Detection¶

Detectors¶

class sdr.ReplicaCorrelator

Implements an clairvoyant replica-correlator detector.

class sdr.EnergyDetector

Implements an energy detector.

Theoretical performance¶

sdr.h0(sigma2: float = 1.0, ...) → rv_continuous

Computes the statistical distribution under the null hypothesis \(\mathcal{H}_0\).

sdr.h1(snr: float, sigma2: float = 1.0, ...) → rv_continuous

Computes the statistical distribution under the alternative hypothesis \(\mathcal{H}_1\).

sdr.p_d(snr: ArrayLike, p_fa: ArrayLike, ...) → NDArray[float64]

Computes the theoretical probability of detection \(P_d\).

sdr.p_fa(threshold: ArrayLike, ...) → NDArray[float64]

Computes the theoretical probability of false alarm \(P_{fa}\).

sdr.threshold(p_fa: ArrayLike, ...) → NDArray[float64]

Computes the theoretical detection threshold \(\gamma\).

sdr.threshold_factor(p_fa: ArrayLike, ...) → NDArray[float64]

Computes the theoretical detection threshold factor \(\alpha\).

sdr.min_snr(p_d: ArrayLike, p_fa, ...) → NDArray[float64]

Computes the minimum input signal-to-noise ratio (SNR) required to achieve the desired probability of detection \(P_d\).

Approximated performance¶

sdr.albersheim(p_d: ArrayLike, p_fa, ...) → NDArray[float64]

Estimates the minimum input signal-to-noise ratio (SNR) required to achieve the desired probability of detection \(P_d\).

sdr.peebles(p_d: ArrayLike, p_fa, ...) → NDArray[float64]

Estimates the non-coherent integration gain for a given probability of detection \(P_d\) and false alarm \(P_{fa}\).

sdr.shnidman(p_d: ArrayLike, p_fa, ...) → NDArray[float64]

Estimates the minimum input signal-to-noise ratio (SNR) required to achieve the desired probability of detection \(P_d\) for the Swerling target model.

Coherent integration¶

sdr.coherent_gain(time_bandwidth: ArrayLike) → NDArray[float64]

Computes the SNR improvement by coherent integration.

sdr.coherent_gain_loss(time: ArrayLike, freq) → NDArray[float64]

Computes the coherent gain loss (CGL) given a time or frequency offset.

sdr.max_integration_time(cgl: ArrayLike, ...) → NDArray[float64]

Computes the maximum integration time that produces at most the provided coherent gain loss (CGL).

sdr.max_frequency_offset(cgl: ArrayLike, ...) → NDArray[float64]

Computes the maximum frequency offset that produces at most the provided coherent gain loss (CGL).

Non-coherent integration¶

sdr.non_coherent_gain(n_nc: ArrayLike, snr, ...) → NDArray[float64]

Computes the SNR improvement by non-coherently integrating \(N_{nc}\) samples.