Parameter Estimation for the Field Strength of Radio Environment Maps

Algorithm 1

Radio environment map field strength estimation.

Step  1

Calculate distance matrix and variogram value matrix G, where and .

  , lag_max = round , , round .

Calculate experimental variogram value ,

for

 h = ;

 SEL = (LAGS == );

 N = sum(sum(SEL == 1));

 R = sqrt(sum((SEL))/());

end for

Step  2

The PSO algorithm is used to fit the theoretical variogram models and using the theoretical variogram models in

Equations (9) and (12),

Initialization: the position and velocity of a particle in -dimensional problem space is randomly generated.

Evaluation of particles: the fitness value of each particle is calculated using Equation (14).

Updating : the particle fitness values are compared with the population optimal value , and if the current value is

better than , the position of is set to the current particle position.

Updating the particle: the velocities and positions of all particles are updated using Equations (15).

Stop condition: return to step for iterations to obtain optimal parameters , , , and . Then, use Equations (9)

and (11) to obtain theoretical variogram models and .

Step  3

   and are calculated using the theoretical variogram model.

Equation (4) is written in matrix form to get .

The estimated value is calculated by Equation (2): .