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Document formatted into pages; contains 53 pages. 502 Thesis (M.S.E.E.)University of South Florida, 2008. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 3 520 ABSTRACT: This thesis analyzes the wireless propagation modeling of a 2.6 GHz band channel around the Tampa Bay area. Different empirical models are compared against measured data, and an adapted model, specific for the Tampa Bay area, is presented that builds on the accuracy of existing models. The effects of the propagation characteristics along bridges are also discussed, and a twoslope model is presented. The proposed models are based on a simple linear regression method, and statistical tests are evaluated for reliability thereof. The analysis also investigates the statistical properties of shadowing effects imposed on the wireless channel. The spatial correlation properties of shadowing effects are investigated in detail, and an extension of existing correlation models for shadowing effects is suggested where the correlation properties are studied in different distance ranges rather than the whole service coverage area. 538 Mode of access: World Wide Web. System requirements: World Wide Web browser and PDF reader. 590 Advisor: Huseyin Arslan, Ph.D. 653 Wireless communications Received signal strength Slow fading Spatial correlation Statistical regression 690 Dissertations, Academic z USF x Electrical Engineering Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.2547 PAGE 1 Analysis and Optimization of Empirical Path Loss Mo dels and Shadowing Effects for the Tampa Bay Area in the 2.6 GHz Band by Julio C. Costa A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Department of Electrical Engineering College of Engineering University of South Florida Major Professor: Hseyin Arslan, Ph.D. Wilfrido Moreno, Ph.D. Thomas Weller, Ph.D. Date of Approval: March 21, 2008 Keywords: Wireless Communications, Received Signal Strength, Slow Fading, Spatial Correlation, Statistical Regression Copyright 2008 Julio C. Costa PAGE 2 DEDICATION To God for allowing me in this world, to my family for caring for me, to my friends for showing me things around it, and to my wife for making me a better man. PAGE 3 ACKNOWLEDGMENTS I am forever in debt to Dr. Arslan and the members of the Wireless Communication and Signal Processing Group particularly Hasari Celebi and Serhan Yarkan for their patience and friendship and the knowledge they have shared with me. Dr. Moreno and Dr. Weller have provided me with great feedback for this thesis and I am grateful for their time and insight. I am very thankful for the opportunity my employer Sprint Nextel has given me, and I am very fortunate to work with my colleagues who have provided me with support and perspectives. I am also humbled to acknowledge my family and fri ends for all they have done in my life to get me where I am today. Finally, I thank God for protecting me in the dark est moments of my life. The Lord is my shepherd; I shall not want Psal m 23:16 PAGE 4 i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT vi CHAPTER 1 INTRODUCTION 1 1.1 Motivation 1 1.2 History 2 1.3 Mobile Radio Propagation 2 1.4 Thesis Organization 3 CHAPTER 2 PROPAGATION MODELS 4 2.1 Introduction 5 2.2 Comparison between Deterministic and Empirical Models 6 2.2.1 HataOkumura Model 6 2.2.2 COST231 HataOkumura Model 7 2.2.3 SUI Model 8 2.2.4 CRCPredict and Deterministic Models 9 2.2.5 Model Comparisons 10 CHAPTER 3 EXPERIMENT 14 3.1 Tampa Bay Environment 14 3.2 Equipment Setup 19 3.3 Rayleigh Fading 21 CHAPTER 4 ADAPTED MODELS FOR TAMPA BAY AREA 25 4.1 Introduction 26 4.2 Regression Analysis 26 4.3 Statistical Parameters for Goodness of Fit of Regression Analysis 28 4.4 Results 29 4.4.1 General Results 29 4.4.2 Bridge Analysis and Model for Tampa Bay Ar ea 31 4.4.3 Suburban Environment Analysis and Model fo r Tampa Bay Area 33 4.4.4 Urban Environment Analysis and Model for T ampa Bay Area 36 CHAPTER 5 SHADOWING EFFECTS FOR TAMPA BAY AREA 39 5.1 LogNormal Shadowing 39 5.2 Shadowing Effects Analysis for Tampa Bay Area 41 5.2.1 Data Analysis 41 5.2.2 Discussion 43 5.3 Correlation Property Analysis for Tampa Bay A rea 44 PAGE 5 ii 5.3.1 Spatial Correlation of Shadowing Effects 4 5 5.3.2 Autocorrelation Properties 46 5.3.3 Data Analysis and Discussion 46 CHAPTER 6 CONCLUSION 50 6.1 Contributions 50 6.2 Future Work 50 REFERENCES 52 PAGE 6 iii LIST OF TABLES Table 1 SUI Models numerical values for different terrain (environment) categories. 9 Table 2 Comparison between different models agains t measured data. 12 Table 3 Site antenna heights and model parameters. 30 Table 4 Oneslope vs. twoslope parameters. 33 Table 5 Path loss exponent and intercept for five suburban sites. 34 Table 6 Mean average of path loss exponent and 1 km intercept for suburban sites. 34 Table 7 RMSE comparison between models. 35 Table 8 Path loss exponent comparisons for transm itter located in downtown Tampa. 37 Table 9 RMSE for urban environment sites in Tampa Bay area. 38 Table 10 Standard deviation in dB of suburban site s. 43 Table 11 Standard deviation in dB of urban sites. 43 PAGE 7 iv LIST OF FIGURES Figure 1 Sample of measured data with channel descr iptions. 5 Figure 2 Empirical models are compared against the regression analysis of the measured data. 11 Figure 3 One of the crane mounts setup with transmi tter for data collection. 15 Figure 4 The Tampa Bay area offers very unique char acteristics such as coastal areas. 16 Figure 5 Building layout of downtown Tampa. 16 Figure 6 Typical Tampa Bay suburban area. 17 Figure 7 Bridges link major metropolitan areas in t he Tampa Bay area. 18 Figure 8 Typical commercial area in Tampa Bay area. 19 Figure 9 Typical transmitter setup. 20 Figure 10 The transmitter was calibrated and values were logged prior to data collection. 21 Figure 11 Sample length of data to be filtered. 22 Figure 12 Sample unfiltered data. 23 Figure 13 Sample filtered data. 23 Figure 14 A small sample of the data showing Raylei gh fading characteristics. 24 Figure 15 Typical scatter plot for a transmitter lo cated in a suburban environment. 27 Figure 16 Path loss exponent as a function of anten na height for suburban area. 31 Figure 17 Data from a cell serving a major bridge i n the Tampa Bay area. 32 Figure 18 Downtown Tampa. 36 PAGE 8 v Figure 19 Regression analysis for sites in downtown Tampa. 37 Figure 20 Lognormal distribution of shadowing effe cts. 40 Figure 21 CDF of the shadowing fading components as a normal probability plot. 41 Figure 22 Shadowing effects as a function of distan ce. 44 Figure 23 Normalized autocorrelation plots for ring 1. 47 Figure 24 These rings suggest the existence of corr elation zones. 48 Figure 25 These rings are the farthest away from th e transmitter. 49 PAGE 9 vi ANALYSIS AND OPTIMIZATION OF EMPIRICAL PATH LOSS MO DELS AND SHADOWING EFFECTS FOR THE TAMPA BAY AREA IN THE 2.6 GHz BAND Julio C. Costa ABSTRACT This thesis analyzes the wireless propagation mode ling of a 2.6 GHz band channel around the Tampa Bay area. Different empirical mod els are compared against measured data, and an adapted model, specific for the Tampa Bay ar ea, is presented that builds on the accuracy of existing models. The effects of the propagation characteristics along bridges are also discussed, and a twoslope model is presented. The proposed models are based on a simple linear regression method, and statistical tests are evalua ted for reliability thereof. The analysis also investigates the statistical properties of shadowin g effects imposed on the wireless channel. The spatial correlation properties of shadowing effects are investigated in detail, and an extension of existing correlation models for shadowing effects i s suggested where the correlation properties are studied in different distance ranges rather tha n the whole service coverage area. PAGE 10 1 CHAPTER 1 INTRODUCTION 1.1 Motivation The advent of Internet has changed the way we comm unicate and share information. No less significant has been the ubiquity of cellular telephony around the world, particularly in less developed countries. A new paradigm is emerging th at promises to bring these two technologies together, an advent that can represent business opp ortunities and higher quality of life in the underdeveloped world. The technologies that are pr imed to bring about these changes have been classified as Worldwide Interoperability for Microw ave Access (WiMAX) or Long Term Evolution (LTE) under the umbrella of proposed spec ifications such as beyond 3G or 4G. Even though these specifications have not yet been clear ly defined, one commonality within these stages is the frequency band where these specific t echnologies may be deployed. Therefore it is advantageous to understand how the channel behaves in different environments in order to deploy these new networks in the most cost effective and e fficient manner. This thesis analyzes the behavior of the wireless channel in the 2.6 GHz ban d using data collected from 29 locations around the Tampa Bay area, and it presents an adapt ed model that provides a better fit than existing models for this specific area. We approac h this problem by using a simple linear regression method to describe the path losses of tr ansmitted radio signals in the Tampa Bay area. In addition, shadowing effects are studied and mode led to provide insight into the deployment design of the network as well as in the optimizatio n phase of the system. We then comment on the variance about the mean of the path loss curve and extend on the existing models that describe shadowing effects. PAGE 11 2 1.2 History In August of 1997 Sprint Nextel announced it would invest more then $3 billion over the next two years to build a WiMAX network to reach 10 0 million people in the United States. Sprint Nextel is the largest holder of the 2.6 GHz Broadband Radio Services (BRS) band licenses that cover about 85 percent of the U.S. population. The BRS band is formerly know as the Multipoint Distribution Service (MDS)/Multichannel Multipoint Distribution Service (MMDS). It was originally allocated for the transmission of data and video programming to subscribers using highpowered systems, also known as wireless cable. In October 1997, the International Telecommunicati on Union (ITUR) included WiMAX technology in the IMT2000 set of standards. This decision may help escalate the opportunities of global deployment in both rural and urban market s to deliver high speed mobile Internet services. These services are mostly likely to be d eployed in the 2.6 GHz band. This band is already available for mobile and fixed services in the U.S. Therefore, the motivation to understand the propag ation characteristics of radio link in this band is warranted. In this thesis we will exp lore the mobile radio propagation characteristics and behaviors in the Tampa Bay area. 1.3 Mobile Radio Propagation The basic characterization of the propagation of t he wireless channel can be described as largescale and smallscale fading. Largescale fa ding deals with spatial characteristics of the channels. Basic propagation models indicate that a verage received signal strength (RSS) power decreases logarithmically with distance. These mod els do not take into account the surrounding environment clutter that exists at different locati ons, such as buildings and tress. This leads to a variation of the measured signal about the mean of the predicted RSS at any particular distance between transmitter and receiver. This phenomenon i s known as lognormal shadowing, and it is studied in more detail in Chapter 5. Smallscale f ading, on the other hand, deals with both spatial PAGE 12 3 and temporal characteristics of the radio signal, a nd it describes the rapid fluctuations of the amplitude, phase, or multipath delays of the RSS ov er a short period of time or distance. This thesis deals exclusively with largescale fading of the mobile radio propagation, and Chapter 3 describes how to remove smallscale fading effects from measured data. 1.4 Thesis Organization Chapter 2 discusses and compares existing determin istic and empirical propagation models. Emphasis is placed on the empirical model. Chapter 3 describes how the experiment is setup and how data is manipulated to filter out sma llscale fading. Chapter 4 describes the proposed model for the Tampa Bay area and shares th e statistical analysis for each type of environment. Chapter 5 goes into the shadowing effe ct of the wireless channel in the Tampa Bay area and discusses the second order statistics of t his effect; that is, the spatial correlation properties of shadowing effects. Chapter 6 revisit s the contributions of this thesis and provides future study directions. PAGE 13 4 CHAPTER 2 PROPAGATION MODELS Propagation models are mathematical tools used by engineers and scientists to design and optimize wireless network systems. The main goal i n the design phase of the wireless network is to predict the probability of signal strength or co verage in a particular location, and avoid interference with neighboring sites. In the optimi zation phase the objective is to make sure the network operates as close as possible to the origin al design by making sure handoff points are close to prediction; coverage is within design guid elines such as indoor, incar, and onstreet RSS; and cochannel interference is low at neighbor ing sites. Also, in the optimization phase measured data collected from the live network may b e used to tune the propagation models utilized in the design phase. Although the propagation models used today have be come more sophisticated due to computer advancement, these models are still very s implified versions of the complex characteristics of the electric and magnetic field in the real world. A complete characterization of the electric magnetic field would involve solving v ery complex equations such as Maxwells Equations. 0e r = E (1) 0 = B (2) t = B E (3) t + = E J B 0 0 0e m m (4) PAGE 14 5 The underlying problem would become even more comp lex when taking into consideration all existing propagation mechanisms s uch as reflection, diffraction, and scattering in a very dynamic environment such as a city. Thes e mechanisms can vary significantly from the mean predicted RSS value at any point between trans mitter and receiver. Some of theses variances are characterized by statistical distribu tions such as Rayleigh and lognormal. Consequently, due to the variance and unpredictabil ity of the radio channel, it is not practical to use theoretical solutions to describe the radio cha nnel but rather statistical methods. Figure 1. Sample of measured data with channel des criptions. On the left, all three phenomena of the channel description are inherited in data: p ath loss, shadowing, and smallscale fading. The plot on the right shows the data with smallscale f ading removed. Nonetheless, the current propagation models offer a very efficient and cost effective way for network planning. They are in fact derived fro m the equations of electromagnetic field theory. A summary of the derivation of these relat ions can be found in [1]. 2.1 Introduction There are two main types of propagation models: sl ope based and deterministic. Slope based models are based on empirical formulas, which themselves are based on measured data and the free space propagation model. The free space p ropagation model is used when line of sight between transmitter and receiver exists and can be represented by the Friss free space equation. L d G G P d Pr t t r 2 2 2) 4( ) (p l= (5) PAGE 15 6 Pt is the transmitted power, Pr(d) is the received power which is a function of the separation between the transmitter and receiver, Gt and Gr is the transmitter and receiver gain respectively, d is the distance separation between the transmitter and receiver in meters, L is system loss factor not related to propagation ( L 1), and l is the wavelength in meters. More detailed information about this equation can be fou nd in [1] Deterministic models use raytracing techniques tha t rely on detailed terrain and clutter database to estimate diffraction calculation based on Huygens principles of physical optics [2]. The prediction generated using deterministic models are very computer intensive. But new development in computer speed and algorithm as well as database accuracy has made deterministic models a good choice for propagation tools especially for inbuilding propagation design. 2.2 Comparison between Deterministic and Empirical Mode ls Understanding the limitations of various propagati on models helps engineers achieve good engineering design. For this reason we will d escribe the most common models used today and then we will provide a brief comparison between deterministic and empirical path loss models. 2.2.1 HataOkumura Model The most common used empirical model is the HataOk umura Model. Hata used predicted signal strength curves obtained by Okumur as data collection experiment throughout Japan to create some basic formulas [3]. These pat h loss formulas (in dB) were based on an urban free space propagation model, with correction factors to account for variation in other types of environment such as suburban, and open areas. T he parameter for correction factors includes the base station and mobile antenna heights and cen ter frequency. R h h a h f Lb m b c p 10 10 10 10log ) log 55.6 9. 44( ) ( log 82. 13 log 16. 26 55. 69 + + = (6) PAGE 16 7 Where cfis the frequency in MHz from 150MHz to 1500MHz, bh is the effective transmitter antenna height in meters ranging from 30m to 200m. mhis the effective mobile receiver antenna height in meters ranging from 1m t o 10m. R is the distance between transmitter and receiver in km, and a(hm) is the correction factor for effective mobile ante nna height, which is a function of the size of the coverage area. For a mediumtosmall city the following correction factor is used. )8.0 log 56.1( )7.0 log 1.1( ) (10 10=c m c mf h f h a (7) For a large city the correction factors used are de scribed below. 1.1 ) 54.1 (log 29.8 ) (2 10=m mh h a MHz fc300£ (8) 97.4 ) 75. 11 (log 2.3 ) (2 10=m mh h a MHz fc300 (9) To obtain the path loss for suburban area the follo wing equation is used. 4.5 28 log 2 } {2 10=c p psf Urban L L (10) And to obtain the path loss for an open area, the e quation is below is used. 94. 40 log 33. 18 log 78.4 } {10 2 10+ =c c p pof f Urban L L (11) 2.2.2 COST231 HataOkumura Model An extension to the Hata model described above is t he COST231 Hata model [1]. This model is designed to be used in the frequency band from 500 MHz to 2000MHz. As the Hata Model, the COST231 is restricted to cell radius gr eater than 1 km and may not be suitable for cells on the order of 1km radius. 231COSTPL = ) ( ) ( log 82. 13 ) ( log 9. 33 3. 4610 10 m b ch a h f+ + m bc R h+ 10 10log )) ( log 55.6 9. 44( (12) PAGE 17 8 For a large city the correction factor a(hm) is used below. 97.4 ) 75. 11 (log 2.3 ) (2 10=m mh h a MHz fc400> (13) For suburban or rural areas the correction factor a(hm) is used in the equation below. )8.0 log 56.1( )7.0 log 1.1( ) (10 10=c m c mf h f h a (14) As noted the a(hm) correction factors are the same for both the origin al Hata model as well as the COST231. 2.2.3 SUI Model Another model which is popular for broadband wirele ss communications is the Stanford University Interim (SUI) or Erceg model [4]. It h as been accepted by the IEEE802.16 Broadband Wireless Access Working Group to evaluate fixed wireless applications air interface performance. The main difference from other models is that the path loss exponent is treated as a random variable in addition to the shadowing effect s. The basic path loss equation for this model along with its correction factors are presented bel ow. s X X d d A PLh f+ + + + =0 10log 10g 0d d> (15) The other parameters are defined below. =l p0 104 log 20 d A (16) b bh c bh a+ =g (17) Here d is the distance between transmitter and receiver a nd 0d is the reference distance at 100m from the transmitter. s is a lognormal distributed factor that is used to account for shadow fading. A is modeled as the freespace path loss formula and g is the random variable path loss exponent that is dependent on the base st ation height bh, and the environment category. PAGE 18 9 The environment categories with corresponding model parameter are shown in Table 1. Table 1. SUI Models numerical values for different terrain (environment) categories. Terrain Category A B C Model Parameter (Hilly/ModeratetoHeavy Tree Density) (Hilly/Light Tree Density of Flat/ModeratetoHeavy Tree Density) (Flat/Light Tree Density) a 4.6 4.0 3.6 B (m1) 0.0075 0.0065 0.005 c 12.6 17.1 20 Also, some correction factors for the operating fre quency fX and for the receiver height hX are provided below. =2000 log 0.610c ff X (18) For terrain category types A and B the following eq uation is used. =2 log 8. 1010r hh X (19) For terrain category type C the following equation is used. =2 log 0. 2010r hh X (20) 2.2.4 CRCPredict and Deterministic Models Deterministic models are raytracing techniques bas ed on geometric optics to estimate signal strength at any particular location. These techniques rely on detailed terrain and clutter databases to estimate diffraction calculations base d on Huygens principle of physical optics. A PAGE 19 10 program known as CRCPredicit has been developed, f or the most part, by the Communications Research Centre in Ottawa, Canada [2]. This progra m is based on several parameters characterizing the local environment of the mobile antenna. It numerically solves the integral for Huygens principle and the field can be calculated using the equation below. n n + =rr1 11 1 1 1 1 1 1 2 1 2 2) ( ) ( ) ( 2 ) (hh ikr ikrdz e z x E dz e z x E x x i kx z x ERp (21) Here l p 2=k is the propagation constant, r is the distance from ( x1,z1) to ( x2,z2), rR is the length of the reflected path, and R is he reflection coefficient of the ground. The accuracy of ray tracing in predicting signal st rength has been increased by the growth in computational capabilities and database storage. 2.2.5 Model Comparisons In [5], the author provides a comparison between de terministic and empirical models. The deterministic models show a difference of 0.75d B and 1.46dB between two popular empirical modes, but a difference of 12.6dB when co mpared against the Hata model. This seems to agree with our analysis since the Hata model ana lysis herein provides a pessimist prediction of the path loss as seen in Figure 2. This difference is due to the more simplistic approach of the Hata model, which accounts for only three correctio n factors and excludes terrain profile and clutter absorption losses. The most common way of predicting diffraction losses caused by terrain and buildings is the use of the Knifeedge diffraction model. In this model the losses caused by obstructions are estimated by the using F resnel Zone Geometry solutions. A detailed analysis on this model is presented in [6]. It is worth mentioning that diffraction models are also incorporated along with terrain and clutter databas es, in tools that support empirical models. Figure 2 shows the path loss for comparison for dif ferent empirical models. No deterministic model is shown on the plot. The reas on being is threefold. First, this thesis focuses on empirically formulated models only. Secondly, d eterministic models require terrain and PAGE 20 11 clutter database in order to make a fair comparison Finally, the lack of access to any specific deterministic tool would make fair comparisons very difficult. The mathematical code for these tools is usually closely guarded and an attempt to simulate the deterministic model using a programming language would be impractical. Figure 2. Empirical models are compared against th e regression analysis of the measured data. The deterministic model, at first, seems to be a mo re accurate way of estimating signal strengths. However, the slope model it is still be ing widely used today. For instance, the SUI model is recommended by the IEEE 802.16 Broadband W ireless Access Working Group as the channel model choice for fixed wireless application s. Furthermore, empirical models have become more accurate as parameter correction factor s are discovered and terrain and clutter databases are integrated in these models. An assum ption may then be made that the deterministic approach is more appropriate to an indoor environme nt, and that the slope model is more appropriate for outdoor environment propagation pla nning. In order for any model to offer a PAGE 21 12 complete picture of the propagation characteristics of specific technologies being deployed, all possible parameters such as the frequency and envir onment types of the Tampa Bay area must be studied in detail. For instance, the extended vers ion of the OkumuraHata model, namely COST231, does not support frequencies beyond 2MHz, and the SUI models do not have a profile for urban environment. By the same token, it is imprac tical to collect data that is capable of covering all the possible parameters and environments. It i s feasible, however, to build upon existing models of the unique characteristics of the environ ment being studied, in this case the Tampa Bay area. Table 2. Comparison between different models agains t measured data. SITE mean err std dev err RMSE mean err std dev err RMSE mean err std dev err RMSE A3.34620.03893.34656.91022.01157.190911.3791.2966 11.451 B5.50450.57365.53366.0790.98636.156810.47850.2825 10.4823 C0.381.5881.61610.44033.618811.036814.89212.9066 15.1671 D10.20851.298910.28911.20132.91363.12215.63052.20 56.0381 E8.07270.64958.09822.27662.59463.43066.75141.8788 7.0025 F10.51812.932410.91070.79795.06015.0683.61344.3544 5.6219 G5.25110.40135.2666.15761.21336.273410.58680.5047 10.5985 H2.59920.04932.59968.00161.81898.201312.48581.101 512.5332 I8.34852.64348.74841.71184.67414.92986.16363.9627 .3038 J6.99682.31947.36333.6044.18765.49038.08813.47028 .7863 K4.37061.23474.5385.68860.7965.742810.14030.08381 0.1407 L 7.93271.27918.03293.10113.0124.30027.57292.2966 7.9062 M1.5221.99362.49099.76610.3419.771914.21221.05231 4.2502 N8.67550.60728.69621.04592.73492.90025.45722.0292 5.8146 O4.34570.91434.43882.16443.82374.35755.92833.2216 6.7304 P3.7883.77545.31915.36741.4945.56719.68892.18539. 9271 Q3.14161.47333.463113.74350.394913.749118.22770. 322518.2305 R5.360.42185.376314.16312.794514.430218.41922.11 3618.5375 S2.24620.64422.334913.77332.22213.947518.18321.5 16518.245 T16.19221.848416.29517.58960.57457.61083.37250.1001 3.3739 U16.37123.19716.67377.59355.56969.38123.33734.88885 .8752 V16.00893.378716.35397.40635.80169.36913.18925.1269 5.9904 W14.34830.769514.36855.19411.51195.4050.87260.82061 .1917 X7.36830.97467.43113.28632.81874.30957.7712.10138 .0441 Y8.27242.22168.55932.07684.16674.61496.55173.4509 7.3874 Z10.64492.782210.99480.69114.84394.84053.74934.133 55.5473 AA4.88361.77395.18923.72024.19685.57417.93733.522 28.6681 BB5.48942.29525.94034.2320.16754.23528.64330.8732 8.6864 CC 6.8055 0.008 6.8055 1.7983 2.4149 2.9898 6.0154 1.7403 6.2568 COST 231SUI TYPE BSUI TYPE C Table 2 shows how the different models fit the meas ured data. RMSE values for the COST231 model ranged from 1.6dB to 16dB; values fo r SUI Type B ranged from 2.9dB to 14.4dB; and values for SUIC ranged from 1.2dB to 1 8.5dB. Positive values for mean error indicate the model is pessimistic, i.e., the path l oss prediction is higher then expected. Negative PAGE 22 13 values indicate the path loss prediction is lower t hen expected. Sites Q, R, and S shows a much higher error rate than the others. This is because these sites are located around bridges. A more detailed explanation is discussed in Chapter 5. Ov erall, SUI Type B model shows a better fit mainly because this model was created to support br oadband wireless applications with parameters closer to the data used for this thesis. PAGE 23 14 CHAPTER 3 EXPERIMENT A crucial part of any experiment study is to make s ure the data collected is consistent throughout the experiment. In order to extract the intended information about the environment, a systematic procedure has to be put in place prior t o the collection of data. During the measurement campaign, the equipment was calibrated and baseline measurements were taken before each data collection. This procedure includ ed a complete log of all information pertaining to site location and equipment type. Gains and los ses about the antennas and cables were noted to effectively calculate the path loss of the propagat ion model. In addition, it was important to take pictures of the surrounding environment. These pic tures can help in determine anomalies in the data and validate clutter and terrain databases. I n this chapter experiment equipment setup and collected data preprocessing analyses are discusse d. 3.1 Tampa Bay Environment In the summer of 2007, RSS data was colleted from 29 locations around the Tampa Bay area. The structure of the 29 sites consisted of e xisting locations towers and rooftops as well as crane mounts as seen in Figure 3. The antenna h eights were in the range of 20m to 58m. PAGE 24 15 Figure 3. One of the crane mounts setup with transm itter for data collection. The sites were located throughout the Tampa Bay ar ea which encompasses of metropolitan areas of Tampa, Clearwater, and St. Pe tersburg. The areas consist of flat terrain with dense residential zones, heavy vegetation, and business districts with tall buildings. Three major bridges spanning over 10km link the major met ropolitan areas, making these routes very important for both commercial and public needs. Th ese bridges are also vital routes for emergency evacuations. Figure 4 depicts one of the unique characteristics of the Tampa Bay area, Clearwater Beach, which is a populated patch of land in between the main coastal areas and a harbor along the Gulf of Mexico. This type of en vironment is very challenging for planning proper coverage and mitigating the Radio Frequency (RF) energy interference created by transmitters near the water. PAGE 25 16 Figure 4. The Tampa Bay area offers very unique cha racteristics such as coastal areas. Although Tampa Bays downtown areas, are relativel y small compared to other major metropolitan areas in the U.S., downtown Tampa has high rises typical of heavy urban environments as shown in Figure 5. Figure 5. Building layout of downtown Tampa. PAGE 26 17 Suburban areas in the Tampa Bay area are similar to those encountered throughout the U.S. which is composed of flat terrain and semiden se tree distribution. These areas usually contains single story homes as shown in Figure 6. Figure 6. Typical Tampa Bay suburban area. One of the main motivations to study the Tampa Bay area was the number of bridges that link the cities such as those shown in Figure 7. B ridges are of major importance due to Tampa Bays heavy traffic volume during business hours. T herefore an adequate quality of service around the bridges is critical. PAGE 27 18 Figure 7. Bridges link major metropolitan areas in the Tampa Bay area. It includes the cities of Clearwater, Tampa, and St. Petersburg. Commercial areas around the Tampa Bay area are comp osed of wide streets and one to two story business units similar to the one in Figu re 8. These environments are the most inclined to have tunnel effects, therefore the need to caref ully filter the data prior to analyzing it. Tunnel effect occurs when RSS is channeled by the building s so that the strongest paths are not necessarily the direct paths diffracted over the ed ge of nearby obstructing buildings, but are found to be from directions parallel to the streets [7]. PAGE 28 19 Figure 8. Typical commercial area in Tampa Bay are a. The Tampa Bay area has a population of about 2.5 mi llion people, which makes an attractive metropolitan area to deploy new networks and services. This area also has unique and diverse environments that can be a challenge to pla n for new networks. The surrounding bodies of water make it hard to contain the RF energy and prevent interference. One of the goals of this thesis is to provide a more optimized model to help mitigate interference and provide a better quality of service around this area. 3.2 Equipment Setup The base stations transmitted a continuous wave (CW ) signal, with an omnidirectional antenna with maximum gain of 8.5 dBi, from a 20 W t ransmitter close to 2.6 GHz. An example of a typical equipment setup is shown in Figure 9. Here the equipment is located on a rooftop somewhere in the Tampa Bay area. The receiver ante nna was placed on a vehicle about 2 m above the ground. The vehicle was driven around th e area. PAGE 29 20 Figure 9. Typical transmitter setup. The transmitter equipment used was a Gator Class A transmitter with maximum output power of 20 W and frequency range of 2.5 GHz to 2.7 GHz. The receiver equipment consisted of a Coyote dual modular receiver which was integrated with commercial software to map the RSS values with GPS information. The test equipment i s shown in Figure 10. PAGE 30 21 Figure 10. The transmitter was calibrated and value s were logged prior to data collection. For every base station experiment a checklist was l ogged with detailed procedures and values such as transmitted power, cable power losse s, and center frequencies. These values were used at a later time for link budget purposes. The se procedures were kept consistent throughout the campaign measurement. As indicated in Chapter 1, there are two major type s of fading in the mobile wireless environment, largescale and smallscale. Although the receiver equipment used was capable of averaging out the smallscale phenomena in real tim e, this was not the case in this experiment. Therefore the averaging had to be completed after t he data was collected. The next section provides the methods used to remove smallscale fad ing from the measured data. 3.3 Rayleigh Fading In order to estimate the local mean received power of the path loss, the smallscale fading characteristics of the radio signal had to be remov ed. The first rule is to determine the proper distance interval that will preserve path loss and shadowing effects statistics. The length of a local mean has to be chosen properly. That is, if t he length is too short, the fast fading is still present after the averaging process. If the length is too long, shadowing effects are removed. PAGE 31 22 Smallscale fading can be modeled by Rayleigh distr ibution assuming the signal has no line of sight (LOS). The measured length of a mobile radio signal necessary to obtain the local mean of the path loss power has been determined to be in th e range of 20 to 40 wavelengths. A detailed derivation of this process can be found in this ref erence [8]. Over 3 million data points in different locations for each transmitter station we re measured in this experiment. A length of 40 wavelengths was used to obtain the local mean as su ggested in [8]. This implies a typical range of standard deviation of 0.06 and a spread of 1 dB. Since the frequency used was 2.6 GHz, the length of 4.5 m was used to obtain the local mean. In Figure 11 a small segment of the raw collected data is shown to illustrate how a very small sample of data needs to be filtered in order to extract the corrected statistical parameters of interest. Figure 11. Sample length of data to be filtered. As seen from Figure 12, the dynamic range from the sample data is about 20 dB in a very short segment of the data. PAGE 32 23 110 100 90 80 70 60Data SampleRSSI (dBm) Figure 12. Sample unfiltered data. After the data is filtered as illustrated in Figure 13 the dynamic range is less then 5 dB; smallscale fading is removed and the path loss and shadowing (variance) effects of the data are preserved. 100 95 90 85 80 75 70 65 60 Data SampleRSSI (dBm) Figure 13. Sample filtered data. Figure 14 is shown to illustrate the statistical ti me varying nature of the received signal which once more shows Rayleigh distribution charact eristics. PAGE 33 24 Figure 14. A small sample of the data showing Rayle igh fading characteristics. Since shortterm fading deals mainly with the relat ionship between the time rate of change in the channel and the transmitted signal, i t is noteworthy to illustrate the received signal as a function of time shown in Figure 14. Please n ote that a more accurate description of the shortterm fading in this signal should not include values approximately between 0 to 50 milliseconds since it clearly shows the signal expe riencing shadowing effects or other phenomena that can not be described by Rayleigh distribution. PAGE 34 25 CHAPTER 4 ADAPTED MODELS FOR TAMPA BAY AREA The main objective of this campaign was to collect RSS data throughout the Tampa Bay are and optimize the existing models. This task is known in the industry as model tuning or propagation model optimization. For the 2.6 GHz band channel, the COST231 Hata model and Stanford University Interim (SUI) models were u sed to compare against the measured data. Again, we are not going to use deterministic models for reasons explained in Chapter 2. Existing models such as SUI and COST231 Hata model are base d on data collected in different areas, and may not fit every possible morphology type. For in stance, the SUI method is based on experimental data collected in several suburban are as in New Jersey and around Seattle, Chicago, Atlanta, and Dallas. None of those areas have char acteristics that resemble the Tampa Bay area. The Hata Model is based on data collected in Japan by Okumura. Moreover, urban areas such as Tokyo are very dissimilar to the urban areas around the Tampa Bay area. Downtown Tokyo extends its high rise buildings for several kilomet ers whereas downtown Tampa consists of tall buildings only within a radius of two kilometers. Therefore, the motivation of this chapter is to provide an adapted model that better describes the propagation characteristics in the Tampa Bay area. The first adapted model is based on a twosl ope based empirical model that is to be used for bridges in the Tampa Bay area. The second adapted m odel is based on regression analysis for the areas suburban environments. The third adapted mo del is also based on regression analysis but uses a much shorter distance for the slope intercep t to account for the urban environment. PAGE 35 26 4.1 Introduction The adapted model proposed here is based on least square regression analysis. We first classify the different types of terrain, and then s ubcategorize based on specific characteristics. The major terrain categories are urban, suburban, a nd rural. Furthermore, we subcategorize the suburban areas as follows: residential only with tr ees, residential/industrial with trees, bridges and coastal. For the bridges, a twoslope method is us ed to provide a better fit than existing models. The twoslope method is used in microcellular desig n, but it can also be used for bridges and highways. In [9] it is suggested that a twoslope method be used to provide a more accurate model particularly for a more efficient system desi gn employing less base stations to achieve the same quality of service. The first step in the process is to average out fa st fading (Rayleigh fading), described in detail in Chapter 3. This is done in order to obta in the local average power, or local mean. The measured spatial length of the RSSI values to obtai n the local average was determined to be in the range of 20 to 40 wavelengths, as described in Sect ion 3.2. In this case for a center frequency of 2.6 GHz, the data is averaged approximately for a d istance segment of 4.5 m. Fastfading is due to multipath effects caused by reflections. Direct lines of sight are superimposed on slow and long term fading signals which are caused by diffraction and distance respectively. The second step was to calculate the path loss exp onent of each site. For this a linear regression using least square was applied to each s ite. The next section gives an overview of the regression analysis that will be used to develop th e adapted models. 4.2 Regression Analysis More in depth material about this section is obtai ned from [10], which proved to be a great resource in understanding the material herein PAGE 36 27 Regression analysis is used to relate variable depe ndence on another. In the specific case of propagation analysis, it helps to explain the RS S dependence as a function of the logarithmic distance between the transmitter and receiver, as i llustrated in Figure 15. Figure 15. Typical scatter plot for a transmitter located in a suburban environment. The red line is the corresponding leastsquare linear regression fit. Using Yi to denote the RSS values in dBm, and Xi to indicate the RSS value corresponding distance in logarithmic scale, we can specify that on the average shown below. i ibX a Y+ = (22) Where a is the intercept and be b the slope (i.e., the path loss exponent). Paramet er extracted from the analysis such as the path loss e xponent and intercept can then be used to make relations between different environments and site c onfigurations. The leastsquare method is the PAGE 37 28 most common procedure in computing these parameters The leastsquare method involves choosing a and b from Equation (21) so that the sum of the squared deviation is minimized. ()2 1=n i i iY Y (23) The parameters a and b can be obtained using the formula below and the de rivation can be found in [10]. () = n X X n Y X Y X bi i i i i i2 2 (24) X b Y a = (25) The derivation of the formulas above requires solv ing partial derivatives and different algorithms may be used to compute these values. Fo r this thesis the MATLAB function polyfit was used to compute coefficients a and b 4.3 Statistical Parameters for Goodness of Fit of R egression Analysis The most common way of determining how a model fit s against the measured data is to use root mean square error (RMSE) calculations, and 2 R which is referred as the coefficient of determination These tests compute the amount of variation that is left over from the distance dependence variation (in path loss case), from the least square fit and the degree of linear association between the variables. 2 R is obtained by taking the ratio of the explained v ariation over the total variation. The largest possible valu e is R2 = 1, and the smallest is R2 = 0. These indicated perfect fit and complete lack of fit resp ectively. =2 2 2) ( ) ( Y Y Y Y Ri i (26) PAGE 38 29 Where iYis the measured RSS value, Y is the sample mean measured RSS value, and Y is the RSS predicted value of the least square fit of the regression analysis. RMSE is also known as Root Average Squared Predict ion Error (RASPE). It gives a summary of the analyzed data in the units of the de pendent variable, which in this case is the RSS in dB units. () n Y Y RMSEn j j j==1 2 (27) A RMSE value closer to 0 indicates a better fit. However, the performance of model is deemed acceptable if it provides an overall RMSE of about 67 dB as stated in [11]. 4.4 Results The parameters obtained from the regression analys is are discussed in this section. First, the general results for all sites are briefly discu ssed. We then classify different environments and adapt the logdistance path loss model to account f or the statistics of the specific areas. More specifically we discuss the propagation characteris tics of bridges, suburban, and urban environments in the Tampa Bay area. 4.4.1 General Results The results presented here show all the parameters for the sites where data was collected. These results have been obtained through regression analysis using leastsquare methods and compared against the different models as shown in T able 3. Please note that the regression analysis is assumed to have zero mean error when co mpared with the models in Chapter 2. The results presented here show the statistical ana lysis of sites located in particular environments or morphologies. Table 3 shows the path loss expone nt, RSS intercept, along with the height of the sites. PAGE 39 30 Table 3. Site antenna heights and model parameters. SITE ANT Height (m)Morphology Path Loss Exponent RSSI Intercept (1 km) Comments SITE A 20 Suburban 3.30 90.08 Flat Terrain/Trees/Houses/Coastal SITE B 27 Suburban 2.29 82.13 Flat Terrain/Trees/House/Industrial/Coastal/Bridges SITE D 27 Suburban 3.56 84.03 Flat Terrain/Heavy Trees/Industrial/Highways/Major Roads SITE E 27 Suburban 4.24 68.90 Flat Terrain/Highway/Bridges/Coastal SITE F 28 Suburban 2.35 81.47 Flat Terrain/Trees/House/Bridges/Coastal/Major Road s SITE G 28 Suburban 3.38 96.34 Flat Terrain/Trees/Industrial/Major Roads SITE H 30 Suburban 3.81 72.73 Flat Terrain / Heavy Trees /Houses/ Industrial / Co astal / Bridges SITE I 30 Suburban 4.93 76.42 Flat Terrain/Condominiums/Coastal SITE J 34 Suburban 2.39 85.12 Flat Terrain/Heavy Trees/House/Industrial/Major Roa ds SITE K 34 Suburban 4.34 77.49 Flat Terrain/Heavy Trees/Industrial/Airport/Major R oads SITE L 34 Suburban 3.26 81.60 Flat Terrain/Condominiums/Coastal SITE N 37 Suburban 2.48 86.17 Flat Terrain/ Hearvy Trees/ Houses/ Industrial SITE O 37 Suburban 3.92 80.53 Flat Terrain/ Heavy Trees/Houses/Industrial/Highway SITE P 37 Suburban 2.87 92.49 Flat Terrain/Heavy Trees/House/Industrial/Major Roa ds SITE Q 39 Suburban 3.43 84.19 Flat Terrain/Heavy Trees/House SITE R 40 Suburban 3.20 81.34 Flat Terrain/Heavy Trees/House/Industrial/Major Roa ds SITE T 43 Suburban 2.55 85.69 Flat Terrain/Heavy Trees/House/Industrial/Major Roa ds SITE U 43 Suburban 3.44 84.25 Flat Terrain/Heavy Trees/Major Roads SITE V 43 Suburban 3.97 86.91 Flat Terrain / Heavy Trees / Heavy Houses / Coastal SITE W 44 Suburban 3.05 81.25 Flat Terrain/Heavy Trees/Coastal SITE X 49 Suburban 2.90 81.47 Flat Terrain/Heavy Trees/Houses/Industrial/Major Ro ads SITE Y 53 Suburban 4.11 78.95 Flat Terrain/Heavy Trees/House/Highway SITE Z 55 Suburban 2.86 78.92 Flat Terrain / Heavy Trees / Heavy Houses SITE AA 55 Suburban 3.50 79.11 Flat Terrain/Heavy Trees/House SITE AB 57 Suburban 3.10 89.64 Flat Terrain/Trees/Houses SITE AC 58 Suburban 3.55 78.11 Flat Terrain/ Heavy Trees/Houses/Major Roads SITE C 27 Urban 2.89 89.61 Flat Terrain/Tall Buildings/Coastal SITE M 36 Urban 2.43 84.76 Flat Terrain/Tall Buildings/Industrial SITE S 40 Urban 2.61 85.09 Flat Terrrain/Tall Buildings The antenna height ranged from 2058 m. The path loss exponent for suburban areas ranged from 2.29 to 4.93. An attempt was made to v alidate the findings of [4] where evidence is shown that the path loss exponent is strongly depen dent on the base station antenna height. Unfortunately, we only had sites with antenna heigh ts ranging from 2058 m, whereas in [4] the heights ranged from 1080 m. This made it very dif ficult to draw any conclusions as shown in Figure 16. PAGE 40 31 Path Loss Exponent for Suburban Area 0.00 1.00 2.00 3.00 4.00 5.00 6.00 010203040506070 Antenna Height (m) Path Loss Exponent Figure 16. Path loss exponent as a function of ante nna height for suburban area. Since the data collected was from an omnidirectio nal transmitter, the possibility of the signal strength serving different environments was very common. In addition to filtering the data as discussed in Chapter 3, we had to filter the dat a to make sure the area being studied was not contaminated by too may types of environment. This approach emphasizes the need to proper ly filter the data before to start analyzing it or mak ing any conclusions. The remanding subsections discuss the specific environments and adapted model s developed in this thesis. 4.4.2 Bridge Analysis and Model for Tampa Bay Some twoslope models have been used to predict co verage in highways [9] but, a specific model in the literature has not been proposed for bridges. This is particularly i mportant to the Tampa Bay area since bridges in this area ar e the major commuter routes among the cities as mentioned in Chapter 3. Also, in an emergency s ituation these bridges are major routes of evacuation, so it is paramount that propagation of radio link is well understood in these areas. PAGE 41 32 Figure 17. Data from a cell serving a major bridge in the Tampa Bay area. The straight lines represents the slope for two different segments whe re the break point is approximately the length of the bridge. Assuming we use the free space loss equation for t he reference distance, i.e. =l po od PL4 log 2010 (28) Then, we can derive the formula below. + < + =BP BP BP Tampa Bridgesd d d d PL d d d PL PL) ( log 0. 75 ) ( ) ( log 0. 2710 10 0 (29) The piecewise equation below can be used to determ ine the path loss before and after and break point distance dBP. As can be seen from the results below, when the tw oslope method is applied to a site serving the three major bridges in Tampa Bay a bett er fit is achieved. The main parameter to this model is the length of the bridge itself. PAGE 42 33 Table 4. Oneslope vs. twoslope parameters. Path Loss Exponent RMSE R2 One Slope s 7.308.750.70 s1 2.303.880.71 s2 8.806.870.37 Path Loss Exponent RMSE R2 One Slope s 5.208.130.49 s1 3.084.490.73 s2 3.107.150.07 Path Loss Exponent RMSE R2 One Slope s 6.309.800.65 s1 3.105.110.74 s2 6.209.020.16 Two Slope SITE A SITE CSITE D Two SlopeTwo Slope The results shown in Table 4 indicate that the fir st slope, which is calculated from the reference distance of one mile to the break point d istance. The break point distance is approximately the distance of the bridge, and the s lope for distance decays much slower than the second slope. This can be explained by the near li ne of sight that is caused by the elevation of the bridges and the attenuation caused by the water whi ch is much lower than in land. The second slope decays much faster and further analysis is re commended to explain the low coefficient of the determination. 4.4.3 Suburban Environment Analysis and Model for T ampa Bay Area The initial results showed that further analysis n eeded to be performed. The data was filtered based on specific locations under the same type of environment. If the majority of the data was collected in a suburban environment, it is possible that a significant number of data points can be located in an urban or rural environm ent. This can contaminate the data and skew the main parameters of interest. For instance, Sit e I showed a path loss exponent value of 4.93. PAGE 43 34 Further investigation of this site shows it is loca ted in a coastal area and it is surrounded by high rise condominiums. After filtering the data the va lues become less spread out. The values for six suburban sites located in the s ame environment are shown in the tables below. As noted, the path loss exponents are withi n very close range. Table 5. Path loss exponent and intercept for five suburban sites. SITE PathLoss Exponent Path Loss 1km (intercept) A 3.20132.14 B 2.86129.72 C 2.97129.54 D 2.90132.64 E 3.20129.58 Table 6. Mean average of path loss exponent and 1 k m intercept for suburban sites. PathLoss Exponent Mean Average Path Loss 1km (intercept) Mean Average 3.02131.72 Suburban Tampa ) log( 2. 30 72. 131_d PLTampa Sub+ = (30) PAGE 44 35 Table 7. RMSE comparison between models. SITETAMPA BAYCOST231SUI TYPE BA 1.308.133.32 B 1.7610.363.01 C 1.5810.944.92 C 0.578.124.16 E 1.028.764.74 RMSE The results in Table 7 show very good agreements wi th the adapted Tampa Bay model with a very close RMSE range between 0.572.18 dB. As expected, the COST231 model did not show a good fit to the data. The SUI Type B provid ed a much closer fit, with RMSE range between 3.014.74 dB. Generally speaking, a model that provides a RMSE between 67 dB is considered a good fit [11]. The values in the urban area were very suspicious since its expected that the path loss exponents will be higher than other areas. The exp lanation here is that 1 km intercept for an urban area may not be appropriate. The figure belo w shows downtown Tampa, which has a dense concentration of tall buildings. Here, an ar bitrary center has been chosen, surrounded by a 1 km radius, the common intercept distance in this case. Most of the data within the area of the circle would be lost if the 1 km intercept distance was used. Also, it should be noted that cell radius is much smaller in the urban area than in th e suburban and rural environment due to the lower antenna height. PAGE 45 36 Figure 18. Downtown Tampa. The new filtered data shows a better agreement wit h the type of environment being studied as it will be shown in the next section. 4.4.4 Urban Environment Analysis and Model for Tamp a Bay Area Transmitters were set up in three different locati ons in downtown Tampa to collect RSS data. The data collected from these transmitters w ere originally analyzed not taking into consideration any filtering. As shown in Figure 18 to completely describe the environment within the downtown area, it is necessary to only c onsider data points within the area of interest. The table below shows the results of the path loss exponent of the sites located in the downtown area after filtering. The height of the sites rang ed from 2740 m. PAGE 46 37 Table 8. Path loss exponent comparison for transmi tter located in downtown Tampa. SITE Path Loss Exponent Before Filtering Data Path Loss Exponent After Filtering Data 100mIntercept (dB) SITE A2.613.4998.55SITE B2.434.93102.60SITE C2.893.9194.00 Site A Site B Site C Figure 19. Regression analysis for sites in downtow n Tampa. The free space path loss for 2.6 GHz at 100 m is a bout 80.4 dB. The average measured path loss at 100 m for the sites in the downtown ar ea was about 98 dB. =l po od PL4 log 2010 (31) PAGE 47 38 + =o Tampa Urband d PL10 _log 1. 41 18. 98 (32) Table 9. RMSE for urban environment sites in the Ta mpa Bay area. SITE Tampa Bay COST231 SITE A6.911.49SITE B6.4813.90SITE C7.228.09 The Tampa Bay model was compared against COST231 and the RMSE is shown on Table 5. Since the SUI model does not have a profi le for the urban environment, no comparison is made against the SUI model. The results of the new adapted model shows a better fit than the existing models. The difference between the models range from 0.87 dB. PAGE 48 39 CHAPTER 5 SHADOWING EFFECTS FOR TAMPA BAY AREA Shadowing effects are very important for link budg et purposes, handoff analysis, cochannel interference and frequency reuse studies, a nd diversity design. The main objective of this chapter is to explore the shadowing effects surroun ding the Tampa Bay area, and to provide insight in the signal variation caused by terrain a nd other obstacles (which is also known as shadowing effect or slow fading). 5.1 LogNormal Shadowing Shadowing effects in empirical models are mainly d escribed as a lognormal distribution [1]. The path loss at any distance from the transmi tter can be described below. sX d PL dB d PL + = ) ( ] )[ ( (33) Where sX is a zeromean Gaussian distributed random variabl e (in dB) with standard deviation s (also in dB). The lognormal distribution describes the random s hadowing effects. They occur over a large number of measurement locations which have th e same distance separation between transmitter and receiver, but have different levels of clutter on the propagation path such as terrain irregularities, buildings, tress, etc. Shadowing effects are shown simply by subtracting t he bestfit path loss regression analysis from each individual measured local mean R SS values [12]. Some authors have described shadowing effects by histograms of excess path loss, which is the expected free space level minus the measured local mean [7]. The histo gram showing this effect is shown in Figure 20 from one of the sites located in the Tampa Bay a rea. Similar patterns to other sites show the PAGE 49 40 same effect, confirming the shadowing effect is log normally distributed. In addition, the plot in Figure 21 shows a linear fit superimposed on a samp le of measured data. The straightline fits show that shadowing effects come from a Gaussian di stribution. Figure 20. Lognormal distribution of shadowing eff ects. The data shows that shadowing effects appears to be Gaussian distributed as is commonly b elieved. PAGE 50 41 Figure 21. CDF of the shadowing fading components as a normal probability plot. The straight line fit shows that shadowing effects is near Gauss ian. 5.2 Shadowing Effects Analysis for Tampa Bay Area As expected, all sites analyzed in the Tampa Bay a rea showed a lognormal distribution about the mean distance dependent value as shown in Figure 20. In this section the techniques applied to determine the standard deviation s for some of the suburban and urban sites will be discussed. 5.2.1 Data Analysis In a mobile radio environment, the received signal envelope consists of large and smallscale fading phenomena. As mentioned before, this thesis is focused only on large scale fading, which is composed of distance dependent signal stre ngth and variability of signal strength about the mean of the distance dependent RSS value. This variability is known as shadowing effects. Statistical analysis of shadowing effects require t he removal of the distance dependence of RSS, PAGE 51 42 or path loss, in addition to the small scale fading as discussed in Chapter 3. In order to accomplish this, we simply subtract the bestfit path loss reg ression analysis from each individual measured local mean RSS values. Figure 20 shows the histog ram of the shadowing effects components. As expected, the mean of this result appears to be concentrated around 0 dB with a standard deviation of about 8 dB. Since the path loss in decibels is assumed to be a random variable with a normal distribution as shown in Equation (32), so is the R SS. The Q function or error function ( erf ) may be used to the determine the probability that the r eceived signal level will exceed (or fall below) a particular level. The Q function is defined below. () ()[ ] 2 2 1 2 2 11 exp ) (2z z xerf dx z Q = =rp (34) The complementary Q function is shown below. ) ( 1 ) (z Q z Q = (35) The probability that the RSS level (in dB) will ex ceed a certain value g can be calculated from the cumulative density function as ( ) s gg) (] ) ( [d P r rrQ d P P= > (36) Similarly, the probability that the RSS level will be below g is given by ( ) s gg= <) () ( [d P r rrQ d P P (37) Typical values for s both for suburban and urban environments are shown on Table 10 and 11 respectively. The values are computed by ca lculating s over distance increments from the transmitter to the receiver. In this case, s was calculated over 1.6 km radius rings, and all values averaged over the total number of rings. PAGE 52 43 Table 10. Standard deviation in dB of suburban site s. SITEStandard DeviationA9.74B10.74C9.94D10.76E8.64F10.47 Table 11. Standard deviation in dB for urban sites. SITE Standard Deviation A9.74B10.72C13.41 5.2.2 Discussion Originally it was suggested that s was a function of distance. Since all values were calculated over 1.6kilometer radius rings, this wa s easily accomplished. The work done by [13] suggested that for rural areas at 900 MHz, sigma va ries with distance. To find the value of s in dB, the following equations are presented for both radial routesLRs and circumferential routes LCs 0.6 ) log( 0.3+ @ dLRs 14 44.0 £ £ d (38) 8.5 ) log( 4.3 + @dLCs 14 44.0 £ £ d (39) Where d is distance in kilometers. Unfortunately, the data did not support a constant picture of this assumption, particularly for data points collected above 10 km as shown in F igure 22. This is due to the fact that enough was collected above 10 km. PAGE 53 44 Figure 22. Shadowing effects as a function of dist ance. Sigma or the standard deviation describing shadow effects was first thought to be d istance dependent. But not enough data was collected to get a constant picture, particularly f or data points collected above 10 km. 5.3 Correlation Property Analysis for Tampa Bay Area The lognormal process of shadowing effects descri bed in the previous section is very useful in the performance analysis of handover proc edures, the design of diversity schemes, and the study of the quality of service in mobile wirel ess systems. However, a better design of wireless systems can be accomplished by a better un derstanding of the spatial correlation properties of shadowing. In this section we do not propose a new model, but analyze the correlation properties of shadow effects in specifi c zones in the service area within the Tampa Bay area. PAGE 54 45 5.3.1 Spatial Correlation of Shadowing Effects Models of spatial correlation properties of shadow ing have been intensely studied since the classical paper of Gudmundson [14] has been pub lished. Therein, the author proposes a simple exponential correlation model for shadowing effects.  2) (k Aa k Rs= (40) D T v Da/e= (41) Where AR is the modeled normalized autocorrelation function 2s is the variance, and De is the correlation between two points separated by D The signal is sampled every T second. Also, v is the mobile velocity and a is the correlation coefficient. This model is cite d quite often in the literature when discussing the topic of correlation shadowing effects. For typical suburban propagation at 900 MHz, it ha s been experimentally verified in [14] that s is approximately 7.5 dB with a spatial correlation of about 0.82 at a distance of 100 m. For typical microcellular propagation at 1700 MHz, [14] shows that s is approximately 4.3 dB with a spatial correlation of 0.3 at a distance of 10 m. The correlation model described above assumes the m obile subscriber is moving in a straight line rather the along a closed route. A t wodimensional sumofsinusoidsbased model for shadowing effects was introduced in [15]. The simulation of shadowing effects along a closed route involves more computational effort rather tha n along a straight line [16]. Therefore, in this section we analyze the correlation properties of sh adowing effects along a closed route; that is, rings of specific widths. In the next section we r eview the properties of autocorrelation functions. PAGE 55 46 5.3.2 Autocorrelation Properties The normalized autocorrelation function (NACF) is estimated by = =+ =1 0 2 1 0) ) ( ( 1 ) ) ( )( ) ( ( 1 ) (N n N k N n N Nm n x N m k n x m n x N k r (42) The function above is normalized to the variance o f the measured data so as to constrain the values in the range 1 to 1. This function is used to calculate the correlation coefficients between one RSS data point to the next. This appro ach generates shadow effects variations that decorrelate exponentially with distance, but cauti on must be taken since it has been shown through extreme value analysis that lognormal shad ows cannot decorrelate exponentially with distance by references in [17]. For the Tampa Bay area spatial correlation analysi s, a function in MatLab called xcorr was used to exploit the autocorrelation properties of the received signal. This function is estimated for a sequence of N length and it is normalized so that the autocorrel ation at zero lag is identical to 1.0. = +=k N n n k n xyy x k R1 0, ) ( 1 ,..., 1,0 = N k (43) The function above computes the autocorrelation fo r the special case of when x = y. 5.3.3 Data Analysis and Discussion The following is a detailed analysis showing the c orrelation properties of RSS as it moves away from transmitter. This process uses concentri c circles to determine the correlation between each incremented area. The plots below help identi fy correlation zones as the receiver moves away from the base station. PAGE 56 47 Figure 23. Normalized autocorrelation plots for ri ng 1. This represents shadow components between 1 to 1.32 kilometers, and the following rin gs are also incremented every 0.32 kilometer. Each sample in the abscissa represents 4.5 meters a ccording to the sampling rate of the equipment. These rings have decorrelation distance s between 100 and 1500 meters. The basic method here is to collect data points wi thin donuts or concentric circles of specific width in this case 0.32 km. This width was selected so as to capture enough samples within each donut without losing possible informati on and correlation patterns. Path loss effects were removed from each point by simply subtracting the measured value by the least square regression analysis of the data The distance between each data point was calculated to be 4.5 m, based on the sampling rate of the equipment and frequency of interest. In all the sites studied, a downward trend in low correlation patterns tends to occur close to the reference distance as it moves away from the transmitter. PAGE 57 48 Figure 24. These rings suggest the existence of co rrelation zones. The shadow effects components seem to behave equally and he decorrela tion distances on the figures above range from 185 to 207 m. When objects are closer to the receiver, such as bu ildings, severe shadow can occur and the signal may go into deep fade. The effect is ob served in Figure 24. The nonperiodic correlation tends to occur between the low correlat ion and slow correlation zones. These patterns are observed to have fairly high peaks from the zer o lag which may be due to effects of street orientation. PAGE 58 49 Figure 25. These rings are the farthest away from the transmitter. They are approximately 10 kilometers away from the transmitter, and decorrel ation distances on the figures above range from 63 to 378 m. Particularly in urban areas it has been observed [1 7] that the radio signal tends to be channeled by the buildings so that a tunnel effect (stronger signal are not necessary line of sight) occurs. Median received signal strength can vary b y as much as 20 dB when near the transmitter station. Slow correlation tends to occur when shad owing objects are not close to the receiver. This phenomenon is observed particularly far from t he base station as seen in Figure 25. PAGE 59 50 CHAPTER 6 CONCLUSION Improvement of accuracy of propagation models will continue to be an integral part of wireless communication systems. This will be even more apparent with the recent convergence of mobile cellular networks and the Internet. In t his thesis the propagation characteristics of the wireless channel in the 2.6 GHz frequency band arou nd the Tampa Bay area are studied. It is shown that an adapted model based on the logarithmi c path loss model provides a better fit than existing empirical models. The shadowing effects w ere studied in detail and the spatial correlation of shadowing effects was investigated. 6.1 Contributions The main contribution of this thesis was to share some insight on the propagation characteristic of the radio link in the Tampa Bay a rea. Adapted models for suburban and urban zones within the Tampa Bay area were presented, inc luding a specific adapted model to support bridges in the Tampa Bay area. These models will h elp to more accurately predict coverage and interference within the area, particularly along th e major bridges in the Tampa Bay area. The proposed adapted methods provide a much better fit than any other existing model, however it is specific for Tampa Bay. Additionally, the log norm al distribution and spatial correlation properties of shadowing effects were discussed. Th e spatial correlation properties of the normalized RSS were exploited in detail using conce ntric zones. 6.2 Future Work The path loss and correlation analyses in this the sis highlight on how the radio signal propagates in the Tampa Bay area. These studies ca n be used to compare future path loss and PAGE 60 51 correlation models. Specifically, correction facto rs for antenna height can be developed. Also, the path loss analysis studied in this thesis could be added as a possible terrain profile to existing models, particularly to the SUI model. In addition it would be interesting to discover a simple spatial correlation function that describes the cor relation zones investigated in Chapter 5. PAGE 61 52 REFERENCES [1] Rappaport, T. 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