Delay Channels
Delay channels offer a simple interface to modeling spatial propagation delays of
signals in a network of distributed Devices
and investigate the delay’s impact on interference and synchronization.
They, by design, do not model any fading effects but do consider signal attenuation according
to Frii’s transmission formula.
classDiagram
class DelayChannelBase {
<<Abstract>>
+realize()
+propagate()
}
class DelayChannelRealization {
<<Abstract>>
+propagate()
}
class RandomDelayChannel {
+realize()
+propagate()
}
class RandomDelayChannelRealization {
+propagate()
}
class SpatialDelayChannel {
+realize()
+propagate()
}
class SpatialDelayChannelRealization {
+propagate()
}
DelayChannelBase o-- DelayChannelRealization : realize()
RandomDelayChannel o-- RandomDelayChannelRealization : realize()
SpatialDelayChannel o-- SpatialDelayChannelRealization : realize()
RandomDelayChannel --|> DelayChannelBase
SpatialDelayChannel --|> DelayChannelBase
RandomDelayChannelRealization --|> DelayChannelRealization
SpatialDelayChannelRealization --|> DelayChannelRealization
click DelayChannelBase href "channel.delay.DelayChannelBase.html"
click DelayChannelRealization href "channel.delay.DelayChannelRealization.html"
click RandomDelayChannel href "channel.delay.RandomDelayChannel.html"
click RandomDelayChannelRealization href "channel.delay.RandomDelayChannelRealization.html"
click SpatialDelayChannel href "channel.delay.SpatialDelayChannel.html"
click SpatialDelayChannelRealization href "channel.delay.SpatialDelayChannelRealization.html"
Currently, two types of DelayChannels are implemented:
RandomDelayChannels and SpatialDelayChannels.
Both generate their own type of DelayChannelRealization, namely RandomDelayChannelRealizations
and SpatialDelayChannelRealizations, respectively.
In general, the delay channel’s impulse response between two devices \(\alpha\) and \(\beta\) featuring \(N^{(\alpha)}\) and \(N^{(\beta)}\) antennas, respectively, is given by
\[\mathbf{H}(t,\tau) = \frac{1}{4\pi f_\mathrm{c}^{(\alpha)}\overline{\tau}} \mathbf{A}^{(\alpha,\beta)} \delta(\tau - \overline{\tau})\]
and depends on the assumed propagation delay \(\overline{\tau}\), the transmitting device’s carrier frequency \(f_\mathrm{c}^{(\alpha)}\) and the antenna array response \(\mathbf{A}^{(\alpha,\beta)}\).
The two implementations differ in the way they generate delay \(\overline{\tau}\) and antenna array response \(\mathbf{A}^{(\alpha,\beta)}\).