A13.1.2 Noise-limited network

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.

    
                     (Eq. 172)

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

                                                                 (Eq. 173)

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: 

where Q  is the cumulative distribution for R_max and the resulting mean path loss (symbol to be inserted) and an additional path loss due to availability or coverage  . 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 standard deviation (symbol to be inserted).

Here are some examples for illustration:

• for 68 % coverage, b = 1;
• for 95 % coverage, (symbol to be inserted) = 1.96;
• for 95.5 % coverage,  (symbol to be inserted)= 2;
• for 99 % coverage, (symbol to be inserted) = 2.58;
• for 99.9 % coverage, (symbol to be inserted) =3.29.
  
  The exact values can be easily determined by using the inverse Gaussian function.

                     (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:

                                   (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)

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.

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