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

WINNER D5.4 v. 1.4
• Model approach is by default stationary. Modelling of non-stationary effects requires extension.
4.3.2 Sum-of-Sinusoids
Example: Jakes’ fading generator, 3GPP SCM
Advantages:
• Correlation across antenna elements and time created implicitly.
• Non-stationary processes potentially easier to integrate.
Disadvantages:
• Requires a large number of sinusoids for realistic modelling and thus computationally expensive.
• Resulting Doppler spectra are peaky (with number of peaks less or equal to number of
sinusoids).
• The SOS approach builds on the assumption that any channel response can be separated into a
sum of reflectors represented as Dirac-functions in time and space.
4.3.3 Problem details
Not all of the above points might be obvious to the reader. In the following, some of the advantages and
disadvantages are thus explained in more details.
4.3.3.1 Stochastic approach
Filtering process. Essentially, the channel response is correlated across space only. This correlation is
characterized by the spatial ACF, which is calculated by numerical integration from the APS. This spatial
ACF is then mapped into two dimensions; the correlation between signals at antenna elements depending
on inter-element spacing, and the correlation between signals in time depending on the movement of the
mobile. This yields a two-dimensional kernel which is then used for filtering uncorrelated Gaussian
samples.
Non-stationary effects. The model is stationary by default. While the incorporation of certain timevariable
parameters is straightforward, e.g. Ricean K-factor, other non-stationary effects, i.e. timeevolution
of Doppler spectrum or angle parameters, requires continuous re-calculation of the filter kernel
and is thus computationally expensive.
4.3.3.2 SOS approach
Number of sinusoids required. In the SOS framework, fading is ensured by defining the position of the
sinusoids in delay and angle in such a way that a minimum number of sinusoids always falls within the
resolution capabilities of the observation system. This minimum number between 4 and 8 [Gald04]
ensures the observation of a close to Rayleigh distribution. If the number of sinusoids drops below this
minimum amount, the observer will first see unusual distributions and finally identify single, discrete
scatterers, both of which is typically not a desired effect. Note that strong discrete scatterers, typically
associated with LOS scenarios, are implemented as an optional additional component (SCM section "Line
of sight") because the power of a single sinusoid is by definition fixed and small (e.g. 1/20 of a tap in
SCM).
In the following, we illustrate this point with an example. In the SOS framework, an APS is generated by
changing the spacing of the sinusoids (because each sinusoid is defined to have equal power). A typical
APS <strong>report</strong>ed for outdoor scenarios is a Laplacian function with a log-normal distributed AS [AIP02].
Next, we determine how to distribute the sinusoids. The lowest density (sinusoids per degree) occurs at
the outer ends of the Laplacian function and for large AS values (we pick 30 degree according to the
reference). Assuming we want to be accurate to -20dB from the peak of the APS, then the angle range is
roughly ±100 degrees from the centre. Let's say the maximum resolution of our observer is 10 degree (for
example by using a highly directive antenna). In these 10 degrees we want to have a minimum of say 5
sinusoids, i.e. a density of 5/10. The total required number of sinusoids then can be derived as 2345 per
delay-tap.
There are two ways to decrease this high number of sinusoids. One is the introduction of variability in
power of the sinusoids. The distribution of taps can then be different to the APS and, with respect to the
previous example, might be more uniform than Laplacian. Hence, in the limiting case of uniform
distribution of taps, the power at each sinusoid would vary according to the Laplace function, and the
resulting number of sinusoids then would be 101.
The second approach for reducing the number of sinusoids is to assume that the AS at each path is not
equal to the total AS (over all paths) but smaller (like in SCM). Following again the example from above
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