Error Vector Magnitude

Inheritance diagram of hermespy.modem.evaluators.ConstellationEVM, hermespy.modem.evaluators.EVMArtifact, hermespy.modem.evaluators.EVMEvaluation

Considering two linked modems denoted by \((\alpha)\) and \((\beta)\), with modem \((\alpha)\) transmitting a symbol sequence

\[\mathbf{s}_{\mathrm{Tx}}^{(\alpha)} = \left[ s_{\mathrm{Tx}}^{(\alpha,1)}, s_{\mathrm{Tx}}^{(\alpha,2)}, \ldots, s_{\mathrm{Tx}}^{(\alpha,B)} \right]^{\mathsf{T}} \in \mathbb{C}^{S}\]

and modem \((\beta)\) receiving a decoded symbol sequence

\[\mathbf{s}_{\mathrm{Rx}}^{(\beta)} = \left[ s_{\mathrm{Rx}}^{(\beta,1)}, s_{\mathrm{rx}}^{(\beta,2)}, \ldots, s_{\mathrm{Rx}}^{(\beta,B)} \right]^{\mathsf{T}} \in \mathbb{C}^{S}\]

Hermes defines the symbol Error Vector Magnitude (EVM) as the root mean square (RMS) of the difference between the transmitted and received symbols

\[\mathrm{EVM}^{(\alpha,\beta)} = \sqrt{\frac{ \lVert \mathbf{s}_{\mathrm{Tx}}^{(\alpha)} - \mathbf{s}_{\mathrm{Rx}}^{(\beta)} \rVert_2^2 }{S}} \ \text{.}\]

In practice, the number of symbols \(S\) may differ between transmitter and receiver. In this case, the longer sequence is truncated to the length of the shorter sequence.

The following minimal examples outlines how to configure this evaluator within the context of a simulation campaign:

 1# Create a new simulation featuring two devices
 2simulation = Simulation()
 3device_alpha = simulation.new_device(bandwidth=1e8, oversampling_factor=8)
 4device_beta = simulation.new_device(bandwidth=1e8, oversampling_factor=8)
 5
 6# Create a transmitting and receiving modem for each device, respectively
 7modem_alpha = TransmittingModem()
 8device_alpha.transmitters.add(modem_alpha)
 9modem_beta = ReceivingModem()
10device_beta.receivers.add(modem_beta)
11
12# Configure the modem's waveform
13waveform_configuration = {
14    'num_preamble_symbols': 10,
15    'num_data_symbols': 100,
16}
17modem_alpha.waveform = RootRaisedCosineWaveform(**waveform_configuration)
18modem_beta.waveform = RootRaisedCosineWaveform(**waveform_configuration)
19
20simulation.add_evaluator(ConstellationEVM(modem_alpha, modem_beta))
21simulation.new_dimension('noise_level', dB(0, 2, 4, 8, 10, 12, 14, 16, 18, 20), device_beta)
22simulation.num_samples = 1000
23result = simulation.run()
24
class ConstellationEVM(transmitting_modem, receiving_modem, confidence=1.0, tolerance=0.0, min_num_samples=1024, plot_scale='log', tick_format=ValueType.LIN, plot_surface=True)[source]

Bases: CommunicationEvaluator

Evaluate the error vector magnitude (EVM) of a constellation diagram.

Parameters:

  • transmitting_modem (TransmittingModem) – Communication modem transmitting information.

  • receiving_modem (ReceivingModem) – Communication modem receiving information.

  • confidence (float) – Required confidence level for the given tolerance between zero and one.

  • tolerance (float) – Acceptable non-negative bound around the mean value of the estimated scalar performance indicator.

  • min_num_samples (int) – Minimum number of samples required to compute the confidence bound.

  • plot_scale (str) – Scale of the plot. Can be 'linear' or 'log'.

  • tick_format (ValueType) – Tick format of the plot.

  • plot_surface (bool) – Enable surface plotting for two-dimensional grids. Enabled by default.

evaluate()[source]

Evaluate the state of an investigated object.

Implements the process of extracting an arbitrary performance indicator, represented by the returned Artifact \(X_m\).

Returns: Artifact \(X_m\) resulting from the evaluation.

Return type:

EVMEvaluation

property abbreviation: str[source]

Short string representation of this evaluator.

Used as a label for console output and plot axes annotations.

property title: str[source]

Long string representation of this evaluator.

Used as plot title.

class EVMArtifact(artifact)[source]

Bases: ArtifactTemplate[float]

Artifact of a error vector magnitude (EVM) evaluation between two modems exchanging information.

Parameters:

artifact (TypeVar(FAT, bound= SupportsFloat)) – Artifact value.

class EVMEvaluation(transmitted_symbols, received_symbols)[source]

Bases: EvaluationTemplate[float, PlotVisualization]

Parameters:

  • transmitted_symbols (ndarray) – Originally transmitted communication symbols.

  • received_symbols (ndarray) – Received communication symbols.

artifact()[source]

Generate an artifact from this evaluation.

Returns: The evaluation artifact.

Return type:

EVMArtifact

property title: str[source]

Title of the visualizable.

Returns: Title string.