A17.7.1.3 Algorithm

For calculation of the path loss according to Recommendation ITU-R P.1546-1 Annex 8 the following procedure is followed:

1 Check range of application of the propagation model regarding time percentage, frequency, distance, and antenna height: 

• • Time percentage :                           1% £< pt £< 50 %
  • Frequency :                                     30 MHz £< f £< 3 000 MHz
  • Distance :                                        0.001 km  £< d £< 1000 km
  • Transmitter antenna height :            0 m £< ht £< 3000 m
  • Receiver antenna height :               1 m £< hr £< 3000 m

2 Determination of lower and higher nominal percentages pt_inf and pt_sup:

If t < 10 then pt_inf = 1 % and pt_sup= 10 % else pt_inf = 10 % and pt_sup= 50 %

3 Determination of the lower and higher nominal frequencies :

If f < 600 MHz then f_inf = 100 MHz and f_sup= 600 MHz else f_inf = 600 MHz and f_sup= 2000 MHz

4 If h_t ³ 10 m: calculate field strength E(f= f, d, h_t, h_r, pt) :

4.1) Calculation of the four following field strengths:

-              E(f= f_inf , d, h_t, h_r, pt_inf)

-              E(f= f_sup , d, h_t, h_r, pt_inf)

-              E(f= f_inf , d, h_t, h_r, pt_sup)

-              E(f= f_sup , d, h_t, h_r, pt_sup)

according to the procedure described in steps 4.1.1. to 4.1.4.

4.1.1) Calculate the dimensionless parameter k, function of the required transmitter height, h_t:

                                              (Eq. 218)

4.1.2) Determine from the following table the set of parameters a₀ to a₃, b₀ to b₇, c₀ to c₆ and d₀ to d₁ to be used according to nominal values of frequencies and time percentages:

Table 85: Parameters a₀ to a₃, b₀ to b₇, c₀ to c₆ and d₀ to d₁

4.1.3) Calculate the unblended to maximum value field strength, E_u, at the distance, d, and transmitting height, h_t, as follows:

                                                                                        (Eq. 219)

where: 

and: 

and: 

where: 

where: 

and: 

4.1.4) Calculate the blended to the free space value of field strength, E_b, at the distance, d, and transmitting height, h_t, as follows:

                                                                                    (Eq. 220)

where:

E_fs is the free-space field strength

E_fs = 106.9 - 20 log(d)   dB(μV/m)

p_bb is a blend coefficient set to value 8.

4.2) Calculation of the field strength E(f, d, h_t, h_r, pt_inf) using log-linear interpolation in frequency range:

                             E = E_inf + (E_sup - E_inf) log(f/f_inf)/log(f_sup/f_inf)     (dB(μV/m))                                  (Eq. 221)

where:

E_inf:       E(f= f_inf , d, h_t, h_r, pt_inf)

E_sup:      E(f= f_sup , d, h_t, h_r, pt_inf)

4.3) Dual calculation for the field strength E(f, d, h_t, h_r, pt_sup) using log-linear interpolation in frequency range:

                             E = E_inf + (E_sup - E_inf) log(f/f_inf)/log(f_sup/f_inf)     (dB(μV/m))                                  (Eq. 222)

where:

E_inf:                       E(f= f_inf , d, h_t, h_r, pt_sup)

E_sup:                      E(f= f_sup , d, h_t, h_r, pt_sup)

4.4) Calculation of the field strength E(f, d, h_t, h_r, pt) using log-linear interpolation formula in time percentage range :

                  E = E_sup (Q_inf- Q_t)/(Q_inf- Q_sup) + E_inf(Q_t - Q_sup)/(Q_inf- Q_sup)     (dB(μV/m))                 (Eq. 223)     

Where: (Q_i (x) being the inverse complementary cumulative normal distribution function):

Q_t     = Q_i (pt/100)

Q_inf       =Q_i (pt_inf/100)

Q_sup  = Q_i (pt_sup /100)

E_inf    = E(f, d, h_t, h_r, pt_inf)

E_sup     =E(f, d, h_t, h_r, pt_sup)

5 For a transmitting/base antenna height h_t less than 10 m, determine the field strength for the required height and distance using following method

The procedure for extrapolating field strength at a required distance d km for values of h_t in the range 0 m to 10 m is based on smooth-Earth horizon distances in km written as d_H(h) = 4.1Öh, where h is the required value of transmitting/base antenna height h_t in metres.

For d < d_H(h_t) the field strength is given by the 10 m height curve at its horizon distance, plus DE, where DE is the difference in field strengths on the 10 m height curve at distances d and the h_t horizon distance.

For d ³ d_H(h_t) the field strength is given by the 10 m height curve at distance Dd beyond its horizon distance, where Dd is the difference between d and the h_t horizon distance.

This may be expressed in the following formulae where E₁₀ (d) is the field strength in dB(µV/m) calculated for transmitter antenna 10 m and for a distance d (km) according to the procedure described in step 4:

E = E₁₀(d_H(10)) + E₁₀(d) - E₁₀(d_H(h_t))                                             dB(µV/m)   d < d_H(h_t)                         

         =    E₁₀(d_H(10) + d - d_H(h_t))                                                dB(µV/m)   d ³ d_H(h_t)                         

If in the latter equation d_H(10) + d - d_H(h_t) exceeds 1 000 km, even though d £ 1 000 km, E₁₀ may be found from linear extrapolation for log(distance) of the curve, given by:

E₁₀  =    E_inf + (E_sup - E_inf) log(d/D_inf)/log(D_sup/D_inf)                        dB(µV/m)                                          

where:

D_inf:                        penultimate tabulation distance (km)

D_sup:                       final tabulation distance (km)

E_inf:                        field strength at penultimate tabulation distance (dB(µV/m))

E_sup:                       field strength at final tabulation distance (dBµV/m))

Note: this recommendation is not valid for distances greater than 1 000 km. This method should be used only for extrapolating for h_t < 10 m.

6 If the receiving antenna height h_r is not equal to the height of representative clutter at its location (denoted R), correct the field strength as follows:

The field-strength values given by the land curves and associated tabulations in this recommendation are for a reference receiving antenna at a height, R (m), representative of the height of the ground cover surrounding the receiving/mobile antenna, subject to a minimum height value of 10 m.

SEAMCAT always assumes the height of local clutter R , depending on the propagation environment set in the model selection window:

Table 86: Default clutter height in the ITU-R P1546-1 model (when clutter height option not activated)

If the receiving antenna height, h_r (m), is different from the assumed R value, as shown in Table 86 , a correction shall be added to the field strength taken from the curve.

Where the receiving antenna is adjacent to land account should first be taken of the elevation angle of the arriving ray by calculating a modified representative clutter height R' (m), given by:

R'            =    R    (m)                                            for h_t <= 6.5d + R                                     (Eq. 224)

               = (1 000 d R – 15 h_t)/(1 000 d - 15 ) (m) for h_t > 6.5d + R                                      (Eq. 225)

where h_t is in metres and distance d is in km.

The value of R' must be limited if necessary such that it is not less than 1 m.

When the receiving antenna is in an urban environment the correction is then given by:

         Correction = (6.03) - J(n)                                               dB                   for h_r < R

= K _hr log(h_r /R')                                             dB                   for h_r ³ R                 (Eq. 226)

where J(n) is given by :

                                           (Eq. 227)

where:

           n                      =                          K_nu Ö (h_dif q_clut)

           h_dif                    =                            R' - h_r         (m)

           q _clut                  =                          arctan (h_dif /27) (degree)

           K _hr                   =                          3.2 + 6.2 log(f)

           K_nu                   =                          0.0108 Ö f

           f                       =                          frequency (MHz)

Where the receiving antenna is adjacent to land in a rural environment the correction is given by the above equation (3) for all values of h_r.

If the required distance is equal to or greater than d₁₀, then again the correction for the required value of h₂ should be calculated using above equation (2) with R' set to 10 m.

If the required distance is less than d₁₀, then the correction to be added to the field strength E should be calculated using:

Correction         = 0.0                                         dB        d £ d (h_r)                                   (Eq. 228)

                                    = (C₁₀) log(d/d_hr)/log(d₁₀/d_hr)         dB        d_hr < d < d₁₀              

where:

C₁₀:       correction for the required value of h_r at distance d₁₀ using equation (2) with R' set to 10 m,

d₁₀:       distance at which the path just has 0.6 Fresnel clearance for h_r = 10 m
calculated as D₀₆(f, h_t, 10) as given in note 2

d_hr:       distance at which the path just has 0.6 Fresnel clearance for the required value of h_r calculated as D₀₆(f, h_t, h_r) as given in note 2

This recommendation is not valid for receiving antenna heights, h_r, less than 1 m.

7 Add a log-normal term G(s_L) corresponding to the variability in the percentage of locations :

Values of standard deviation for digital systems having a bandwidth less than 1 MHz and for analogue systems are given as a function of frequency by:

                               s_L = K + 1.6 log(f)          dB                                                               (Eq. 229)

where :

K          =          2.1 - for mobile systems in urban locations;

3.8 - for mobile systems in suburban locations or amongst rolling hills;

5.1 - for analogue broadcasting systems.

For digital systems having a bandwidth of 1 MHz or greater, a standard deviation of 5.5 dB should be used at all frequencies.

8 If necessary, limit the resulting field strength to the maximum value calculated as follows:

The field strength must not exceed a maximum value E_max given by:

  E_Max = E_fs                                               dB(mV/m)      for land paths

where E_fs is the free space field strength for 1 kW e.r.p. given by:

                               E_fs = 106.9 - 20 log(d)     (dB(mV/m))                                       (Eq. 230)

9 Convert field strength to path loss using following formula:

             Lb = 77.2 – E 20 log f     (dB)                                                  (Eq. 231)

where:

Lb: basic transmission loss (dB)

E: field strength in dB(mV/m) measured with a transmitting power of 1 W e.i.r.p.

f: frequency (MHz).

Note 1: The following approximation to the inverse complementary cumulative normal distribution function, Qi(x), is valid for 0.01 <= x <= 0.99 :

Q_i(x) = T(x) –x(x)                     if x £ 0.5

Q_i(x) = -{T(1-x) – x(1-x)}            if x > 0.5

where:

                                                                       C₀ = 2.515517

                                                                       C₁ = 0.802853

                                                                       C₂ = 0.010328

                                                                       D₁ = 1.432788

                                                                       D₂ = 0.189269

                                                                       D3 = 0.001308

Note 2: the path length which just achieves a clearance of 0.6 of the first Fresnel zone over a smooth curved Earth, for a given frequency and antenna heights h_t and h_r, is given approximately by:

where:

                      D_f:        frequency-dependent term

                     =                          km                                                                              

                     D_h:        asymptotic term defined by horizon distances

                     =                               km                                                                              

                        f:        frequency (MHz)

                  h_t, h_r:        antenna heights above smooth Earth (m)

In the above equations, the value of h_t must be limited, if necessary, such that it is not less than zero. Moreover, the resulting values of D₀₆ must be limited, if necessary, such that it is not less than 0.001 km.

Note 3: the case h_t is less than zero described in the recommendation is not handled.

Note 4: no correction due to terrain clearance angle is implemented.