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 fr

eque

ncy

slic

es 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