Block Error Rate¶

Inheritance diagram of hermespy.modem.evaluators.BlockErrorEvaluator, hermespy.modem.evaluators.BlockErrorArtifact, hermespy.modem.evaluators.BlockErrorEvaluation

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 \(L\) bit block segments of equal length

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

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

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

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(bandwidth=1e8, oversampling_factor=8)
device_beta = simulation.new_device(bandwidth=1e8, oversampling_factor=8)

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

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

simulation.add_evaluator(BlockErrorEvaluator(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 BlockErrorEvaluator(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, Serializable

Evaluate block errors between two modems exchanging information.

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.