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Path Loss Models for Microwave Links Unraveled


Free Space Model


     The free space model only accounts for the loss in signal power due to spreading of energy over a 3-dimensional space.

FSPL of FSL = (4*pi*f*d/c)^2



Where:
f - frequency
d - distance
c - speed of light
Wavelength (lambda) - c/f

     We notice from the formula that as the frequency increases, the loss becomes greater, which is intuitive since more wavelengths are needed to cover a given distance compared to the lower frequency wavelengths. Naturally, as the distance increases, the loss becomes greater as well.




ITU Terrain Model


     This model considers the Fresnel zone, aside from the free space loss at distances (-20*Cn+10) and closer (where Cn is the normalized terrain clearance).


Total Loss = -20*Cn + 10 + FSL




Where:
Cn = (h1-h2)/sqrt((lambda*d1*d2/(d1+d2)));
h1 - height of LOS link
h2 - height of obstruction
d1 - distance to obstruction from TX 1
d2 - distance to obstruction from TX 2
lambda - wavelength


Weissberger's Model


Total Loss = FSL + 1.33*(f^0.284)*(d^0.588)


-if (14<d<=400)

Total Loss = FSL + 0.45*(f^0.284)*d 


-if (0<d<=14)



Where:

d - depth of foliage along path

     Once again, we observe that frequency and distance share a direct relationship with the total loss.





Hata Model (Urban)


Path Loss in Urban Area = 69.55 + 26.16*log(f) - 13.82*log(hb) - Ch + (44.9 - 6.55*log(hb))*log(d)^b




Where:

f - frequency
hb - antenna height of base station
Ch - antenna height correction factor
d - distance
b - recommendation ITU-R P.529-3 Adjustment factor

     Again, frequency and distance share a direct relationship with the total loss. However, the antenna height is also considered to decrease the loss (inverse relationship).





Hata Model (Suburban)


Path Loss in Suburban Area = Path Loss in Urban Area - 2*log(f/28)^2-5.4



     We can observe that the considered loss due to frequency is decreased with the suburban model.





Hata Model (For Open Areas)


Path Loss in Open Area = Path Loss in Urban Area -4.78*log(f)^2 +18.33*log(f)-40.97






Cost 231 Extended Hata Model


Total Loss = 46.33 + (44.9 - 6.55*log(hb))*log(d) + 33.9*log(f) - a(h) -13.82*log(hb) + C




hb - height of base station
h - mobile station height in meters
d - distance in kilometers
f - frequency in Megahertz
C = 0 for Suburban areas
C = 3 for Metropolitan Centers





Empirical Cost-Walfisch-Ikegami Model (Non-LOS)


Total Loss = FSL + Rooftop-to-street diffraction loss + Multi-screen diffraction loss






Empirical Cost-Walfisch-Ikegami Model (LOS)


Total Loss = 42.64 + 26*log(d) + 20*log(f)



Where:
d - distance in kilometers
f - frequency in megahertz

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