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

WINNER D5.4 v. 1.4
where t is the time, the full polarimetric (2x2) transfer matrix, κ ( t)
, includes the losses and
depolarisation of all physical processes (reflection, diffraction, scattering, etc) of each multipath
r
r
components, xT,
s is the position of the antenna element s of transmit antenna array, x Ru , is the position
of the antenna element u of the receive antenna array u, and ν
l is the Doppler component. Note that all
parameters are in general time variant, which is not shown for simpler presentation.
4.1.4.1 Inter-segment modeling
The radio channel is in general not stationary. Nevertheless, over short periods of time and space, channel
parameters vary very little, and the assumption of short-term stationarity is often a very good
approximation. The parameters characterizing our channel model are called bulk parameters. The time
durations, over which these bulk parameters are constant, are denoted channel segment a.k.a. drops in the
nomenclature of the SCM. Over time and space, bulk parameters change and we characterize this
variability statistically.
For simulation purposes, the first goal typically is to experience the range of variability of the channel
rather than the medium-term evolution behaviour. Thus, the initial focus is mainly on the joint
distributions of bulk parameters. Between channel segments, i.e. realizations of these random variables,
independence is assumed. The physical interpretation is that channel segments are relatively short channel
observation periods that are significantly separated from each other in time or space.
Each term of the matrix channel is a sum of L multipath components that can be described by the time
htτφθϕϑ , , , , , , given as:
varying double-directional delay spread function (D 3 SF), ( )
L
ht (, τφθϕϑ , , , , ) = ∑ αn() t δφ ( −φn, θ −θn, ϕ −ϕn, ϑ−ϑn, τ −τn)
. (4.2)
n=
1
The instantaneous power double-directional-delay spectrum (PD 3 S) can be written as:
L
2
PI(, t τφθϕϑ , , , , ) = ∑ αn() t δφ ( −φn, θ −θn, ϕ −ϕn, ϑ−ϑn, τ −τn)
, (4.3)
n=
1
where ⋅ is the absolute value of the argument. The per channel segment (local) average PD 3 S, which
represents channel characteristics per channel segment, can be defined as:
P
( τφθϕϑ , , , , ) = E { P ( t, τφθϕϑ , , , , )}
s t I
L
∑
= p δφ ( −φ , θ −θ , ϕ −ϕ , ϑ−ϑ ) δτ ( −τ
)
n=
1
n n n n n n
In (4.4), the variables {L, p n , φ n , θ n , ϕ n , ϑ n , τ n } are the bulk parameters introduced above. The L paths are
characterized by the orientation of the last-bounce scatterer as seen from transmitter and receiver, as well
as the total delay. This approach stems from superresolution parameter estimation techniques (e.g.,
MUSIC, ESPRIT, SAGE) which decompose a measured channel response based on the above model.
The D 3 SF characterizes the dispersive behaviour of the mobile radio channel in delay domain and
direction domain seen either at transmitter or receiver sides. The equations are valid regardless of which
terminal is the transmitter, either BS or MS and which terminal is the receiver either MS or BS. All
parameters in (4.4) are random variables, since scatterers’ locations change with movement of the MS.
Hence, the D 3 SF is a random process, which is described by joint distribution of its random variables. The
statistics of multipath components amplitudes, delays, and azimuth and elevation angles at both ends are
generally not separable. Hence, they have to be described in joint probability density functions (pdf).
However, multidimensional joint pdf is not tractable mathematically. Therefore, simplifications are
needed for simulation purposes. As a result, only partial dependencies of distributions of different
parameters are usually assumed.
One of the most common assumptions is uncorrelated scattering (US). We assume independence of all
parameters for different paths, i.e., different n. Therefore, (4.4) is characterized by the joint distribution
f( pn, φn, θn, ϕn, ϑn, τ
n)
, which is independent of n.
The expectation in (4.4) is over short periods of time, where channel parameters vary only slightly, and
the assumption of short-term stationarity is valid. The over segments (global) average PD 3 S is obtained
by taking the expectation of the per channel segment (local) average PD 3 S over all bulk parameters
(4.4)
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