Radar Signals Tutorial 3 LFM Coherent Train and

Radar Signals Tutorial 3 LFM, Coherent Train and Frequency Coding

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

LFM review

LFM 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 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 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 LFM 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 M contiguous time slices tb

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 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 d. B

Exhaustive search of Costas codes

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

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

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

Low auto-cor sidelobes High sidelobes at high Doppler cuts

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