Radar theory of radio wave

1. Radar Signals
Tutorial 3
LFM, Coherent Train and Frequency Coding

2. Outline
 More on LFM
 Range sidelobe reduction
 Coherent train of identical pulses
 Large improvement in Doppler resolution
 Frequency-modulated pulse (besides LFM)
 Costas code
 Nonlinear FM

3. LFM review

4. LFM range sidelobe reduction
 Amplitude weighting Square-root of Hamming window

5.  To maintain matched filtering, the weight should be
split between the transmitter and receiver
 Yet a linear power amplifier is required

6. LFM Hamming-weighted LFM
Sidelobe suppression and mainlobe broadening

7. A train of pulses
 A coherent train of identical unmodulated pulses
 Signal
 Complex envelop
 Unmodulated pulse

8. 6 pulses and duty cycle = 0.2

9. Large improvement in Doppler resolution

10. Resolutions and Ambiguities

11. Frequency-modulated pulses
 Previously discussed LFM
 The volume of AF concentrates in a slowly decaying
diagonal ridge
 An advantage when Doppler resolution is not
expected from a single pulse
 Relatively high autocorrelation sidelobe
 Other frequency-modulation schemes
 Better Doppler resolution
 Lower autocorrelation sidelobes

12. Matrix representation of quantized LFM
M contiguous time slices tb
M
frequency
slices
Δf
There is only one dot in each
column and each row.
The AF can be predicted
roughly by overlaying a copy of
this binary matrix and shifting it
to some (delay, Doppler).
A coincidence of N points
indicates a peak of N/M

13. Costas coding (1984)
The number of coinciding dots
cannot be larger than one for
all but the zero-shift case.
A narrow peak at the origin and
low sidelobes elsewhere

15.  A Costas signal
 Hopping frequency
 Complex envelope

16. Check whether Costas
If all elements in a row of the difference matrix are
different from each other, the signal is Costas.

17. Peak sidelobe is
-13.7 dB

18. Exhaustive search of Costas codes

19. Construction of Costas code
 Welch 1 (Golomb & Taylor, 1984)
 Applicable for M = p – 1 where p can be any prime
number larger than 2.
 Let α be a primitive element in GF(p)
 Numbering the columns of the array j = 0,1,...,p-2
and the rows i = 1,2,...,p-1. Then we put a dot in
position (i, j) if and only if i = αj

20.  M = 4
 p = M + 1 = 5
 GF(5) = {0 1 2 3 4}
 Use α = 2:
 Use α = 3:
{1 2 4 3}
{1 3 4 2}

21. Nonlinear Frequency Modulation
 Stationary-phase concept
 The energy spectral density at a certain frequency is
relatively large if the rate of the change of this
frequency is relatively small
 Design the phase (frequency) to fit a good spectrum

23. Low auto-cor
sidelobes
High sidelobes at
high Doppler cuts

24. Future talks
 Phase-coded pulse
 Barker codes
 Chirplike phase codes
 Our codes
Thank you
Sep. 2009