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11-2 Propagation Effects for Vehicular and Personal Mobile Satellite Systems regression fits to data models describe probability distributions of fades based on experimental measurements. The second class, probability distributions models, are based on the utilization of a composite of several probability density functions customarily used in radio wave propagation; namely, Rayleigh, Ricean, and lognormal statistics. Among these, some combine densities based on physical reasoning about the propagation process, while others add the use of fade state or fade state transition probabilities. The third class of models employs geometrical analytical procedures for predicting the effects of single and multiple scatterers. The choice as to which model is most appropriate depends very much on the intended application and which propagation phenomenon one wants to predict. Of the different types, empirical models do not provide insight into the physics of propagation processes, but they characterize the sensitivity of the results to important parameters. Statistical models build upon an understanding of the processes that cause signal variations, but with simplifying assumptions. Analytical models attempt to describe a particular propagation scenario deterministically, but then have to use statistics to extend the results to realistic situations. In this chapter, we present background information associated with the important elements of model development. Also described are the dominant LMSS propagation models of the above types, their input and output parameters, as well as their advantages and limitations. 11.2 Background Information Associated with Model Development 11.2.1 Diffusely Scattered Waves To explain signal variations specific to LMSS transmissions between a satellite and a moving vehicle, the interactions of two important signal components have to be considered: line-of-sight and diffusely scattered waves. We ignore the ground reflected waves since it is presumed that for LMSS scenarios, any energy directed towards the antenna near the horizontal will be outside its beamwidth and be filtered out by the low gain pattern function values. The direct wave may be approximated by a plane wave propagated along the lineof-sight path, with most of the power transmitted through the first Fresnel zone. It may be completely obscured by obstacles such as mountains, buildings, or overpasses, or partially shadowed by roadside trees or utility poles. Absorption, diffraction, scattering, or a combination thereof may explain the shadowing process. The frequency of the direct wave is also shifted by an amount proportional to the relative speed between the satellite and the vehicle. A scenario for diffuse scattering for mobile reception may be described as follows. Transmissions from a satellite illuminate obstacles in the vicinity of the vehicle resulting in reflected energy emanating from multiple scatterers. Waves from these scatterers arrive at the receiving antenna with random polarizations, amplitudes, and phases, and the individual contributions are delayed by the amount of time corresponding to the extra
Theoretical Modeling Considerations 11-3 path traveled. In addition, the individual contributions undergo a Doppler shift proportional to the relative speed between any particular scatterer and the vehicle. It is limited to a band of frequencies relative to the zero speed center frequency given by v Δ f D = ± (11-1) λ where v is the vehicle speed in m/s and λ is the wavelength in m. The positive sign denotes an increase in frequency that occurs when the vehicle moves towards the illuminated obstacle. The negative sign corresponds to a decrease in frequency occurring when the vehicle moves away from the illuminated object. This, of course, represents a worst case scenario that may occur at locations where there are sharp bends in the road. As an example, a vehicle traveling at 25 m/s ( ≈ 55 mph) receiving L-Band (1.5 GHz or λ = 0.2 m), will experience Doppler shifts limited to ± 125 Hz. 11.2.2 Faraday Rotation Faraday rotation effects [Davies, 1990; Flock, 1987] are potential contributors to signal strength variations which can be neglected for LMSS systems which employ circular polarization and L-Band or above frequencies. The ionosphere contains free electrons in the relatively static Earth’s magnetic field. This combination causes polarization rotation of linearly polarized waves as given by (for f > 100 MHz) 6 Be ⋅TEC φ = 1. 35 ⋅10 ( ° ) , 2 (11-2) f where f is the frequency in Hz and Be is the effective earth's magnetic field in Webers/m 2 assumed constant as a simplifying assumption and defined by B = B cosθ , (11-3) e B where B is the true Earth’s magnetic flux density at a location in the ionosphere along the Earth-satellite path and θ B is the angle between the direction of propagation and the earth's magnetic flux density vector. TEC is the total electron content (number of electrons/m 2 ) given by ∫ 3 TEC = N dl ( number of electrons / m ) , (11-4) where l is the path length through the ionosphere and N (number of electrons/m 3 ) is the electron density along the path. Assuming extreme values of TEC and Be given by [ITU- R, 1986b (Report 263-6)] and for an angle of transversal of 30° 18 TEC = 1. 86 ⋅10 (number/m 2 ), (11-5)
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A2A-98-U-0-021 (APL) EERL-98-12A (E
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Table of Contents 1 Introduction __
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10 Optical Methods for Assessing Fa
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Table of Contents 1 Introduction __
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1-2 Propagation Effects for Vehicul
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Table of Contents 2 Attenuation Due
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Chapter 2 Attenuation Due to Trees:
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Attenuation Due to Trees: Static Ca
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Table of Contents 3 Attenuation Due
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Figure 3-23: Fade distributions at
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3-4 Relative Signal Level (dB) 5 0
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3-10 Percent of Distance the Fade >
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3-12 Propagation Effects for Vehicu
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3-14 3.4.3 Austin, Texas at K-Band
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3-20 Relative Signal Level (dB) 5 0
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3-24 Percentage of Distance Fade >
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3-26 and where 1 2 Propagation Effe
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3-28 Percentage of the Time Fade >
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3-32 3.7.5 Comparative Summary of M
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Chapter 4 Signal Degradation for Li
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Table of Tables Table 4-1: Summary
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4-4 Percentage of Distance Fade > A
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4-14 Percentage of Distance or Time
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Table of Contents 5 Fade and Non-Fa
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Chapter 5 Fade and Non-Fade Duratio
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Fade and Non-Fade Durations and Pha
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Table of Contents 6 Polarization, A
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Chapter 6 Polarization, Antenna Gai
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Polarization, Antenna Gain and Dive
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Table of Contents 7 Investigations
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was derived from measurements over
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7-6 7.3 Belgium (PROSAT Experiment)
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7-10 Probability Fade > Abscissa (%
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7-14 Percentage of Time Fade > Absc
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7-24 Probability (%) > Abscissa 100
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Chapter 8 Earth-Satellite Propagati
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Table of Figures Figure 8-1: Maximu
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Chapter 8 Earth-Satellite Propagati
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Earth-Satellite Propagation Effects
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Chapter 9 Maritime-Mobile Satellite
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Figure 9-7: Fading depth versus pat
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12-14 Standard Deviation (dB) 4 3 2
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12-18 Fade Depth (dB) 7.0 6.5 6.0 5
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Index 13-1 Index 2 2-state Markov m
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Index 13-3 Jongejans, A. et al., 3-
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