Multipath Fading Channel

Allows for the direct configuration of the Multipath Fading Channel’s parameters

\[\begin{split}\mathbf{g} &= \left[ g_{1}, g_{2}, \,\dotsc,\, g_{L} \right]^\mathsf{T} \in \mathbb{C}^{L} \\ \mathbf{k} &= \left[ K_{1}, K_{2}, \,\dotsc,\, K_{L} \right]^\mathsf{T} \in \mathbb{R}^{L} \\ \mathbf{\tau} &= \left[ \tau_{1}, \tau_{2}, \,\dotsc,\, \tau_{L} \right]^\mathsf{T} \in \mathbb{R}^{L} \\\end{split}\]

directly.

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
delays = 1e-9 * np.array([0, 0.3819, 0.4025, 0.5868, 0.4610, 0.5375, 0.6708, 0.5750, 0.7618, 1.5375, 1.8978, 2.2242, 2.1717, 2.4942, 2.5119, 3.0582, 4.0810, 4.4579, 4.5695, 4.7966, 5.0066, 5.3043, 9.6586])
powers = 10 ** (np.array([-13.4, 0, -2.2, -4, -6, -8.2, -9.9, -10.5, -7.5, -15.9, -6.6, -16.7, -12.4, -15.2, -10.8, -11.3, -12.7, -16.2, -18.3, -18.9, -16.6, -19.9, -29.7]) / 10)
rice_factors = np.zeros_like(delays)
channel = MultipathFadingChannel(delays, powers, rice_factors)
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()

# 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(0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20), beta_device)

# Run simulation and plot resulting SNR curve

class MultipathFadingChannel(delays, power_profile, rice_factors, correlation_distance=inf, num_sinusoids=20, los_angle=None, doppler_frequency=0.0, los_doppler_frequency=None, antenna_correlation=None, gain=1.0, seed=None)

Bases: Channel[MultipathFadingRealization, MultipathFadingSample], Serializable

Base class for the implementation of stochastic multipath fading channels.

Parameters:

• delays (Union[ndarray, List[float]]) – Delay in seconds of each individual multipath tap. Denoted by \(\tau_{\ell}\) within the respective equations.

• power_profile (Union[ndarray, List[float]]) – Power loss factor of each individual multipath tap. Denoted by \(g_{\ell}\) within the respective equations.

• rice_factors (Union[ndarray, List[float]]) – Rice factor balancing line of sight and multipath in each individual channel tap. Denoted by \(K_{\ell}\) within the respective equations.

• correlation_distance (float) – Distance at which channel samples are considered to be uncorrelated. \(\infty\) by default, i.e. the channel is considered to be fully correlated in space.

• num_sinusoids (int) – Number of sinusoids used to sample the statistical distribution. Denoted by \(N\) within the respective equations.

• los_angle (float | None) – Angle phase of the line of sight component within the statistical distribution.

• doppler_frequency (float) – Doppler frequency shift of the statistical distribution. Denoted by \(\omega_{\ell}\) within the respective equations.

• antenna_correlation (AntennaCorrelation | None) – Antenna correlation model. By default, the channel assumes ideal correlation, i.e. no cross correlations.

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

• seed (int | None) – Seed used to initialize the pseudo-random number generator.

Raises:

• ValueError – If the length of delays, power_profile and rice_factors is not identical.

• ValueError – If delays are smaller than zero.

• ValueError – If power factors are smaller than zero.

• ValueError – If rice factors are smaller than zero.

classmethod Deserialize(process)

Deserialize an object’s state.

Objects cannot be deserialized directly, instead a Factory must be instructed to carry out the deserialization process.

Parameters:

process (DeserializationProcess) – The current stage of the deserialization process. This object is generated by the Factory and provides an interface to deserialization methods supporting multiple backends.

Return type:

MultipathFadingChannel

Returns:

The deserialized object.

_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:

MultipathFadingRealization

serialize(process)

Serialize this object’s state.

Objects cannot be serialized directly, instead a Factory must be instructed to carry out the serialization process.

Parameters:

process (SerializationProcess) – The current stage of the serialization process. This object is generated by the Factory and provides an interface to serialization methods supporting multiple backends.

Return type:

None

property antenna_correlation: AntennaCorrelation | None

Antenna correlations.

Returns:

Handle to the correlation model. None, if no model was configured and ideal correlation is assumed.

property correlation_distance: float

Correlation distance in meters.

Represents the distance over which the antenna correlation is assumed to be constant.

property delays: ndarray

Delays for each propagation path in seconds.

Represented by the sequence

\[\left[\tau_{1},\, \dotsc,\, \tau_{L} \right]^{\mathsf{T}} \in \mathbb{R}_{+}^{L}\]

of \(L\) propagtion delays within the respective equations.

property doppler_frequency: float

Doppler frequency in \(Hz\).

Represented by \(\omega\) within the respective equations.

property los_angle: float | None

Line of sight doppler angle in radians.

Represented by \(\theta_{0}\) within the respective equations.

property los_doppler_frequency: float

Line of sight Doppler frequency in \(Hz\).

Represented by \(\omega\) within the respective equations.

property max_delay: float

Maximum propagation delay in seconds.

property num_resolvable_paths: int

Number of dedicated propagation paths.

Represented by \(L\) within the respective equations.

property num_sinusoids: int

Number of sinusoids assumed to model the fading in time-domain.

Represented by \(N\) within the respective equations.

Raises:

ValueError – For values smaller than zero.

property power_profile: ndarray

Gain factors of each propagation path.

Represented by the sequence

\[\left[g_{1},\, \dotsc,\, g_{L} \right]^{\mathsf{T}} \in \mathbb{R}_{+}^{L}\]

of \(L\) propagtion factors within the respective equations.

property rice_factors: ndarray

Rice factors balancing line of sight and non-line of sight power components for each propagation path.

Represented by the sequence

\[\left[K_{1},\, \dotsc,\, K_{L} \right]^{\mathsf{T}} \in \mathbb{R}_{+}^{L}\]

of \(L\) factors within the respective equations.