Error Vector Magnitude

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:

# Create a new simulation featuring two devices
simulation = Simulation()
device_alpha = simulation.new_device()
device_beta = simulation.new_device()

# Create a transmitting and receiving modem for each device, respectively
modem_alpha = TransmittingModem(device=device_alpha)
modem_beta = ReceivingModem(device=device_beta)

# Configure the modem's waveform
waveform_configuration = {
    'symbol_rate': 1e8,
    'num_preamble_symbols': 10,
    'num_data_symbols': 100,
}
modem_alpha.waveform = RootRaisedCosineWaveform(**waveform_configuration)
modem_beta.waveform = RootRaisedCosineWaveform(**waveform_configuration)

simulation.add_evaluator(ConstellationEVM(modem_alpha, modem_beta))
simulation.new_dimension('noise_level', dB(0, 2, 4, 8, 10, 12, 14, 16, 18, 20), device_beta)
simulation.num_samples = 1000
result = simulation.run()

class ConstellationEVM(transmitting_modem, receiving_modem, plot_surface=True)

Bases: CommunicationEvaluator

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

Parameters:

• transmitting_modem (TransmittingModem) – Modem transmitting information.

• receiving_modem (ReceivingModem) – Modem receiving information.

• plot_surface (bool, optional) – Plot the surface of the evaluation result in two-dimensional grids. Defaults to True.

evaluate()

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

Short string representation of this evaluator.

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

property title: str

Long string representation of this evaluator.

Used as plot title.

class EVMArtifact(artifact)

Bases: ArtifactTemplate[float]

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

Parameters:

artifact (AT) – Artifact value.

class EVMEvaluation(transmitted_symbols, received_symbols)

Bases: EvaluationTemplate[float, PlotVisualization]

Parameters:

• transmitted_symbols (np.ndarray) – Originally transmitted communication symbols.

• received_symbols (np.ndarray) – Received communication symbols.

artifact()

Generate an artifact from this evaluation.

Returns: The evaluation artifact.

Return type:

EVMArtifact

property abbreviation: str

property title: str

Title of the visualizable.

Returns: Title string.