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 t b M frequency slices Δ f 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 = α j

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