Cellular Systems Cellular Concepts The cellular concept was a ...

EE5401 Cellular Mobile Communications
EE5401 Cellular Mobile Communications
Coverage Problems
Revision:
- Recall that the mean measured value,
⎛ d ⎞
PL(
d)
dB = PL(
d0)
dB + 10n
log
⎜
⎟ or
⎝ d0
⎠
P r ( d)
dB = PtdB
− PL(
d)
dB
[ P ( γ ]
β ( γ ) = P r R)
> - cell boundary coverage,
β ( γ )
∞
= ∫
γ
1
2πσ
X dB
⎛ ⎞
⎜γ
− P
= r ( R)
Q ⎟
⎜ ⎟
⎝
σ X dB ⎠
⎡
2⎤
⎢ 1 ⎛
⎞
⎜ X −
− dB Pr
( R)
exp
⎟ ⎥dX
⎢ ⎜
⎟ ⎥ dB
2
⎢⎣
⎝
σ X dB ⎠ ⎥⎦
where Q(x) is the standard normal distribution.
• must know how to use the table.
- Measurement shows that at any value of d, the
path loss PL (d)
at a particular location is random
and distributed log-normally (normal in dB) about
this mean value.
Pr ( d)
dB = Pr
( d)
dB + X σ
where X σ is a zero-mean Gaussian distributed
random variable (in dB) with standard deviation σ
(in dB).
Boundary coverage
Cell coverage
• Proportion of locations within the area defined by the
cell radius R, receiving a signal above the threshold γ.
1
U ( γ ) = ∫ P[ Pr
( r)
> γ ] dA
A
A
1
R 2π
⎛ P r ⎞
Q⎜γ
− r ( )
= ∫ ∫
⎟ ⋅ rdr ⋅ dθ
2
πR
⎜
X
⎟
0 0 ⎝
σ
dB ⎠
2
R ⎛ P r ⎞
Q⎜γ
−
=
r ( )
∫
⎟ ⋅ rdr
R ⎜
X
⎟
0 ⎝
σ
dB ⎠
• Therefore, there will be a proportion of locations at
distance R (cell radius) where a terminal would
experience a received signal above a threshold γ. (γ is
usually the receiver sensitivity)
The solution is given in the Rappaport p.107 (1 st
edition).
Institute for Infocomm Research 59 National University of Singapore
Institute for Infocomm Research 60 National University of Singapore