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Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms

1SLIDEBen-Gurion Univ. Jan 26, 2016

Periodic and a-periodic on-off coded waveforms for

non-coherent RADAR and LIDAR

Nadav Levanon

Tel Aviv University, Israel

Radar SymposiumBen-Gurion Univ., 25 January 2016

With contributions from:

Itzik Cohen, Tel Aviv univ.; Avi Zadok and Nadav Arbel, Bar-Ilan univ.; J. Mike Baden, GTRI



With the knowledge accumulated in coherent radar, we enrich the branch of non-coherent radar.

http://www.thales-electron-devices.de/images/about/new/magnetron.jpg

http://www.thales-electron-devices.de/images/about/new/magnetron.jpg



Non-coherent pulse compression

• On-off keying transmitted signal +.

Can utilize saturation amplifier, pulsed oscillator (e.g., magnetron) and especially laser +.

Random phase of each sub-pulse is acceptable and even advantageous.

• Basic compression codes+:

Bipolar a-periodic or periodic codes (Barker, Ipatov, Legendre, m-sequences …)

• Simple envelope detection in receiver +.

Doppler tolerance + (but no Doppler information -).

SNR loss due to non-coherency -.

Sensitivity to multi-scatterer targets -.

• Non-coherent integration of many pulses (summing) is much

simpler + than coherent integration (which requires FFT), but less efficient -.

• Low-sidelobe response requires mismatched processor.

Additional SNR loss because of the mismatch -.



Receiver block diagram

BPF | |p

bn b2

∑Output

Rectified output b1

p =1 Magnitude detector

p =2 Magnitude square detector



PERIODIC NON-COHERENT WAVEFORMS



Periodic on-off waveforms (Example: Laser range finder)

Classical approach: Time Of Flight (TOF); Amplitude (power) limited (Amax)

time

A

0 tpTr

Target illumination time,i rT M T

1max 2

, unambiguousrangerR CT

, rangeresolutionpR t

2 2

average max2p r pP A t T A t C R

2 2 2 2 2 2

on target max

Assumes the beam apperture on target is smaller than the target

4p r p i r p iP MA t T A t T T A t TC R

2 2 2

on target max4p iP A t TC R

Implies a conflict between power-on-

target and unambiguous range.

Increasing A:

• Complicates hardware

• Increases probability of intercept

Possible solution:

Add more pulses within Tr without

reducing the unambiguous range.



Example of periodic on-off waveform: Barker 13 !!

Perfect Periodic Cross-Correlation (PPCC)

S = 1 1 1 1 1 0 0 1 1 0 1 0 1

R = 1 1 1 1 1 b b 1 1 b 1 b 1 , b=-2



N 3 4 5 7 11 13

b -1 -2 -3 -1 -1 -2

N = 4 5 13

Code type m-seq & Legendre m-seq & Legendre Legendre

22 1 4 1 1 32 1 4 2 1 4 3 1

All unipolar Barker codes can exhibit PPCC (with the proper b in their reference)

All unipolar m-sequences exhibit PPCC, with their corresponding bipolar reference (b = -1).

m-sequences are available at lengths , N. Takeuchi, et. al. “Random modulation

cw lidar,” Applied Optics, Vol. 22, No. 9, 1 May 1983, pp 1382-1386.

2 1, 2,3,4,...mN m

m-sequences (shift register sequences)

Legendre sequences

All unipolar Legendre sequences exhibit PPCC, with their corresponding bipolar reference (b = -1).

Legendre sequences are available at lengths 4 1, 1,2,3,4,... ; is a primeP k k P

All unipolar modified Legendre sequences exhibit PPCC, with their corresponding bipolar reference

(b = -1).

Modified Legendre sequences are available at lengths 4 3, 2,3,4,... ; is a primeP k k P

Modified Legendre sequences

Ipatov sequences



function [s,r] = perfect_periodic_Legendre_on_off( N )

% Generates a periodic coded signal using Legender and modified Legendre sequences

% The signal exhibits perfect periodic crosscorrelation with its reference

% N is any odd prime

Nspt=sprintf('%g element Legendre on-off waveform ',N);

if isprime(N)==0

disp('Not a prime')

return

end

s=ones(1,N);

if rem((N+3)/4,1)==0 % modified Legendre

s(mod((1:N-1).^2,N)+1)=0;

r=s*2-1;

s(1)=0;

else % Legendre

s(mod((1:N-1).^2,N)+1)=0;

r=s*2-1;

end

d=abs(ifft(fft(s).*conj(fft(r))));

figure, plot(d, 'k')

title(['Periodic cross-correlation of ' Nspt ]);

end



On-off signal based on Legendre 19

>>[s,r]=perfect_periodic_Legendre_on_off(19);

>> disp([s' r'])

1 1

0 -1

1 1

1 1

0 -1

0 -1

0 -1

0 -1

1 1

0 -1

1 1

0 -1

1 1

1 1

1 1

1 1

0 -1

0 -1

1 1

On-off signal based on modified Legendre 17

>>[s,r]=perfect_periodic_Legendre_on_off(17);

>> disp([s' r'])

0 1

0 -1

0 -1

1 1

0 -1

1 1

1 1

1 1

0 -1

0 -1

1 1

1 1

1 1

0 -1

1 1

0 -1

0 -1



Example of periodic on-off waveform: m-sequence 15

S = 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1

R = b 1 1 1 1 b b b 1 b b 1 1 b 1, b=-1

Perfect Periodic Cross-Correlation (PPCC)



Interference between two targets (simulations: m-sequence 127, Legendre 131)

In CW waveforms the returns from two targets always coincide, even if the delay difference is large.

The on-off non-coherent case is especially sensitive to the resulting interference.

The simulation included different random phase of each sub-pulse out of the 650,000 subpulses.

(code-length * number of periods processed * number of averages 650,000 ).

No additive noise.



The modulo-2 sum of an m-sequence and another phase (i.e. time-delayed version)

of the same sequence yields yet a third phase of the sequence.



18 averages using the same code 18 averages of using 18 different codes



Performances with noise (simulation), Ipatov 121

Periodic Cross-correlation

output. The reference

contained 3 periods.

Section of signal ( 60 elements),

5 samples per code element



Laser range finder experiment setup outside the Music Department at Bar-Ilan campus.



Experimental results with a laser range finder (4003 element on-off Legendre signal)

R2=R0

R

R1=R0 -1.139m

R3=R0 +1.229m

R0 = 273m

R 1.2m

Optical transmitted power = 22.5dBm.

Sub-pulse width = 1ns dR=15cm

Output after averaging 1000

consecutive measurements.

Target illumination time = 0.2s

(= 10-9 4003 49 1000)

Unambiguous range = 600m

Target (white paper) relative forward

power reflectivity = 0.07 .



Unique noise behavior[s‘ r']

1 1

0 -1

1 1

1 1

0 -1

0 -1

0 -1

0 -1

1 1

0 -1

1 1

0 -1

1 1

1 1

1 1

1 1

0 -1

0 -1

1 1

In each period, (N+1)/2 envelope

detected samples (all positive),

are multiplied by 1 and (N-1)/2

samples are multiplied by -1 .



Sadogursky, A. and Levanon, N. “Performances of Marcum’s (S+N)-N integration scheme

with fluctuating targets”, IEEE Trans. AES, Vol. 50, No.1, Jan. 2014, pp. 319-328.



Noise only. Correlation

with {1,-1} reference.

Noise only. Correlation

with {1,0} reference.

Field trial at Tel Baruch coast, with a

modified FURUNO magnetron marine

radar (magneton project with Elisra.

Project manager Erez Ben-Yaacov).



Extending the un-ambiguous range of a simple magnetron radar by a factor of 3

Transmitted non-coherent pulse train: 1 1 0 1 1 0 1 1 0 …... (every 3rd pulse is blocked)

Reference pulse train: 1 1 -1 1 1 -1 1 1 -1 …...

Clutter and targets will

replicate after 3 PRIs,

rather than after 1 PRI.

PRI

Legendre 3 and

its reference

Pulse fluctuations can

slightly distort the

perfect periodic cross-

correlation.



Field trial near the port of Ashdod, with a

modified FURUNO magnetron marine radar

(magneton project with Elisra. Project

manager Erez Ben-Yaacov).



Near-clutter

replicating at a

range of 12km

(corresponding

to the PRI)

Ship target at a

range of 13.1 km

Correlation with {1,0} reference



Correlation with {1,-1} referenceShip target at a

range of 13.1 km



A-PERIODIC NON-COHERENT WAVEFORMS

Example: Compressing a single long pulse by internal on-off coding



Manchester Encoded Unipolar Barker 13

1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0

Trans

Ref

Unipolar Barker 13: 1 1 1 1 1 0 0 1 1 0 1 0 1



A-periodic cross-correlations between a unipolar Barker 13 and a mismatched reference

Unipolar Barker 13: 1 1 1 1 1 0 0 1 1 0 1 0 1

The mismatched filter

(MMF) used, is a

sequence of length

65 (=5*13) optimized

for minimum integrated

sidelobes (SL), with

higher weight given to

the minimization of the

near SL.

The MMF can get any

value, both positive

and negative.



Reduced duty cycle of the sub-pulses (1) Better range resolution (2) Higher bandwidth

(3) Lower energy in the compressed pulse



Fig. 1. Flow cytometry

setup implementing spatial

modulated emission.

ON-OFF SIGNAL - USE IN OPTICAL MASKS



Thank you

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