Formulas For System Planning; Free Space Path Loss; Fresnel Zone Boundary; Theoretical Signal Strength - GE MDS 4790M Installation And Operation Manual

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8.3 Formulas for System Planning

The following standard formulas are provided for assistance in determining
system installation parameters.

Free Space Path Loss

α
= 92.4 + 20
fs
α
= free space loss in dB
fs
d = path distance in kilometers
ƒ = frequency in GHz

Fresnel Zone Boundary

⋅
nd d
1
F = 17.3 ------------------- -
n
fD
F = Fresnel zone boundary in meters
n
d = distance from one end of the path to the Fresnel zone boundary (in
1
kilometers)
d = distance from the other end of the path to the Fresnel zone
2
boundary (in kilometers)
D = total path distance (d
ƒ = frequency in GHz
n = Fresnel zone, 1 (for 1st) is used here

Theoretical Signal Strength

EIRP α
RSSI = –
RSSI = signal strength at the receiver in dBm
EIRP = RF power output in dBm + G
α
= free-space path loss in dB
fs
G = receive antenna gain in dBi
ra
L = receive feedline loss in dB
rfl
L = transmit feedline loss in dB
tfl
G = transmit antenna gain in dBi
ta

Probability of System Fading

× ×
FProb = a b
FProb = probability of fading more than F
a = terrain factor
• 4 is used for very smooth terrain, such as over water
• 1 is used for average terrain, with moderate roughness
• 0.25 is used for mountainous or very rough terrain
b = climate factor
• 0.5 is used for a hot, humid climate
• 0.25 is used for temperate or northern areas
• 0.125 is used for a very dry climate
ƒ = frequency in GHz
d = path length in km
F = fade margin in dB
MDS 4790M (MPT 1411) I/O Guide
log f + 20 log d
10 10
2
where:
+d ) in kilometers
1 2
+ G – L
where:
fs ra rfl
–L
ta tfl
7 – 3
× × ×
6.0 10 f d
where:
– ( ) 10 ⁄
F
×
10
where:
MDS 05-3628A01, Rev. B