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Methods for Path Loss Prediction School of Mathematics and Systems Engineering Reports from MSI - Rapporter från MSI Methods for Path loss Prediction Cem Akkaşlı October MSI Report 09067 2009 Växjö University ISSN 1650-2647 SE-351 95 VÄXJÖ ISRN VXU/MSI/ED/E/--09067/--SE Abstract Large scale path loss modeling plays a fundamental role in designing both fixed and mobile radio systems. Predicting the radio coverage area of a system is not done in a standard manner. Wireless systems are expensive systems. Therefore, before setting up a system one has to choose a proper method depending on the channel environment, frequency band and the desired radio coverage range. Path loss prediction plays a crucial role in link budget analysis and in the cell coverage prediction of mobile radio systems. Especially in urban areas, increasing numbers of subscribers brings forth the need for more base stations and channels. To obtain high efficiency from the frequency reuse concept in modern cellular systems one has to eliminate the interference at the cell boundaries. Determining the cell size properly is done by using an accurate path loss prediction method. Starting from the radio propagation phenomena and basic path loss models this thesis aims at describing various accurate path loss prediction methods used both in rural and urban environments. The Walfisch-Bertoni and Hata models, which are both used for UHF propagation in urban areas, were chosen for a detailed comparison. The comparison shows that the Walfisch-Bertoni model, which involves more parameters, agrees with the Hata model for the overall path loss. Keywords: path loss, prediction, wave propagation, rural, urban, Hata, Walfisch-Bertoni. Email: [email protected] Acknowledgments I would like to express my sincere thanks to my supervisor Prof. Sven-Erik Sandström, Växjö University for his support and helpful suggestions for this thesis work. I also would like to express my special thanks to my family and friends. Table of Contents 1. INTRODUCTION .................................................................................................................................. 1 2. THEORETICAL BACKGROUND ....................................................................................................... 2 2.1 RADIATED AND RECEIVED POWER ................................................................................................... 2 2.1.1 Radiated Power .................................................................................................................................... 2 2.1.2 Radiation Resistance and Received Power .......................................................................................... 6 2.1.3 Friis Transmission Equation ................................................................................................................ 7 2.2 PROPAGATION MODELING .................................................................................................................. 10 2.2.1 Overview of Channel Modeling ........................................................................................................ 10 2.2.2 Path loss Models due to Propagation Mechanisms ............................................................................ 14 2.2.2.a Path loss due to reflection and the Two Ray model ................................................................ 14 2.2.2.b Path loss due to diffraction ..................................................................................................... 19 3. PROPAGATION MODELS ................................................................................................................. 28 3.1 PROPAGATION MODELS FOR RURAL AREAS ............................................................................... 28 3.1.1 Deterministic Multiple Edge Diffraction Models ............................................................................ 28 3.1.2 Approximate Multiple Edge Diffraction Models ............................................................................ 30 3.1.2.a The Bullington method ........................................................................................................... 30 3.1.2.b The Epstein Petersen method .................................................................................................. 31 3.1.2.c The Japanese method ............................................................................................................... 32 3.1.2.d The Deygout method............................................................................................................... 33 3.1.2.e The Giovanelli method ............................................................................................................ 33 3.1.3 The Slope UTD method ................................................................................................................... 35 3.1.4 The Integral Equation approach ...................................................................................................... 42 3.1.5 The Parabolic Equation method ...................................................................................................... 48 3.2 PROPAGATION MODELS FOR URBAN AREAS .............................................................................. 52 3.2.1 The Okumura model ....................................................................................................................... 52 3.2.2 The Hata model ............................................................................................................................... 54 3.2.3 The Walfisch - Bertoni model ......................................................................................................... 55 4. SIMULATION ...................................................................................................................................... 63 4.1 The Hata model........................................................................................................................................ 63 4.2 The Walfisch - Bertoni model .................................................................................................................. 64 4.3 Comparison of the Hata model and the Walfisch - Bertoni model .......................................................... 66 APPENDIX A ............................................................................................................................................... 69 APPENDIX B ................................................................................................................................................ 79 APPENDIX C ............................................................................................................................................... 81 APPENDIX D ............................................................................................................................................... 85 REFERENCES ............................................................................................................................................. 89 1. INTRODUCTION In radio propagation channels, spatial and temporal variations of signal levels are usually observed on three main scales. Signal variation over small areas (fast fading), variations of the small area average (shadowing), and variations over very large distances (path loss). Path loss prediction plays a crucial role in determining transmitter-receiver distances in mobile systems [1]. This thesis aims at describing various accurate path loss models that are used in rural and urban areas. In Chapter 2, the theoretical origins of the propagation phenomena and the received power concept are introduced. The difference between the range dependent path loss and fast/slow fading, as well as the basic path loss models are introduced. Basic models are also simulated by using MATLAB. Chapter 3 focuses on describing various accurate models for rural and urban areas, respectively. For the rural case, deterministic and approximate multiple edge diffraction models, as well as models with other approaches, are introduced. For the urban case the Walfisch-Bertoni and the Okumura-Hata models are chosen for a detailed comparison. The Walfisch-Bertoni model is described in detail via MATLAB simulations. A detailed description of the repeated Kirchoff-Integral which is used in this model is given in Appendix A. The standard Hata model is chosen as a reference for the results of the Walfisch-Bertoni model. In Chapter 4, the proposed models are compared for various parameters and simulated in MATLAB. 1 2. THEORETICAL BACKGROUND 2.1 RADIATED AND RECEIVED POWER 2.1.1 Radiated Power From the Maxwell equations for a homogeneous, isotropic, linear and lossless dielectric medium, the magnetic vector potential A can be obtained as [2, 3]: J jkR A e dv' , (2.1.1) 4 v R where, R |r r' | , (2.1.2) is the distance from the source point to the field point. The free space wave number is, k . 00 (2.1.3) Assuming a Hertzian dipole source one has the current as, i( t ) Re{ Ie jt } . (2.1.4) Figure 2.1.1 – The Hertzian dipole. Considering Figure 2.1.1 and replacing Jdv ' in equation (2.1.1) with zˆ Idz' it can be written, I jkR A e dz ' zˆ . (2.1.5) 4 c R Assuming that the current is constant over the infinitesimal length l of the dipole ()Rr , and that the point of observation is far away, one has, 2 Il jkr A e zˆ . (2.1.6) 4r This expression suggests that the wave is propagating radially, in the direction of rˆ , with the phase constant
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