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

WINNER D5.4 v. 1.4
• Cross-polarization ratio (XPR). No distinction is made between clusters and segments in the
current model. Therefore, the resulting variability of XPR is equivalent if evaluated across
clusters or across segments.
• Total angle-spread and delay-spread. These parameters characterize the power dispersion in
angle and delay domain across clusters. Note that this is a high-level characterization. The more
detailed properties of angle and delay dispersion are each defined by a set of two variables. This
is firstly, a mean angle and a delay offset for each single cluster, and secondly, an angle-spread
and a delay-spread for each cluster. Here,
• The angle-spread per cluster and delay-spread per cluster values are constants.
• The mean angle per cluster and the delay offset per cluster distributions are functions of
the total (per segment) angle-spread and the total (per segment) delay-spread.
Large-scale parameters of the channel have clear influence on the channel characteristics. This can be
noticed in delay domain characteristics through the RMS delay spread and in the angle domain through
the RMS angle-spread in departure and in arrival. The RMS delay spread has influence on power delay
spectrum and on the probability density function (pdf) of path delays through the parameter r τ .. The
statistical distributions that generate spatial properties of the ZDSCs are functions of RMS angle-spread
through azimuth angle propationality factor ( r ϕ ) and RMS azimuth angle-spread ( σ ϕ ) in the arrival side,
and through departure angle proportionality factor ( r φ ) and RMS departure angle-spread ( σ φ ) in the
departure side. The dispersion parameters σ ϕ and σ φ are sometimes correlated with log-normal
shadowing (LNS), which is important for interference calculations, handover algorithms, etc. For each set
of RMS delay spread and RMS angle-spread departure, RMS angle-spread departure arrival and LNS
within each channel segment, correlation between them has to be considered. These large-scale
parameters are often <strong>report</strong>ed in literature to have log-normal distributions.
Our framework allows for any distribution for the large-scale parameters and also introduces a modelling
of the auto-correlation over the service area. This is achieved by using scenario and parameter specific
g ⋅ to transform the large-scale parameters into a domain where they can be treated as
transformations ( )
Gaussian. The mean, µ , cross-correlation and auto-correlation matrix R ( 0)
are then defined in the
transformed domain. The realizations of the large-scale parameters are then obtained as
−1
0.5
−1
0.5
0.5
5
g R ? x, y + µ
⋅
R 0 is obtained as R ( 0) = EΛ
0.
( ( ) ), where g ( ) is the inverse transform, and ( )
T
from the eigen-decomposition R( 0 ) = EΛE
of R ( 0)
. The auto-correlation is achieved by generating m
( m = 6 for A1, and m = 4 for all other scenarios) independent Gaussian random processes,
? x, y = ξ1 x,
y Kξ
m
x,
y , each one with mean zero and variance one in the positions x, y where the
( ) [ ( ) ( )] T
mobiles are located. The auto-correlation of the process c
( x,
y)
2
E{ ξ ( x y ) ξ ( x , y )} = exp( − r / λ ), where ( ) ( ) 2
c
1, 1 c 2 2
∆
c
∆ r =
no auto-correlation mode (NACM) in which the parameters
the random variable ?( x, y) [ ξ ( x,
y) ( x y)
] T
1
Kξ
m
,
x
1 − x0
+ y1
− y0
m
ξ is given by
. However, we also define a
λ , K ,λ are all set to zero, or equivalently,
= , is randomized independently for each location. The
required parameters for generating the correlated large-scale parameters are thus the transformation
~
s ( x , y)
= g( s( x,
y)
) (or actually its inverse), the mean µ and correlation R ( 0)
of the transformed largescale
parameters, and the de-correlation distance parameters λ , K 1
,λm
.
This information is available in Table 3.1 to Table 3.5. Table 3.1 lists the distribution function for each
modelled parameter in each scenario. For normally distributed random variables the original and
transformed variable is identical, except for the delay-spread in scenario B3, where the transformation is a
9
multiplication with a factor 10 (for numerical reasons). For parameters of log-Gumbel and log-Logistic
distribution, the transformation (and their inverse) are given by:
~
−
s = g s = −Q
1 F log s ,ν ,ς
(3.1)
and
( ) (
Gumbel( 10
( ) ))
−1
( ~ −1
s = g s ) = exp log(10) F Q(
~ s ),ν ,ς
Gumbel
−
1
( ( ))
1 ( F Logistic 10
)
−1
( log(10) F ( Q(
~ s ),ν ,ς ))
−
( s) = −Q
( log ( s)
,ν ,ς )
(3.2)
~
s = g
, (3.3)
−1
s = g ( ~ s ) = exp
Logistic
−
(3.4)
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