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Radar Signals

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

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Radar Signals

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  1. Radar Signals Tutorial 3LFM, 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. Hamming-weighted LFM 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 There is only one dot in each column and each row. M frequency slices Δf 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 M contiguous time slices tb

  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

  14. A Costas signal • Hopping frequency • Complex envelope

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

  16. Peak sidelobe is -13.7 dB

  17. Exhaustive search of Costas codes

  18. 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

  19. 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}

  20. 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

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

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

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