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

WINNER D5.4 v. 1.4
and choosing an AS of 3 degrees, the required number of sinusoids is 239 for equal amplitude sinusoids
and 11 for sinusoids with varying amplitude.
Peaky Doppler spectrum. Due to the fixed velocity, each scatterer can be attributed a single Doppler
frequency component. The resulting Doppler spectrum is simply the addition of these components, which
are limited in number by the amount of sinusoids per path. Ways to mitigate this are to use a high number
of sinusoids, to shorten the time-duration of the drops (frequency resolution decreases), or introduce
instationarity of the velocity.
Discrete Scatterer Framework. The assumption that any channel response can be separated into a sum
of reflectors represented as Dirac-functions in time and space implies infinite accuracy. The measurement
system to obtain these parameters would need infinite bandwidth, antennas, and power. The
parameterization is thus problematic from an exact physical interpretation point of view.
4.3.4 Comparison
It is important to note that both approaches converge to each other with increasing number of sinusoids
for SOS and decreasing length of stationary segments for the stochastic approach. Hence, the essential
question is which model is preferable for reasonable assumptions about the channel and implementation
parameters. Channels that can not even be assumed short-term stationary will be more difficult to
implement (with equal computational complexity) as a stochastic model than with SOS. On the other
hand, channels with large AS per tap will be more difficult to implement (with equal computational
complexity) as SOS than with a stochastic model.
The WINNER Channel Model follows the SOS approach. It is seen as flexible framework and it enables
more easily advanced future modelling features like time evolution of channel model parameters.
4.3.5 Kronecker correlation
Many stochastic MIMO channel models apply what is called the Kronecker assumption for the antenna
correlation matrices. This assumption states that the correlation matrix, obtained as C = E{ vec(H)
vec(H) H }, can be written as a Kronecker product, i.e. C = C Rx ⊗ C Tx , where C Rx and C Tx are receive and
transmit correlation matrices, respectively. The Kronecker property is useful in many ways; most
importantly it significantly reduces the number of model parameters, and it greatly simplifies the
analytical treatment (such as for capacity evaluation). It implies that the joint transmit and receive APS
function can be written as a product of two independent APS at transmitter and receiver.
Other publications [HOHB02] based on measurement results have made a point that this assumption
could not be verified empirically in all scenarios evaluated. In reaction to that, researchers have tried to
come up with new methods that represent a compromise between the abstraction and simplification of the
Kronecker assumption and the rather complex case with no assumptions at all. In [OHWW03], an
approach is presented where the condition of a separable APS is alleviated into the condition of
independent eigenbasis of receiver to the transmit weights, and vice versa.
Our preliminary analysis shows that, while both arguments certainly have significance, it is in practice
important to carefully examine the underlying basis that the correlation matrix is computed on. We start
with the most detailed model. In case of a wideband system, the channel is represented as a tapped delay
line, i.e. H(τ) = H 1 δ(τ - τ 1 ) + … + H n δ(τ - τ n ). Furthermore, each delay-tap matrix can be split into a
sum of contributions from different angle clusters, i.e. H i = H i1 + … + H im . We can now argue that with
sufficient splitting and thus subdivision of the delay-angle domain, we can always reach a point such that
all the smallest parts H ij have a separable APS and thus a Kronecker correlation matrix. Any system with
a resolution capability less than that will observe only linear combinations of H ij which might well not
hold up to the Kronecker assumption. Thus we can always define a channel model based on Kronecker
correlated components, while a system employing this model might not observe such properties.
In summary this means that we can build a channel model by defining a set of clusters (in delay-angle
domain) along with their independent APS at transmitter and receiver.
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