1. Eliminating range ambiguity
Pulse compression
Coherence
Pulsed Doppler
Exercises
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2. 1. Eliminating range ambiguity
EEE381B Aerospace Systems & Avionics
1. Eliminating range ambiguity
Ramb = c / (2 PRF) = cTp / 2
Recall the range ambiguity problem of a simple pulsed radar; namely that target returns beyond the PRF distance yield ambiguous ranges.
In fact, if target returns beyond this range are detectable, all target ranges are ambiguous!
Ramb = c / (2 PRF)
60 km
110 km
10 km
Target range = ?
50 km
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3. 1.1 Range ambiguity strategies [2]
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1.1 Range ambiguity strategies [2]
Choose a low PRF such that Ramb > Rmax
In general, not practical
“Tag” each pulse with an identifier
Difficult implementation, and severe limitations
PRF jittering
Small changes in successive pulses
PRF switching
Switching among n PRfs
Stimson chapter 12, page 155.
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4. EEE381B Aerospace Systems & Avionics
1.2 PRF Jittering
By making slight changes in PRF in successive pulses (alternating between two close PRFs), the apparent range of targets beyond the ambiguous range will change while the apparent range of targets within the ambiguous range will not change.
apparent range 1
ambiguous range 1
PRF1
true range
apparent range 2
ambiguous range 2
PRF2
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5. EEE381B Aerospace Systems & Avionics
1.3 PRF Switching
An extension of PRF jittering, PRF switching involves interleaving n different PRF values. Knowing each PRF value and the amount by which the apparent ranges change, it is possible to calculate true ranges well out beyond the separate ambiguous ranges.
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6. EEE381B Aerospace Systems & Avionics
1.3.1 Range bins
Assume a pulsed radar with a PRF of 75kHz; this yields an ambiguous range of 20km. However we want to detect targets out to 100km, 5 times this range.
Define a bank of 80 range bins where each bin represents a range interval of ¼km.
Now if a target is detected in bin 24 then the targets apparent range is 24x¼ = 6km. However the true range could be 6, 26, 46, 66, or 86.
••• ••• 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36
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7. EEE381B Aerospace Systems & Avionics
1.3.2 Switch PRF
Now to determine the true range, switch to a second PRF such that it is just lower enough to yield a new ambiguous range equal to exactly ¼km longer than the original ambiguous range (increase it by 1 range bin).
The target’s apparent range will either stay in the same bin number or shift n bins to the left.
If it stays in the same bin number that is its true range
If it shifts to the left n bins, its true range is computed as:
Rtrue = n Ramb1 + Rapparent1
In our example, if the target moves to bin 21, its true range is 3x20km + 6km = 66 km.
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8. EEE381B Aerospace Systems & Avionics
1.3.3 Ghosts
PRF switching can lead to another form of ambiguity known as ghosting. If two targets are detected at the same azimuth and elevation angle and their velocities are nearly equal, one or both of the targets will move to different range bins when the PRF is switched.
This will cause each to have two possible ranges, one is their true range and the other is a ghost.
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9. EEE381B Aerospace Systems & Avionics
1.3.3 Ghost ambiguity
Returning to our example, assume that range bins 24 and 26 are filled with PRF1, while range bins 22 and 24 are filled with PRF2. Which moved where?
The two targets are either at:
46 km and 46.5 km or
6 km and 86.5 km
PRF1
••• ••• 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 A B
PRF2
Target A: 2x = 46 km, or 6 km
Target B: 2x = 46.5 km, or 4x = 86.5 km
••• ••• 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36
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10. EEE381B Aerospace Systems & Avionics
1.3.4 Eliminating Ghosts
Introduce a third PRF, this time at a value just larger enough to yield an ambiguous range one range bin less than the original range ambiguity. This will cause the apparent ranges to shift n bins to the right if it is not the true range. This allows the ghosts to be identified.
Back to our example, if the targets now appear in range bins 26 and 28, the true targets are at 46 and 46.5 km.
Target A: 2x = 46 km
Target B: 2x = 46.5 km
PRF1
••• ••• 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 A B
PRF2
••• ••• 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36
PRF3
••• ••• 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 A B
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11. EEE381B Aerospace Systems & Avionics
1.3.5 PRF switching summary
Depending upon how great the detection range, the range of operational PRFs, and the potential number of ghosts, it may be necessary to introduce N switch PRFs. However, for most fighter aircraft applications it is usually sufficient to use 3 switch PRF values.
The introduction of PRF switching have some inconvenients:
there is a linear reduction in received signal integration time.
the radar complexity is increased, increasing the overall cost and decreasing the system reliability.
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12. EEE381B Aerospace Systems & Avionics
2. Pulse compression
Recall a second concern with pulsed radar, range resolution. Range resolution decreases as a function of decreasing pulse width, however decreasing pulse width also decreases radar range and increases receiver bandwidth.
For example, in order to achieve a 5m range resolution, a 0.033sec pulse width is required. This results in a very wide receiver bandwidth (60 MHz), and a large drop in radar range unless peak power or PRF is increased accordingly.
Pulse compression at the receiver is a solution.
Rres = c/2
 = 2(5m)/(300,000,000 m/s) = sec
BWRx = 2/ = MHz
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13. 2.1 Principle of pulse compression
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2.1 Principle of pulse compression
“Chirp”
In order to achieve pulse compression at the receiver, the transmitted pulse must first be frequency modulated; for example it might be linearly increased over the duration of the transmitted pulse. The target return carries virtually the same signal modulation.
The “magic” in the receiver filter is that a time delay is applied to the incoming waveform such that, the lower the frequency, the greater the time delay. The frequency-delay rate is inversely proportional to the frequency deviation in the transmitted pulse. This gives the effect of slowing down the leading edge lower frequencies of the received signal such that the trailing edge higher frequencies “catch up” – effectively compressing the received pulse!
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14. 2.2 Pulse compression ratio [2]
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2.2 Pulse compression ratio [2]
Pulse compression ratio:
return from target A f F 
comp
return from target B
where
Define:
 - uncompressed transmitted pulse width;
comp - compressed received pulse width;
f – receiver frequency sensitivity; the receiver can not resolve differences in frequency lower than this value; and
F – maximum frequency deviation over duration of transmitted pulse.
therefore
The value f represents the receiver frequency sensitivity, in other words the minimum discernable frequency difference between two signals. For pulses to be resolved, the frequency difference must be at least half the bandwidth of the uncompressed pulse, 1/.
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15. 2.3 Merits of pulse compression
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2.3 Merits of pulse compression
Linear frequency modulation, or “chirp”, has the following advantages:
significantly increased range resolution
target signal-to-noise ratio (SNR) is increased
enables large compression values ( )
comparatively simple
and the following disadvantage:
slight ambiguity between range and Doppler frequency shifts (although the Doppler shifts are relatively much smaller).
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16. PD radar - range ambiguity
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PD radar - range ambiguity
As strictly a function of PRF, we see that unambiguous range decreases rapidly with increasing PRF (ignoring any improvement techniques such as PRF switching).
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17. PD radar – Doppler ambiguity
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PD radar – Doppler ambiguity
Maximum unambiguous Doppler
fd_max = PRF – (2VR/)
Just as for range ambiguity, the frequency returns become ambiguous as a function of the PRF; in this case it is offset by the region of negative frequency sidelobe clutter.
Just as for range ambiguity, the frequency returns become ambiguous as a function of the PRF; in this case it is offset by the region of negative frequency sidelobe clutter.
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18. PD radar – Doppler ambiguity
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PD radar – Doppler ambiguity
For a 10 GHz pulse Doppler radar, on a platform travelling at 1000 knots, we see the maximum unambiguous Doppler is a step like function of PRF.
1 knots = km/hr
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19. EEE381B Aerospace Systems & Avionics
PRF Considerations
In the context of pulsed Doppler radar, it is interesting to note that no single value of PRF provides universally good performance.
Thus an airborne radar must either be designed with selectable* PRF or equipped with more than one radar.
* Selectable PRF does not necessarily imply by a human operator.
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20. Combining ambiguities
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Combining ambiguities
Combining both range ambiguity and doppler ambiguity for this typical PD radar / scenario, we see that no single PRF provides both good unambiguous range and good unambiguous doppler, in fact the regions of each are nearly mutually exclusive. This just confirms that stated previously that a range of PRFs are typically required.
Combining both range ambiguity and doppler ambiguity for this typical PD radar / scenario, we see that no single PRF provides both good unambiguous range and good unambiguous doppler, in fact the regions of each are nearly mutually exclusive. This just confirms that stated previously that a range of PRFs are typically required.
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21. EEE381B Aerospace Systems & Avionics
Categories of PRF
PRF
Range
Doppler
High
Ambiguous
Unambiguous
Medium
Low
The categorization of PRF is based not upon their values, but instead upon whether or not range or Doppler is unambiguous.
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22. EEE381B Aerospace Systems & Avionics
Low PRF
A low PRF is one for which the maximum range of the radar is unambiguous in the first range zone (first return).
Advantages
Limitations
Good air-to-air look-up, ground mapping
Poor air-to-air look-down
Precise ranging
Ground moving targets a problem
Simple pulse delay ranging is possible
Doppler ambiguities too severe to be resolved
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High PRF
A high PRF is one for which the observed Doppler frequencies of all significant targets are unambiguous.
Advantages
Limitations
Good noise-aspect capability with high closing-rate targets
Poor detection range especially against low-closing targets
High average power without pulse compression.
Precludes simple pulse delay ranging (requires PRF switching)
Targets can be resolved within main lobe clutter.
Zero-closing rate targets may be missed
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24. EEE381B Aerospace Systems & Avionics
Medium PRF
A medium PRF is one for which both the range and Doppler frequencies are ambiguous.
Advantages
Limitations
Good all-aspect capability (compromise), good for tail-aspect targets
Poor detection range against both low- and high-closing targets
Ground moving targets eliminated
Must resolve both ambiguities
Pulse delay ranging sometimes possible
May require PRF switching
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25. Exercices

26. Resolving range ambiguity
EEE381B Aerospace Systems & Avionics
Resolving range ambiguity
Consider a pulsed radar with a nominal PRF of kHz and a maximum detection range of 150 km. Introduce two switch PRFs, one for resolving ambiguity and one for deghosting; the former adds one range bin, while the latter removes one.
If the nominal number of range bins is 128, what are the two switch PRFs?
Given PRF1 bins 43 & 49, and PRF2 bins 41 & 42, what are the possible target ranges?
Resolve the target ranges with PRF3 bins 44 & 57
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27. Pulse compression advantage
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Pulse compression advantage
Consider a pulsed radar with a pulse width of 1sec.
What is the improvement in range resolution that can be achieved employing pulse compression if the maximum frequency deviation of the transmitted pulse is 20MHz?
What is the compression ratio?
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