Spatial Delay Channel

The spatial delay channel requires both linked devices to specify their assumed positions. Its impulse response between two devices \(\alpha\) and \(\beta\) featuring \(N^{(\alpha)}\) and \(N^{(\beta)}\) antennas, respectively, is given by

\[\mathbf{H}(t,\tau) = \frac{1}{4\pi f_\mathrm{c}^{(\alpha)}\overline{\tau}} \mathbf{A}^{(\alpha,\beta)} \delta(\tau - \overline{\tau})\ \text{.}\]

The assumed propagation delay between the two devices is given by

\[\overline{\tau} = \frac{\|\mathbf{p}^{(\alpha)} - \mathbf{p}^{(\beta)}\|_2}{c_0}\]

and depends on the distance between the two devices located at positions \(\mathbf{p}^{(\alpha)}\) and \(\mathbf{p}^{(\beta)}\). The sensor array response \(\mathbf{A}^{(\alpha,\beta)}\) depends on the device’s relative orientation towards each other.

The following minimal example outlines how to configure the channel model within the context of a Simulation:

# Initialize two devices to be linked by a channel
simulation = Simulation()
alpha_device = simulation.new_device(
    carrier_frequency=1e8,
    pose=Transformation.From_Translation(np.array([0, 0, 0])),
)
beta_device = simulation.new_device(
    carrier_frequency=1e8,
    pose=Transformation.From_Translation(np.array([1, 0, 0])),
)

# Create a channel between the two devices
channel = SpatialDelayChannel()
simulation.set_channel(alpha_device, beta_device, channel)

# Configure communication link between the two devices
link = SimplexLink()
alpha_device.transmitters.add(link)
beta_device.receivers.add(link)

# Specify the waveform and postprocessing to be used by the link
link.waveform = RRCWaveform(
    symbol_rate=1e8, oversampling_factor=2, num_data_symbols=1000,
    num_preamble_symbols=10, pilot_rate=10)
link.waveform.channel_estimation = SCLeastSquaresChannelEstimation()
link.waveform.channel_equalization = SCZeroForcingChannelEqualization()
link.waveform.synchronization = SCCorrelationSynchronization()

class SpatialDelayChannel(model_propagation_loss=True, gain=1.0, **kwargs)

Bases: DelayChannelBase[SpatialDelayChannelRealization]

Delay channel based on spatial relations between the linked devices.

Parameters:

• model_propagation_loss (bool, optional) – Should free space propagation loss be modeled? Enabled by default.

• gain (float, optional) – Linear power gain factor a signal experiences when being propagated over this realization. \(1.0\) by default.

• **kawrgs – Channel base class initialization arguments.

_realize()

Generate a new channel realzation.

Abstract subroutine of realize. Each Channel is required to implement their own _realize() method.

Returns: A new channel realization.

Return type:

SpatialDelayChannelRealization

recall_realization(group)

Recall a realization of this channel type from its HDF serialization.

Parameters:

group (h5py.Group) – HDF group to which the channel realization was serialized.

Return type:

SpatialDelayChannelRealization

Returns: The recalled realization instance.

class SpatialDelayChannelRealization(model_propagation_loss, sample_hooks, gain)

Bases: DelayChannelRealization

Realization of a spatial delay channel.

Generated from SpatialDelayChannel's realize routine.

Parameters:

• model_propagation_loss (bool) – Should free space propagation loss be modeled?

• gain (float) – Linear power gain factor a signal experiences when being propagated over this realization.

static From_HDF(group, sample_hooks)

Return type:

SpatialDelayChannelRealization