CFAR detection

CFAR consumes nonnegative power, not complex amplitudes. It returns four full-size arrays: a boolean detection mask, estimated noise, threshold, and SNR in decibels.

CA-CFAR

For \(N\) exponentially distributed training cells, CA-CFAR estimates their mean \(\hat{P}_n\) and uses threshold

\[ T=\alpha\hat{P}_n, \qquad \alpha=N\left(P_\mathrm{FA}^{-1/N}-1\right). \]

This relation gives the configured false-alarm probability under independent, homogeneous complex Gaussian noise.

GOCA and SOCA

Greatest-of and smallest-of CFAR split the training region into leading and trailing halves:

\[ \hat{P}_\mathrm{GOCA}=\max(\hat{P}_L,\hat{P}_R), \qquad \hat{P}_\mathrm{SOCA}=\min(\hat{P}_L,\hat{P}_R). \]

GOCA is conservative at clutter boundaries. SOCA can preserve a target beside a high-clutter region but may increase false alarms.

OS-CFAR

OS-CFAR sorts the \(N\) training powers and chooses rank \(k\). The multiplier is solved from the exact Laplace transform of the exponential order statistic:

\[ P_\mathrm{FA}=\prod_{i=0}^{k} \frac{N-i}{N-i+\alpha}. \]

rankFraction selects \(k\) and is commonly set near 0.75. OS-CFAR is useful when other targets contaminate some training cells.

Two-dimensional behavior

cfar_2d treats Doppler as circular and range as bounded. Range edge cells whose full training window is unavailable are invalid and receive NaN noise, threshold, and SNR. Optional 3x3 peak grouping performs deterministic NMS.

result = rsp.cfar_2d(
    rdPower,
    method="os",
    trainingCells=(10, 4),
    guardCells=(2, 1),
    rankFraction=0.75,
    pfa=1e-4,
    peakGrouping=True,
)
bins = np.argwhere(result.detections)

There is no top-N fallback when no cell passes CFAR. An empty detection set is a valid result and must remain empty. maxDetections only caps genuine detections after sorting by SNR in the model pipeline.

Statistical validation

An empirical PFA test should disable peak grouping, draw independent exponential power, discard invalid range edges, and compare the observed false-alarm count to a binomial confidence interval around the configured PFA. Structured clutter and correlated FFT bins do not satisfy the ideal CA-CFAR assumptions.