Radar Signals
Tutorial 3LFM, Coherent Train and Frequency Coding
OutlineOutline
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 reviewLFM review
LFM range sidelobe reductionLFM range sidelobe reduction
Amplitude weighting Square-root of Hamming window
To maintain matched filtering, the weight should be split between the transmitter and receiver
Yet a linear power amplifier is required
LFM Hamming-weighted LFM
Sidelobe suppression and mainlobe broadening
A train of pulsesA train of pulses
A coherent train of identical unmodulated pulses Signal
Complex envelop
Unmodulated pulse
6 pulses and duty cycle = 0.2
Large improvement in Doppler resolution
Resolutions and Ambiguities
Frequency-modulated pulsesFrequency-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
Matrix representation of quantized LFMMatrix representation of quantized LFM
M contiguous time slices tb
M f
requ
ency
sli
ces 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
Costas coding (1984)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
A Costas signal Hopping frequency Complex envelope
Check whether CostasCheck whether Costas
If all elements in a row of the difference matrix are different from each other, the signal is Costas.
Peak sidelobe is -13.7 dB
Exhaustive search of Costas codesExhaustive search of Costas codes
Construction of Costas codeConstruction 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
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}
Nonlinear Frequency ModulationNonlinear 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
Low auto-cor sidelobes
High sidelobes at high Doppler cuts
Future talksFuture talks
Phase-coded pulse Barker codes Chirplike phase codes Our codes
Thank youSep. 2009
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