Final report on link level and system level channel models - Winner

WINNER D5.4 v. 1.4
( ) { }
P φ = LE p| φ f( φ)
(4.18)
( ) { }
P θ = LE p| θ f( θ)
(4.19)
( ) { }
P ϕ = LE p| ϕ f( ϕ)
(4.20)
( ) { }
where E{ p|
τ }, E{ p|
φ } , E{ p|
θ }, E{ p|
ϕ } , and { | }
P ϑ = LE p| ϑ f( ϑ)
, (4.21)
E p ϑ are the expected power of the
multipath components conditioned on their delays, azimuth departure angle, elevation departure angle,
azimuth arrival angle, elevation arrival angle, respectively.
4.1.4.1.1 Expected power conditioned on delay
The estimated expected power of multipath components conditioned on delays can be obtained from
(4.17) as:
{ } ( )
E p| τ ∝ P τ / f( τ)
. (4.22)
In order to make the concept of the generic channel model approach clear, we can think of the case when
both P ( τ ) and f ( τ ) are exponential decaying functions. The one-side exponential decaying function
P τ is expressed as:
that describes the ( )
where
P
( τ )
( −τ
σ ),
⎧ exp
τ
for τ > 0
⎪
∝ ⎨
⎪
⎩0,
otherwise
(4.23)
σ
τ is the RMS delay spread. The exponential function that describes the probability density
f τ is expressed as:
f τ ∝ exp −τ
~
, (4.24)
function of the delays ( )
where
σ ~
τ
( ) ( )
is standard deviation of the path delays. Hence, the expected power conditioned on delay
(4.25) can be written as:
Now, let us define a parameter r τ as follows:
use (4.26) in (4.25), we get:
σ τ
⎛ σ%
τ
−σ
⎞
τ
Pn
= E{ p| τ}
∝exp
⎜−τ ⎟. (4.25)
⎝ σσ %
τ τ ⎠
σ ~
τ
r
τ
=
(4.26)
στ
⎛ rτ
−1⎞
Pn
= E{ p| τ}
∝exp⎜−τ
⎟
⎝ rτσ
τ ⎠ . (4.27)
Thus, the expected power of multipath components conditioned on delay depends on the RMS delay
spread and the parameter that describes the ratio between the path delays standard deviation and the RMS
delay spread.
For the case when P ( τ ) is exponential as in (4.24) and the f ( τ ) is uniform U ( 0,
τ )
power conditioned on delay (4.22) can be written as:
Pn
4.1.4.1.2 The power azimuth-delay spectrum
max
, the expected
⎛ τ ⎞
= E{ p| τ}
∝exp⎜−
⎟
⎝ στ
⎠ , τ ≤ τ
max
(4.28)
We will focus our discussion on azimuth angles at both transmitter and receiver. Now, we call the double-
P φ , ϕ,
τ and its corresponding
directional-delay spectrum as the double-azimuth-delay spectrum, i.e., ( )
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