Mathematics and workflow for converting a mixed pulse stream into pulse descriptor words, PRI families, emitter tracks and usable ELINT intelligence.
An EW receiver rarely sees one clean radar. It sees a crowded pulse environment: search radars, fire-control radars, navigation emitters, datalinks, repeaters, reflections and noise triggers. Deinterleaving is the process that separates that mixed stream into individual emitter pulse trains.
The input is usually a sequence of pulse descriptor words. Each PDW is a compact measurement record: time of arrival, RF, pulse width, amplitude, angle of arrival, modulation flags and measurement quality. The deinterleaver searches for structure across those measurements.
A dense pulse stream is sorted into emitter tracks by combining TOA regularity with RF, PW, amplitude and AOA consistency.
A PDW is not the waveform itself. It is the receiver's measurement summary of a detected pulse. Good PDW quality is the foundation of good deinterleaving.
Formula reading: TOA is time of arrival, RF is measured carrier frequency, PW is pulse width, A is amplitude, AOA is bearing or angle estimate and q is a quality flag. The difference between adjacent TOAs is the first clue to pulse repetition interval, but adjacent pulses may belong to different emitters.
A radar pulse train is often recognized by repeated TOA spacing. Deinterleaving searches for a PRI hypothesis that explains many pulses while rejecting incompatible pulses.
Formula reading: a constant-PRI emitter produces pulses at a start time t0 plus integer multiples of PRI. en is timing residual. A pulse is accepted into the train if its residual falls inside the timing gate. The gate must include receiver timestamp error and radar jitter, but too wide a gate admits wrong pulses.
When many emitters are interleaved, adjacent TOA differences are misleading. Histogram and difference methods compare many pulse pairs and look for repeated spacings that reveal PRI families.
Formula reading: every pair of pulses contributes a time difference. H(T) is a histogram or accumulator at candidate interval T. b is bin half-width. Weights wij can reward similar RF, PW or AOA, and reduce contributions from unlikely pulse pairs.
Modern deinterleaving cannot rely on PRI alone. Emitters may share similar PRIs, skip pulses, stagger PRIs or change frequency. Clustering combines timing with RF, PW, AOA and amplitude behavior.
Formula reading: x is the measured feature vector for a pulse or pulse group. μ is the expected emitter feature center. Σ describes measurement variance and natural agility. The squared Mahalanobis distance D2 tells whether the pulse is statistically compatible with an emitter track.
Real radars often avoid simple fixed PRI. They may use stagger, jitter, dwell-and-switch, frequency agility or pulse compression. The deinterleaver must recognize patterns without forcing every emitter into a constant-PRI model.
Formula reading: jitter adds random or pseudo-random variation around a nominal PRI. Stagger cycles through a set of PRI values. Dwell-switch holds one value for several pulses, then changes. These patterns are intentional radar design choices and important emitter identification features.
Receivers miss pulses due to sensitivity, blanking, overlap, antenna scan loss or thresholding. They also create false PDWs from noise and interference. Track scoring prevents the deinterleaver from building fragile or imaginary emitters.
Formula reading: Pobs is the observed-pulse fraction. If the model predicts 20 pulses but only 12 are found, Pobs = 0.6. The total score S combines timing, frequency, pulse width and angle consistency using weights selected for the receiver and mission.