How do I calculate the velocity resolution of a pulsed Doppler radar from the coherent processing interval?
Pulsed Doppler Velocity Resolution
Velocity resolution is critical for: distinguishing closely spaced targets in the Doppler domain (e.g., two aircraft flying in formation with slightly different speeds), separating slow-moving targets from clutter (ground clutter has near-zero velocity; detecting a walking person (1 m/s) in clutter requires delta_v less than 1 m/s), and weather radar (distinguishing wind velocities within a storm cell).
| Parameter | Pulsed | CW/FMCW | Phased Array |
|---|---|---|---|
| Range Resolution | c/(2B) | c/(2B) | c/(2B) |
| Velocity Resolution | PRF dependent | Direct from Doppler | Coherent processing |
| Peak Power | High (kW-MW) | Low (mW-W) | Moderate per element |
| Complexity | Moderate | Low | High |
| Typical Application | Surveillance, weather | Altimeter, automotive | Tracking, multifunction |
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
Frequently Asked Questions
How does this compare to FMCW velocity resolution?
For an FMCW radar: the velocity resolution is the same formula: delta_v = lambda/(2×T_frame), where T_frame is the time over which multiple chirps are collected for Doppler processing (equivalent to T_CPI). For a 77 GHz automotive FMCW radar with 128 chirps at 10 kHz chirp rate: T_frame = 12.8 ms. delta_v = 0.0039/(2×0.0128) = 0.15 m/s. The shorter wavelength (77 GHz vs. 10 GHz) provides approximately 8× better velocity resolution for the same CPI.
What is the velocity ambiguity?
The maximum unambiguous velocity: v_max = lambda × PRF / 4. For 10 GHz, PRF = 10 kHz: v_max = 0.03 × 10000/4 = 75 m/s (270 km/hr). Targets moving faster than v_max alias (fold over) into the velocity spectrum, appearing at the wrong velocity. To avoid ambiguity: increase the PRF (but this reduces the unambiguous range), or use multiple PRFs and resolve the ambiguity using the Chinese Remainder Theorem approach.
How many pulses are practical?
Typical CPI lengths: airborne fighter radar: 16-128 pulses (CPI = 1-10 ms). Short CPI for fast scan rate and maneuvering target tracking. Ground-based air surveillance: 10-30 pulses per dwell (limited by beam scan rate). Weather radar: 32-256 pulses (CPI = 10-80 ms for fine velocity resolution of wind fields). GMTI (ground moving target indication): 16-64 pulses. Space-based radar (SAR): thousands to millions of pulses (synthetic aperture depends on integration time). The practical limit is: the dwell time available (scan rate determines how long the beam stays on target), and the target coherence time (how long the target's Doppler is stable).