Module metrics 

The metrics of a declarative link.

The metrics compare the samples at the end of the link with the transmitted symbols. The samples must be at one sample per symbol and aligned on the symbols (after decimation and, when the receiver introduces a delay, frame synchronisation). The comparison uses the symbols $n$ with $s_{\mathrm{start}} \le n < N - s_{\mathrm{end}}$ (skip_start, skip_end) that no block excluded (pilots, preambles).

metrics:
  report: [ber, ser, snr_db, gmi]   # default [ber, ser, snr_db]
  skip_start: 64                    # edges of the filters
  skip_end: 64
  scale: power                      # power (default), ls or none

The names of the metrics and of the scalings are read without case. Before the decisions the samples $z_{n}$ are scaled:

• power: to the power of the transmitted symbols $x_{n}$ on the window (blind);
• ls: by the least-squares complex gain $\sum_{n} x_{n} z_{n}^{*} / \sum_{n} \lvert z_{n} \rvert^{2}$, which also removes a constant phase (genie-aided);
• none: as they are.

Metric	Kind	Definition
ber	rate	hard-decision bit errors (Gray labels) over the window
ser	rate	symbol errors
snr_db	mean	$10 \log_{10} \left( \sum \lvert x \rvert^{2} / \sum \lvert z - x \rvert^{2} \right)$ per trial, after the scaling (metrics::snr_db; a trial without error gives $+\infty$, which the record drops and counts)
snr_eff_db	mean	$10 \log_{10} \left( \rho^{2} / (1 - \rho^{2}) \right)$, $\rho^{2} = \lvert \sum z x^{*} \rvert^{2} / \left( \sum \lvert z \rvert^{2} \sum \lvert x \rvert^{2} \right)$ per trial: the effective SNR after the least-squares gain of $x$ onto $z$ (Häger & Pfister; independent of the scaling)
evm	mean	$\sum \lvert z - x \rvert^{2} / \sum \lvert x \rvert^{2}$ per trial (power ratio, metrics::evm_data_aided)
mse	mean	the mean of $\lvert z - x \rvert^{2}$ per trial (metrics::mse)
gmi	mean	generalised mutual information (bits/symbol) per trial
ngmi	mean	GMI per bit of information, $\mathrm{GMI} / H(X)$
entropy	mean	entropy $H(X)$ of the source (bits/symbol): $\log_{2} M$, or less with shaping
mi	mean	symbol-wise mutual information (bits/symbol) per trial
coded_ber	rate	information bits decoded in error (fec_decode)
bler	rate	coded blocks with at least one information bit in error
air	mean	rate of a decoder that uses the receiver’s own posterior (bits/symbol)
air_bmd	mean	the same with the bit-wise LLRs of that posterior
air_opt, air_bmd_opt	mean	the same with the best scaling $s$ of the posterior, per block
posterior_calibration	mean	$\hat{\sigma}^{2}$ over the mean of $\lvert z - x \rvert^{2}$: 1 for a calibrated receiver, below 1 for an over-confident one

The air metrics need a block that declares the receiver’s posterior (a learned receiver, or noise_estimate after a classic receiver) and use the samples as they are, without scaling (see metrics::posterior_rates). Compared with mi and gmi (genie gain and variance), they show what the receiver loses by its own estimates.

With a shaped source (source with mb_lambda, or pas_encode), the information rates, the soft demapper and the posterior use the probabilities of the points, and awgn_ebn0 counts the energy per bit of information (the entropy $H(X)$).

The information rates use the least-squares channel gain of metrics::information_rates (consistent at every SNR, independent of the scaling), not the power normalisation of OptiCommPy’s estimators.

With two polarisations (source with pols: 2) the metrics pool both: the samples of x then those of y, against the symbols of x then those of y, the window (skip_start, skip_end) applying to each polarisation.

The coded metrics compare the decoded information bits with the transmitted ones and need no aligned symbols: a coded link may report them alone.

The rates are counted over all the trials (Wilson intervals, usable by the min_errors stopping rule); the other metrics are means of per-trial values.

Structs

Metrics

The metrics of a link (see the module documentation).

Enums

Metric

A metric of a declarative link (see the module documentation).

Constants

METRICS

The names of the metrics a link can report, in the order of Metric::ALL.