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11-22 11.4.5.1 Discussion Propagation Effects for Vehicular and Personal Mobile Satellite Systems The model has been shown to fit measured fade distributions, when the propagation parameters were determined by tailoring the data to the model. Calculation procedures are straightforward. 11.4.6 Models With Fade State Transitions 11.4.6.1 Two- and Four-State Markov Modeling Cygan et al. [1988] used a 2-state Markov model (Gilbert-Elliot model) for nonshadowed (good) and shadowed (bad) channel conditions and a 4-state Markov model, also with good and bad states and qualified by either short or long duration, to predict error rates in the land mobile satellite channel. Channel states are related to the presence or absence of shadowing conditions and both models describe the transition probabilities between states. Model parameters are determined from data collected in L-Band satellite propagation experiments carried out in a variety of environments at elevation angles between 21° and 24°. The data set on which the parameters are based is the same as the one used for the derivation of the total shadowing model. The 2-state model has a total of four parameters, of which two are signal level dependent error rates and two are state transition probabilities. A summary of its parameters for three propagation scenarios is given in Table 11-6. The derived bad lengths appended to the table may be reasonable in the urban environment where much of the shadowing is due to blockage by buildings. For tree shadowing prevalent in the suburban environment, the 2-state model is lacking in predicting the effects of many short fades observed in real channel measurements. Table 11-6: Parameters for 2-State Model Parameter Remark Urban Suburban Highway PGB Transition probability from “good” to “bad” state 3.95x10 -4 PBG Transition probability from “bad” to “good” state 1.05x10 -4 ε G Error rate in “good” state 2.1x10 -4 2.1x10 -4 1.54x10 -4 3.4x10 -4 2.96x10 -5 1.29x10 -4 1.1x10 -4 ε B Error rate in “bad” state 0.317 0.298 0.194 LG Derived “good” length (m) 24 45 704 LB Derived “bad” length (m) 88 60 161 At the price of being more calculation intensive, the 4-state model is capable of providing a more realistic statistical simulation of error bursts. It has a total of thirteen parameters, of which eight are state transition probabilities, two express the transitional durations between short and long, good or bad states, and three are measures for the error probabilities in all good as well as short and long bad states. Typical values of the transitional durations for good/bad states are 0.46/1.85 m for urban, 0.92/0.65 m for suburban, and 5.2/2.5 m for highway driving, respectively. Error probabilities range
Theoretical Modeling Considerations 11-23 −4 −4 from 1⋅ 10 to 3. 5⋅ 10 for the good states to 0.16 … 0.37 for the bad states, with the short bad state's error rate about 30% below the long bad state. While the discussion of error probabilities is beyond the scope of this text, these models give an indication of the level of complexity that may be required for successfully modeling the LMSS channel. 11.4.6.2 Markov Transitions, Multipath And Fade Depth Model By combining three distinct concepts into one LMSS propagation model, Wakana [1991] has modeled fading and its spatial characteristics. Fading due to multipath is rendered by Ricean statistics (11-29), while fading of the line-of-sight signal due to tree shadowing is described in terms of a Markov model for the transitions between fade states and an attenuation algorithm for the fade depth. Like the 4-state model described above, this Markov model considers transition probabilities between four fade states: fade or nonfade, short or long, but with a total of only six as opposed to eight independent parameters. Of two attenuation models introduced, one linking the attenuation to the fade state, the other to the fade duration, the former alternative was used. Besides the six state transition probabilities, four other parameters are required. They are the Ricean K-factor for the multipath scattering, attenuation levels for short and long fades, and a lowpass filter time constant to smooth the transitions between fade and non-fade states. The ten model parameters were determined for a specific suburban propagation path geometry with an optimization procedure performed on data collected in a helicopter experiment. Simulated data produced using these parameters are qualitatively similar to real data when time series are compared and have, of course, similar cumulative distributions of fades, fade durations, and non-fade durations. Typical parameter values are in the range of 0.13 to 0.97 for the transition probabilities, 10.7 dB attenuation for both fade states, a 13 dB K-factor, and a 22 Hz lowpass filter cut-off frequency, corresponding to a spatial filter of about 1 m. Variations of the signal level at near line-of-sight power, which may be due to diffraction at the fade state transition zone and specular reflection from the ground near the vehicle have not been considered in the model development and therefore are not replicated by the simulator. Until parameters are determined for a variety of environments and elevation angles, the modeling results cannot readily be applied to other propagation geometries. 11.5 Geometric Analytic Models Geometric analytic models are useful for gaining physical insight of the mechanism of fading and characteristics of signal retrieval. They may also be used to achieve timeseries fades that may be interfaced with simulation techniques. Unfortunately, the complexities of “real life” scenarios do not lend themselves to analytic models and only simplified and idealized scenarios are considered.
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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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3-28 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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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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9-6 Roughness Parameter, u (Rad) 28
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9-8 Cθ = ( θo − 7) / 2 dB for
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9-10 Fading Depth (dB) 6 5 4 3 2 1
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9-12 Fading Depth (dB) 6 5 4 3 2 1
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9-18 Mean Fade Occurrence Interval,
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9-20 Mean Fade Duration, T D (sec)
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9-22 Fade Depth (dB) 7.0 6.5 6.0 5.
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