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(Eq. 172)
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where the path loss is defined by a median loss plus an additional term representing the distribution
(Eq. 173)
where:
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The distribution of the path loss can be expressed in a general way by the following equation:
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where Q is the cumulative distribution for Rmax and the resulting mean path loss (symbol to be inserted)
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Here are some examples for illustration:
- for 68 % coverage, b = 1;
- for 95 % coverage, (symbol to be inserted)
= 1.96;Mathinline body $b$ - for 95.5 % coverage, (symbol to be inserted)
= 2;Mathinline body $b$ - for 99 % coverage, (symbol to be inserted)
= 2.58;Mathinline body $b$ - for 99.9 % coverage, (symbol to be inserted)
=3.29.Mathinline body $b$
The exact values can be easily determined by using the inverse Gaussian function.
(EQ to be inserted) Mathinline
(Eq. 174)body $v({{R}_{\max }})={{P}_{VLT}}+{{g}_{VLT}}+{{g}_{VLR}}-sen{{s}_{VLR}}-{{F}_{median}}({{f}_{VLR}},{{h}_{VLR}},{{h}_{VLT}},{{R}_{\max }},env)-b\sigma $
The determination of the zero of function v, is made through a recursive method such as regula-falsi used in logarithmic scale which should yield a better precision. The solution of such a method provides the following equation:
(EQ to be inserted) (Eq. 175)
In this case, formulas given for need to be inverted.
Then the equation:
(Eq. 165)
The determination of the zero of function v, is made through a recursive method such as regula-falsi used in logarithmic scale which should yield a better precision. The solution of such a method provides:
(Eq. 166
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In this case, formulas given for (EQ to be inserted - only half is copied with math tool) need to be inverted.
Note 1: The inverse of the normalised Gaussian cumulative distribution is implemented through a piece approximation.
Note 2: Ro is to be set to 1 m (0.001 km)
Note 3: If after running a simulation it appears that the resulting coverage radius is equal or very close to the minimum distance or the maximum distance used in the calculation of the coverage radius, it is likely that there is a mistake in the values provided. This can be solved by reducing the minimum distance or increasing the minimum distance used in the calculation, so that the algorithm can calculate the corresponding coverage radius.
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