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A13.1.2 A13.1.2

Assuming that the received power is equal to the sensitivity of the victim link receiver, then the radius R_max can be determined for the wanted radio path by the following equation. 

Image Added    
Image Removed                                  (Eq. 163172)

...

where the path loss is defined by a median loss plus an additional term representing the distribution

 

                                                                                                                    (Eq. 164173)

where: 

• F_median: propagation loss not including slow fading, i.e. path loss without variations option;
• F_slowfading(X%): slow fading margin for X% coverage loss;

...

The distribution of  the path loss  can be expressed in a general way by the following equation: Image Removed

Unit
body $Q(\mu +a,{{R}_{\max }})=y$

                                                                                         

where Q  is the cumulative distribution for R_max and the resulting mean path loss

Mathinline
body $\mu $

 and an additional path loss

Mathinline
body $a$

 due to availability or coverage  

Mathinline
body $y$

. The availability y of the system is linked to the coverage loss through the simple relation y = 1 – x. Assuming that slow fading can be approximated by log-normal distribution, i.e. median  mean, the relation  can be introduced where  b stands for a multiple of the well known standard deviation (sigma). A few

Mathinline
body $\sigma $

.

Here are some examples for illustration: At a

• for 68 % coverage, b = 1;
• for 95 % coverage,

...

• Mathinline
  body $b$

   = 1.96;
• for 95.5 % coverage,

  Mathinline
  body $b$

  = 2;
• for 99 %

...

• coverage,

  Mathinline
  body $b$

   = 2.58

...

• ;
• for 99.9 %

...

• coverage,

  Mathinline
  body $b$

   =3.29.
  
  

The exact values can be easily determined by using the inverse Gaussian function.

 

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Then the equation:

Image Removed                (Eq. 165)

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 $

  (Eq. 174)

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:

   Image Removed                                 (Eq. 166)

...

           

Mathinline
body ${{\tilde{R}}_{\max }}={{R}_{\max 0}}-\frac{{{R}_{\max 0}}-{{R}_{\max 1}}}{v({{R}_{\max 0}})-v({{R}_{\max 1}})}v({{R}_{\max 0}})$

  (Eq. 175)

In this case, formulas given for  have (EQ to be inserted - only half is copied with math tool)  need to be inverted.

 

Note 1: Inverse The inverse of the normalised Gaussian cumulative distribution is implemented through a piecewise piece approximation. 

Note 2: Ro is to be set to 1 m (0.001 km) 

Note 3: If after running the 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 you provided. This can be solved by reducing the minimum distance or increasing the minimum distance used in the calculation, so that the algorithm may find can calculate the corresponding coverage radius. 

Note 4: When setting the R_min, R_max values, please observe the validity range as appropriate for the selected propagation model. Otherwise SEAMCAT will produce the error a warning message when starting a the simulation starts.