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Orthogonal Frequency Coding for SAW Device Applications. D.C. Malocha 1 , D. Puccio, and D. Gallagher, Electrical & Computer Engineering Department, University of Central Florida, Orlando, FL, 32816-2450 [email protected] 1. Orthogonal Frequency Coding (OFC) Introduction. - PowerPoint PPT Presentation
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Orthogonal Frequency Coding for SAW Device
Applications
D.C. Malocha1, D. Puccio, and D. Gallagher,
Electrical & Computer Engineering Department, University of Central Florida, Orlando, FL, 32816-2450
Orthogonal Frequency Coding (OFC) Introduction
Fixed time length for a chip, , and fixed chip carrier frequency, fC.
Fixed relationship between time length and center frequency or where N = # of carrier cycles per chip.
Relationship between chip time and chip nullbandwidth, NBW: fc/NBWc=2N or Fc/NBWc=2N+1.
There will be multiple chips in a bit.
C
NcfC 1/2NcfC
Orthogonal Frequency Coding (OFC) Six Element Basis Set
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.5
1Orthogonal Frequencies
Relative Frequency
Rel
ativ
e Am
plitu
de
•Chip length sets the bandwidth; NBW=2/Tc
•fc*Tc=N
•Null frequencies @ fc1 occur at peak of fc2
0 80 160 240 320 400
40
20
0Linear Chirp Frequency Response
Frequency (MHz)
dB (N
orma
lized
)
0 100 200 300 4000
1
2
3Linear Chirp Group Delay
Frequency (MHz)
Grou
p Dela
y (u
sec)
Linear Stepped ChirpFrequency Response - 7
Chips/Bit
1 0 1 2 3 4 5 6 7 8 9 101
0
1Linear Stepped Chirp
Time - Normalized to chip length
Am
pli
tude
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.2
0.4
0.6
0.8
Normalized Frequency
Mag
nit
ude (
Lin
ear)
Schematic of OFC SAW ID TagDefining an OFC Bit
0 1 2 3 4 5 6 71
0.5
0
0.5
1
Normalized Time (Chip Lengths)0 1 2 3 4 5 6 7
1
0.5
0
0.5
1
Normalized Time (Chip Lengths)
Piezoelectric Substrate
f1 f4 f6 f0f2 f5 f3
Linear Stepped Chirp Time Response with 7 Chips
Conventional PN CodingSingle Carrier Frequency BPSK 7 Chip Barker Code
1 0 1 2 3 4 5 6 7 8 9 101
0
1BPSK 7 bit Barker Code
Time ( Normalied to chip length)
Am
plitu
de
0 50 100 150 200 250 300 350 400 450 500
40
20
0Frequency Response - 7 bit Barker Code
Frequency (MHz)
dB N
orm
aliz
ed
1 Chip
Auto CorrelationPN Coding Single Carrier BPSK 7 Chip Barker Code
1 0 1 2 3 4 5 6 7 8 950
40
30
20
10
0Autocorrelation 7 Chip Barker Code
Normalized Time
Nor
mal
ized
Am
plitu
de (
dB)
•Single Carrier Frequency
•Processing gain is proportional to chips/bit
•Sidelobes dependent on code
OFC Time/ Frequency Response
7 Chip
1 0 1 2 3 4 5 6 7 8 9 10 11 121
0
1OFC Time Response 7 bit Barker Code
Time ( Normalied to chip length)
Am
plitu
de
0 50 100 150 200 250 300 350 400 450 500
40
20
0OFC Frequency Response
Frequency (MHz)
dB N
orm
aliz
ed
1 Chip
PN-OFC vs. Single Carrier BPSK PN-OFC vs. Single Carrier PN
0 0.5 1 1.5 2 2.550
40
30
20
10
0
7 Chip OFCSingle Carrier
OFC and Single Carrier
Normalized Frequency
dB N
orm
aliz
ed to
Pea
k of
Sin
gle
Car
rier
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.850
40
30
20
10
0
7 Chip OFCSingle Carrier
OFC and Single Carrier
Normalized Frequency
dB N
orm
aliz
ed to
Pea
k of
Sin
gle
Car
rier
For PN, PG=7
For OFC, PG=49
OFC 7-Chip vs. Single Carrier BPSK Frequency Response
OFC 7-Chip vs. Single Carrier PN Code Frequency Response
Time Autocorrelation Comparison
0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 71
0.5
0
0.5
1
7 bit Barker Code OFC7 bit Barker Code Single Carrier
Time Normalized to a Chip Length
Nor
mal
ized
Am
plitu
de
For PN, compressed pulse width is 2 chips
For OFC, compressed pulse width is 0.29 chips
0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.51
0.5
0
0.5
1
7 bit OFCSingle Carrier
Time Normalized to a Chip Length
Nor
mal
ized
Am
plitu
de
OFC 7-Chip vs. BPSK Single CarrierTime Autocorrelation
OFC vs. Single Carrier PN with 7 ChipsTime Autocorrelation
2 Differing OFC CodesTime Domain Code Diversity
1 0 1 2 3 4 5 6 7 8 9 101
0
1OFC Time Response
Time ( Normalied to chip length)
Am
plit
ude
2 Differing OFC CodesFrequency Domain
Code Diversity
Autocorrelation of OFC7 Chip Barker CodeNo-PN Code and With PN-Code
0.5 0.05 0.6 1.15 1.7 2.25 2.8 3.35 3.9 4.45 525
20
15
10
5
0Autocorrelation of OFC 7Bit Braker Code
Normalized Time
Nor
mal
ized
Am
plitu
de (d
B)
0.5 0.05 0.6 1.15 1.7 2.25 2.8 3.35 3.9 4.45 525
20
15
10
5
0Autocorrelation of OFC No Code
Normalized Time
Nor
mal
ized
Am
plitu
de (d
B)
OFC 1 Bit Long, 7 Chips/BitWith No PN Coding
0.5 0.35 0.2 0.05 0.1 0.25 0.4 0.55 0.7 0.85 10
0.2
0.4
0.6
0.8
1Autocorrelation of OFC
Time Normalized to a Chip Length
Nor
mal
ized
Am
plitu
de (d
B)
2 1.29 4.57 7.86 11.14 14.43 17.71 2150
40
30
20
10
0
Cross CorrelationAutocorrelation
Auto and Cross Correlation
Time Normalized to Chip Length
Nor
mal
ized
Am
plit
ud
e (d
B)
OFC 1 Bit Long, 7 Chips/BitWith PN Coding
2 0.3 2.6 4.9 7.2 9.5 11.8 14.1 16.4 18.7 2150
40
30
20
10
0
Cross CorrelationAutocorrelation
Auto and Cross Correlation
Time Normalized to Chip Length
Norm
aliz
ed A
mplitu
de
(dB
)
0.5 0.35 0.2 0.05 0.1 0.25 0.4 0.55 0.7 0.85 10
0.2
0.4
0.6
0.8
1Autocorrelation of OFC
Time Normalized to a Chip Length
Nor
mal
ized
Am
plitu
de (d
B)
OFC 3 Bit Long, 7 Chips/BitNo PN Coding
2 0.3 2.6 4.9 7.2 9.5 11.8 14.1 16.4 18.7 2150
40
30
20
10
0
Cross CorrelationAutocorrelation
Auto and Cross Correlation
Time Normalized to Chip Length
No
rmal
ized
Am
pli
tud
e (d
B)
0 50 100 150 200 250 300 350 400 450 500
40
20
0OFC Frequency Response 7 Bit Barker Code
Frequency (MHz)
dB
No
rmal
ized
0.5 0.35 0.2 0.05 0.1 0.25 0.4 0.55 0.7 0.85 10
0.2
0.4
0.6
0.8
1
Autocorrelation of OFCtrace 2
Autocorrelation of OFC
Time Normalized to Chip Length
No
rmal
ized
Am
pli
tud
e
OFC 3 Bit Long, 7 Chips/BitWith PN Coding
OFC System Schematic
Upchirp TAG
DownchirpCorrelatorOutput
fo
TX
RX
OFC Tag SchematicReflector Structure
Piezoelectric Substrate
f1 f4 f6 f0f2 f5 f3
0 5 10 15 20 25 302
0
2
4
6
8
10
Original OFCConvolution of OFC with ChirpOFC after Chirp Deconvolution
7 bit PN OFC
Time - Normalized to chip length
Am
plitu
de
Plots of 3 Bit, 7 Chips/Bit OFC System Simulation
Ideal OFC TAG
OFC with Chirp
OFC with |Chirp|2
Tag Return Signal is28 Bits long
3 Bit, 7 Chips/Bit SimulationIdeal vs. System Autocorrelation
2 0 2 4 6 8 10
0
0.2
0.4
0.6
Upper: Auto Correlation - SystemLower: OFC-OFC Autocorrelation
Time - Normalized to Chip Length
Am
plitu
de
OFC Auto and Cross Correlation
3 Bits, 7 Chips/Bit
5 0.5 6 11.5 17 22.5 28 33.5 39 44.5 5025
20
15
10
5
0
Cross correlationAuto Correlation
OFC Auto and Cross Correlation
Time
Nor
mal
ized
Am
plitu
de (
dB)
Conclusions and Discussion OFC SAW Technique
a viable way of tagging multi-sensors inherent processing gain reduces pulse ambiguity for sensor inherent security – OFC and PN coding
Implementable in transducers or reflectors Modeling shows expected results First SAW sensor embodiment is successful
(Puccio, et.al. this symposium)
