Post on 16-Jan-2016
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A Unified Understanding of the Many Forms ofOptical Code Division Multiplexing
Eli YablonovitchRick Wesel
Bahram JalaliMing Wu
Ingrid Verbauwhede
Can FPGA’s + Modulator/PhotoDetector ArrayMimic any form of OCDMA?
PrincetonUSC
Matched Filtering in Time Domain (non-coherent)
UC DavisTelcordia
Purdue Univ.
Matched Filtering in the Spectral Domain (coherent)
Block Diagram
DW
DM
DE
MU
X
Photodetectors FPGADataFrom
Network
Vo
ltag
eTime
ThresholdLevel(validdata)
Mu
lti-wave
leng
thL
aser So
urce
Wav
elen
gth
Time
Wav
elen
gth
Time DW
DM
MU
XTo Network
Transmitter
Receiver
Wav
elen
gth
Modulators
FPGAData
Code
Time
PLL
Switch Matrix
Delay Module
Code Generator
System clock
LVD
S O
utput
LVD
S Input
Protocol
Input clock
Input data
Output clock
Output data
LVDS: Low Voltage Differential Signaling
PLL: Phase-Locked Loop
FPGA Encryption
Therefore FPGA’s + Modulator/PhotoDetector Array can easily duplicate the performance of Matched
Filtering in Time Domain (non-coherent)
Therefore Princeton scheme andUSC scheme can
be emulated by our FPGA approach
thresholddetector
Spectral P
hase Decoder
Wavelength M
UX
Wavelength M
UX
Data
Fre
quen
cy
timet
Photo-receiverarray
Buffer
Dela
y
Sum
Data
FPGA
time
Fre
quen
cy
t
Equivalence Between Spectral Phase Encoding And Time Sequential Encoding:
(a) Sequential brief individual pulses, have a broad spectrum as indicated by the colors. The plus and minus signs in (a) indicate various phase shifts induced on the spectral components of one pulse. The phase shifts can be decoded by a matched filter, producing a single big pulse that can be monitored by a threshold detector.
(b) With no loss of generality, the pulses can be spectrally filtered, and each spectral component sent to a phase sensitive photo-receiver. The retrieved information can be stored and processed in a Field Programmable Gate Array, which is fully equivalent to direct-sequence radio CDMA.
(a)
(b)
Figure 1: Coherent detection without a local oscillator. The ring is a carrier add/drop separation filter.
sidebands + carrier
sidebands
sidebands
carrier
carrier
opticalelectrical
+
Figure 4: Tandem single side band receiver, not requiring a local oscillator, avoids duplicate side-bands.
180hybrid
coupler
carrieradd/drop
EDFA
opticalelectrical
sidebands
carrier
carrier2
+ +
in-phasesignal
quadraturesignal
sidebands
cos2(t) code2(t)signal(t)=
(1/2)signal(t)
1
-1time
chip time
local codegenerator
code(t)
Transmittercarrier wave
cos(t)
cos(t) code(t) signal(t)code(t) signal(t)code(t)
signal(t)
Receiverlocal
oscillatorcos(t)
local oscillatorcos(t)
cos(t) code(t) signal(t)
cos2(t) code(t)signal(t)
time
time
mixer
mixermixer
mixer
A Direct Sequence radio CDMA system imposes random phase shifts +1 or –1 on the signals in much the same way as the channelized optical spectral phase decoder/encoder, described in a previous vugraph.
Direct Sequence Spread Spectrum:
Therefore FPGA’s + Modulator/PhotoDetector Array can do Spectral Phase Encoding if Coherent detectors
are used
Therefore UC Davis scheme andTelcordia scheme and
Purdue scheme can be emulated by
our FPGA approach
freq
uenc
y
ttime
freq
uenc
y
time t
chip time
channel 1
channel 2
freq
uenc
y
ttime
time between pulses
The different approaches are all equivalent since, the frequency time rectangular cell changes shape, but its area is preserved, in accordance with the “Uncertainty Principle”.
Conventional Wavelength/Time matrix. Frequency and time are treated on an equal footing.
Spectral Phase Encoding. Each color of each pulse will be coded with a different phase shift, producing narrow slicing of the spectrum, but relatively long periods between pulses.
Direct-Sequence Time-Domain Spread-Spectrum CDMA. Each channel occupies a broad frequency spectrum corresponding to the inverse of the chip time.
Successive Decoding
• We can decode the first user by treating others as noise, then the first user’s ones become erasures for the other users. Proceed in this way until finish decoding all the users.
• This is called successive decoding. For binary OR channel, this process does not lose capacity as compared to joint decoding.
Successive Decoding: The Z-Channel • Successive decoding for n users:
– User with lowest rate is decoded first– Other users are treated as noise– The decoded data of the first user is used in the
decoding of the remaining users
• First user sees a “Z-channel”
• Where i = 1-(1-p)n-i is the probability that at least one of the n-i remaining users transmits a 1
1
11 0x
1x
0y
1y
Simple codes
• In order to have a hardware demo working for the May meeting, some very simple codes were produced.
• This demo consists of two transmitter and two receivers
• Both receivers decode the information independently
Simple Codes for Demo• Short codes have been designed for a
simple demo for 2 users• These were chosen to be as simple to
encode and decode as possible • Each bit is encoded separately• Bit synchronism is assumed, blocked
asynchronism is allowed• Coordination is required• These codes are error free
Simple codes for Demo (2)
Receiver 1 looks for position of 0 (which always exists)
If 1 or 2, decide 1
If 3 or 4, decide 0
Source 1
1 2 3 4
0
1
Rate 1/4
Source 2
1 2 3 4 5 6
1
0Rate 1/6
0
1
Receiver 2 looks forFIRST position of 0.If 1, 3 or 5, decide 1If 2, 4 or 6, decide 0
Worst Case :
block i block i+1
Sum Rate 5/12
FPGA Setup for initial successive decoding Demo
DataGenerator
Encoder
FPGA
Modulator
CWLaser
DataGenerator
Encoder
FPGA
Modulator
CWLaser
WavelengthCoupler
Photodetector
Bit ErrorRate Tester
Decoder
FPGA
Photodetector
Bit ErrorRate Tester
Decoder
FPGA
Transmitter 1
Transmitter 2
Receiver 1
Receiver 2