Frame Error Rate

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

\[\mathbf{b}_{\mathrm{Tx}}^{(\alpha)} = \left[ b_{\mathrm{Tx}}^{(\alpha,1)}, b_{\mathrm{Tx}}^{(\alpha,2)}, \ldots, b_{\mathrm{Tx}}^{(\alpha,B)} \right]^{\mathsf{T}} \in \lbrace 0, 1 \rbrace^{B}\]

and modem \((\beta)\) receiving a bit stream

\[\mathbf{b}_{\mathrm{Rx}}^{(\beta)} = \left[ b_{\mathrm{Rx}}^{(\beta,1)}, b_{\mathrm{Rx}}^{(\beta,2)}, \ldots, b_{\mathrm{Rx}}^{(\beta,B)} \right]^{\mathsf{T}} \in \lbrace 0, 1 \rbrace^{B}\]

which can be partitioned into \(L\) frame segments of equal length

\[\begin{split}\mathbf{b}_{\mathrm{Tx}}^{(\alpha)} &= \left[ b_{\mathrm{F,Tx}}^{(\alpha,1)\mathsf{T}}, b_{\mathrm{F,Tx}}^{(\alpha,2)\mathsf{T}}, \ldots, b_{\mathrm{F,Tx}}^{(\alpha,L)\mathsf{T}} \right] \in \lbrace 0, 1 \rbrace^{B} \\ \mathbf{b}_{\mathrm{Rx}}^{(\beta)} &= \left[ b_{\mathrm{F,Rx}}^{(\beta,1)\mathsf{T}}, b_{\mathrm{F,Rx}}^{(\beta,2)\mathsf{T}}, \ldots, b_{\mathrm{F,Rx}}^{(\beta,L)\mathsf{T}} \right] \in \lbrace 0, 1 \rbrace^{B}\end{split}\]

Hermes defines the frame error rate (FER) as the exepcted number of block errors between the streams, i.e.,

\[\mathrm{FER}^{(\alpha,\beta)} = \mathbb{E} \lbrace \| b_{\mathrm{F,Tx}}^{(\alpha,l)} - b_{\mathrm{F,Rx}}^{(\alpha,l)} \|_2^2 > 0 \rbrace \ \text{.}\]

In practice, the number of bits \(B\) may differ between transmitter and receiver. In this case, the shorter bit stream is padded with zeros.

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

class FrameErrorEvaluator(transmitting_modem, receiving_modem, plot_surface=True)

Bases: CommunicationEvaluator, Serializable

Evaluate frame errors between two modems exchanging information.

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:

FrameErrorEvaluation

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.

yaml_tag: Optional[str] = 'FrameErrorEvaluator'

YAML serialization tag

class FrameErrorArtifact(artifact)

Bases: ArtifactTemplate[float]

Artifact of a frame error evaluation between two modems exchanging information.

Parameters:

artifact (AT) – Artifact value.

class FrameErrorEvaluation(evaluation)

Bases: EvaluationTemplate[ndarray]

Frame error evaluation of a single communication process between modems.

artifact()

Generate an artifact from this evaluation.

Returns: The evaluation artifact.

Return type:

FrameErrorArtifact

property title: str

Title of the visualizable.