Radar Signals

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Radar Signals
Tutorial 3LFM, Coherent Train and Frequency
Coding
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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

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LFM review
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LFM range sidelobe reduction

• Amplitude weighting

Square-root of Hamming window
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• To maintain matched filtering, the weight should
  be split between the transmitter and receiver
• Yet a linear power amplifier is required

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Hamming-weighted LFM
LFM
Sidelobe suppression and mainlobe broadening
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A train of pulses

• A coherent train of identical unmodulated pulses
• Signal
• Complex envelop
• Unmodulated pulse

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6 pulses and duty cycle 0.2
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Large improvement in Doppler resolution
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Resolutions and Ambiguities
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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

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Matrix representation of quantized LFM
There is only one dot in each column and each row.
M frequency slices ?f
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
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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
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• A Costas signal
• Hopping frequency
• Complex envelope

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Check whether Costas
If all elements in a row of the difference matrix
are different from each other, the signal is
Costas.
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Peak sidelobe is -13.7 dB
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Exhaustive search of Costas codes
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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 a 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
  aj

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• M 4
• p M 1 5
• GF(5) 0 1 2 3 4
• Use a 2
• Use a 3

1 2 4 3
1 3 4 2
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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

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Low auto-cor sidelobes
High sidelobes at high Doppler cuts
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Future talks

• Phase-coded pulse
• Barker codes
• Chirplike phase codes
• Our codes

Thank you Sep. 2009