A17.9.2 Algorithm

The terminal designations

This propagation model is not reciprocal with respect to designations of the transmitting/base station and the receiver/mobile station/terminal. It is primarily intended for use with broadcasting and mobile services where the transmitter/base antenna is above the level of local clutter.

When it is used to calculate the coverage of, or for the coordination of, broadcasting and/or base-to-mobile stations, then the actual transmitting/base station should be treated as the “transmitting/base”. For this the SEAMCAT user has to deselect the “Terminal designation” switch.

In other cases, whch is the default setup in SEAMCAT, where there is no a priori reason to consider either terminal as the transmitting/base, then the selection of which terminal to designate as the transmitting/base station for the purposes of this propagation model can be as follows:

a)         if both terminals are below the levels of clutter in their respective vicinities, then this model will not give accurate predictions to the problem at hand. Users should seek guidance from other, more appropriate, ITU-R Recommendations. Note that SEAMCAT will prompt you with a warning message;

b)         if one terminal is in an open location or above the surrounding clutter, whereas the other terminal is below the level of clutter, then the open/uncluttered terminal should be treated as the transmitting/base station for the purposes of actual identity as the transmitter/base or receiver/mobile;

c)         if both terminals are open/uncluttered, then the terminal with the greater effective height should be treated as the transmitting/base station for the purposes of this Recommendation.

As noted above, this model is not reciprocal. However, in some special cases, it may be treated as such. For these particular cases, for example, which may be encountered for the monitoring and prediction of receiver/mobile-to-transmitter/base coverage and/or interference, it may be useful, under items b) and c) of the previous discussion, to designate that terminal in the open location, which should also always have the higher effective height, as the transmitter/base as the “high” antenna, whilst designating the terminal in the cluttered location as the receiver/mobile as the “low” antenna, without regard to which terminal is actually the transmitter/base and receiver/mobile. Users of this model should note, for the purposes of calculation, that if these “high” and “low” designations are to be used, the high antenna termination will always be synonymous with (and equivalent to) the transmitter/base station’s effective height, h1, whilst the low antenna termination will always be synonymous with (and equivalent to) the receiver/mobile’s height, h2, with the same qualifier, in the subsequent calculation of field strength or basic transmission loss.

Maximum field-strength values

The field strength must not exceed a maximum value E_max as described in ITU-R P. 1546-1. In principle any correction which increases a field strength must not be allowed to produce values greater than these limits for the family of curves and distance concerned. However, limitation to maximum values should be applied only where indicated in Annex 6 of the ITU-R P.1546-4.

Determination of transmitting/base antenna height, h1

The transmitting/base antenna height, h₁, to be used in the calculation depends on the type and length of the path and on various items of height information, which may not all be available.

For land paths, the effective height of the transmitting/base antenna, h_eff, is defined as its height in metres over the average level of the ground between distances of 3 and 15 km from the transmitting/base antenna in the direction of the receiving/mobile antenna. Where the value of effective transmitting/base antenna height, h_eff, is not known it should be estimated from general geographic information. This model is not valid when the transmitting/base antenna is below the height of surrounding clutter.

The value of h₁ to be used in calculation should be obtained using the method given in § 3.1, 3.2 or in § 3.3 of P1546-4 as appropriate.

Land paths shorter than 15 km

For land paths less than 15 km, the following method is used:

Terrain information not available

In SEAMCAT, no terrain information is available. Therefore, the value of h₁ is calculated according to path length, d, as follows:

                                        (Eq. 241)

      m for d <= 3 km

                                                m for 3 km < d < 15 km

where h_a is the antenna height above ground (e.g. height of the mast).

Land paths of 15 km or longer

For these paths:

                          m     (Eq. 242)

Transmitting/base antenna height, h1, in the range 10 m to 3 000 m

If the value of h₁ coincides with one of the eight heights for which curves are provided, namely 10, 20, 37.5, 75, 150, 300, 600 or 1 200 m, the required field strength may be obtained directly from the plotted curves or the associated tabulations. Otherwise the required field strength should be interpolated or extrapolated from field strengths obtained from two curves using:

        dB(μV/m)  (Eq. 243)

where:

                       h_inf :        600 m if h₁ > 1200 m, otherwise the nearest nominal effective height below h₁

                      h_sup :        1200 m if h₁ > 1200 m, otherwise the nearest nominal effective height above h₁

                      E_inf :        field-strength value for h_inf at the required distance

                     E_sup :        field-strength value for h_sup at the required distance.

The field strength resulting from extrapolation for h₁ > 1200 m should be limited if necessary such that it does not exceed the maximum defined in § 2 of Recommendation ITU-R P.1546-4.

This model is not valid for h₁ > 3000 m.

Transmitting/base antenna height, h1, in the range 0 m to 10 m
For a land path, the field strength at the required distance d km for 0 <= h1 < 10 m is calculated using:

          (Eq. 244)

where:

             (Eq. 245)

                                    dB  (Eq. 246)

: the correction Ch1 in dB calculated using equation (12) in § 4.3 of ITU-R P.1546-4 at the required distance for h1 =  10 m
E₁₀ and E₂₀ : the field strengths in dB(μV/m)  calculated according to § 4.1 of ITU-R P.1546-4 at the required distance for h1 = 10 m and h1 = 20 m respectively..

Note that the corrections C₁₀₂₀ and  should both evaluate to negative quantities.

Transmitting/base antenna height, h₁, in the range 0 m to 10 m

For a land path, the field strength at the required distance d km for 0 £ h₁ < 10 m is calculated using:

Interpolation of field strength as a function of distance

Figures 1 to 24 of Recommendation ITU-R P.1546-4 show field strength plotted against distance, d, the range 1 km to 1 000 km. No interpolation for distance is needed if field strengths are read directly from these graphs. For greater precision, and for computer implementation, field strengths should be obtained from the associated tabulations (see Annex 1 of ITU-R P.1546-4, § 3). In this case, unless d coincides with one of the tabulation distances given in Table 1, the field strength, E (dB(μV/m)), should be linearly interpolated for the logarithm of the distance using:

          dB(μV/m)    (Eq. 247)

where:

                         d :        distance for which the prediction is required

                       d_inf :        nearest tabulation distance less than d

                      d_sup :        nearest tabulation distance greater than d

                      E_inf :        field-strength value for d_inf

                     E_sup :        field-strength value for d_sup.

This model is not valid for values of d less than 1 km or greater than 1 000 km.

Interpolation and extrapolation of field strength as a function of frequency

Field-strength values for the required frequency should be obtained by interpolating between the values for the nominal frequency values of 100, 600 and 2000 MHz. In the case of frequencies below 100 MHz or above 2 000 MHz, the interpolation must be replaced by an extrapolation from the two nearer nominal frequency values. For most paths interpolation or extrapolation for log (frequency) can be used, but for some sea paths when the required frequency is less than 100 MHz it is necessary to use an alternative method.

For land paths, and for sea paths where the required frequency is greater than 100 MHz, the required field strength, E, should be calculated using:

                               dB(μV/m)                (Eq. 248)

where:

                         f :        frequency for which the prediction is required (MHz)

                       f_inf :        lower nominal frequency (100 MHz if f < 600 MHz, 600 MHz otherwise)

                      f_sup :        higher nominal frequency (600 MHz if f < 600 MHz, 2 000 MHz otherwise)

                      E_inf :        field-strength value for f_inf

                     E_sup :        field-strength value for f_sup.

The field strength resulting from extrapolation for frequency above 2 000 MHz should be limited if necessary such that it does not exceed the maximum value given in § 2 of Recommendation ITU-R P.1546-4.

For sea paths where the required frequency is less than 100 MHz an alternative method should be used, based upon the path lengths at which 0.6 of the first Fresnel zone is just clear of obstruction by the sea surface. An approximate method for calculating this distance is given in § 17 of  Recommendation ITU-R P.1546-4.

The alternative method should be used if all of the following conditions are true:

• The path is a sea path.
• The required frequency is less than 100 MHz.
• The required distance is less than the distance at which a sea path would have 0.6 Fresnel clearance at 600 MHz, given by D₀₆(600, h₁, 10) as given in § 17 of P1546-4.

If any of the above conditions is not true, then the normal interpolation/extrapolation method given by equation (14) should be used.

If all of the above conditions are true, the required field strength, E, should be calculated using:

                  dB(μV/m)                                                                           for d <= d_f

                       dB(μV/m)         for d > d_f

where:

                    E_max :        maximum field strength at the required distance as defined in § 2 of P1546-4

                            maximum field strength at distance d_f as defined in § 2 of P1546-4

                         d₆₀₀ :       distance at which the path has 0.6 Fresnel clearance at 600 MHz calculated as D₀₆(600, h₁, 10) as given in § 17 of P1546-4

                        d_f :       distance at which the path has 0.6 Fresnel clearance at the required frequency calculated as D₀₆( f, h₁, 10) as given in § 17 of P1546-4

                    Ed600      field strength at distance d₆₀₀ and the required frequency calculated using equation (14).

Interpolation of field strength as a function of percentage time

Field-strength values for a given percentage of time between 1% and 50% time should be calculated by interpolation between the nominal values 1% and 10% or between the nominal values 10% and 50% of time using:

               dB(μV/m)   (Eq. 249)

where:

                         t :        percentage time for which the prediction is required

                       t_inf :        lower nominal percentage time

                      t_sup :        upper nominal percentage time

                      Q_t =        Q_i (t/100)

                    Q_inf  =        Q_i (t_inf/100)

                    Q_sup =        Q_i (t_sup/100)

                      E_inf :        field-strength value for time percentage t_inf

                     E_sup :                field-strength value for time percentage t_sup

where Q_i (x) is the inverse complementary cumulative normal distribution function.

This model is valid for field strengths exceeded for percentage times in the range 1% to 50% only. Extrapolation outside the range 1% to 50% time is not valid.

A method for the calculation of Q_i (x) is given in Annex 5, § 15 of ITU-R P.1546-4.

Correction for receiving/mobile antenna height

The field-strength values given by the land curves and associated tabulations in this model are for a reference receiving/mobile 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. Examples of reference heights are 20 m for an urban area, 30 m for a dense urban area and 10 m for a suburban area.

Table 90: Default clutter height in the ITU-R P.1546-4 model(when clutter height option not activated)

Where the receiving/mobile antenna is on 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:

           m     (Eq. 250)

where h₁ and R (m) and distance d (km). Note that for h₁ < 6.5d + R, R′ ≈ R. The value of R' must be limited if necessary such that it is not less than 1 m.

when the receiving/mobile antenna is in an urban environment the correction is then given by:

(Eq. 251)

Correction              dB    for h₂ < R′

                           dB      for h₂ ≥ R′

where J(n) is given by equation (12a), and:

             v =     

                      m         

              =    degrees          

            f:        frequency (MHz).

In cases in an urban environment where R' is less than 10 m, the correction should be reduced by K_h2 log(10/R′). Where the receiving/mobile antenna is on land in a rural or open environment the correction is given by equation   for all values of h₂ with R' set to 10 m.

Correction for short urban/suburban paths

If a path of length less than 15 km covers buildings of uniform height over flat terrain, a correction representing the reduction of field strength due to building clutter should be added to the field strength. The correction is given by:

                               Correction =    (Eq. 252)

where h_a is the antenna height above ground (m) (i.e. height of the mast) and R is representative of the height of the ground cover surrounding the receiving/mobile antenna as defined in § 9 of P1546-4, which also represents the height of ground cover surrounding the transmitting/base antenna. This correction only applies when d is less than 15 km and h₁ − R is less than 150 m.

Variation in path loss

Values of standard deviation are dependent on frequency and environment, and empirical studies have shown a considerable spread. Representative values for areas of 500 m ´ 500 m are given by the following expression (In SEAMCAT it is understood that the below equation only applies to the Mobile system and not to the Broadcasting systems):

                                                              dB  (Eq. 253)

where:

                K =       1.2, for receivers with antennas below clutter height in urban or suburban environments for mobile systems with omnidirectional antennas at car-roof height

                       K =        1.0, for receivers with rooftop antennas near the clutter height

                       K =        0.5, for receivers in rural areas 

                         f :        required frequency (MHz).

In SEAMCAT depending on the selected system the standard deviation is defined as follow:

Mobile: when “< 2 km radius” and “< 50 km radius” is selected, 4 dB and 8 dB are added to the calculated standard deviation respectively. This responds to the note of the Recommendation stating that if the area over which the variability is to apply is greater than 500 m ´ 500 m, or if the variability is to relate to all areas at a given range, rather than the variation across individual areas, the value of s_L will be greater. Empirical studies have suggested that location variability is increased (with respect to the small area values) by up to 4 dB for a 2 km radius and up to 8 dB for a 50 km radius.

Broadcasting, digital: the standard deviation is set to a constant value of 5.5 dB. No correction is added.

Broadcasting, analogue: The standard deviation is defined as follow and no correction is added:

                                                  dB (Eq. 254)

In addition, SEAMCAT allows you to select a standard deviation value which overwrites any predefined value when selecting the “use user specified standard deviation” switch.