Random Delay Channel

Delay channel assuming a uniformly distributed random propagation between the linked devices. 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 is drawn from the uniform distribution

\[\overline{\tau} \sim \mathcal{U}(\tau_{\mathrm{Min}}, \tau_{\mathrm{Max}})\]

and lies in the interval between \(\tau_\mathrm{Min}\) and \(\tau_\mathrm{Max}\). The sensor array response \(\mathbf{A}^{(\alpha,\beta)}\) is always assumed to be the identity matrix.

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)
beta_device = simulation.new_device(carrier_frequency=1e8)

# Create a channel between the two devices
channel = RandomDelayChannel((1e-8, 10e-8))
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()

# Configure a simulation to evaluate the link's BER and sweep over the receive SNR
simulation.add_evaluator(BitErrorEvaluator(link, link))
simulation.new_dimension('noise_level', dB(20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40), beta_device)

# Run simulation and plot resulting SNR curve
simulation.num_samples = 1000

class RandomDelayChannel(delay, decorrelation_distance=inf, **kwargs)

Bases: DelayChannelBase[RandomDelayChannelRealization]

Delay channel assuming random propagation delays.

Parameters:

• delay (float | Tuple[float, float]) – Assumed propagation delay in seconds. If a scalar floating point, the delay is assumed to be constant. If a tuple of two floats, the tuple values indicate the mininum and maxium values of a uniform distribution, respectively.

• decorrelation_distance (float, optional) – Distance in meters at which the channel decorrelates. By default, the channel is assumed to be static in space.

• **kwargs – Channel base class initialization parameters.

_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:

RandomDelayChannelRealization

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:

RandomDelayChannelRealization

Returns: The recalled realization instance.

property decorrelation_distance: float

Distance in meters at which the channel decorrelates.

Raises:

ValueError – If the decorrelation distance is set to a negative value.

property delay: float | Tuple[float, float]

Assumed propagation delay in seconds.

If set to a scalar floating point, the delay is assumed to be constant. If set to a tuple of two floats, the tuple values indicate the mininum and maxium values of a uniform distribution, respectively.

Raises:

• ValueError – If the delay is set to a negative value.

• ValueError – If the delay is set to a tuple of two values where the first value is greater than the second value.

class RandomDelayChannelRealization(consistent_realization, delay_variable, delay, model_propagation_loss, sample_hooks, gain)

Bases: DelayChannelRealization

Realization of a random delay channel.

Generated from RandomDelayChannel'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, delay_variable, sample_hooks)

Return type:

RandomDelayChannelRealization

to_HDF(group)

Serialize the channel realization to HDF5.

Parameters:

group (Group) – HDF5 group to serialize the channel realization to.

Return type:

None

property delay: float | Tuple[float, float]

Assumed propagation delay in seconds.

If set to a scalar floating point, the delay is assumed to be constant. If set to a tuple of two floats, the tuple values indicate the mininum and maxium values of a uniform distribution, respectively.

Raises:

• ValueError – If the delay is set to a negative value.

• ValueError – If the delay is set to a tuple of two values where the first value is greater than the second value.