Radar Detection Performance Monte Carlo
Compute probability of detection (Pd) vs range for pulsed radar systems. Select Swerling target model (0–IV), specify antenna gains, noise figure, pulse parameters, and rain rate. Monte Carlo over RCS fluctuations and system uncertainties produces Pd confidence bands and ROC curves.
How It Works
The radar range equation gives single-pulse SNR as a function of range:
SNR = (Pt × Gt × Gr × λ² × σ) / ((4π)³ × R⁴ × kT₀BFL)
Non-coherent integration of n pulses provides an approximate gain of n0.8 (Barton's formula) over a single pulse.
The Swerling models describe how target RCS fluctuates scan-to-scan (slow, I/III) or pulse-to-pulse (fast, II/IV). Swerling I/II assumes a Rayleigh-amplitude target (chi²(2) RCS). Swerling III/IV uses chi²(4). Swerling 0 is non-fluctuating (ideal metal sphere).
The CFAR detection threshold is set by requiring P(false alarm) = Pfa under H₀ (noise only). The threshold equals the (1–Pfa) quantile of the chi²(2n) distribution.
The Monte Carlo sweeps RCS fluctuation (Swerling sampling), receiver noise figure (±0.5 dB), and transmit power (±0.3 dB) to produce Pd confidence bands at each range.
Related Calculators
FAQ
What is the difference between Swerling I and Swerling II?+
Both model a Rayleigh-amplitude target (sum of many small scatterers with no dominant component, giving exponential RCS distribution). Swerling I is "slow fading" — the RCS is constant across all n integrated pulses in a dwell. Swerling II is "fast fading" — RCS is independently resampled for each pulse. Slow fading is more common for scan-to-scan changes; fast fading models pulse-agile or highly fluctuating targets.
Why does Pd increase with more integrated pulses?+
Non-coherent integration averages out noise fluctuations. Each additional pulse adds signal energy while noise averages down. The integration gain is approximately n^0.8 for non-coherent processing (compared to n for ideal coherent processing). Diminishing returns occur because noise fluctuations decrease as √n while the threshold also adjusts to maintain constant Pfa.
What do the p5/p50/p95 confidence bands represent?+
The bands come from the Monte Carlo simulation sweeping RCS fluctuations (Swerling sampling), receiver noise figure (±0.5 dB σ), and transmit power (±0.3 dB σ). The p5 curve is the worst-case 5th percentile — 5% of manufactured/operating scenarios perform worse than this. p95 is the best-case. For system margin allocation, design to the p5 curve.