas with a low density of buildings depends mainly on the topography and the land usage (clutter) For rural area, two rays model, Hata-Okumura model, Parabolic Equation model, Hata-Okumura with Knife Edge Diffraction are usually used to compute the received field - Urban area: Propagation of electromagnetic waves in urban scenarios is influenced by reflections and diffractions at the buildings Typically the multipath propagation is very important in urban environments Therefore, several empirical model like Hata-Okumura Model, Walfish Ikegami Model and Ray Optical Propagation model are offered to compute the received field - Indoor area: Propagation of electromagnetic waves inside buildings is influenced mainly by the walls Phenomena like multi-path propagation, reflection, diffraction and shadowing have a significant influence on the received power So the propagation models should consider these phenomena to obtain accurate results Simple empirical propagation models are therefore not sufficient In this situation, One Slope Model, Montley Keenan Model, COST 231 Multi Wall Model are usually applied to compute received field [13] - Tunnel: The propagation of electromagnetic waves in tunnels differs significantly from the propagation in outdoor environments Therefore new approaches to the modeling of the scenario are required to obtain accurate prediction results [12] The following propagation models can be used: One Slope Model, Montley Keenan Model, COST 231 Multi Wall Model - Other scenarios: satellite communication, vehicles, combined scenarios, etc In this project, we have focused on investigating the propagation models for rural area Student: Trinh Xuan Dung Page Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Some softwares have been developed to calculate the coverage map Two of the most popular products are designed by AWE Communication [13] and Akosim [14] Figure 1-1a and 11b show graphical interfaces of ProMan (product of AWE Communication) and FUN (product of Akosim) Figure 1-1: Graphical Interface of coverage map computation softwares (a) FUN (b) ProMan For rural area, Hata-Okumura with Knife Edge Diffraction Extension is the most popular propagation model It is widely used in most of propagation softwares In this project, I try to suggest another model: Fast Far Field Approximation (FAFFA) to compute the received field We evaluate the efficiency of Hata-Okumura with Extension and FAFFA in terms of accuracy and computation load We then find out the advantages and disadvantages of FAFFA compared to HataOkumura with Extension Model Finally, we implement the FAFFA on a real map (2 dimension map) Student: Trinh Xuan Dung Page Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan However, the computation of scattered field is more complicated We need to calculate the induced current Jm=1:N and use the induce currents to compute the scattered field Integral Equation method requires the terrain information has the resolution from λ/4 to λ/10 This made the numbers of terrain points vary from 10000 to 50.000 The original Integral Equation method has the complexity equivalent to O(N3) Therefore, we need at least 100003 ~ 1012 computations to compute the induced currents This is an extremely huge computation and it requires several months for computation with a standard PC With the assumption that most energy comes to the observation points are from one direction (forward direction) This allows us to omit backward scattering energy Consequently, all upper triangle components of impedance matrix turn to zero and make the impedance matrix has the triangle form as shown by following equation: ˢ# ˢ$ ˢ% ˢ I## I$# I%# I # Ŵ I$$ I%$ I $ Ŵ Ŵ I%% I % I Ŵ Ŵ Ŵ # Ŵ Ŵ Ŵ I H# H$ H% (3-4) H We first find induced current J1 Then J1 is used to compute J2, and so on Finally, we can compute JN from all previous Jk=1:N-1: H# (3-5a) H$ (3-5b) H & (3-5c) This can be implemented easily by a FOR LOOP By using the forward scattering assumption, we reduce the complexity of the algorithm into 0(N2) With the value of induced currents, we can compute the scattered field: ˗ {˭{ {${ (# H" { } Ȏ zzzȎ′ }{ H (3-6) Finally, we add the scattered field with directed field to get the received field ˗ {˭{ Student: Trinh Xuan Dung ˗ {˭{ - ˗ {˭{ (3-7) Page 29 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan 3.1.3 Fast Far Field Approximation Similar to Integral Equation method, FAFFA requires the path has a high resolution Therefore, we first have to increase the resolution of the path The method is presented in previous section [3.2.3] FAFFA separates the computation of Zmn in to near field points and far field points (defending on the position of these points to the point m that we need to compute Zmn): (# I H # (# I H - I H (3-8) Therefore, we have to compute the near field and far field separately and then add them together We suppose that we have to compute the field of all points in group J For the far field points, we have to divide the path into M groups as illustrated in figure 3-10 Each group contents N/M points Figure 3-10: Points grouping Next, we compute the scattered field from each of “previous” groups (A,B, ) to center of group J by the summation: ˠ I H ˫  $ ˥ H (3-9) Where “i” represents “previous” groups and M is the center of group J This process is demonstrated in figure 3-11 Now, we can compute the field scattered from far field group to every point in group J by multiplying the summation Tij by “shifting function” Sij: ˟ ˥ zzzzzzzzzzȎ zzzzzzzzzzzzzȎ  (3-10) Where M is the center of group J, Ni is the center of “group i” and m is a point of group J that we need to compute the scattered field Student: Trinh Xuan Dung Page 30 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Group J Group A T1j Group B (a) Group J Group A Group B T2j (b) Figure 3-11: Demonstration of Tij calculation We get the total field scattered from far field points to m: ˘˘ This process is illustrated in figure 3-12 ˟ ˠ (3-11) Figure 3-12: Illustration of computing scattered field from far field points We then compute the scattered field from near field point NFm Adding FFm and NFm, we get the total scattered field at point m From this scattered field, we can compute the induced current at point m ˚˘ H (3-12) I ˟IIˮˮ˥J˥ˤ ˘˩˥ˬˤ{˭{ Student: Trinh Xuan Dung ˘˘ - ˚˘ (3-13) Page 31 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan 3.2 Dimension Implementation 3.2.1 Find path Algorithm In order to compute the received power at the receiver in dimension map, we must find the path between the transmitter and receiver and extract height information along that path Figure 313 is an illustration for the find path algorithm The idea of the algorithm is very simple It uses the Thales theorem to make decision From the transmitter, we find the path to the receiver, step by step The dotted line is the “imagine line” from the transmitter to receiver because the map is a digital image, it is not continuous We cannot get the “dotted line” Therefore, we must find a closest path along the dotted line From the transmitter, we find the intersection point between the “imagine line” and the line connect points 1,2,3 Then we can compute the distance from the intersection point to point Basing on this distance, we will make decision to choose the closest point to the “imagine line”: ˖˩JˮIJI˥ ŵ {˲ ˲ { {˳ ˳ { If (distance ≤ 0.5): point is chosen If (0.5 < distance ≤ 1.5): point is chosen If (distance > 1.5): point is chosen Figure 3-13: Illustration of find path algorithm (a) step (b) step Student: Trinh Xuan Dung Page 32 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Because “0.5 < Distance < 1.5”, point is chosen Now, we can store (x,y) position and the height of the point We continue to find the next point In figure (b), we need to choose the closest point to the path from point 4, 5, Similarly to previous step, we will find the intersection point between the “imagine line’ and the horizontal line 4-5-6 Then we will compute the distance from the intersection point to point 1’: ˖˩JˮIJI˥ Ŷ {˲ ˲ { {˳ ˳ { If (distance ≤ 1.5): point is chosen If (1.5 < distance ≤ 2.5): point is chosen If (distance > 2.5): point is chosen Because (distance ≤ 1.5), point is chosen We will store the (x,y) position and height of point Similarly, the algorithm will run to the position of receiver We will get the final result as illustrated in figure 3-14: Receiver (R) Transmitter (T) Figure 3-14: Result of find path algorithm Student: Trinh Xuan Dung Page 33 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan However, in order to apply this algorithm to all points in the whole map, we need to divide the map into different corners as illustrated in figure 3-15 The points in corner can be computed like those in corner 1, we just need to change the position of transmitter and receiver Similarly, the points in Corner can be computed like those in Corner Figure 3-15: Division of map into corner There is a small difference between the finding path algorithm in Corner and Corner With the points in Corner 1, all x position of the path is smaller than x position of transmitter While in Corner 2, all x position of the path is greater than x position of transmitter We apply this algorithm to a real map The real map is downloaded from the website of US Geology Survey www.usgs.gov with the resolution 30x30 m The result is shown in figure 3-16 50 45 40 35 30 25 100 200 300 400 500 600 700 800 900 1000 100 48 70 200 46 65 300 44 60 55 400 42 50 500 40 600 38 45 40 36 700 35 30 34 800 200 400 600 800 1000 1200 32 900 1000 100 200 300 400 500 600 700 800 900 50 100 150 200 250 300 350 1000 Figure 3-16: Result of the find path algorithm when it applies to real map Student: Trinh Xuan Dung Page 34 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan 3.2.2 Path Linearization Unfortunately, we cannot apply the Fast Far Field Approximation to compute the received field on the map we get from the algorithm “find path” because the path that we found is non-linear A closer look to the map is shown in figure 3-17 Non-linear 70 65 60 55 50 45 40 35 30 200 400 600 800 1000 1200 Figure 3-17: Non-linearity of the path- side view We can recognize that the distance between adjacent points are non-linear The x-y distance between adjacent points is not a constant, it can be or 1,414 (standardization) This is caused by the “find path algorithm” In figure 3-18, we can recognize that the x-y distance of the adjacent points along the path is not linear Figure 3-18: Non-linearity of the path- top view Student: Trinh Xuan Dung Page 35 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Therefore, we must “linearize” the path We will use the interpolation technique to the linearization Figure 3-19 is an illustration of the linearization of the path At first, we need to find the previous and next point in the non-linear path In figure 3-19, for example, we need to find the height position of “position 41”, we need to know two adjacent points of it in non-linear map, particularly point at x-y “position 40.522” and 41.936 From these two points, we can compute the height of “position 41” It is similar to compute the “position 42” and “position 43” 41 42 40.522 43 41.936 43.35 Figure 3-19: Linearization of the path This interpolation technique is apply to the non-linear path and we receive the result in figure 3-20 This figure plots both of linear and non-linear paths on the same graph We can see that they match perfectly 70 65 60 55 50 45 40 35 30 200 400 600 800 1000 1200 Figure 3-20: Result of linearization Student: Trinh Xuan Dung Page 36 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan 3.2.3 Improvement of FAFFA in the 2D computation Fast Far Field Approximation requires a considerable computation The computer needs several minutes to compute the received power for one path In a real map, we have several thousand paths from the transmitter Consequently, we need several thousand minutes to compute the power map This is a big disadvantage of FAFFA compared to other method In this section, we will try to remove this disadvantage of FAFFA method in 2D map We recognize that the computation of induced current J takes lots of calculation time Therefore, we will try to re-use the induced J for the several adjacent paths We suppose that we have paths which are close together They are called Path_1 and Path_2 At first, we will compute the induced current J1 on Path_1 using FAFFA Then, we use J1 to compute the induced current J2 on Path_2 This saves lots of computation time because the complexity of FAFFA is equivalent to O(N2) while the complexity of the reusing induced current is only O(N) The idea is quite simple We need to find the relationship of the induced currents on Path_1 and those on Path_2 In the equation of J [Section 2.3], we discover the connection between the induced current J and incident field Ei We have the estimation: H Moreover: J {${ J {${ H {${ H {#{ H { { {#{ { { { { {#{ H { { ˥ Ә { { {#{ { { { { % H { { % { { {#{ { { ˥ Ә { { { { ә (3-14) ŵ, equation (3-14) becomes: { { { { ә (3-15) When we have the induced current on Path_2, we can easily compute the received field of the points on Path_2 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 Figure 3-21: Fast Implementation of FAFFA on 2D Map Student: Trinh Xuan Dung Page 37 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan CHAPTER 4: RESULTS In this chapter, we will discuss about the results of our implementation in previous section, including: - Evaluating the efficiency of different method to compute received field: o Hata-Okumura with Epstein Peterson KED Extension o Integral Equation Method o FAFFA - Evaluating the efficiency of fast implementation of FAFFA on real map All of the algorithms run on a standard laptop with the configuration: o CPU: Core Duo Intel T5450 o Memory: GB 4.1 Dimension MAP 4.1.1 FAFFA and Integral Equation method FAFFA is the fast implementation of Integral Equation method Therefore, we have to compare the efficiency of FAFFA and Integral Equation method We will focus on two important criteria: accuracy and calculation time Terrain Information 60 50 H e ig h t( m ) 40 30 20 10 0 1000 2000 3000 4000 5000 dist anc e (m) 6000 7000 8000 7000 8000 Comparison of FAFFA and IE Method -20 -40 Loss (dB) -60 -80 -100 -120 -140 1000 2000 3000 4000 5000 distance (m) 6000 Figure 4-1: Comparison of IE Method and FAFFA Method Frequency: 144 MHz Scenario: Hadsund, Denmark Student: Trinh Xuan Dung Page 38 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan In figure 4.1, we can recognize that the result of FAFFA completely match that of Integral Equation method For other cases, we can see in table 4.1 and 4.2 FAFFA is a good approximation of Integral Equation method in terms of accuracy In table 4.1 and 4.2, at the columns of calculation time, the calculation time of FAFFA is much smaller than that of Integral Equation method, ex: in scenario of Hadsund, at frequency of 144 MHz: - Calculation time of FAFFA: 121 s - Calculation time of Integral Equation method: 13047 s The numbers of points in a group are 100 points In theory, we can save the computation #%"& time 100 times This result agrees with the theory: ŵŴŻ % ŵŴŴ #$# FAFFA save large computation time compared to Integral Equation method We can conclude that FAFFA is a good approximation of Integral Equation method in both terms of accuracy and calculation time Method Integral Equation Hata-Okumura and Epstein Peterson KED FAFFA Frequency (MHz) Calculation Time (s) Standard Deviation (dB) Calculation Time (s) Standard Deviation (dB) Calculation Time (s) Standard Deviation (dB) 144 28432 5.27 208 5.27 0.35 5.5 435 - - 1363 5.49 0.34 7.3 970 - - 7471 7.27 0.34 9.09 Table 4-1: Comparison of different methods Scenario: Hjorring, Denmark Method Integral Equation Hata-Okumura and Epstein Peterson KED FAFFA Frequency (MHz) Calculation Time (s) Standard Deviation (dB) Calculation Time (s) Standard Deviation (dB) Calculation Time (s) Standard Deviation (dB) 144 13047 3.69 121 3.69 0.33 6.59 435 - - 1058 5.55 0.33 11.35 970 - - 5251 9.79 0.33 11.74 Table 4-2: Comparison of different methods Scenario: Hadsund, Denmark Student: Trinh Xuan Dung Page 39 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan 4.1.2 FAFFA and Hata-Okumura with Epstein Peterson KED Extension Similar to the comparison of IE method and FAFFA, we will compare FAFFA and HataOkumura with Extension (a short name of Hata-Okumura method with Epstein Peterson Knife Edge Diffraction Extension) in criteria: accuracy and calculation time In table 4.1 and table 4.2, we can see that calculation time of Hata-Okumura with Extension method is always smaller than 1s at all frequencies In contrast, calculation time of FAFFA method is directly proportional to frequency I Hence, as the frequency The relationship of the frequency and wavelength is: 9˦ increases, the wavelength will decrease However, the required resolution of the path is related to wavelength: J˥JJˬ˯ˮ˩JJ ÈŸ ÈŵŴ Therefore, the resolution will decrease equivalent to the decrease of wavelength This comes to the number of points will increase and hence the computation time increases In all experiments, the smallest calculation time of FAFFA is 121 seconds It is still much greater than calculation time of Hata-Okumura with Extension method Thus, in terms of calculation time, Hata-Okumura with Extension is absolutely better than FAFFA method Terrain Information 40 35 H e ig h t(m ) 30 25 20 15 10 2000 4000 6000 distance (m) 8000 10000 12000 Comparison of FAFFA, Hata-Okumura with KED and measurement data -20 FAFFA Hata Okumura with Epstein Peterson KED Extension Measurements -40 Loss (dB) -60 -80 -100 -120 -140 -160 2000 4000 6000 distance (m) 8000 10000 12000 Figure 4-2: Comparison of FAFFA Method, Hata Okumura with Epstein Peterson KED Extension and measurement data Scenario: Hjorring, Denmark Frequency: 144 MHz Student: Trinh Xuan Dung Page 40 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Terrain Information 60 50 H e ig h t (m ) 40 30 20 10 0 1000 2000 3000 4000 5000 distanc e (m) 6000 7000 8000 Comparison of FAFFA, Hata-Okumura with KED and measurement data -20 FAFFA Hata Okumura with Epstein Peterson KED Extension Measurements -40 Los s (dB ) -60 -80 -100 -120 -140 1000 2000 3000 4000 5000 distance (m) 6000 7000 8000 9000 Figure 4-3: Comparison of FAFFA Method, Hata Okumura with Epstein Peterson KED Extension and measurement data Scenario: Hadsund Frequency: 144 MHz Now, we continue to compare FAFFA and Hata-Okumura with Extension in terms of accuracy Figure 4.2 and 4.3 illustrate the received field measured by different methods in scenarios: Hadsund and Hjorring We can see that FAFFA has a better result compared to HataOkumura with Extension method However, we need some statistic numbers to make the comparison more clearly In table 4.1 and 4.2, at columns of “Standard Deviation”, we can see that in all cases, FAFFA is more accurate than Hata-Okumura with Extension method (about 2dB) Generally, FAFFA is more accuracy than Hata-Okumura with Extension method However, the calculation time of FAFFA is still greater than that of Hata-Okumura with Extension Therefore, in order to make FAFFA be applicable in real, we need more improvement Student: Trinh Xuan Dung Page 41 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan 4.2 Dimension MAP In table 4.1 and 4.2, we can see that FAFFA at least several minutes to compute the received field for path In real situation, we have a dimension map and we need to compute FAFFA for thousand paths If we use FAFFA, we need several thousand minutes to compute the received field for whole map This calculation time is quite large and impractical Therefore, we have developed a fast implementation for FAFFA in 2D map 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 Figure 4-4: Fast Implementation of FAFFA on Dimension Map At first, we compute the induced current J1 on Path_1 using FAFFA method Then we will compute induced current J2 on Path_2 using J1 Finally, we compute the received field on Path_2 using J2 The result is sketched in figure 4.5 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 200 400 600 800 1000 1200 Figure 4-5: Result of Fast Implementation of FAFFA on 2D Map In figure 4.5, we compare the received field on Path_2 computed by FAFFA with that computed by using the induced current J1 We can see the “enhanced method” has especially good result with the points near the transmitter While the points move far from transmitter, the result is also good However, when the terrain has a fast variation of height, the received field computed by “enhanced method” is not robust Student: Trinh Xuan Dung Page 42 Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan In terms of calculation time, the complexity of computation on Path_2 becomes O(N) This makes the computation time on Path_2 decrease from several minutes to less than second This is a huge improvement and it makes FAFFA be practical However, this is a tradeoff When we decrease the computation time, the error raises In order to save the calculation time without increase of error, I suggest following methods: - Method 1: This method is rather simple We recognize that the “enhanced method” has especially good result with the points near the transmitter Therefore, we can apply the “enhanced method” for all points near the transmitter The points which are far from the transmitter will use FAFFA normally This method is illustrated in figure 4.6 Terrain Information 60 50 H eight (m ) 40 30 20 10 0 1000 2000 3000 4000 5000 distance (m) 6000 7000 8000 Figure 4-6: A suggestion to reduce error of “enhanced method” - Method 2: This method is more complicated to implement We see that the “enhanced method” becomes inaccuracy as the terrain has a fast variation in height Therefore, we will apply the FAFFA for the points that have fast variation in height For other points, we will apply the “enhanced method” This method is illustrated in figure 4.7 Terrain Information 60 50 H eight (m ) 40 30 20 10 0 1000 2000 3000 4000 5000 distance (m) 6000 7000 8000 Figure 4-7: Another suggestion to reduce error of “enhanced method” By applying these methods, we can save the calculation time and not make the error increase Student: Trinh Xuan Dung Page 43 ... power of all points in the map to compute the coverage map The problem of coverage map calculation turns into problem of received field computation Propagation models are developed to compute. .. the propagation models for rural area Student: Trinh Xuan Dung Page Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan Some softwares have been developed to. .. Page ii Application of Propagation Models to compute coverage map Instructor: Dr Conor Brennan ABSTRACT Integral Equation (IE) method is a deterministic method to compute the UHF terrain pathloss