Implements an clairvoyant replica-correlator detector.

Notes¶

The replica-correlator detector is a clairvoyant detector that assumes perfect knowledge of the signal $s[n]$. The complex noise $w[n]\sim \mathcal{CN}(0,{\sigma }^2)$. The null and alternative hypotheses are given by:

The test statistic $T(x)$ is given by:

where $\mathcal{E}$ is the received energy $\mathcal{E}=\sum _{n=0}^{N-1}{|s[n]|}^2$.

The probability of detection $P_D$, probability of false alarm $P_{FA}$, and detection threshold ${\gamma }^{\prime }$ are given by:

References¶

• Steven Kay, Fundamentals of Statistical Signal Processing: Detection Theory, Sections 4.3.2 and 13.3.1.

Methods¶

static roc(enr, ...) → tuple[NDArray[float_], NDArray[float_]]

Computes the receiver operating characteristic (ROC) curve.

static p_d(enr: ArrayLike, p_fa: ArrayLike, ...) → NDArray[float_]

Computes the probability of detection $P_D$.

static p_fa(threshold: ArrayLike, energy, ...) → NDArray[float_]

Computes the probability of false alarm $P_{FA}$.

static threshold(p_fa: ArrayLike, energy, ...) → NDArray[float_]

Computes the threshold ${\gamma }^{\prime }$.