additional_clutter_loss_rural.md

Estimate Additional cluster loss for Rural via ITU-R P.452-16

Reference: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.452-16-201507-S!!PDF-E.pdf

The additional loss due to protection from local clutter is given by the expression:

$$ A_h = 10.2 F_{fc} .e^{-d_k}(1-tanh(6(h/h_a-0.625)))-0.33 $$

where

• $d_k$ is distance (km) from nominal clutter point to antenna
• $h$ is antennal height(m) above ground level
• $h_a$ is nominal clutter height (m) above local ground level

where

$$ F_{fc} = 0.25 +0.375(1+tanh[7.5(f-0.5)]) $$

f Frequency (GHz)

From table 4 in FCC ref document - the Nominal clutter heights and distances for Clutter set as the Village centre

• $h_a$ = 5 meters
• $d_k$ is 0.07 km.

$A_{ht}$ Transmitter $A_{hr}$ Receiver

$$ \begin{align} A_{ht} = 10.2 F_{fc} .e^{0.07}(1-tanh(6(h_t/5-0.625)))-0.33 \hspace{100cm} \\ \text{where } \\ h_t = \text{height of transmitter antenna (Wifi AP)} \end{align} $$

and

$$ \begin{align} A_{hr} = 10.2 F_{fc} .e^{0.07}(1-tanh(6(h_r/5-0.625)))-0.33 \hspace{100cm} \\ \text{where } \\ h_r = \text{height of receiver antenna (Microwave Tower) (interference)} \end{align} $$

clutter_loss.md

Estimate cluster loss for Rural

ITU-R P.452-16 is a recommendation that provides a prediction method for the evaluation of interference between stations on the surface of the Earth at frequencies above about 0.1 GHz. It does not specifically provide clutter loss values for different environments like ITU-R P.2108-0 does.

As per the FCC document note 165

See Table 4 of ITU-R P.452-16, Prediction procedure for the evaluation of interference between stations on the surface of the Earth at frequencies above about 0.1 GHz. Reference: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.452-16-201507-S!!PDF-E.pdf

(If this is not rendering properly see at https://gist.github.com/alexcpn/b88865b090856b2537ea2cd3e4c559f7)

$$ A_h = 10.2 F_{fc} .e^{-d_k}(1-tanh(6(h/h_a-0.625)))-0.33 $$

where $d_k$ is distance (km) from nominal clutter point to antenna $h$ is antennal height(m) above ground level $h_a$ is nominal clutter height (m) above local ground level

where

$$ F_{fc} = 0.25 +0.375(1+tanh[7.5(f-0.5)]) $$

As per the FCC document, the ITU-R P.452-16 should use the village centre as the default clutter category.

from table 4 in FCC ref document $h_a$ = 5 meters and $d_k$ is 0.07 km.

$A_{ht}$ Transmitter $A_{hr}$ Receiver

$$ A_{ht} = 10.2 F_{fc} .e^{0.07}(1-tanh(6(h_t/5-0.625)))-0.33 \\ \text{where } \\ h_t = \text{height of transmitter antenna (Wifi AP)} $$

and

$$ A_{hr} = 10.2 F_{fc} .e^{0.07}(1-tanh(6(h_r/5-0.625)))-0.33 \\ \text{where } \\ h_r = \text{height of receiver antenna (Microwave Tower) (interference)} $$

Putting these in the final basic transmission loss not exceed for p% time $L_b$ (dB) as given by

$$ L_b = -5log(10^{-0.2L_{bs}} +10^{-0.2L_{bam}}) + A_{hr} +A_{ht} $$

Where $L_{bam}$ dB is the modified basic transmission loss, which takes diffraction and LoS or ducting/layer-reflection enhancements into account: and $L_{bs}$ The basic transmission loss due to tropo-scatter

Unclear/Complex parts

• Height of transmitter antenna is unknown (? check)
• It is not clear if $A_{hr}$ or $A_{ht}$ has to be added only if they are in village region
• Calculation of $L_{bs}$ is complex and need mean temperature and pressure (see below)
• Calculation of $L_{bam}$ is still more complex and involve multiple formulae

Calculation of $L_{bam}$

$$ \begin{align} L_{bam} = L_{bda} + (L_{minb0p} -L_{bda} )F_j \\ \end{align} $$

Calculate L_{minb0p}

$$ L_{minb0p} = \begin{cases} L_{b0p} + (1-\omega)L_{dp} \text{ for } p \le \beta_0 \\ L_{bd50} + (L_{b0\beta} + (1-\omega)L_{dp} -L_{bd50} ).F_i \text{ for } p \ge \beta_0 \end{cases} $$

Calculate L_{b0p} $$ \begin{align} \text{Basic transmission loss not exceeded for time percentage, p%, due to LoS propagation:} L_{b0p} = L_{bfsg} + E_{sp} \ E_{sp} = 2.6[1-exp(-0.1{d_{lt} +d_{lr}})]log(p/50) \ L_{bfsg} = 92.5 + 20 log(f) + 20log(d) + A_g \ \text{Ag : total gaseous absorption (dB): } \ A_g = [\gamma_o + \gamma_w(p)]d \ \end{align} $$

Calculating diffraction loss

The diffraction loss $L_{dp}$ not exceeded for p% time, for 0.001% ≤ p ≤ 50%, is then calculated using a limiting or interpolation procedure described in § 4.2.4.The diffraction loss is calculated by the combination of a method based on the Bullington construction and spherical-Earth diffraction

The diffraction model calculates the following quantities required in § 4.6:

• $L_{dp}$: diffraction loss not exceeded for p% time
• $L_{bd50}$: median basic transmission loss associated with diffraction
• $L_{bd}$: basic transmission loss associated with diffraction not exceeded for p% time.

Calculate L_{dp} diffraction loss not exceeded for p% time $$ $$

Calculate L_{bd50} $$ $$

Calculation of $L_{bs}$

$L_{bs}$ The basic transmission loss due to tropo-scatter, Lbs (dB)

$$ L_{bs} = 190 + L_f + 20 log(d) + 0.573θ – 0.15 N_0 + L_c + A_g – 10.1[– log ( p / 50)]^{0.7} dB $$

where $L_f$ : frequency dependent loss:

$$ L_f = 25 log f – 2.5 [log ( f / 2)]^2 $$

and

$L_c$ : aperture to medium coupling loss (dB):

$$ L_c =0.051.e^{0.055( G_t + G_r)} $$

where $G_t$ $G_r$ is the gain (linear) of the transmitting and receiving antenna (dBi)

$$ \begin{align} A_g = [\gamma_o + \gamma_w(p)]d \\ p \text{ water vapour density } = 7.5 +2.5 \omega \\ \omega = \text{fraction of the total path over water} \end{align} $$

where

$\gamma_o$ $\gamma_w(p)$ specific attenuation due to dry air and water vapour, respectively, and are found from the equations in Recommendation ITU-R P.676

and when we go there https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.676-10-201309-S!!PDF-E.pdf and select the Annexe 2 approximation (Approximate estimation of gaseous attenuation in the frequency range 1-350 GHz )

We get the following

For f ≤ 54 GHz:

$$ \gamma_o = [7.2r_t^{2.8}/(f^2+0.34 r_p^2 r_t^{1.6}) +0.62\xi_3/((54-f)^{1.16\xi_1} + 0.83\xi_2)]f^2r_p^2*10^{-3} \rightarrow \text{Equation (22a)} $$

where

$$ \begin{align} \xi_1 = \varphi (r_p ,r_t ,0.0717, -1.8132,0.0156, -1.6515) \\ \xi_2 = \varphi (r_p ,r_t,0.5146, -4.6368, -0.1921, -5.7416) \\ \xi_3 = \varphi (r_p ,r_t,,0.3414, -6.5851,0.2130, -8.5854) \ \\ \varphi (r_p ,r_t,a,b,c,d) = r_p^ar_t^b \times exp[c(1-r_p)+d(1-r_t)] \end{align} $$

Where

f: frequency (GHz)

$r_p = p_{tot}/1013$, where $p_{tot}$ represents total air pressure

$r_t = 288/(273 + t)$

p: pressure (hPa)

t: temperature (°C), where mean temperature values can be obtained from maps given in Recommendation ITU-R P.1510, when no adequate temperature data are available.

ITU-R P.1510 https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.1510-1-201706-I!!PDF-E.pdf