A STUDY OF THE EFFECTS OF PHYSICAL ENVIRONMENT ON CAMPUS WIRELESS NETWORKS: A CASE STUDY OF UNIVERSITY OF NIGERIA NSUKKA [LIONET].

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1 A STUDY OF THE EFFECTS OF PHYSICAL ENVIRONMENT ON CAMPUS WIRELESS NETWORKS: A CASE STUDY OF UNIVERSITY OF NIGERIA NSUKKA [LIONET]. A PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF MASTER OF ENGINEERING (M.ENG) IN ELECTRONIC ENGINEERING (COMMUNICATION OPTION) BY NWAWELU, UDORA NWABUOKU PG/M.ENG./09/51008 UNIVERSITY OF NIGERIA, NSUKKA FACULTY OF ENGINEERING DEPARTMENT OF ELECTRONIC ENGINEERING MAY,

2 APPROVAL PAGE This is to certify that the project entitled A Study of the Effects of Physical Environment on Campus Wireless Networks: a Case Study of University of Nigeria Nsukka [Lionet] was submitted to the Department of Electronic Engineering, University of Nigeria Nsukka, for the award of Degree of Master of Engineering, (M. Eng.) in Telecommunication Engineering. 2

3 DEDICATION TO: God almighty, the comforter of the afflicted and my beloved parents Mr. & Mrs. E.C. Nwawelu who taught me that learning never ends. 3

4 ACKNOWLEDGEMENTS My gratitude goes to God Almighty for His awesomeness, whose by His approval this work saw the light of the day. I will like to express my gratitude to my supervisor, Professor A.N. Nzeako, for his excellent guidance and teaching, in the course of the research. It has been a great privilege and rewarding experience to work under him. I extend my heart-felt gratitude to Dr. G.C.E. Mbah of Department of Mathematics, University of Nigeria, Nsukka. Despite his engagements, he squeezed out time to look into my work and made his contributions. My thanks go to Dr. Mrs. Nwadinigwe of Botany Department of the University of Nigeria, Nsukka. My special thanks go to the management and staff of the Centre for Basic Space Science, University of Nigeria, Nsukka for their technical support, the staff of M.I.S and Database Centre of the University of Nigeria, Nsukka for providing me with all the necessary information needed in the course of this research. My thanks also go to all the staff of the Department of Electronic Engineering of the University of Nigeria Nsukka and my colleagues for providing me with assistance. I thank my lovely parents Mr. E. C. and Mrs. N. F. Nwawelu, for providing me with abundant love, encouragement, and advice. Thank you Engr. and Mrs. I. F Okafor for your generous love and help throughout this sojourn. My special thanks go to Eze Nkeiru for all her encouragement and prayers throughout this sojourn. My unreserved gratitude goes to Mr. Daniel Okoh for his excellent guidance in the course of learning MATLAB programme. I thank in a special way Engr. M. A. Ahaneku for his contribution towards the successful completion of this research. I thank my brothers and sisters for their moral and financial supports. Finally, time would not permit me to mention all that have been in one way or other contributed to the successful completion of this research, all I have to say is thank you million times. 4

5 ABSTRACT Campus environment of the University of Nigeria, Nsukka, is characterized by the existence of ornamental trees, massive buildings and other man made infrastructures. This work studied the effects of physical environment (trees and buildings) obstructions on the Lionet in Nsukka campus of the University of Nigeria. The effects of these obstructions were measured by the variation in path loss and received signal strength as functions of distance using computer simulation and field measurement. The simulation results were compared with the field measurement results, conducted under free space condition and where the Lionet signal was obstructed by trees and buildings. The results show that trees and buildings have significant effects on the path loss and the received signal strength of the Lionet. The study therefore recommends that the power level of the Lionet should be improved for efficient performance, more access points should be deployed at locations where obstructions are prevalent, and Lionet should possibly migrate from wireless to fibre optic network. 5

6 TABLE OF CONTENTS Approval Page Dedication Acknowledgements Abstract Table of Contents List of Figures List of Tables i ii iii iv v ix xi CHAPTER ONE: INTRODUCTION Introduction Background to the Study Aim of the Study Statement of Problem Significance of the Study Limitations of the Study 4 CHAPTER TWO: LITERATURE REVIEW Introduction Overview of Electromagnetic Waves Electromagnetic Wave Theory The Poynting Vector Radio Wave Effects Reflection Reflection from Dielectrics Brewster Angle Diffraction Scattering Absorption Review of Free-Space Path Loss Prediction Review of Propagation Models Okumura Model Hata Model 17 6

7 2.8.3 Durkins Model Walfisch-Bertoni Model PCS Extension to Hata Model Attenuation Factor Model Longley-Rice Model Radio Signal Transmission through a Tree Radio Signal Transmission through a Building 21 CHAPTER THREE: MODEL DEVELOPMENT Introduction Suggested Tree Path Loss Propagation Model Expectation Value of the Total Cross Section Method of Obtaining the Expectation Value of the Total Cross Section Suggested Building Path Loss Propagation Model Free Space Loss Model Building Loss Factor Penetration Losses Method of Obtaining the Window Penetration Loss Method of Obtaining Parameters for the Penetration Losses Indoor Losses Distance Dependence Losses 43 CHAPTER FOUR: THE SIMULATION AND EXPERIMENTS Introduction Path Loss Flow Chart Models Simulation Method of Simulating the Tree Path Loss Method of Simulating the Building Path Loss Experimental Setup and Measurements 51 CHAPTER FIVE: RESEARCH RESULTS AND DISCUSSIONS Introduction Presentation of Results 54 7

8 5.1.1 Free Space Path Loss Model Suggested Tree Path Loss Model Suggested Building Path Loss Model Results Presentation and Discussion Simulated Path Loss as a Function of Transmitting and Receiving Antennas Distance for the Models Simulated Received Power Level in db as a Function of Transmitting and Receiving Antennas Distance for the Models Measured Received Power Level in db as a Function of Transmitting and Receiving Antennas Distance under Free Space, and Non Line-of-Sight Condition Measured Path Loss in db as a Function of Transmitting and Receiving Antenna Distance under Free Space, and Non Line-of-Sight Condition Comparison of the Simulated Results with Practical Field Data of the Path Loss for the Three Scenarios Comparison of the Simulated Results with Practical Field Data for the Received Power Level in db for the Three Scenarios Statistical Analysis of Results Statistical Analysis of Variation in Path Loss with Distance at Frequency of 2400 MHz Statistical Analysis of Variation in Received Power Level with Distance at Frequency of 2400 MHz 70 CHAPTER SIX: CONCLUSION AND RECOMMENDATIONS Conclusion Recommendations Limitations of the Study Suggestions for Further Work 75 REFERENCES 76 Appendix A 81 Appendix B 82 Appendix C 84 Appendix D 86 8

9 Appendix E 91 Appendix F 96 9

10 LIST OF FIGURES Figure 1.0: Aerial view of the University of Nigeria Nsukka. Figure 2.0: Spectrum of Electromagnetic Waves. Figure 2.1: Schematic Representation of Radio Wave Effects Figure 2.2: Geometry for calculating reflection coefficients between two dielectrics Figure2.3: Axes for orthogonal polarized components. Parallel and perpendicular components are related to the horizontal and vertical spatial coordinates. Wave is shown propagating out of the page toward the reader. Figure 2.4: Scattering of electromagnetic wave by a scatterer. Figure 2.5: Transmission between two Antennas. Figure 3.0: Access Point Sited Close to a Tree within the Campus. Figure 3.1: Geometry of Tree Canopy Volume. Figure 3.2: Incident wave on a Single Leaf or a Single Branch of the Tree Canopy. Figure 3.3: Access Point Sited Close to a Building within the Campus. Figure 3.4: Geometry of Lionet Signal Transmission through a Building. Figure 3.5: Configuration for Lionet Signal Penetrating the Glass Window. Figure 3.6: Configuration for Lionet Signal Penetrating the Wall. Figure 4.0: Flow Chart of the Computer Simulation for the Path Loss Prediction. Figure 4.1: Free Space Condition. Figure 4.2: Obstruction of Lionet Signal by a Single Tree. Figure 4.3: Obstruction of Lionet Signal by a Building. Figure 5.0: Plots of Simulated Path Loss with Distance for the Three Models at Frequency of 2400 MHz. Figure 5.1: Plots of Simulated Received Power Level with Distances for the Three Models at Frequency of 2400 MHz. Figure 5.2: Plots of the Measured Received Power Level with Distance for the Three Scenarios at Frequency of 2400 MHz. Figure 5.3: Plots of the Measured Path Loss with Distances for the Three Scenarios at Frequency of 2400 MHz. Figure 5.4: Plots of the Simulated and Measured Path Loss with Distances for the Three Scenarios at Frequency of 2400MHz. Figure 5.5: Plots of the Simulated and Measured Received Power with Distance for the Three Scenarios at Frequency of 2400 MHz. 10

11 LIST OF TABLES Table 3.1: The Number of Leaves and Branches per Unit Volume of a Tree Canopy. Table 3.2: Summary of the Window Penetration Loss Parameters and Formulas. Table 3.3: Summary of the Wall Penetration Loss Parameters and Formulas. Table 5.0: Results of the Simulated Path loss under Free Space Condition and under the Effect of a Single Tree or a Building at Frequency of 2400 MHz. Table 5.1: Results of the Simulated Received Power Level under Free Space Condition and under the Effect of a Single Tree or a Building at Frequency of 2400 MHz. Table 5.2: Measured Received Power Level as a Function of Distance between the Transmitting and Receiving antennas under Free Space, and where the Lionet signal is obstructed by a Single Tree or a Building. Table 5.3: Results of the Measured Path loss under Free Space and the effect of a Single Tree or Building at Frequency of 2400 MHz. Table 5.4: Simulated and Measured Path loss under Free Space and the effect of a Single Tree or Building at Frequency of 2400 MHz. Table 5.5: Simulated and Measured Received Power Level under Free Space and the effect of a Single Tree or Building at Frequency of 2400 MHz. Table 5.6: Summary of the Descriptive Statistics for the Variation of Path Loss with Distance at Frequency of 2400 MHz. Table 5.7: Summary of Post Hoc Tests on the Variation of Path loss at different Distances at Frequency of 2400 MHz. Table 5.8: Summary of Homogeneous Subset Tests on the Variation of Path Loss under Free Space, Effect of a Tree or Building at Frequency of 2400 MHz. Table 5.9: Summary of Correlations of Path Loss under Free Space, Effect of a Tree or Building with Distance at Frequency of 2400 MHz. Table 5.10: Summary of the Coefficients of Path loss under Free Space, Effect of a Tree or Building with Distance at Frequency of 2400 MHz. Table 5.11: Summary of the Descriptive Statistics for the Variation of Received Power Level with Distance at Frequency of 2400 MHz. Table 5.12: Summary of Post Hoc Tests on the Variation of Received Power Level at different Distances at Frequency of 2400MHz. Table 5.13: Summary of Homogeneous Subset Tests on the Variation of Received Power Level under Free Space, Effect of a Tree or Building at Frequency of 2400 MHz. 11

12 Table 5.14: Summary of Correlations of Received Power Level under Free Space, Effect of a Tree or Building with Distance at Frequency of 2400 MHz. Table 5.15: Summary of the Coefficients of Received Power Level under Free Space, Effect of a Tree or Building with Distance at Frequency of 2400 MHz. 12

13 1.0 Introduction CHAPTER ONE INTRODUCTION Wireless communication system refers to any system that uses electromagnetic waves to transfer information from one point to another without using wires [1]. In communication systems where antennas are used to transmit information from one point to another, the medium between (and around) the transmitter and receiver has a major influence on the quality and performance of the transmitted signal. This is because radio wave propagation is very sensitive to the properties and effects of the medium located between the transmitting and the receiving antennas [2]. The presence of trees or buildings in the path of the communication link is expected and usual. This will have significant effects on the quality of the received signal besides other attenuating factors such as the terrain. Therefore, the establishment of a reliable link between antennas of wireless systems is often desired while having to deal with path loss due to obstructions existing in the vicinity [3]. Moreover, the characteristics of trees such as growth over time will affect the condition of the link even if the link is performing well at the moment. Removing all the obstructing trees or buildings is an unrealistic solution. This scenario is that of the dilemma encountered in the deployment of a campus wireless communication networks in the University of Nigeria, Nsukka. The University of Nigeria Nsukka is located in Enugu State. Its land mass is about hectares in an asymmetrical shape lying to the Northeast of Nsukka town [4]. The bulk of the buildings in the campus occupy the Western half of the site leaving the gently slopping valley, lying between the Northeast and Southern hills relatively free of buildings. These areas are the three covered hills at the extreme Northern tip of the campus, the large hill to the Northeast and the Northern slopes of the hill to the South [4]. There are many ornamental trees which add aesthetic values to the campus environment. Figure 1.0 shows the aerial view of the University of Nigeria, Nsukka. 13

14 Figure 1.0: Aerial view of the University of Nigeria Nsukka. [Google TM 2011] Buildings are the main source of signal attenuation but vegetation elements such as trees can also have some reducing effects on a propagating radio signal. When a radio signal impinges on obstacles such as vegetation, buildings or hills, it can be absorbed, reflected, diffracted, or refracted. In the case of radio wave propagation between antennas that are located on heights, it will in principle be the tree canopy that affects the attenuation. For the trees, their appearance in the path of the communication link has significant effects on the quality of the received signal. This is because, discrete scatterers of the tree such as the randomly distributed leaves, twigs, branches and tree trunks can cause attenuation, scattering, diffraction, and absorption of the radiated propagating waves [5]. Foliage can introduce attenuation, broadening of the beam and depolarization of the electromagnetic waves [2]. The transmission losses through trees are functions of the frequency of transmission, dielectric constant, density, size and shape of the vegetation, transmit and receive antenna heights, and the transmit and receive antenna separation distance [6]. Also, transmission losses through buildings are functions of the frequency of transmission, the type of construction materials used, transmit and receive antenna heights, the internal layout of the building, and the transmit and receive antenna separation distance [7]. To have a campus wireless networks with good quality of service (QoS) parameters, it must be designed carefully from the very beginning. The design process of a campus wireless network will be to determine the access point (AP) location and frequency plan, both of 14

15 which are chiefly dependent on the environmental and climatic characteristics of the service area [8]. 1.1 Background to the Study In campus environment where the presence of ornamental trees, buildings and other man made infrastructure are expected and usual, indiscriminate positioning of access points (AP) without proper site survey may likely results to poor signal reception. The same applies to the University of Nigeria Nsukka whose topography has been described extensively in section 1.0; the poor signal reception is due to the obstruction of the radio wave (Lionet signal) by the trees, buildings e.t.c. which have different refractive indices. This affects the signal strength that would be received by the individual client in various areas of the service area. For the trees, Lionet signal propagating through them is attenuated because of absorption of power by the leaves and branches. There are also losses in the transmitted waves due to scattering of power out of the beam by the components of the tree canopy. For the buildings, scattering, absorption and diffraction of the Lionet signal when it interacts with the buildings may be the main cause of signal degradation and fluctuation. Because the propagated Lionet signal is being obstructed by trees and buildings, the signal is thus prevented from covering the maximum expected range. Effects of vegetation and buildings on the transmitted radio signal have been studied. Most researches show that vegetations and buildings have significant effects on the received signal strength and path loss [6][9][10]. The present study is motivated by the undesirable poor signal reception, loss of data packets, and delay in uploading and downloading of data, frequently experience from the radio wave signal transmitted by the Lionet within the University environment. 1.2 Aim of the Study The objective of this research is to develop an empirical propagation model for the University of Nigeria Nsukka wireless network (Lionet), for predicting the path loss and received signal strength of the Lionet; also to proffer solutions on ways of improving the quality of the Lionet signal in the presence of trees or buildings for its efficient performance. 15

16 1.3 Statement of Problem As campus wireless network is becoming the preferred network option which enhances staff and student s mobility in the IT driven environment, poor reception of its signal has made network experts to study the factors that contribute to the network impairment. Although Lionet stands out as cost effective, installation and configuration flexible, but the quality of service (QoS) and the efficient performance of such wireless network are affected by the presence of physical environment between (or around) its communication path. Preliminary investigations around the Lionet access points revealed that the subscribers usually receive the signal better around the trees nearer to the access points. This is evidence that the propagated Lionet signal is being obstructed by trees and buildings, thus preventing it from covering its maximum expected range. Since the presence of trees and buildings affect the quality of the received signal, it is therefore necessary to properly account for these effects in the design of a new radio communication link by the radio frequency (RF) experts. 1.4 Significance of the Study The result obtained from this research will serve as a reference to all the campus wireless network designers in; a. Planning and designing a reliable radio link for campus wireless network, by determining the power level and the signal strength of the received signal within the service area. b. Proper determination of the site location, number of access points (AP), and signal coverage within the service area. c. Suggesting possible ways of improving the quality of their signals in terms of increased power level in areas where physical environment causes signal attenuation. 1.5 Limitations of the Study This research is limited to the effects of trees and buildings on the Lionet operating at transmission frequency of 2400 MHz, and for a maximum distance of 100 meters away from the Lionet Access Point (AP). Although there are other environmental and climatic factors that can attenuate the Lionet signal such as rain, wind, terrain profile, and other manmade structures. 16

17 6.0 Introduction CHAPTER TWO LITERATURE REVIEW In this chapter, overview of electromagnetic wave is presented. Phenomena of radio wave effects and propagation are reviewed. The free space propagation model is reviewed. Some of the propagation models are reviewed, which include; Longley-Rice Model, Okumura Model, Durkin s Model, Hata Model, PCS Extension to Hata Model, Walfisch and Bertoni Model, and Attenuation Factor Model. Finally, transmission of radio signal through a tree and building are reviewed. 2.1 Overview of Electromagnetic Waves Electromagnetic waves are produced as a result of the oscillation or acceleration of an electric charge. This oscillation or acceleration creates a wave which has both an electric and a magnetic component [11]. Figure 2.0, shows electromagnetic spectrum, ranges from gamma rays to radio waves. Figure 2.0: Spectrum of Electromagnetic Waves [11]. 17

18 2.1.1 Electromagnetic Wave Theory From the principle of electromagnetism, change in the electric field is accompanied by a change in the magnetic field, and vice versa. These phenomena were described in 1865 by James Clerk Maxwell in four equations, which have come to be known as the Maxwell equations [11]. The four Maxwell equations in the general form are [1]; x H = μ 0 J + ε 0 dd dt x E = db dt (2.1) (2.2). B = 0 (2.3). D = ρ ε 0 (2.4) Where H = H r, t is magnetic field intensity, r is the position vector, t is the time, and the bar under the variables is the symbol for a three-dimensional vector. The other vector field quantities are the electric field intensity, E r, t, electric flux density, D r, t, and magnetic flux density, B r, t, J and ρ are current density (a vector) and volume charge density respectively, ε 0 is the permittivity of free space, and μ 0 is permeability of free space The Poynting Vector Poynting vector is a quantity that defines the power density (W/m 2 ) associated with an electromagnetic field. Considering an electromagnetic field E, H, the magnitude and direction of the rate of transfer of electromagnetic energy at all points in space is quantified by the Poynting vector given as [11]; S = E x H (2.5) The Poynting vector is very important in propagation, absorption and scattering problems of electromagnetic waves. For time-harmonic fields, S is a rapidly varying function of frequency. With regards to the rapid oscillations of the Poynting vector, it is more convenient to apply the time-averaged Poynting vector for time-harmonic fields. This is written as [11]; S av = 1 2 Re E x H 2.6 Where H denotes the complex conjugate of the magnetic field vector. For isotropic condition, the propagation power is directed perpendicular to the electric and magnetic field. Equation 2.6 is a general formula for computing the average power density of a propagating electromagnetic wave. 18

19 2.2 Radio Wave Effects Radio waves are subject to the influence of the environment in which they are propagated. When a radio wave impinges on an obstruction, some of the energy can be reflected back into the initial medium, some may be transmitted into the second medium, some may be absorbed by the medium, some may be diffracted and some may be scattered. The interaction of radio waves with the environment causes multipath fading at a specific location and the strength of the signal received decreases as the distance between the transmitter and receiver increases. Figure 2.1 is the schematic representation of radio wave effects. Incident wave Scattering Reflected waves Absorption Transmitted waves Figure 2.1: Schematic Representation of Radio Wave Effects [11]. Reflection occurs when a propagating electromagnetic wave impinges upon an object whose dimensions are large compared to the wavelength of the propagating wave. The radio wave could be reflected by any kind of obstacle, such as mountains, vehicles, aircraft, and buildings [12]. Diffraction occurs when the radio path between the transmitter and the receiver is obstructed by a surface that has irregularities. This gives rise to a bending of waves around the obstacle, making it possible to receive the signal even when a line-of-sight path does not exists between the transmitter and the receiver. At high frequencies, diffraction, like reflection, depends on the geometry of the object as well as the amplitude, phase, and polarization of the incident wave at the point of diffraction [12]. 19

20 Scattering is the redirection of electromagnetic energy by the target. It occurs when the medium through which the wave travels consists of a large number of objects whose dimensions are small compared to the wavelength. Objects such as leaves and branches from trees, traffic signs, and rough surfaces will spread out the energy in all directions [12]. Absorption occurs when the radio signal passes into a medium like large buildings and foliage which are not totally transparent to radio signals [13]. When a radio wave strikes the obstacle, part of the radio signal energy is dissipates as heat. 2.3 Reflection When a radio wave propagating in one medium impinges upon another medium having different electrical properties, the wave is partially reflected and partially transmitted. If the plane wave is incident on a perfect dielectric, part of the energy is transmitted into the second medium and part of the energy is reflected back into the first medium, and there is no loss of energy in absorption. If the second medium is a perfect conductor, then all incident energy is reflected back into the first medium without loss of energy. The electric field intensity of the reflected and transmitted waves may be related to the incident wave in the medium of origin through the Fresnel reflection coefficient (Г). The reflection coefficient is a function of the material property, and generally depends on the wave polarization, angle of incidence and the frequency of the propagating wave [6]. In general, electromagnetic waves are polarized, meaning they have instantaneous electric field components in orthogonal direction in space. A polarized wave may be mathematically represented as the sum of two spatially orthogonal components, such as vertical and horizontal, or left-hand or right- hand circularly polarized components. For an arbitrary polarization, superposition may be used to compute the reflected fields from a reflecting surface [14]. 20

21 2.3.1 Reflection from Dielectrics E i E r E i E r H i H r H i H r θ i θ r Ԑ 1,μ 1,ζ 1 θ i θ r Ԑ 1,μ 1,ζ 1 θ t Ԑ 2,μ 2,ζ 2 θ t Ԑ 2,μ 2,ζ 2 E t E t (a) (b) Figure 2.2: Geometry for calculating reflection coefficients between two dielectrics [8]. (a) E-field parallel in the plane of incidence. (b) E-field normal to the plane of incidence. Figure 2.2 shows an electromagnetic wave incident at an angle θ i with the plane of the boundary between two dielectric media. As shown in the figure, part of the energy is reflected back to the first media at an angle θ r, and part of the energy is transmitted (refracted) into the second media at an angle θ t. The nature of reflection varies with the direction of polarization of the E-field. The behavior for arbitrary direction of polarization can be studied by considering the two distinct cases shown in figure 2.3. The plane of incidence is defined as the plane containing the incident, reflected, and transmitted rays. In figure 2.2a, the E-field polarization is parallel with the plane of incidence (that is, the E-field has a vertical polarization, or normal component, with respect to the reflecting surface) and in figure 2.2b, the E-field to the plane of incidence (that is, the incident E-field is pointing out of the page towards the reader, and is perpendicular to the page parallel to the reflecting surface). In figure 2.2, the subscripts i, r, and t refer to the incident, reflected, and transmitted fields respectively. Parameters ε 1, μ 1, and ζ 1, and ε 2, μ 2, and ζ 2 represent the permittivity, permeability, and conductance of the two media, respectively. Often, the dielectric constant of a perfect (lossless) dielectric is related to a relative value of permittivity, ε r, such that ε = ε 0 ε r where ε 0 is a constant given by 8.85 x F/m. If a dielectric material is lossy, it will absorb power and may be described by a complex dielectric constant given by 21

22 where ε = ε 0 ε r j ε * (2.7) ε = ζ 2πf (2.8) and ζ is the conductivity of the material medium measured in Siemens/meter. The terms ε r and ζ are generally, dependent on the operating frequency of the wave. Because of superposition, only two orthogonal polarizations need be considered to solve general reflection problems. The reflection coefficients for the two cases of parallel and perpendicular E-field polarization at the boundary of two dielectric are given by [8]. Г parallel = E r E i = η 2 sinθ t η 1 sinθ i η 2 sinθ t + η 1 sinθ i (2.9) where Г is the reflection coefficient for E-field parallel in plane of incidence. Г perpendicular = E r E i = η 2 sinθ i η 1 sinθ t η 2 sinθ i + η 1 sinθ t (2.10) where Г is the reflection coefficient for E-field normal to the plane of incidence. where η i : is the intrinsic impedance of the i th medium (i = 1, 2 ) and is given by μ i ε i, the ratio of electric field for a uniform plane wave in the particular medium. The velocity of the electromagnetic wave is given by 1 μ ε, and the boundary conditions at the surface of incidence obey Snell s law which, referring to figure 2.2, is given by μ 1 ε 1 sin(90 θ i ) = μ 2 ε 2 sin(90 θ t ) (2.11) The boundary condition from Maxwell s equations are used to derive equations (2.9), (2.10), as well as equations (2.12), (2.13) and (2.14) θ i = θ r 2.12 And E r = ГE i (2.13) E t = (1 + Г)E i (2.14) Where, Г is either parallel or perpendicular, depending on whether the E-field is in vertical or normal horizontal to the plane of incidence. For the case when the first medium is free space and μ 1 = μ 2, the reflection coefficients for the case of vertical and horizontal polarization can be simplified to; Г parallel = ε rsinθ i + ε r cos 2 θ i (2.15) ε r sinθ i + ε r cos 2 θ i 22

23 And Г perpendicular = sinθ i ε r cos 2 θ i sinθ i + ε r cos 2 θ i (2.16) For the case of elliptical polarized waves, the wave may be broken (depolarized) into its vertical and horizontal E-field components and superposition may be applied to determine transmitted and reflected wave. In the general case of reflection and transmission, the horizontal and vertical axes of the spatial condition may not coincide with the perpendicular and parallel axes of the propagating waves. Parallel Vertical axis Perpendicular θ Horizontal axis Figure 2.3: Axes for orthogonal polarized components. Parallel and perpendicular components are related to the horizontal and vertical spatial coordinates. Wave is shown propagating out of the page toward the reader [6]. An angle θ measured counter-clock wise from the horizontal axis is defined as shown in figure 2.3 for a propagating wave out of the page (towards the reader). The vertical; and horizontal field components at a dielectric boundary may be related by [14]; E H d E V d = RT D C R E H i E V i (2.17) where, E d H and E d V are the depolarized fields components in the horizontal and vertical i i directions respectively, E H and E V are the horizontally and vertically polarized components of the incidence wave, respectively, E d H, E d i i V, E H and E V are time varying components of the E-field which may be represented as phasors. R is a transformation matrix which is perpendicular and parallel to the plane of incidence. The matrix R is given by [14]; 23

24 cosθ. sinθ R = sinθ. cosθ where θ is the angle between the two sets of axes, as shown in figure 2.4. The depolarization matrix D c is given by; D perp..0 D c = 0. D para Brewster Angle The Brewster angle is the angle at which no reflection occurs in the medium of origin. At Brewster's angle, the reflected light is completely polarized Perpendicular to the plane of incidence. The transmitted ray contains all of the Parallel component and about 85% of the perpendicular component. Brewster's angle, θ B depends on the indices of refraction of the incident medium and the reflecting medium. It occurs when the incident angle θ B is such that the reflection coefficient Г (parallel ) is equal to zero. The Brewster angle is given by the value of θ B which satisfies [15]; sin θ B = ε 1 ε 1 + ε When the first medium is free space and the second medium has a relative permittivity ε r, equation (2.18) becomes; sin θ B = ε 1 1 ε r Diffraction Diffraction describes the amount that a radio signal propagates around and over an obstruction. Depending on the severity of the diffraction, the radio signal may be impaired. As a general rule of thumb, the larger the obstruction the greater the diffraction, or rather attenuation [16]. The phenomenon of diffraction can be explained by Huygens, principle, which states that all points on a wavefront can be considered as point sources for the production of secondary wavelength and that these wavelets combine to produce a new wavefront in the direction of propagation [8]. 24

25 2.5 Scattering Scattering is accompanied by absorption. Scattering of light is a fundamental factor in our visual perception of the world. Our perception of phenomenon such as the blue sky, rainbows, clouds, snow, fog, milk, red sunsets, and white paint are examples of the influence of scattering. It removes energy from a beam of light traversing the light. If light traverses a perfectly homogenous medium, it is not scattered. Only inhomogeneities cause scattering. The most important property of the scattered wave is its intensity. By intensity, it means the flux per unit area i.e. the total energy flux in this solid angle [17]. The actual received signal in a mobile radio environment is often stronger than what is predicted by reflection and diffraction models alone. This is because when a radio wave impinges on a rough surface, the reflected energy is spread out in all directions due to scattering [15]. Objects such as lamp posts and trees tend to scatter the energy in all directions, thereby providing additional radio energy at a receiver [8][15]. Figure 2.4 illustrates the scattering of incident wave. Scattered wave Incident wave Scattering angle Scatterer Figure 2.4: Scattering of Electromagnetic Wave. The roughness of such surface often induces propagation effects different from the specular reflection. Surface roughness is often tested using the Rayleigh criterion which defines a critical height (h c ) of surface protuberances for a given angle of incidence θ i, given by [3]; h c = λ 8sin θ i (2.20) A surface is considered smooth if its minimum protuberance h is less than h c and is considered rough if the protuberance is greater than h c. For rough surface, the flat surface reflection coefficient needs to be multiplied by a scattering loss factor, ρ s, to account for the diminished reflected field. The surface height h is a Gaussian distributed random variable with a local mean and found ρ s to be [3]; 25

26 ρ s = e 8 πδ h sin θ i λ 2 (2.21) where δ h is the standard deviation of the surface height about the mean surface height. The scattering loss factor derived above was modified to give better agreement with measured results, and is given found as [3]; ρ s = e 8 πδ h sin θ i λ 2 I 0 8 πδ h sin θ i λ 2 (2.22) where I 0 is the Bessel function of the first kind and zero order. The reflected E-fields for h > h c can be solved for rough surface using modified reflection coefficient given as; Г rough = ρ s Г (2.23) 2.6 Absorption Absorption of radio wave can be described as the way energy is taken up by a medium. The energy is transformed to other forms of energy for example, to heat. Usually, the absorption of waves does not depend on their intensity, although in certain conditions (usually, in optics), the medium changes its transparency dependently on the intensity of waves going through [18]. There are number of ways to quantify how quickly radio wave is absorbed in a certain medium, for example: (1) Absorption coefficient Attenuation coefficient, which is sometimes but not always synonymous with absorption coefficient. Absorption cross section and scattering cross section are closely related to absorption coefficient and attenuation coefficient, respectively. Extinction, which is equivalent to the attenuation coefficient. (2) Penetration depth and Skin depth. (3) Propagation constant, attenuation constant, and complex wave number. (4) Complex refractive index and extinction coefficient. (5) Complex dielectric constant. All these quantities measure, at least to some extent, the same thing, how well a medium absorbs radiation. However, practitioners of different fields and techniques tend to conventionally use different quantities drawn from the list above [18]. 26

27 2.7 Review of Free Space Path Loss Prediction Free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight path between them. The model predicts that the received power decays as a function of the transmitter-receiver separation distance raised to some power (i.e. a power law function) [19]. The antennas at each end of a path direct the electromagnetic energy towards each other as shown in figure 2.5. z Recieving antenna direction of propagation Ø y θ Pointing direction of antenna x Figure 2.5: Transmission between two Antennas [1]. The equation for free space propagation between two antennas is given by the Friis transmission equation [20]; P R P T = G T G R λ 2 4πR 2 g T θ, g R θ, (2.24) where, P T = Transmitted power P R = Received power G T = Transmitting antenna gain G R = Receiving antenna gain λ = Wavelength of the electromagnetic wave d = distance between the antennas g T θ, g R θ, = Relative directive gains at the spherical angles (θ, ) measure from the pointing direction of each antenna with a convenient reference direction. 27

28 The transmission loss (free space path loss) equation is often expressed in decibels: P R = P T G TG R λ 2 4πR 2 g T θ, g R θ, (2.25) 10log 10 P R = 10log 10 P TG T g T G R g R λ 2 4πR 2 (2.26) P R = P T + G T + g T + G R + g R + 20log 10 λ 20log 10 R 22 (2.27) The basic transmission loss is just the free-space loss, which is the loss between two isotropic antennas. 2.8 Review of Propagation Models Below are the reviews of some propagation models which can be employed on wireless communication systems Okumura Model The Okumura model is one of the most widely used models for signal prediction in urban areas. This model is applicable for frequencies in the range, 150MHz to 1920MHz and distances of 1 km to 100 km. it can be used for base station antenna heights ranging from 30 m to 1000 m [8]. The Okumura model is formally expressed as: L = L FSL + A MU H MG H BG K correction (2.28) Where, L is the median path loss in (db), L FSL is the free space loss in (db), A MU is the median attenuation in (db), H MG is the mobile station antenna height gain factor, H BG is the base station antenna height gain factor, and K correction is the correction factor gain (such as type of environment, water surface, isolated obstacles etc.) [21]. Furthermore, Okumura found that H BG varies at the rate of 20 db/decade and H MG varies at the rate of 10 db/decade for heights less than 3m. H BG = 20 log H B 200 For 30m < H BG < 100m For H M 3m H MG = 10 log H M 3 H MG = 20 log H M 3 (2.29) (2.30) (2.31) 28

29 Okumura s model is very practical and has become a standard for system planning in modern land mobile radio system. The disadvantages of Okumura s model are: it is slow in response to rapid changes in terrain, the model is based on measured data and does not provide analytical explanation, and it does not provide a means to measure the free-space loss. However, any standard method for calculating the free space loss can be used [21] Hata Model Hata model is an empirical model derived from a technical report by Okumura so that the result could be in computational model [15]. It is the most widely used radio frequency propagation model for predicting the behavior of cellular transmissions in built up areas. This model incorporates the graphical information from Okumura model and develops it further to realize the effects of diffraction, reflection and scattering caused by city structures [22]. This model is valid from 150 MHz to 1500 MHz. Hata presented the urban area propagation loss as a standard formula and supplied correction. The standard formula for median path loss in urban areas is given as [23]; L 50 (urban) = logfc 13.82log h te a(h re )f + ( log h te )log d (2.32) Where fc is the frequency (in MHz) from 150 MHz 1500 MHz; h te is the effective transmitter antenna height (in meters) from 30 m to 200 m, h re is the effective receiver antenna height (im meters) ranging from 1 m to 10 m, d is the T-R, separation distance (Km) and a(h re ) is the correction factor for effective mobile antenna height which is a function of the size of the coverage area. For a small to medium sized city, the mobile antenna correction factor as [8]; a(h re ) = 1.1 log f c 0.7 h re 1.56logf c 0.8 db (2.33) and for a large cities, it is given by; a(h re ) = 8.29 log1.5h 2 re db (2.34) for f c 300 MHz a(h re ) = 3.2 log11.75h 2 re 4.97 db (2.35) for f c 300 MHz To obtain the path loss in a suburban area, the standard Hata formula in equation (2.32) is modified as; L 50 db = L 50 urban 2 log (f c

30 and for the path loss in open rural areas, the formula is modified as; L 50 db = L 50 urban 4.78 logf 2 c logf c (2.37) This model is well suited for large cell mobile system, but not personal communications, which have cells on the order of 1 km radius. Though based on the Okumura Model, the Hata model does not provide coverage to the whole range of frequencies covered by Okumura Model. Hata model does not go beyond 1500 MHz while Okumura provides support for up to 1920 MHz Durkins Model Durkins model adopts a propagation prediction approach similar to that of Longley-Rice [24]. The models consist of two parts; (1) Ground profile: Which is reconstructed from topographic data of proposed surface along radial joining transmitter and receiver Which models LOS & diffraction derived from obstacles & local scatters Which assume all signal received along radial (no multipath) (2) Expected path loss calculated along the radial By moving receiver location to deduce signal strength contour By being pessimistic in narrow valleys By identifying weak reception areas well The disadvantages of Durkin s model are that it cannot adequately predict propagation effects due to foliage, buildings, other than ground reflection, so additional loss factor are often included [6] Walfisch-Bertoni Model The Walfisch-Bertoni model is used widely for predicting the average path loss for mobile systems in urban areas. It considers the impact of rooftops and building height by using diffraction to predict average signal strength at street level [25]. The model considers the path loss (db) S, to be a product of three factors. Path loss = S = P 0 Q 2 P 1 (2.38) where; P 0 represents freespace Path Loss between isotropic antennas given by 30

31 P 0 = λ 4πR 2 (2.39) The factor Q 2 gives reduction in rooftop signal due to row of buildings that immediately shadow hill. P 1 is based on diffraction and determines signal loss from roof top to street [25]. The path loss is given in (db) as; where; S db = L 0 + L rts + L ms (2.40) L 0 represents the free space loss L rts represents the rooftop-to-street diffraction and scatters loss and L ms denotes multiscreen diffraction loss due to the rows of buildings [26] PCS Extension to Hata Model The Cost-231 model was formed by European Co-operative Scientific & Technical (EUROCOST). It extend Hatas model to 2GHz [23]. It has been used extensively in typical sub-urban environment where the building heights are quasi-uniform. Designers of public mobile radio system (e.g GSM, PCS etc) often use the model. This model also takes into account free space loss, loss due to diffraction down to the street, and the street orientation factor. The model for path loss is given in equation (2.41), [27]. L 50 (urban)(db) = logf c logh te (h re ) + ( h te )logd + C M (2.41) Where, h re is defined as in equations (2.15), (2.16), (2.17). For medium sized cities, C m = 0dB, for metropolitan centers C M = 3dB. The COST-231 extension of the Hata Model is restricted to the range of parameters f c = frequency from 1500MHz - 2GHz h te = 30m-200m h re = 1m-10m d = 1km-20km Attenuation Factor Model Attenuation Factor Model is an indoor site specific propagation model that includes effect of building type and variations caused by obstacles by and have been used to accurately deploy in door and campus network [24][28][29]. The models reduced the standard deviation for path loss to 4dB as compared to the standard deviation for path loss with log distance model which is 13dB. The attenuation factor model is given by; 31

32 PL db = PL d 0 db + 10n sf log d + FAF db + PAF db (2.42) d 0 Where, n SF is the exponent value for same floor measurement, FAF represents floor attenuation factor for different floors, and PAF represents partition attenuation factor for obstruction encountered by primary ray tracing [24] Longley-Rice Model The Longley-Rice model is applicable to point-to-point communication systems in the frequency range from 40 MHz to 100 GHz, over different kinds of terrain. This model is particularly useful in predicting propagation losses over irregular terrain for which knife-edge diffraction losses are significant. The model predicts long-term median transmission loss over irregular terrain relative to free space transmission loss [30]. Longley-Rice model accounts for transmission losses (Path Loss) associated with a number of factors, which include; free space path loss, losses due to scattering and diffraction effects, path geometry of the terrain profile, the refractivity of the troposphere and diffraction losses over isolated obstacles. Thus, A TL = L F + A Diff + A Sca + G ht + G hr where, A TL = Transmission loss [db] L F = Free space path loss [db] A Diff = Attenuation due to diffraction [db] A Scat = Attenuation due to scattering [db] G ht, G hr = Height of transmitting and receiving antennas with gains respectively (Terrain heights) km The Longley-Rice model operates in two models. A model for predictions over an area and a model for point-to-point link predictions. A model for prediction over an area is used when terrain path profiles are not available while a point-to-point link prediction is used when detailed terrain profile or path specific parameters are known. One of the shortcomings of the Longley-Rice model is that it does not account for losses due to environmental factors, such as the losses contributed by the existence of buildings and vegetation particularly between two antennas [6][30]. 32

33 2.9 Radio Signal Transmission through a Tree A vegetation canopy tree is a bounded medium consisting of many discrete, randomly distributed and oriented, dielectric inclusions (branches, leaves e.t.c.) in a homogeneous background material (air). Tree canopy consist of an ensemble of leaves and branches. Leaves are modeled as thin lossy dielectric disks and branches as finite lossy dielectric cylinders [32]. From the standpoint of radio wave propagation, trunks, leaves, and branches of individual tree scatter or absorb electromagnetic waves [1][5][32][33][34][35]. Numerous studies on the effects of vegetation on the transmitted wave signals have been done. Propagation measurements through vegetation over a range of frequencies have been accounted in the rain forests of India between MHz, through a single tree between 1 and 4 GHz, in a forested urban park between 0.9 and 1.8 GHz, in various foliage and weather condition between 2 and 60 GHz [36]. The effects of vegetation on GSM signal propagation in rural areas has been studied [6]. The signal degradation due to tree shadowing was found to be between 11 and 16 db [36]. Also, the study on the fading characteristics of RF signals due to foliage in frequency bands from 2 to 60 GHz showed that, RF propagation through trees between 2 and 60 GHz is strongly frequency and wind speed dependent [10]. In [37], study on the influence of trees on radio channel at frequencies of 3 and 5 GHz has been done. It was found that the excess path loss was between 1 and 16 db. These are evidence that the effects of trees are significant on the path loss and received power level. The transmission losses through vegetation are affected by various parameters such as the number and species of trees along the path, transmit and receive antenna height, transmit and receive antenna distance, transmission frequency, dielectric constant, density, physical size and shape of the vegetation [1][38][39] Radio Signal Transmission through a Building A great number of authors have studied the transmission of radio signal through a building. From the information collected to predict the attenuation suffered by radio signals transmitted through a building, most existing models treat the buildings as being completely opaque to radio signals [7]. This means that the amount of radio signal, which could be received from transmitter after traversing a building, is negligible. According to [40][41], it has been found that this is not a valid assumption in some cases. In [40], the possibility of transmission through buildings could produce an over-estimation of the shielding provided by a building, 33

34 which will result in the possibility of unexpected interfering events occurring. In [41], the field strength measured behind a building could be seriously underestimated because as was said above, the models developed to predict the field strength in the shadow of a building tend to assume the building to be an impenetrable obstacle. Also, loss as a result of transmission of radio wave through building is often significant behind the building obstructing the line-of-sight (LOS) to the base station antenna [42][43][44],. For the measurements carried out in the residential areas and homes for the transmission frequency in the 5.85 GHz band, building penetration attenuation was reported at an average of 14 db [36]. 34

35 3.0 Introduction CHAPTER THREE MODEL DEVELOPMENT In this chapter, a mathematical model is developed for the path loss prediction of the Lionet signal transmission through a tree. This model accounts for the contribution of absorption and scattering of radio signals by the canopy of a single tree. Also a mathematical model is developed for prediction of the attenuation suffered by the Lionet signal transmitted through a building. The models developed for the purpose of this research are based on the information obtained from Longley-Rice propagation model. 3.1 Suggested Tree Path Loss Propagation Model Figure 3.0 is a photograph of an access point sited close to a tree at the Nsukka campus of the University of Nigeria. Figure 3.0: Access Point Sited Close to a Tree within the Campus. 35

36 Path loss prediction of Lionet signal passing through a tree includes; free space loss plus tree loss factor (L tree ). The tree loss factor is included in the model to account for the increase in attenuation of the received signal when the receiver is placed behind a tree. The expression for the path loss from the transmitting antenna to a receiving antenna in the presence of a tree is written as [36]; PL tree = L FS + L t 3.1 where; PL tree = Path loss in the presence of a tree. L FS = Free space loss. L t = Tree loss factor. The overall geometric representation of the event is shown in figure 3.1. P i P a P s H t Access Point r P r Receiving antenna H r Figure 3.1: Geometry of tree Canopy Volume. A tree canopy is modeled as a hemispherical volume, which contains randomly distributed and oriented branches and leaves that fill most of the canopy space. In this research, branches are modeled as circular cylinders while the leaves are modeled as thin disks [32]. The branches in the tree canopy are classified into five size categories denoted as N b. The number 36

37 of leaves and branches are represented by n l and n b respectively, where the subscript b is an element of b 1, b Nb and b N is used to denote branches of the nth size category. Attenuation of radio wave propagating through a tree is primarily due to scattering and absorption caused by both leaves and branches. Though trunks also have some influence on the attenuation, the surface area occupied by the trunks is much smaller than that of the leaves and branches of the tree and are at a height lower than the antenna heights. Thus, the loss due to the trunk as a result of diffraction was considered negligible [39]. Some assumptions made while trying to reduce the complexity of the model include: Loss due to the trunk as a result of diffraction is considered negligible [39]. The tree is so tall that there is no diffraction. The leaves are assumed to be identical and homogenous Multiple scattering is negligible. The tapered nature of the individual branches is neglected. The geometry of the propagation model is illustrated in figure 3.1. As illustrated in the figure, access point of height H t radiates a spherical wave that can reach a client at a height H r behind a tree, r is the separation distance between the transmitting and the receiving antenna, P i corresponds to the power emitted (incident power) from the transmitting antenna, P r is the received signal strength (received power level) by the receiving antenna, P s and P a correspond to the power scattered and power absorbed by the elements of the tree canopy. From figure 3.1, the power balance in the volume is; P i = P r + P s + P a (3.2) For brevity, P l = P s + P a (3.3) where P l is the total power loss by the elements of the tree canopy, therefore; P i = P r + P l (3.4) For a sphere of radius r with center at the ray intersection, the beam subtends an area A on the sphere surface. The solid angle is given by [45]; Ω = A r 2 (3.5) The infinitesimal element of solid angle can also be written in terms of elementary area da on any surface. The element of solid angle is; 37

38 dω = da r 2 (3.6) The incident power P i is readily related to power density S(r), the magnitude of the timeaverage pointing vector as [6]; P i = S av r A = S av (r)nr 2 dω (3.7) Here n is the normal of the first surface and r 2 dω is the surface area where dω is the differential solid angle, dω = sinθ dθd. Since the symmetry is spherical, the projection of the average power density is written as [39]; S av r = S av r n (3.8) In order to simplify the notation, the average power density will be represented as S r instead of S av r. Therefore the average power density is written as; P i = S r r 2 dω (3.9) The received power level can be written as [39]; P r = S r + dr (r + dr) 2 dω 3.10 As the incident power travels downwards in the tree canopy, it undergoes both absorption and scattering by the leaves and branches of the canopy [6]. The loss contributed by randomly oriented leaves and branches that fill most of the canopy space, reduce the potential for the radio waves getting to the receiving antenna. The power loss as a result of both absorption and scattering for a single leaf or branch is; P l = P i ( ζ s l,b + ζ a l,b ) (3.11) The power loss contributed by the scattering and absorption of incident power by the leaves, represented by their number n l and branches classified into N b different size categories represented by their number n b per unit volume is: P l = P i n l ζ s l + ζ a l + n b ζ s b + ζ a b b=b 1,.,b N b dv (3.12) Superscripts b and l refer to leaves and branches of the canopy. For brevity, n l ζ s l + ζ a l + n b ζ s b + ζ a b b=b 1,..,b N b = ς η Therefore equation (3.12) becomes; P l = P i ς η dv (3.13) In order to calculate the volume of the tree canopy, the element of volume of the sphere is given as [46][47]; 38

39 dv = dr rdθ r sinθ d (3.14) dv = r 2 sinθ dθ d dr (3.15) where sinθ dθd = dω Equation (3.15) simplifies as; dv = r 2 drdω (3.16) Substituting equation (3.16) into equation (3.13), we have; P l = P i ς η r 2 drdω (3.17) Substituting equation (3.9), (3.10) and (3.17) into equation (3.2), we have; S r r 2 dω = S r + dr r 2 dω + S r ς η r 2 drdω (3.18) Dividing equation (3.18) by dω, we have; S r r 2 = S r + dr r 2 + S r ς η r 2 dr (3.19) Dividing equation (3.19) by dr, we have; This simplifies as; S r r 2 S r + dr r2 = + S r ς η r 2 (3.20) dr dr Integrating, we have This simplifies as; S r + dr r 2 S r r 2 + S r ς η r 2 = 0 dr (3.21) d dr S r r2 = S r ς η r 2 (3.22) d dr S r = S r ςη (3.23) ds r S r = ςη dr (3.24) ln S r = ς τ r + c (3.25) S r = exp ( ς τ r + c) (3.26) S r = De ςη r (3.27) where D = S iso r is the emitted power density in a spherical wave generated by an isotropic antenna with a time-average transmitted power P t, [1]. S iso r = P t 4πr 2 (3.28) where, 4πr 2 = Area of a sphere. Substituting equation (3.28) into equation (3.27) we have; 39

40 S r = P t 4πr 2 e ςη r, r 0 (3.29) For realistic antenna, the radio wave is not only transmitted in the desirable direction but also in other less desirable direction. A commonly used parameter to measure the overall ability of an antenna to direct radiated power in a given direction is their directive gain [39]. It is the ratio of the energy propagating in the specified direction to the energy that would have been transmitted in that direction by an isotropic antenna. For the power coming out from a point source, the radiated energy will move in the direction pointed to by the antenna and with an angle of directivity relevant to the propagation wavelength and antenna [48]. S r, θ, = P t 4πr 2 G Dt θ, (3.30) Substituting equation (3.30) into equation (3.29), we have; S r, θ, = P te ςη r 4πr 2 G Dt θ,, r 0 (3.31) At the receiving end, the power level of the radiated signal collected is subjected to the receiver antenna s effective area. The effective area A eff θ, of a receiving antenna is the ratio of the average power delivered to a matched load to the time average power density of the incident electromagnetic wave at the antenna [48]. Thus, P L = A eff S (3.32) where P L is the maximum average power transferred to the load (under matched condition) with the receiving antenna properly oriented with respect to the polarization of the incident wave [49]. The directivity of an antenna has its relationship with the effective surface area of the antenna (receiver) as; G Dr θ, = 4π λ 2 A eff θ, (3.33) where, λ = wavelength = c f Solving for A eff, we have; A eff θ, = G Dr θ, λ 2 4π (3.34) By multiplying the transmitted time average power density of (3.32) with the receiving antenna s effective area, A eff θ,, an expression for the received power can be obtain as [50]; 40

41 P r = P te ςη r 4πr 2 G Dt A eff (3.35) Substituting equation (3.34) into equation (3.35), we have; P r = P tλ 2 G Dt G Dr 4πr 2 e ςη r, r 0 (3.36) A desirable property during transmission between two antennas is that the ratio between the transmitted and received power should be as high as possible. In order to achieve such, the transmitting antenna and receiving antenna are directed to have the maximum value of the directive gain. Therefore equation (3.37) is restated as; P r P t = λ2 D t D r 4πr 2 e ςτ r, r 0 (3.38) where D t and D r are the directive gain of the transmitting and receiving antenna. The equation (3.38) can only be employed when the leaves and branches occupied all spaces between the transmitting and receiving antenna. To get a more realistic expression for the attenuation of the emitted radio wave, we considered a case whereby the radio signal traversed estimated number of leaves and branches before getting to a receiver i.e, some part of the distance between the two antennas consists of free space. If the total distance between the transmitting and receiving antennas is r and the radio signal traversed estimated number of leaves and branches of a tree canopy, the improved formula of equation (3.38) becomes P r P t = λ2 D t D r 4πr 2 e ςτ, r 0 (3.39) Transforming equation (3.39) into decibels and expressing it in the path loss form yields; PL tree [db] = 10 log P t P r = 10log 4πr 2 λ 2 D t D r e ςτ (3.40) Since n l ς s l + ς a l + n b ς s b + ς a b = ς τ, we have; b=b 1,..,b N b PL tree [db] = 10 log P t P r Let = 10log 4πr 2 λ 2 D t D r e n l ς s l + ς a l + n b ς s b + ς a b b=b 1,..,b N b (3.41) ς s l + ς a l = ς tl ς s b + ς a b = ς tb 41

42 Therefore equation (3.41) reduces to; PL tree db = 10 log P t P r = 10log 4πfr 2 c 2 D t D r e n l ς tl + n b ς tb b=b 1,...,b N b (3.42) where; P t = Transmitted power (w) P r = Received power level (w) r = Distance from the transmitter antenna to the receiver antenna m f = Frequency of transmission (MHz) c = Velocity of light in air = (m/s) D t = Directive gain of the transmitting antenna. D r = Directive gain of the receiving antenna. N b = Branches of different size categories n l = Number of leaves of the tree canopy n b = Number of branches of the tree canopy ς tl = Cross section of a single leaf ς tb = Cross section of a single branch From equation 3.42 an expression for the attenuation of a tree canopy (tree loss factor) was found from [39], L t = 10 log e n l ς tl + n b ς tb b=b 1..b N b n l ς tl + n b ς tb b=b 1..b N b (3.43) 3.2 Expectation Value of the Total Cross Section Cross section is a quantity that shows the ability of an object to scatter or absorb incident power density [39]. The total cross section ( ς t ) is the sum of the cross section due to absorption and scattering of incident power density by a single leaf and a single branch. It is written as; ς t = ς tl + ς tb (3.44) The value of total cross section depends on canopy attributes such as size, shape, dielectric properties of leaves and branches, and orientation of leaves and branches in relation to the direction of the propagation of radio wave [32][48][51]. For the purpose of this research, we 42

43 Pi assumed that the total cross section is a function of orientation angles, the number of leaves and branches, the size of the leaves and branches, and the shape of the leaves and branches. To shade light on how we obtained the mean value of the total cross section of leaves and branches of the tree canopy, figure 3.2 shows the interaction of incident power with a single leaf or a single branch. Z V i m, n H v θ ϕ X Y Figure 3.2: Incident Wave on a Single Leaf or a Single Branch of the Tree Canopy. The orientation of leaves and branches determine how radio wave is being intercepted and absorbed as it traverses the tree canopy. For the orientation angle of the leaves and branches with respect to the reference frame, we used two variables (θ, ϕ) to describe it. where; θ = Elevation orientation angle of leaves and branches of the tree canopy. ϕ = Azimuthal orientation angle of leaves and branches of the tree canopy. The normal of the disc is denoted by n and the symmetry axis of the cylinder by m. From figure 3.2, the normal vector which also is valid for the symmetry axis of the cylinder can be written as; n = X cos θ cos ϕ Y cos θ sin ϕ + Z sinθ (3.45) Method of Obtaining the Expectation Value of the Total Cross Section Analysis was carried out on a tree standing between the Lionet communication path at the campus of the University of Nigeria Nsukka. The following parameters and method of obtaining them are described. In a hemispherical tree canopy of leaves and branches with varying orientations, the general expression for the expectation value of total cross section of a single leaf and a single branch of the tree canopy is 43

44 ϕ 2 θ 2 ς t = ς t θ, ϕ f l,b Ω θ, ϕ dω (3.46) ϕ 1 θ 1 where dω = cosθ dθ dϕ is the solid angle, f Ω l,b θ, ϕ equals the probability density function for the azimuthal and elevation orientation angle of the leaves and branches of the tree canopy. Aiming at obtaining the expectation value of the leaves and branches of a tree canopy, we calculated the total cross section for different orientations of the leaves and branches. Based on the fact that leaves and branches in the canopy are randomly placed, we employed a statistical based approach to characterize the leaves and branches of the canopy. This relation takes the form of probability density function. The probability density for the leaves and branches in the azimuthal coordinate ϕ is assumed to be uniformly distributed over the tree canopy volume from 0 ϕ < 2π. Also, the probability density for the leaves and branches in elevation coordinate θ is considered to be uniformly distributed. For the purpose of this study, we assumed a uniform probability function of the form; f θ l,b θ = 1 θ 2 θ 1, if θ 1 < θ < θ 2 0, otherwise (3.47) Elevation and azimuthal orientation angle of leaf in the tree canopy: None of the leaves in the tree canopy were found to exhibit a preferred azimuthal orientation angle; also the leaves have no preferred elevation orientation angle. Thus, the cross sections of the leaf are averaged over ϕ and θ with 0 ϕ < 2π, f ϕ l ϕ = 1, π 2 θ < π 2, f θ l θ = 1. The mean cross section of a single leaf of a tree canopy is 2π π 2 ς tl = ς tl θ, ϕ f θ l θ f ϕ l ϕ cosθ dθ dϕ 0 π 2 (3.48) Substituting f ϕ l ϕ = 1 and f θ l θ = 1 into equation (3.48), we have 2π π 2 ς tl = ς tl θ, ϕ cosθ dθ dϕ (3.49) 0 π 2 Elevation and azimuthal orientation angle of the branch in the tree canopy: None of the branches of the tree were found to exhibit a preferred azimuthal orientation angle; also the branches have no preferred elevation orientation angle. Thus, the cross-sections of the branch 44

45 are averaged over ϕ and θ with 0 ϕ < 2π, f ϕ b ϕ = 1, π 2 θ < π 2, f θ b θ = 1. The mean cross section of a single branch of a tree canopy is 2π π 2 ς tb = ς tb θ, ϕ f θ b θ f ϕ b ϕ cosθ dθ dϕ 0 π 2 (3.50) Substituting f ϕ b ϕ = 1 and f θ b θ = 1 into equation (3.50), we have 2π π 2 ς tb = ς tb θ, ϕ cosθ dθ dϕ 0 π 2 (3.51) By combining equation (3.49) and (3.51) for the case of mean cross section of a single leaf and a single branch of a tree canopy; we obtain an expression for the equivalent cross section of the leaves and branches of the tree canopy as; n ς eq = n l ς tl + n b ς tb (3.52) b=b 1 As previously said, the cross section of a single leaf and a single branch are ς tl and ς tb ; the number of leaves and branches of a tree canopy are n l and n b ; and b = b 1, b 2,.. b n is the number of branches of different size categories. In order to get an estimated value of the number of leaves and branches per unit volume of the tree canopy, the number of branches grouped into five categories and the number of leaves that are attached to the individual branch are counted. The estimated number of leaves and branches with their corresponding radius and length/thickness per unit volume of the tree canopy is listed in the table 3.1. Table 3.1: The Number of Leaves and Branches per Unit Volume of a Tree Canopy. Scatterer Type Radius (m) Length/thickness (m) Number Branch 1 = b Branch 2 = b Branch 3 = b Branch 4 = b Branch 5 = b leaf

46 3.3 Suggested Building Path Loss Propagation Model Figure 3.3 is a photograph of an access point sited close to a building at the Nsukka campus of the University of Nigeria. Figure 3.3: Access Point Sited Close to a Building within the Campus. Path Loss prediction of the Lionet signal passing through a building includes; free-space loss plus building loss factor. The building loss factor is included in the model to account for the increase in attenuation of the received signal when the receiver is placed behind a building. The expression for the path loss from the transmitting antenna to the receiving antenna in the presence of a building is; PL building = L FS + L buiding 3.53 where; PL building = Path loss in the presence of building. L FS = Free space loss. L building = Building loss factor. 46

47 Modeling Lionet signal transmitted through a building involves three steps; the first step relating the output of the Lionet signal from the transmitter to the building, the second step is called an indoor event, and the third step relating the propagation of the signal down to the receiver antenna. The overall geometric explanation of the event is shown in figure 3.4. In the model, a transmitting antenna of height H t radiates rays that can reach a receiving antenna located at a height H r above the ground behind a building. Though there are several paths through which Lionet signal can get to the receiving antenna, but for the purpose of this research, only the signal that passed through the window and wall is considered. Values we used in calculating the building path loss are; the transmission frequency (f) equals 2400MHz, the height of the transmitting antenna (H t ) equals 7m, the height of the receiving antenna (H r ) equals 1.5m, the width of the building (w b ) equals 10m, the distance from the transmitting antenna to the building (d 1 ) is 10m, the distance from the building to the receiving antenna (d 2 ) varies from m, window thickness (t 1 ) equals 0.008m and wall thickness (t 2 ) equals 0.27m. Penetrati on Losses Penetrati on Losses P i d t θ εr, ζ εr, ζ d in θ H t dr Transmitter antenna t t P r θ d 1 w b d 2 r Receiver antenna H r Figure 3.4: Geometry of Lionet Signal Transmission through a Building. In order to model a Lionet signal transmission through a building, we made some assumptions to reduce the complexity of the model. The access point is assumed to be in a transmitting mode, while the receiver is assumed to be in the receiving mode. 47

48 The length of the building is assumed to be infinitely large, so no diffraction effects could happen due to the corners of the building. The building window and wall are made of certain kind of material, which had relative permittivity ε r and conductivity ζ. The height of the building is so high compared to the transmit antenna height, so no propagation over the roof exists. The Lionet signal comes from outside the building, penetrates into it through a window and wall. Likewise the signal going from inside the building to outside. The direction of signal propagation does not change for the signal moving inside the building. The internal layout of the building was not specified. 3.4 Free Space Loss Model The free-space loss between the transmitting antenna and receiving antenna has been derived extensively in section 3.1, and it is given as; P r P t = c2 D t D r 4πfr 2 (3.54) where P t is the transmitted power, P r is the received power, D t and D r are the directivity gains of the transmitting and receiving antenna, r is the transmit and receive antenna distance of separation, c is the velocity of light, and f is the transmission frequency. Transforming equation (3.54) into decibels yields; L FS [db] = 10 log P t P r = 10log 4πfr 2 c 2 D t D r (3.55) 3.5 Building Loss Factor As previously said, building loss factor is included in the model to account for the increase in attenuation of the received signal when the receiver is placed behind a building. Due to the fact that the side of the building we are considering has only two partitions, the Lionet signal here is taken to traversed two paths before getting to the receiving antenna. Assuming the same elevation angle, the signal incident on the window and wall of the building. For the two scenarios, their signal strengths are summed up. The angle that the Lionet signal made with the window and wall is obtained from sin θ = H t H r d t + d in + d r (3.56) 48

49 where H t equals the transmitting antenna height, H r equals the receiving antenna height, d t equals the path length from the transmitting antenna to the building in the direction of signal propagation, d in equals the path length inside the building in the direction of signal propagation, d r equals the path length from the building to the receiving antenna in the direction of signal propagation, and θ equals the incidence angle on the window and wall of the building. For brevity, r which denotes the transmitting antenna and receiving antenna distance of separation is given as; where; r = d 1 + t + w b + t +d 2 (3.57) d 1 = distance from the transmitting antenna to the building, measured in the perpendicular direction from the antenna to the building. t = the thickness of the window and wall. w b = width of the building. d 2 = distance from the building to the receiving antenna, measured in the perpendicular direction from the receiving antenna to the building. From basic Pythagoras theorem, d t + d in + d r = H t H r 2 + r From equation (3.57), expression for the elevation angle is θ = sin 1 H t H r H t H r 2 + r 2 (3.59) Once the elevation angle is known, the expressions that relate the distances d t, d in, and d r with θ are d 1 d t = cos θ w b d in = cos θ (3.60) 3.61 d r = d 2 cos θ (3.62) Building loss factor include; penetration losses, when the radio signal went from outside the building to inside it; indoor losses, losses due to the propagation of radio signal inside the building; penetration losses again, when the signal moved from inside the building to outside; 49

50 distance dependence losses with an exponent equals 2, when the signal passed from the building to the receiving antenna. An expression for the building loss factor is written as: L building = L pen + L in + L pen + L dd (3.63) where; L pen = Penetration losses L in = Indoor losses L dd = Distance dependent losses The description of different losses, which the Lionet signal experienced during transmission from a building down to the receiving antenna, are described in section 3.4.1, 3.4.2, and Penetration Losses Losses as a result of Lionet signal coming from outside to the inside of a building are group into two; window penetration loss and wall penetration loss. These losses were modeled using Fresnel Transmission Coefficient (FTC). This parameter characterizes the level of signal strength coming from outside into the building. From [52], the Fresnel Reflection Coefficient was given as; R s = sin ε r cos 2 (3.64) sin + ε r cos 2 where; Ø = Angle between the reflecting surface and the direction of propagation of the incident or reflected ray. ε r = Complex relative permittivity The angle in equation (3.64) can be related with the elevation angle θ in figure 3.4. When both are expressed in degrees, we have; θ = 90 From equation (3.64), R s as a function of elevation angle, is restated as; R s = cosθ ε r sin 2 θ (3.65) cosθ + ε r sin 2 θ For equation (3.65), the complex relative permittivity used in the equation is written as; ς ε r = ε j ε j60λς (3.66) wε 0 50

51 where; R s = Reflection coefficient. ε r = Relative permittivity, which depends on the type of construction materials of the building. ε 0 = Permittivity of the vacuum ζ = Conductivity, which depends on the type of construction materials of the building. Since value for ε 0 = F/m, the product 60λς will be very small, so it can be negligible. Therefore, the complex relative permittivity becomes; ε r = ε The Fresnel Transmission Coefficient can be derived from the Reflection Coefficient as [52]; T S = R S + 1 (3.67) Substituting equation 3.65 into equation 3.67 we have; T S = cosθ ε r sin 2 θ cosθ + ε r sin 2 θ + 1 (3.68) T S = cosθ ε r sin 2 θ + cosθ + ε r sin 2 θ cosθ + ε r sin 2 θ The expression for the Fresnel Transmission Coefficient becomes; T S = cos θ + 2 cos θ ε r sin 2 θ (3.69) (3.70) By normalization, the dependence of penetration losses with the Fresnel Transmission Coefficient is; L pen = 1 T S 2 (3.71) The penetration losses are the same both when the signal is coming from outside the building, and when is coming from inside to outside of the building due to reciprocity law [52] Method of Obtaining the Penetration Losses As previously said, the side of the building we are considering has only two partitions, therefore the Lionet signal is taken to traversed two paths before getting to the receiving antenna. Thus, we present below a method of obtaining the window penetration loss and wall penetration loss. The parameters needed for the prediction of the building losses have been derived extensively in section 3.4 and

52 Window Penetration Loss The Lionet signal penetrates two windows made of glass before getting to the receiving antenna positioned at a distance away from the transmitting antenna. The window penetration is illustrated in Figure 3.5. dt Window Penetration loss Window Penetration loss Pi θ εr1 εr1 din θ Ht dr Transmitter antenna Pr θ d1 t1 wb t1 d2 r Receiver antenna Hr Figure 3.5: Configuration for Lionet Signal Penetrating the Glass Window. Table 3.2 is the summary of the parameters and formulas employed for predicting the window penetration loss. Table 3.2: Summary of the Window Penetration Loss Parameters and Formulas Parameters θ (degrees) Formulas θ = sin 1 H t H r r (meters) r = d 1 + t 1 + w b + t 1 + d 2 d t (meters) d in (meters) d r (meters) T S1 (dimensionless) d 1 d t = cos θ w b d in = cos θ d r = T S1 = d 2 cos θ cos θ + H t H r 2 + r 2 2 cos θ ε r1 sin 2 θ From the information given in the table 3.1, loss as a result of the penetration of the Lionet signal through a glass window is; 52

53 1 L 1 = 2 T (3.72) S1 where L 1 is the window penetration loss, ε r1 is the relative permittivity of the window made of glass, and T S1 is the Fresnel Transmission Coefficient of the window. Wall Penetration Loss The Lionet signal penetrates two walls made of concrete before getting to the receiving antenna positioned at a distance away from the transmitting antenna. The wall penetration is illustrated in Figure 3.6. P i d t Wall Penetration loss Wall Penetration loss θ εr2 εr2 d in θ H t dr Transmitter antenna P r d 1 t 2 w t 2 d 2 θ r Receiver antenna H r Figure 3.6: Configuration for Lionet Signal Penetrating the Wall. Table 3.3 is the summary of the parameters and formulas employed for predicting the wall penetration loss. 53

54 Table 3.3: Summary of the Wall Penetration Loss Parameters and Formulas Parameters θ (degrees) Formulas θ = sin 1 H t H r r (meters) r = d 1 + t 2 + w b + t 2 + d 2 d t (meters) d in (meters) d r (meters) T S2 (dimensionless) d 1 d t = cos θ w b d in = cos θ d r = T S2 = d 2 cos θ cos θ + H t H r 2 + r 2 2 cos θ ε r2 sin 2 θ From the information given in the table 3.2, loss as a result of the penetration of the Lionet signal through a wall made of concrete is; L 2 = 1 T S2 2 (3.73) where L 2 is the wall penetration loss, ε r2 is the relative permittivity of the wall made of concrete, and T S2 is the Fresnel Transmission Coefficient of the wall. Combining equation 3.72 and 3.73, we have an expression for the penetration losses as; L pen = 1 T S T S2 2 (3.74) Due to reciprocity law, the general expression for the penetration losses is L pen = 2 1 T S T S2 2 (3.75) Method of Obtaining Parameters for the Penetration Losses In order to evaluate the Fresnel Transmission Coefficient, which measures the quantity of the building penetration loss, the relativity permittivity of the materials of interest is considered. Since it is practically impossible to know the exact value of this parameter, suitable values were gotten from literature [53]. Glass has been found to vary strongly with glass composition not with frequency. For glass, its relative permittivity has been found to be 4 [53]. Therefore, the relative permittivity of the 54

55 window made of glass (ε r1 ) is assumed as 4. For the wall made of concrete, the relative permittivity at 1.7 GHz and 18 GHz are 4.62 and 4.11 respectively [53]. From these results, it is obvious that the relative permittivity of the concrete wall does not vary significantly due to frequency changes, therefore the relative permittivity of the concrete wall (ε r2 ) is assumed as Indoor Losses Indoor attenuation is characterized as the losses due to the propagation of radio signal totally inside the building [19]. The expression for the indoor loss which includes the effect of building type as well as the variations caused by obstacles has been shown by many researchers to obey the distance power law [1]. Expression of indoor losses becomes; L in = d t + d in d t n (3.76) n = the path loss exponent value for the same floor measurement, and it depends on the surroundings and the building type. From [7], values of the path loss exponent, n, were found varying between 3.5 and 4.0 for the same floor measurement. Therefore, the model value for the path loss exponent, n, is assumed as Distance Dependence Losses Distance dependence losses are dependent on the distance from the building to the receiving antenna. The path loss dependence with distance from the building to the receiver was chosen equal to 2 as in the case of free-space loss because it obeys power decays law [1][7]. The resultant expression is; where; L dd = propagation. d t + d in + d r d t + d in 2 (3.77) d r = path length from the building to the receiving antenna in the direction of signal By combining equations (3.75), (3.76), and (3.77), an expression for the building loss factor becomes; 55

56 L building = 2 1 T S T S2 2 + d t + d in d t n + d t + d in + d r d t + d in 2 (3.78) Also combining equations (3.56) and (3.79), an expression to predict the path loss that the Lionet signal suffered when transmitted through the building becomes; PL building = P r P t = c2 D t D r 4πfr T S T S2 2 + d t + d in d t n + d t + d in + d r d t + d in 2 (3.79) where; P t = Transmitted power (w) P r = Received power level (w) f = Frequency of transmission (MHz). r = Distance from the transmitting antenna to the receiving antenna (m). c = Velocity of light in air = (m/s). D t = Directivity gain of the transmitting antenna. D r = Directivity gain of the receiving antenna. T s1 = Fresnel Transmission Coefficient of the window made of glass. T s2 = Fresnel Transmission Coefficient of the wall made of concrete. d t = Path length from the transmitting antenna to the building (m). d in = Path length inside the building (m). d r = Path length from the building to the receiving antenna (m). n = Path loss exponent value for the 'same floor' measurement. 56

57 4.0 Introduction CHAPTER FOUR THE SIMULATION AND EXPERIMENTS In the preceding chapter, we derived the models for the prediction of the path loss of Lionet signal transmitted through a tree and building. In this chapter, the flow chart of the computer simulation and the simulation proper are presented. Finally, the experimental setup for the data collection is described. 4.1 Path Loss Flow Chart Figure 4.0 is a flow chart for computer simulation of the path loss for the free space condition, and where Lionet signal is obstructed by a tree and building. Start Input value for the distance & height \ Input value for transmission frequency No Obstacle encountered? Yes Tree identified? No No Yes \ Get tree parameters Is the tree parameter Complete? Yes Process the total cross section of the leaves & branches Building identified? Yes \ Get building parameters Is the building parameter Complete? Yes No No Calculate Path loss \ Output Path loss End Figure 4.0: Flow Chart of the Computer Simulation for the Path Loss Prediction. 57

58 4.2 Models Simulation In sub-section (4.2.1) and (4.2.2), we described an effective procedure employed in simulating the path loss of a Lionet signal propagating through a tree or a building. The code used for the simulation is written in MATLAB. The reason for choosing MATLAB includes; Its commands match very closely to the steps that are used to solve engineering problems. It solves technical computing problems faster than traditional programming languages. It is flexible in processing mathematical expressions Method of Simulating the Tree Path Loss Attenuation of Lionet signal due to the contributions of leaves and branches of the tree canopy could be found by following these steps; Step 1: Evaluation of the Equivalent Value of the Total Cross Section of Leaves and Branches of the Tree Canopy. The equivalent value of the total cross section of leaves and branches of the tree canopy is given as n ς eq = n l ς tl + n b ς tb (4.3) b=b 1 where ς tl equals the cross section of a single leaf, ς tb is the cross section of a single branch, n l is the number of leaves of a tree canopy, n b is the number of branches of a tree canopy, and b = b 1, b 2,.. b n is the number of branches of different size categories. We first evaluate the mean value of cross section of a single leaf from 2π π 2 ς tl = ς tl θ, ϕ f θ l θ f ϕ l ϕ cosθ dθ dϕ 0 π 2 (4.4) The leaf cross section is averaged over angles ϕ and θ with 0 ϕ < 2π, f ϕ l ϕ = 1, π 2 θ < π 2, and f θ l θ = 1. Therefore equation 4.4 becomes 58

59 2π π 2 ς tl = ς tl θ, ϕ cosθ dθ dϕ (4.5) 0 π 2 Since the program has the limitation that it does not generate continuous values of the total cross section, a discrete form of the total cross section will be needed. For the leaves this becomes N 1l N 2l ς tl = ς tl θ i, ϕ j cosθ i (4.6) i=1 j=1 N 1l and N 2l are the sample points on a surface that cover ¼ of a sphere. In this research, N 1l and N 2l were done for 120 points on a surface that cover ¼ of the sphere, i.e in figure 3.2 we took values in the regions 0 < θ < 90 and 0 < ϕ < 90. We obtained the values of the cross sections on the other parts of the sphere due to spherical symmetry in order to calculate the equivalent values of the cross section of the leaves of the entire tree canopy. Next, we evaluate the mean value of cross section of the branches from; 2π π 2 ς tb = ς tb θ, ϕ f θ b θ f ϕ b ϕ cosθ dθ dϕ (4.7) 0 π 2 The branches cross section is averaged over angles θ and ϕ with 0 ϕ < 2π, f ϕ b ϕ = 1, π 2 θ < π 2, and f θ b θ = 1. Therefore equation 4.7 becomes 2π π 2 ς tb = ς tb θ, ϕ cosθ dθ dϕ (4.8) 0 π 2 Since the program has the limitation that it does not generate continuous values of the total cross section, a discrete form of the total cross section will be needed. For the branches this becomes N 1b N 2b ς tb = ς tb θ i, ϕ j cosθ j (4.9) i=1 j=1 N 1b and N 2b are the sample points on a surface that cover ¼ of a sphere. In this research, N 1b and N 2b were done for 30 points on a surface that cover ¼ of the sphere, i.e in figure 3.2 we took values in the regions 0 < θ < 90 and 0 < ϕ < 90. We obtained the values of the 59

60 cross sections on the other parts of the sphere due to spherical symmetry in order to calculate the equivalent values of the cross section of the leaves of the entire tree canopy. Next, we evaluate the equivalent value of the total cross section of the entire tree canopy from n ς eq = n l ς tl + n b ς tb (4.10) b=b 1 In this research we grouped the size of the branches of the entire tree canopy into 5 categories, thus equation 4.10 becomes 5 ς eq = n l ς tl + n b ς tb (4.11) b=b 1 For the practical values we use for the calculation of the equivalent values of the total cross sections of the leaves and branches per unit volume of the tree canopy, see table 1 of chapter 3. Finally, we evaluate the attenuation of the mean value of the total cross section per unit volume of the tree canopy using the expression in equation 3.43; 5 L t = (n l ς tl + n b ς tb ) (4.12) b=b 1 Step 2: Evaluation of the Free Space Loss The free space loss is given as; L FS = 4πfr 2 c 2 D t D r (4.13) Where r equals the distance from the transmitting antenna to the receiving antenna (in meters), f equals the frequency of transmission (in MHz), c equals the velocity of light in air (in m/s), D t equals the directivity gain of the transmitting antenna, and D r equals the directivity gain of the receiving antenna. Next, we multiply the result gotten from the free space loss and result from attenuation of the mean value of the total cross section per unit volume of the tree canopy, i.e; 4πfr 2 c n D t D l ς tl + n b ς tb r 5 b=b 1 60

61 Therefore, the tree path loss converted to decibels (db) is given as; PL tree = 10log 4πfr 2 5 c n D t D l ς tl + n b ς tb (4.14) r b=b 1 For listing of MATLAB code used, see Appendix B Method of Simulating the Building Path Loss An analysis was carried out on a building standing in the path of the Lionet communication link. The necessary parameters and method of obtaining them for the computation of the building path loss are described below. Step 1: Evaluation of the Free Space Loss The free space loss is given as; L FS = 4πfr 2 c 2 D t D r (4.15) where d 1 equals the distance from the transmitting antenna to the receiving antenna (in meters), f equals the frequency of transmission (in MHz), c equals the velocity of light in air (in m/s), D t equals the directivity gain of the transmitting antenna, and D r equals the directivity gain of the receiving antenna. Step 2: Evaluation of the Incidence Angle The incidence angle is given as; θ = sin 1 H t H r H t H r 2 + r 2 (4.16) Where H t equals the transmitting antenna height (in meters), H r equals the receiving antenna height (in meters), r equals the access point and receiving antenna distance of separation (in meters), and θ equals the incidence angle. Step 3: Evaluation of Window Penetration Loss The window penetration loss is given as; 61

62 L 1 = 1 2 cos θ cos θ + ε r1 sin 2 θ 2 (4.17) Where θ equals the incidence angle and ε r1 equals the relative permittivity of the window made of glass. Step 4: Evaluation of Wall Penetration Loss The wall penetration loss is given as; L 2 = 1 2 cos θ cos θ + ε r2 sin 2 θ 2 (4.18) where θ equals the incidence angle and ε r2 equals the relative permittivity of the wall made of concrete. Next, we add L 1 and L 2, i.e; L 1 + L 2 Next we multiply the preceding result by 2, i.e; 2 (L 1 + L 2 ) Therefore, the building penetration losses are; L pen = 2 (L 1 + L 2 ) Step 5: Evaluation of the Indoor Loss The indoor loss is given as; L in = d t + d in d t n (4.19) where d t equals the path length from the transmitting antenna to the building (in meters), d in equals the path length inside the building (in meters), and n equals the path loss exponent value for the 'same floor' measurement. Step 6: Evaluation of the Distance Dependence Loss The distance dependence loss is given as; L dd = d t + d in + d r d t + d in 2 (4.20) 62

63 where d r equals the path length from the building to the receiving antenna (in meters). Step 7: Evaluation of the Building Loss Factor The building loss factor is given as; L building = 2 1 T T d t + d in d t n + d t + d in + d r d t + d in 2 (4.21) Step 8: Evaluation of the Building Path Loss The building path loss is given as; PL building = c2 D t D r 4πfr T T d t + d in d t n + d t + d in + d r d t + d in 2 (4.22) Finally, we transformed the PL building into decibels, i.e; PL building db = 20log 4πfr c + 10log(D t ) + 10log(D r ) 2 20log T log T nlog d t + d in d t + 20log d t + d in + d r d t + d in (4.23) For listing of MATLAB code used, see Appendix C. 4.3 Experimental Setup and Measurements The experimental setup for the prediction of the path loss and received power level under free space condition and where a single tree or a building obstructs the Lionet signal are shown in figures 4.1, 4.2, and 4.3, respectively. At the transmitting section, omni-directional antenna (WBS 2400) with transmitting power of 19 db is mounted at the top of 7m height mast H t. Along the transmission path lays either a tree or a building, which obstructs the Lionet signal as in the case shown in figure 4.2 and 4.3. The receiving section consisted of a spectrum analyzer (SPECTRAN HF 6080) that was connected to a Laptop (HP G62) for data logging, and Uninterruptible Power Supply (UPS) to provide emergency power whenever there is any occurrence of power disruption, which may eventually result in data loss. One of the major concerns with this kind of measurement is ensuring that the signal intercepted by the receiving antenna comes from one access point. To achieve that, we selected an isolated access point by its SSID and MAC Address. 63

64 The access point of interest is partly impeded by a tree and a building as shown in the figures 4.2 and 4.3, while part of the access point is free from any kind of obstruction as shown in the figure 4.0. We measured the received power level with SPECTRAN HF 6080 via an omnidirectional antenna (WBS 2400). The SPECTRAN HF 6080 was adjusted to a frequency of 2400 MHz at sampling rate of 5000 ms. The receiving antenna is directional while the transmitting antenna has no restriction. Finally, from the measured received power level, we obtained the measured path loss for the three scenarios shown in figures 4.1, 4.2, and 4.3. Access Point Receiving Antenna Figure 4.1: Free Space Condition. 64

65 Access Point Receiving Antenna Figure 4.2: Obstruction of Lionet Signal by a Single Tree. Access Point Receiving Antenna Figure 4.3: Obstruction of Lionet Signal by a Building. 65