If the radar transmits a new pulse before the echo from a distant target has returned, it does not know which pulse the echo belongs to. The target then appears at a wrong, too short range: a ghost target.
In practiceRadars therefore switch PRF. A real target stays in the same place at every PRF; a ghost jumps around. The same applies to velocity: a radar with too low a PRF can assign the wrong velocity to a fast target.
The terms ambiguous and unambiguous have already come up at several points in this chapter — with the maximum unambiguous range (Maximum Unambiguous Range) and with the blind speeds of MTI (Pulse-Doppler radar and Moving Target Indicator). This section puts the concept itself at the centre, because it is one of the most fundamental — and most confusing — concepts in radar engineering.
What do ambiguous and unambiguous mean?
A measurement is unambiguous if there is only one reality that can explain the result. A measurement is ambiguous if several different realities produce exactly the same result — the radar then cannot tell from the measurement itself which one is correct.
Look only at the minute hand of a clock: it points at the 3. You know unambiguously that it is quarter past — but quarter past what? 09:15, 10:15 and 11:15 give exactly the same hand position. The minute hand is unambiguous within one hour, and ambiguous beyond it. A radar measurement works in exactly the same way: unambiguous within a certain interval, ambiguous beyond it.
Why does a radar suffer from this? Because a pulse radar is not a continuous observer but a sampler: it looks at a fixed rhythm — the PRF (Pulse Repetition Frequency). Anything that repeats between two looks, or reaches further than one looking interval, folds back into that interval:
- In the time domain: the radar measures travel time only within one PRI. An echo that is under way for longer than one PRI is attributed to the wrong pulse → range ambiguity (Ambiguity in range).
- In the frequency domain: the radar samples the Doppler frequency at the PRF. Doppler frequencies that are more than the PRF apart cannot be distinguished → Doppler ambiguity (Ambiguity in velocity (Doppler)).
Ambiguity does not mean the measurement is wrong — the measurement is correct, but it has several valid interpretations. "Unambiguous" means: within this interval exactly one interpretation is possible. The size of that interval is determined entirely by the PRF — and that makes the choice of PRF the design compromise of the pulse radar (Choosing the PRF: low, medium and high PRF).
Ambiguity in range
The radar assumes that every echo belongs to the most recently transmitted pulse (Maximum Unambiguous Range). That is only guaranteed to be correct for targets within the maximum unambiguous range:
A target beyond that limit produces a second-time-around echo: its echo arrives after the next pulse has left and is linked to that pulse. The radar shows the target at the measured travel time minus one (or more) whole PRIs — so far too close:
How do you make the measurement unambiguous again? By testing the radar's assumption: change the PRI (PRI modulation). A real target within Rmax,unamb stays at the same apparent range; a second-time-around echo jumps in step with the PRI change. By using two or three different PRFs and checking which true range fits all measurements, the radar reconstructs the correct n — and with it the true range.
Ambiguity in velocity (Doppler)
The same phenomenon exists in the velocity domain, and the cause is again the PRF. A pulse(-Doppler) radar does not see the Doppler shift continuously but in samples: one phase measurement per pulse, so at a sampling frequency equal to the PRF. Signal theory then tells us that only Doppler frequencies within a window the size of the PRF can be distinguished from each other:
A target moving faster than the unambiguous window "folds back": the radar measures the true Doppler minus a whole number of times the PRF. The target appears to move much more slowly than it does, or even in the opposite direction. This is exactly the clock analogy of What do ambiguous and unambiguous mean?, but in frequency instead of time.
You have already met two familiar faces of Doppler ambiguity:
- Blind speeds (Pulse-Doppler radar and Moving Target Indicator): a target whose Doppler falls exactly on a multiple of the PRF cannot be distinguished from stationary clutter (Doppler "0") and is filtered out — ambiguity in its most harmful form.
- Apparent velocities: a pulse-Doppler radar with too low a PRF can show an approaching target as receding — until the processing has resolved the ambiguity.
The solution is the same as for range: several PRFs. Each PRF gives a different fold-back; the true velocity is the value that is consistent with all measurements. Staggered PRI (PRI modulation) also shifts the blind speeds from pulse pair to pulse pair, so that no velocity is permanently invisible.
Choosing the PRF: low, medium and high PRF
Now everything comes together. Range ambiguity calls for a low PRF (long listening time → large unambiguous range); Doppler ambiguity calls for a high PRF (fast sampling → large unambiguous velocity range). These two wishes fundamentally conflict — you cannot have both at their maximum. This is the famous PRF trade-off:
| PRF regime | Range | Doppler / velocity | Typical use |
|---|---|---|---|
| Low PRF (~300 Hz – 4 kHz) | unambiguous | ambiguous (many blind speeds) | surveillance / early warning (Characteristics of the Early Warning (EW) radar): looking far and unambiguously |
| Medium PRF (~4 – 30 kHz) | ambiguous | ambiguous | multifunction and fighter radars: both ambiguous, but both resolvable with PRF switching |
| High PRF (~30 – 300 kHz) | ambiguous (heavily) | unambiguous | pulse-Doppler look-down (Pulse-Doppler radar and Moving Target Indicator): unambiguous velocity, maximum clutter suppression |
Note what medium PRF does: it accepts double ambiguity and resolves both by working through several PRFs per observation (PRI modulation). That costs time and computing power, but gives the best balance for a radar that has to measure both the range and the velocity of low-flying targets — the reason modern combat aircraft radars have medium-PRF modes.
A radar's PRF therefore reveals to the ESM operator not only the radar type but also what the radar is doing: low PRF = searching at range, high PRF = Doppler work such as look-down or CW-like illumination, alternating PRF blocks = a multifunction radar resolving its ambiguities. And conversely: anyone who wants to place jamming or false targets has to know in which domain the radar measures unambiguously — a false target outside the unambiguous window folds back to a place the jammer does not control.