p for r ( b0

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where R is either the maximum accepted path loss or the noise oor gure of the system. We must note that for the case of infrequent light shadowing, the model shows the best t around the median region and some deviation near the tails of the distribution (see Fig. 14.5). The results of the model showed a slightly higher shadowing effect than those from measured data. For the combined results (see both Figs. 14.5 and 14.6), the t was poor about the median but reasonably good in the

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45.0 0.01 0.1 1.0 10 30 50 70 90 99 99.9 99.99 % of time received signal envelope > ordinate

FIGURE 14.5. Loo s envelope model and measurement for heavy shadowing at f 18:925 GHz.

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45.0 0.01 0.1

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FIGURE 14.6. Loo s phase model and measurement for heavy shadowing at f 18:925 GHz.

LAND SATELLITE COMMUNICATION LINKS

weak signal range, which is most important for fade margin calculations. The model parameters were obtained by trial and error to t the measured values. The results indicate that the model shows a correlation between the rate of change of the envelope due to multipath and foliage attenuation both for heavy shadowing and for light shadowing. The disadvantage of this model is that the measurements were made up to 30 , model parameters for higher elevation angles are not available. 14.3.2. Extended Suzuki Model In literature, the product of a Rayleigh process combined with a lognormal process is de ned as the Suzuki process [10]. It is well known that such a process is a suitable and widely accepted statistical model for the random variations of the envelope of the received signal of frequency nonselective macrocell land mobile terrestrial channel. The Suzuki process is an adequate statistical model [10], which is usually used in land mobile communication channels, where often it is assumed that a direct line-ofsight component is absent. For mobile-satellite communication channels, where for most of the time a direct line-of-sight component is present, an extension of the Suzuki process was proposed as combination of Rician and lognormal processes. The extended Suzuki process Z t will be introduced here as a product process of the Rician process x t (see de nitions in 1) with cross-correlated components and the lognormal process t , that is, Z t x t t Then the PDF of the extended Suzuki process, Z t , pZ z , is [10] pZ z

14:6

1 z px ; y dy jyj y

14:7

where px x; y denotes the joint PDF of the processes x t and t at the same time t, y is the variable of integration, and x z=y. The Rician process, x, and the lognormal process, y, are statistically independent, that is, px x; y px x p y 14:8

Thus, (14.7) can be written using the PDF of the Rician process and the PDF of the lognormal process: z pZ z p 2pc0 s

1 0

1 f z=y 2 p2 = 2c0 g zp ln y m 2 = 2s2 e e I0 dy; y3 yc0

z!0 14:9

STATISTICAL MODELS

Here, c0 is a mean of the Rician random variable x, p is a LOS component, m and s are the mean and standard deviation of random variable y. To test the accuracy of this model, a special experiment was carried out where the transmitter with a radiated frequency of 870 MHz was assembled on a helicopter at a xed elevation angle of 15 with respect to the receiver. As the test route, a rural area was chosen with about 35% tree coverage, and the rest was cleared land. A test was performed for two different situations. In one, the test route was lightly shadowed and in the other it was heavily shadowed by a dense tree cover. It was shown that, using the extended Suzuki model, the cumulative e distribution function PZ x=y is in agreement with the measurements [10]. For both situations, light and heavy shadowing, the simulation results of the e cumulative distribution function PZ x=y of the simulation system are in an extremely good agreement with the analytical results. As was mentioned in Reference [10], an extended Suzuki process is proposed for modeling frequency of nonselective fading mobile-satellite radio channels. Such an extended Suzuki process is a product of a Rician process and a lognormal process, where the inphase and quadrature components describing the Rician process are mutually correlated. In addition, the model can also take into consideration a Doppler shift of the direct line-of-sight component. 14.3.3. Corazza Vatalaro Model This model may be considered as an extension of the Loo s model for the case, where the direct and the multipath (diffuse) components of the shadowed signal are lognormally distributed [11]. In particular, the model is applied to nongeostationary satellite channels, such as low-Earth orbit (LEO) and medium-Earth orbit (MEO) channels, in which for a given user located in a generic site the elevation angle changes continuously. Again, it combines a Rician and lognormal statistics, with shadowing affecting both direct and diffuse components. Therefore, it is suitable for all types of environment (rural, suburban, urban) simply by tuning the model parameters. The PDF of the received signal envelope, r, can be presented as [11]:

1 0