Orthogonal Frequency Coding for SAW Device Applications
description
Transcript of Orthogonal Frequency Coding for SAW Device Applications
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)