**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.

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**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).

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**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**

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

-if (14<d<=400)

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**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)**

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**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)**

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**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**

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**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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