# Ideal Channel#

The Ideal Channel is the default Channel Model assumed by Simulations. It is completely deterministic and lossless, introducing neither phase shifts, amplitude changes nor propagation delays in between the linked Devices.

classDiagram direction LR class IdealChannel { _realize() : IdealChannelRealization } class IdealChannelRealization { +propagate(Signal) : ChannelPropagation } IdealChannel --o IdealChannelRealization : realize() click IdealChannel href "channel.ideal.IdealChannel.html" "IdealChannel" click IdealChannelRealization href "channel.ideal.IdealChannelRealization.html" "IdealChannelRealization"

Considering two devices $$\alpha$$ and $$\beta$$ featuring $$N_\alpha$$ and $$N_\beta$$ antennas respectively, the ideal Channelâ€™s impulse response

$\begin{split}\mathbf{H}(t, \tau) = \delta(\tau) \left\lbrace\begin{array}{cr} \left[1, 1,\,\dotsc,\, 1 \right] & \text{for } N_\beta = 1 \\ \left[1, 1,\,\dotsc,\, 1 \right]^\mathsf{T} & \text{for } N_\alpha = 1 \\ \begin{bmatrix} 1, & 0, & \dots, & 0 \\ 0, & 1, & \dots, & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0, & 0, & \dots, & 1 \end{bmatrix} & \text{otherwise} \end{array}\right\rbrace \in \mathbb{C}^{N_\beta \times N_\alpha}\end{split}$

depends on the number of antennas of the devices and is independent of the time $$t$$. For channels with an unequal number of antennas, the ideal Channelâ€™s impulse response is a diagonal matrix with ones on the diagonal, padded with zeros to match the dimensions of the channel matrix. Therefore, the device with the bigger amount of antennas will receive / transmit nothing from the additional antennas.