1. LFM Pulse Compression Sidelobe Reduction Techniques
EECS 725
Weizhi Shaun Chua

2. Outline Introduce Pulse Compression:
Concept and system
Advantage and Disadvantage
Present Three LFM techniques to reduce sidelobes:
Windowing applied to matched filter
Amplitude Tapering in TX pulse
Phase Predistortion in TX pulse

3. Pulse Compression (PCMP)
Traditional pulse bandwidth dependent on pulse length.
B = 1/T
Short pulses, require high PT
PCMP: “compresses” more bandwidth into pulse by modulating TX pulse.
TX pulse mod: LFM, NLFM, binary/polyphase coding.
LFM very prevalent in modern radar.
Less PT needed for same SNR and range resolution performance.
ΔR = c/2B

4. Pulse Compression (PCMP)
s(t)
y(t)
sr(t)
Example:
TX signal: s(t) =
Matched filter: h(t) = (time reverse and conjugate s(t)
Range result: y(t) = sr(t)*h(t) (convolution)

5. LFM waveform LFM: Linear Frequency Modulation (chirp)
Easy to implement: DDS, FPGA, DAC, VCO
S(t) = exp{ j2π(fot + 0.5BTt2) } for |t| ⋜ T/2
f = [-B/2 B/2] for this case
Time Bandwidth Product (TB): affects chirp spectrum. f1 t1

6. LFM Spectrum – TB
Fresnel Ripples
High TB: chirp spectrum approximates a rectangular spectrum
Low TB: not so.
Higher TB, smaller the Fresnel Ripple.
Keep in mind: will show in future slides how reducing Fresnel ripple can help in sidelobe reduction.

7. Pulse Compression of LFM
y(t) = s(t)*h(t) ~ essentially an autocorrelation function
Y(t) has sinc shape. Y(f) is rectangular, ∴ y(t) sinc
↓ mainlobe width ↑ range resolution
Mainlobe width = 1/B
Problem: high sidelobes
Peak sidelobe is -13 dB, poor dynamic range, mask weak echo returns.

8. Windowed Matched Filter
* matched filter weights
hw(t) = w(t)*h(t)
Windowing shapes the rectangular spectrum of the matched filter.
More gradual rise times, less sidelobes.
Plethora of windows to choose from: Tukey, Hamming, Blackman Harris…
Drawbacks: increased rise time, reduce bandwidth, mainlobe widens.
Drawbacks: reduced SNR.

9. Windowed Matched Filter
Hamming Window applied.
Sidelobe only -44 dB.
Mainlobe widens
Taken a hit in SNR

10. Distant Range Sidelobes
Windowing the matched filter does not reduce distant range sidelobes (T/2).
A function of TB and ∴ a function of Fresnel Ripples.
↑ TB ↓ distant range sidelobe magnitude
For fixed TB, equivalent performance can be achieved by reducing Fresnel ripples.

11. Amplitude Tapering of TX pulse
s(t) = tukey(t)* exp{ j2π [fot + 0.5BTt2] } | t | ⋜ T/2
Amplitude tapering can reduce the Fresnel ripple in the chirp spectrum
Chirp spectrum more rectangular in shape

12. Amplitude Tapering of TX pulse
Combined with windowed matched filter to get best of both worlds.
Extremely low distant sidelobes.
Suffering from more SNR hit due to less illumination of target.
Peak sidelobe near mainlobe slightly higher. Right tapering ratio has to be chosen.
Example: CReSIS’ radars typically use 0.1 Tukey tapering ratio along with Blackman Harris internal windowing

13. Phase Predistortion
Leaves amplitude constant, modulates phase of chirp signal
Cubic phase predistortion.. There are others too..
Goal is to similarly reduce Fresnel Ripples.. not as good as amplitude tapering
Does not suffer SNR hit as much as amplitude tapering

14. Phase Predistortion Combined with internal windowing.
Reduced distant sidelobe amplitude
Amplitude tapering has better performance in sidelobe reduction
Peak sidelobe near mainlobe does not change as compared to internal windowing case.

15. Summary
LFM methods to suppress sidelobes in pulse compression were discussed.
Three more common methods were discussed.
Other modes of PCMP exist: NLFM, binary/poly phase coding…
Modern digital technology allows ease of implementation of many theoretical modulation schemes..

16. THANKS!! QUESTIONS AND COMMENTS
If have time.. Go to bonus slides..

17. Bonus – CReSIS Stuff
Real time amplitude modulation of waveform ( MHz update rate)
Can be used for amplitude tapering, DDS sinc output spectrum compensation, and radar TX chain S21 (transmit coefficient)

18. Bonus – CReSIS Stuff DDS Chassis: power supplies (switchers)
Power routing hub
RS232 level shifter and signal buffer
Chirp BPF
CLK Generator (PLL technology)
Dual 4 channel DDS board.

19. Bonus – CReSIS Stuff Radar GUI NI LabVIEW Waveform control Tapering
Quick look feature
Pulse Compression result

20. Bonus – CReSIS Stuff UWB-ICE Radar System
RX & Digitizer (NI PXIe 1085)
24 Channels
DDS Chassis
UWB-ICE Radar System

21. THANKS!! QUESTIONS AND COMMENTS