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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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
2SLIDEBen-Gurion Univ. Jan 26, 2016
With the knowledge accumulated in coherent radar, we enrich the branch of non-coherent radar.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
3SLIDEBen-Gurion Univ. Jan 26, 2016
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 -.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
4SLIDEBen-Gurion Univ. Jan 26, 2016
Receiver block diagram
BPF | |p
bn b2
∑Output
Rectified output b1
p =1 Magnitude detector
p =2 Magnitude square detector
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
5SLIDEBen-Gurion Univ. Jan 26, 2016
PERIODIC NON-COHERENT WAVEFORMS
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
6SLIDEBen-Gurion Univ. Jan 26, 2016
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.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
7SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
8SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
9SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
10SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
11SLIDEBen-Gurion Univ. Jan 26, 2016
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)
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
12SLIDEBen-Gurion Univ. Jan 26, 2016
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.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
15SLIDEBen-Gurion Univ. Jan 26, 2016
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.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
16SLIDEBen-Gurion Univ. Jan 26, 2016
18 averages using the same code 18 averages of using 18 different codes
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
17SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
18SLIDEBen-Gurion Univ. Jan 26, 2016
Laser range finder experiment setup outside the Music Department at Bar-Ilan campus.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
19SLIDEBen-Gurion Univ. Jan 26, 2016
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 .
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
20SLIDEBen-Gurion Univ. Jan 26, 2016
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 .
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
21SLIDEBen-Gurion Univ. Jan 26, 2016
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.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
22SLIDEBen-Gurion Univ. Jan 26, 2016
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).
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
23SLIDEBen-Gurion Univ. Jan 26, 2016
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.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
24SLIDEBen-Gurion Univ. Jan 26, 2016
Field trial near the port of Ashdod, with a
modified FURUNO magnetron marine radar
(magneton project with Elisra. Project
manager Erez Ben-Yaacov).
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
25SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
26SLIDEBen-Gurion Univ. Jan 26, 2016
Correlation with {1,-1} referenceShip target at a
range of 13.1 km
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
27SLIDEBen-Gurion Univ. Jan 26, 2016
A-PERIODIC NON-COHERENT WAVEFORMS
Example: Compressing a single long pulse by internal on-off coding
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
28SLIDEBen-Gurion Univ. Jan 26, 2016
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
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
29SLIDEBen-Gurion Univ. Jan 26, 2016
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.
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
30SLIDEBen-Gurion Univ. Jan 26, 2016
Reduced duty cycle of the sub-pulses (1) Better range resolution (2) Higher bandwidth
(3) Lower energy in the compressed pulse
Nadav Levanon, Tel-Aviv UniversityOn-Off Waveforms
31SLIDEBen-Gurion Univ. Jan 26, 2016
Fig. 1. Flow cytometry
setup implementing spatial
modulated emission.
ON-OFF SIGNAL - USE IN OPTICAL MASKS