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FIGURE 14.7. An LMSS propagation environment and classi cation of propagation states [19].
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state transition characteristics based on a Markov model were obtained by this approach. States A, B, and C represent the LOS condition, slight shadowing by trees and/or small obstacles such as utility poles, and full shadowing by large obstacles such as buildings as is shown in Figure 14.7 prepared according to Reference [19]. A fading channel model is discussed in Reference [19] for the quantitative assessment of signal degradation due to shadowing and multipath propagation in various fading environments. On the basis of previously developed channel models and taking the three states into account, we will present an improved channel model. Each state consists of various propagation elements. In Figure 14.8(a), notation a1 represents a case of the direct wave component, without shadowing, a2 denotes the slight shadowing, and a3 denotes perfect shadowing. Similarly, b represents the multipath wave component caused by the ground (b1) and scattered waves from land obstructions (b2). Notice that both kinds of waves, b1 and b2, contain a coherently re ected component and an incoherently scattered component, which were de ned in 5. Now, we consider statistical signal level characteristics in terms of the PDF. A few useful PDF models have been developed for LMSS. State A can be expressed by the Nakagami Rician fading model (also called the Rician model). As for Loo s model, it presents the PDF of the direct wave component following a lognormal distribution and PDF of the re ected wave component following the Rayleigh distribution. Loo s model can be a good representation of State B. Moreover, we can assign a Rayleigh fading model for the PDF of State C. As the model we present is characterized by a three states, it can be expected to have a more exible expression
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State A [ Pr ,A ] State B [m, ,Pr ,B ] State C [Pr ,C [
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FIGURE 14.8. A three-state propagation channel model according to [19]: (a) Propagation impairment factor. (b) Statistical channel model. (Reprinted with permission # 1997 IEEE)
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for LMSS propagation environments composed to States A, B, and C. So, the resultant channel model proposed in Reference [19] can be written as shown in Figure 14.8(b) with the state occurrence probability functions, pA , pB , pC , where pA pB pC 1. The calculations of A, B, and C are following: pA 1 90 y 2 =a; ( for urban areas pC =4; pC 4pC ; for suburban areas where y is the elevation angle of the satellite, 10 y 90 , and & for urban areas 7:0 103 ; a for suburban areas 1:66 104 ; 14:29a 14:29b
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14:30
In order to understand the state duration statistics, such as the mean duration of State A during which high quality communication is maintained, a model capable of
STATISTICAL MODELS
p AA
State A
State B
p AB pCA pBC pCB
p AC
State C
FIGURE 14.9. The three-state Markov model.
expressing time-variant characteristics is necessary. A Markov model is useful for this purpose. Since the model we are proposing is a three-state model, the Markov model can also be expressed as a three-state model as shown in Figure 14.9 according to Reference [19]. According to our de nitions of fading (see 1), there are two types of signal level variations: short-term variations in terms of instantaneous uctuations followed by the given PDF in each state and long-term variations represented by state transitions. For the purpose of satellite diversity assessment, understanding of the long-term variations is adequate at the rst stage of assessment as mentioned before. Therefore, we formulate a Markov model for simulating the long-term variations (namely, state-to-state variations). Figure 14.10(a) (c) shows examples of satellite constellations where at least one, two, and three satellites simultaneously cover every point on the Earth s surface
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