Final report on link level and system level channel models - Winner
Final report on link level and system level channel models - Winner
Final report on link level and system level channel models - Winner
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WINNER D5.4 v. 1.4<br />
where t is the time, the full polarimetric (2x2) transfer matrix, κ ( t)<br />
, includes the losses <strong>and</strong><br />
depolarisati<strong>on</strong> of all physical processes (reflecti<strong>on</strong>, diffracti<strong>on</strong>, scattering, etc) of each multipath<br />
r<br />
r<br />
comp<strong>on</strong>ents, xT,<br />
s is the positi<strong>on</strong> of the antenna element s of transmit antenna array, x Ru , is the positi<strong>on</strong><br />
of the antenna element u of the receive antenna array u, <strong>and</strong> ν<br />
l is the Doppler comp<strong>on</strong>ent. Note that all<br />
parameters are in general time variant, which is not shown for simpler presentati<strong>on</strong>.<br />
4.1.4.1 Inter-segment modeling<br />
The radio <strong>channel</strong> is in general not stati<strong>on</strong>ary. Nevertheless, over short periods of time <strong>and</strong> space, <strong>channel</strong><br />
parameters vary very little, <strong>and</strong> the assumpti<strong>on</strong> of short-term stati<strong>on</strong>arity is often a very good<br />
approximati<strong>on</strong>. The parameters characterizing our <strong>channel</strong> model are called bulk parameters. The time<br />
durati<strong>on</strong>s, over which these bulk parameters are c<strong>on</strong>stant, are denoted <strong>channel</strong> segment a.k.a. drops in the<br />
nomenclature of the SCM. Over time <strong>and</strong> space, bulk parameters change <strong>and</strong> we characterize this<br />
variability statistically.<br />
For simulati<strong>on</strong> purposes, the first goal typically is to experience the range of variability of the <strong>channel</strong><br />
rather than the medium-term evoluti<strong>on</strong> behaviour. Thus, the initial focus is mainly <strong>on</strong> the joint<br />
distributi<strong>on</strong>s of bulk parameters. Between <strong>channel</strong> segments, i.e. realizati<strong>on</strong>s of these r<strong>and</strong>om variables,<br />
independence is assumed. The physical interpretati<strong>on</strong> is that <strong>channel</strong> segments are relatively short <strong>channel</strong><br />
observati<strong>on</strong> periods that are significantly separated from each other in time or space.<br />
Each term of the matrix <strong>channel</strong> is a sum of L multipath comp<strong>on</strong>ents that can be described by the time<br />
htτφθϕϑ , , , , , , given as:<br />
varying double-directi<strong>on</strong>al delay spread functi<strong>on</strong> (D 3 SF), ( )<br />
L<br />
ht (, τφθϕϑ , , , , ) = ∑ αn() t δφ ( −φn, θ −θn, ϕ −ϕn, ϑ−ϑn, τ −τn)<br />
. (4.2)<br />
n=<br />
1<br />
The instantaneous power double-directi<strong>on</strong>al-delay spectrum (PD 3 S) can be written as:<br />
L<br />
2<br />
PI(, t τφθϕϑ , , , , ) = ∑ αn() t δφ ( −φn, θ −θn, ϕ −ϕn, ϑ−ϑn, τ −τn)<br />
, (4.3)<br />
n=<br />
1<br />
where ⋅ is the absolute value of the argument. The per <strong>channel</strong> segment (local) average PD 3 S, which<br />
represents <strong>channel</strong> characteristics per <strong>channel</strong> segment, can be defined as:<br />
P<br />
( τφθϕϑ , , , , ) = E { P ( t, τφθϕϑ , , , , )}<br />
s t I<br />
L<br />
∑<br />
= p δφ ( −φ , θ −θ , ϕ −ϕ , ϑ−ϑ ) δτ ( −τ<br />
)<br />
n=<br />
1<br />
n n n n n n<br />
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<br />
characterized by the orientati<strong>on</strong> of the last-bounce scatterer as seen from transmitter <strong>and</strong> receiver, as well<br />
as the total delay. This approach stems from superresoluti<strong>on</strong> parameter estimati<strong>on</strong> techniques (e.g.,<br />
MUSIC, ESPRIT, SAGE) which decompose a measured <strong>channel</strong> resp<strong>on</strong>se based <strong>on</strong> the above model.<br />
The D 3 SF characterizes the dispersive behaviour of the mobile radio <strong>channel</strong> in delay domain <strong>and</strong><br />
directi<strong>on</strong> domain seen either at transmitter or receiver sides. The equati<strong>on</strong>s are valid regardless of which<br />
terminal is the transmitter, either BS or MS <strong>and</strong> which terminal is the receiver either MS or BS. All<br />
parameters in (4.4) are r<strong>and</strong>om variables, since scatterers’ locati<strong>on</strong>s change with movement of the MS.<br />
Hence, the D 3 SF is a r<strong>and</strong>om process, which is described by joint distributi<strong>on</strong> of its r<strong>and</strong>om variables. The<br />
statistics of multipath comp<strong>on</strong>ents amplitudes, delays, <strong>and</strong> azimuth <strong>and</strong> elevati<strong>on</strong> angles at both ends are<br />
generally not separable. Hence, they have to be described in joint probability density functi<strong>on</strong>s (pdf).<br />
However, multidimensi<strong>on</strong>al joint pdf is not tractable mathematically. Therefore, simplificati<strong>on</strong>s are<br />
needed for simulati<strong>on</strong> purposes. As a result, <strong>on</strong>ly partial dependencies of distributi<strong>on</strong>s of different<br />
parameters are usually assumed.<br />
One of the most comm<strong>on</strong> assumpti<strong>on</strong>s is uncorrelated scattering (US). We assume independence of all<br />
parameters for different paths, i.e., different n. Therefore, (4.4) is characterized by the joint distributi<strong>on</strong><br />
f( pn, φn, θn, ϕn, ϑn, τ<br />
n)<br />
, which is independent of n.<br />
The expectati<strong>on</strong> in (4.4) is over short periods of time, where <strong>channel</strong> parameters vary <strong>on</strong>ly slightly, <strong>and</strong><br />
the assumpti<strong>on</strong> of short-term stati<strong>on</strong>arity is valid. The over segments (global) average PD 3 S is obtained<br />
by taking the expectati<strong>on</strong> of the per <strong>channel</strong> segment (local) average PD 3 S over all bulk parameters<br />
(4.4)<br />
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