1/19 2008, Graz, Austria Power Spectral Density of Convolutional Coded Pulse Interval Modulation Z....

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Transcript of 1/19 2008, Graz, Austria Power Spectral Density of Convolutional Coded Pulse Interval Modulation Z....
2008, Graz, Austria 1/19
Power Spectral Density of Convolutional Coded Pulse
Interval Modulation
Z. Ghassemlooy, S. K. Hashemi and M. Amiri Optical Communications Research Group,
School of Computing, Engineering and Information Sciences,Northumbria University,
Newcastle, U.K.Web site: http://soe.unn.ac.uk/ocr
2008, Graz, Austria 2/19
Outline
Aims and Objectives  Motivations
Introduction
DPIM and Convolutional Coded DPIM
Power Spectral Density of CCDPIM
Results
Conclusions
2008, Graz, Austria 3/19
Aims and Objective – Motivation
Carry out analysis for the power spectral density for the convolutional coded DPIM and investigate: Bandwidth efficiency DC component.
Compare the results with both the uncoded and coded DPIM
2008, Graz, Austria 4/19
Indoor Optical Wireless Communications
Definition: OWC is wireless transmission of light i.e. infrared radiation
through the medium of the air.
Some advantages are: Higher bandwidth. Unregulated bandwidth. Immunity to electromagnetic interference. High security compared with RF. Absence of multipath fading (due to the use of IM/DD). Complementary to RF.
2008, Graz, Austria 5/19
Modulation Techniques
Pulse Time Modulation
Analogue Digital
Isochronous Anisochronous Isochronous AnisochronousPIMPIWMPFMSWFM
PWMPPM
PPMMPPMDPWMPCM
DPIMDPIWMDHPIMDPPM
2008, Graz, Austria 6/19
Digital Modulation Schemes
Information
Frame 4
1 1 1
Frame 3
1 1 0
Frame 2
0 1 0
Frame 1
0 0 0
DPIM
2008, Graz, Austria 7/19
Digital Pulse Interval Modulation
DPIM signal is defined :
p(t)  rectangular pulse shape,
Ts  slot duration an  set of random variables
representing a pulse/no pulse in the nth Ts
L = 2M, hence for M = 2, L = 4 slots.
00
01
10
11
4DPIM Symbols
NGS 1GS
SourceData
GSL
NGBLo
Lavg
1)3(5.0
)1(5.
n
sn nTtpatx
2008, Graz, Austria 8/19
DPIM  Convolutional Coding
Linear block codes like Hamming code, Turbo code and Trellis coding are difficult (if not impossible ) to apply in PIM because of variable symbol length.
Hence, Convolutional coding
 since it acts on the serial input data rather than the block.
2008, Graz, Austria 9/19
Convolutional Coding
Defined as (n,k,K), where k and n are the input (1) and output bits (i.e. 2), and K is the memory element.
Code rate is defined as k/n = 1/3.
Constraint length (K)=3; The Generator Function:
G0 = [111]
G1 = [101]
Z1 Z1
Output 1
Output 2
Data Sequence
(Ik)Z1 Z1
Output 1
Output 2
Data Sequence
(Ik)
2008, Graz, Austria 10/19
Convolutional Coded DPIM
][1
mL
Average symbol length of code data:
P[.]  probability function and },,,{ 110 LLLL
10 ][ LL
For LDPIM
avg
L
LLLL
LL
2
1
2
)1(11
1
1
and
For CCDPIM symbol length
)}2(2,,8,6{ L
Lave = L + 5
.
2008, Graz, Austria 11/19
DPIM  Convolutional Coding
2 empty slots / symbol  to ensure that the memory is cleared after each symbol.
Trellis path is limited to 2.
2008, Graz, Austria 12/19
DPIM  Decoder
Viterbi ‘Hard ‘ decision decoding The Chernoff upper bond on the error probability
is:
where Pse is the slot error probability of uncoded DPIM.
)1(4,1
),(
sese ppDII
IDTPb
It is also possible not use Viterbi algorithm instead one can use a simple lookup table.
2008, Graz, Austria 13/19
Power Spectral Density
Generally signals can be divided into two models: Deterministic Model  No uncertainty about signal’s time
dependent behaviour at any instance of time. Random or Stochastic Model – Uncertain about signal’s
timedependent behaviour at any instance of time. However certain on the statistical behaviour of the signal on overall.
Power of Random Signal Deterministic signals  Instantaneous power is x2(t). Random signals – There is no single number to associate
with the instantaneous power i.e. x2(t) is a random variable for each time. The expected instantaneous power of x2(t) need to obtained.
2008, Graz, Austria 14/19
PSD of CCDPIM
A DPIM pulse train may be expressed as [12]:
which is cyclostationary, where p(t) is the rectangular pulse shape, Ts is the slot duration and for all n is a set of random variables that represent the presence or absence of a pulse in the nth time slot.
xc(t) can be stationarized with the introduction of a continuous variable to give xs(t) = xc(t + ), where is equally distributed over [0, Ts] and is independent of an. The distribution of stationarization depends on the length probabilities given as:
.
n
snc nTtpatx
}1,0{na
k
avg LLkp
][)( 01
2008, Graz, Austria 15/19
PSD of CCDPIM
The general expression for the spectral distribution expressed by the spectral density is given as:
Where T is the input period of the {an} (the sequence !!),
P(f) is the Fourier transform of p(t), the rectangular pulse shape P(f)2 = T2Sinc2(fT)
mmmccvs ffTfFfTRfP
TfR )()()()(
1)(
2
2008, Graz, Austria 16/19
PSD of CCDPIM (Contd.)
The continuous Spectrum of the CCDPIM Sequence {an}is evaluated as:
Where z = ei2Πu, is the greatest common divisor.
The Discrete part of the spectrum is defined as:
Where
,])()([2)()()(2
zBzAzAzCuRc
muezzAuF mui
mmmcm ,,)()( 22
mzVzA )()(
)()()()( zUzzXmzVzB
)(][)()( 1 zVpdiagzVzC
2008, Graz, Austria 17/19
PSD of CCDPIM (Contd.)
)(/)()( zgzhzX
1
0
)()(k
kzkpzh
0
)(k
kzpzg
0
)(k
kzzU
][ mLp
],,,1[)( 1 zzzV
,
2008, Graz, Austria 18/19
PSD of CCDPIM  Simulation
8CCDPIM using (37), Pulse shape p(t)  rectangular with 100%
duty cycle.
2008, Graz, Austria 19/19
Results (1)
PSD of 8CCDPIM with 100% pulse duty cycle against the normalised frequency: (a) predicted, and (b) simulated
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5160
140
120
100
80
60
40
20
0
20
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Normalised Frequency (fT)
Rvs
(fT
)/T
Clock (slot)DC level
2008, Graz, Austria 20/19
Results (2)
0 1 2 3 4 5 6 7 8 9 10160
140
120
100
80
60
40
20
0
20
Normalised Frequency (fT)
Rvs
(fT
)/T
(dB
)
PSD of 8CCDPIM with 50% pulse duty cycle against the normalised frequency: (a) predicted, and (b) simulated
1 2 3 4 5 6 7 8 9 10
Clock (slot)DC level
2008, Graz, Austria 21/19
Results (1&2)  Observation
Slot (clock) component  Phase locked loop to recover it at the receiver.
The nulls at normalised frequencies (fT)0 = ±1, ±2,… are poles on the unit circle.
It is followed by two symmetrically close poles on both sides at (fT)0 = ±1.5.
With information on nulls and poles, filter H(z) can be implemented as an Auto Regressive Moving Average (ARMA) filter.
DC level – may result in the baseline wander effect due to highpass filtering of the ambient light.
2008, Graz, Austria 22/19
Results (3) Spectral Comparison
0 0.5 10
0.2
0.4
0.6
0.8
1
fT
8CCDPIM
0 0.5 1 1.5 20
0.05
0.1
0.15
0.2
0.25
fT
8DPIM
Rvs
(fT
)/T
High DC component
2008, Graz, Austria 23/19
Results (4)  Slot Error Rates
• Higher bit resolution provides better performance ( at the expense of bandwidth)
• The code gain is 0.6 higher for bit resolution of 5 compared to 3.
2008, Graz, Austria 24/19
Packet Error Rates
2 1 0 1 2 3 4 5 6 7 8Electrical SNR (dB)
Pro
babi
lity
of P
ack e
t err
or,
PE
R8,16,32DPIM with one guard band @ R=100Mbps
Uncoded8DPIM
Coded UpperBound 8DPIMUncoded 32DPIM
Coded UpperBound 32DPIM
Uncoded16DPIMCoded UpperBound 16DPIM
1010
108
106
104
1012
2008, Graz, Austria 25/19
Conclusions
PSD of CCDPIM has been derived analytically based on the stationarisation of variable length word sequence.
Close match between predicted and simulated results.
Clock components can used for synchronisation. DCPIM > DCPPM, more susceptible to baseline
wander Convolutional coding has improved PER
performance of DPIM scheme.
2008, Graz, Austria 26/19
Thank You!