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Applications of Wavelet Transform and Artificial Neural Network in Digital Signal Detection for
Indoor Optical Wireless Communication
Sujan Rajbhandari
1
Sujan Rajbhandari
Supervisors
Prof . Maia AngelovaProf. Z. Ghassemlooy
Prof. Jean-Pierre Gazeau
Optical Wireless Communication
Sujan Rajbhandari
2
Light as the carrier of information
Also popularly known as free space optics (FSO) or Free Space Photonics (FSP) or open-air photonics .
Indoor or outdoor
Transmission Format
Transmitted signal ‘1’ presence of an optical pulse ‘0’ absence of an optical pulse
Sujan Rajbhandari
0 2 4 6 8 100
0.2
0.4
0.6
0.8
1
Transmitted OOK
Normalized Time
Am
pitu
de
0 1 1 0 0 0 11 0 1
Links
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Non-LOS
Multipath Propagation Intersymbol interference (ISI) Difficult to achieve high data
rate if ISI is not mitigated.
Non-LOS
Multipath Propagation Intersymbol interference (ISI) Difficult to achieve high data
rate if ISI is not mitigated.
RxRxTxTx
LOSLOS
No multipath propagation Noise and device speed
are limiting factors Possibility of blocking
TxTx
RxRx
Received Signal
Sujan Rajbhandari
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Non-LOSNon-LOS
0 2 4 6 8 10-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Normalized Time
Am
plit
ud
e
Received signal for non-LO OOK
LOSLOS
0 2 4 6 8 10
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Received OOK for LOS links
Normalized Time
Am
plit
ud
e
Classical Digital Signal Detection
Set a threshold level.
Compared the received signal with the threshold level
Set ‘1’ if received signal is greater than threshold level
Set ‘0’ is received signal is less than threshold level.
Sujan Rajbhandari
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Classical signal detection techniques: Assumptions
The statistical of noise is known.
Maximise the signal to noise ratio for unknown noise with known statistics.
Channel characteristics are known( at least partially ) and generally assume to be linear.
Digital signal Reception:Problem of feature extraction and pattern
classification
8
Received signal ‘1’ signal + interference ‘0’ interference only (noise and intersymbol
interference (ISI)) .
Interference only signal + interference
0 0.2 0.4 0.6 0.8 1-0.5
0
0.5
1
1.5
2
2.5
Normalized Time
Am
plit
ud
e
0 0.2 0.4 0.6 0.8 1-1
-0.5
0
0.5
1
1.5
Normalized Time
Am
plit
ud
e
Sujan Rajbhandari
Receiver from the Viewpoint of Statistics9
Testing a Null Hypothesis of
a) Received signal is interference only
against
b) Alternative Hypothesis of received signal is signal
plus interference
Sujan Rajbhandari
Problem of Feature Extraction and Pattern Classification
10
Receiver Block diagram
OpticalReceiver
Wavelet Transform
Artificial Neural Network
Threshold Detector
Feature ExtractionFeature
ExtractionPattern
ClassificationPattern
Classification
Sujan Rajbhandari
Time- Frequency analysis
Fourier Transform
Time-frequency mapping
What frequencies are present in a signal but fails to give picture of where those frequencies occur.
No time resolution.
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Time- Frequency analysis
Windowed Fourier Transform (Short time Fourier
transform)
Chop signal into equal sections
Find Fourier transform of each section
Disadvantages
Problem how to cut a signal
Fixed time and frequency resolution
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Time- Frequency analysis
Continuous Wavelet Transform (CWT) Vary the window size to vary resolution
(Scaling). Large window for precise low-frequency information,
and shorter window high-frequency information Based on Mother wavelet. Mother Wavelet are well localised in time.(Sinusoidal
wave which are the based of Fourier transform extend from minus infinity to plus infinity)
Sujan Rajbhandari
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Continues Wavelet Transform
Where are wavelets and s and τ are scale and
translation. Translation time resolution scale frequency resolution Wavelets are generated from scaling and translation
the Mother wavelet.
dtttfs s )(*)(),( ,
)(1
)( ,, s
t
st ss
dsdtstf s )(),()( ,
CWT of Signal f(t) and reconstruction is given by
)(, ts
Discrete Wavelet Transform
• Dyadic scales and positions• DWT coefficient can efficiently be obtained by filtering and down sampling1
1 Mallat, S. (1989), "A theory for multiresolution signal decomposition: the wavelet representation," IEEE Pattern Anal. and Machine Intell., vol. 11, no. 7, pp. 674-69
Artificial Neural Network
Fundamental unit : a neuron
Based on biological neuron
Capability to learn
Sujan Rajbhandari
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).(1
n
kkk wxbfy
b
wn y
x1
f(.)∑
w1
Output
xn
.
.
.
Artificial Neural Network
Input layer , hidden layer(s) and
output layer
Extensively used as a classifier
Supervised and unsupervised
learning.
Weight are adjust by
comparing actual output and
target output
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Input Layer
Hidden Layer 1
Hidden Layer 2
Output
Input Layer
Hidden Layer 1
Hidden Layer 2
Output
Feature Extraction:Discrete Wavelet Transform
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DWT of Interference onlyDWT of Interference only DWT of signal +InterferenceDWT of signal +Interference
0 2 4 6 8 10 12 14 16 18 20-1
0
1
a 3
0 2 4 6 8 10 12 14 16 18 20-1
0
1
d3
0 5 10 15 20 25 30 35 40-1
0
1
d2
0 10 20 30 40 50 60 70 80-1
0
1
d1
0 2 4 6 8 10 12 14 16 18 200
1
2
a 3
0 2 4 6 8 10 12 14 16 18 20-0.5
0
0.5
d3
0 5 10 15 20 25 30 35 40-0.5
0
0.5
d2
0 10 20 30 40 50 60 70 80-0.5
0
0.5
d1
• Significant difference in approximation coefficient ,a3.• No difference in other details coefficients. (Details coefficient are due to the high frequency component of signal , mainly due to noise.)
• Significant difference in approximation coefficient ,a3.• No difference in other details coefficients. (Details coefficient are due to the high frequency component of signal , mainly due to noise.)
Denoising
The high frequency component can be removed or suppressed.
Two Approach Taken
1. Threshold approach in which the detail coefficients are suppressed by either ‘hard’ or ‘soft’ thresholding.
2. Coefficient removal approach in which detail coefficients are completely removed by making it zero.
Sujan Rajbhandari
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De-noised Signal
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LOS LinksLOS Links
0 2 4 6 8 10-0.5
0
0.5
1
1.5
Normalized Time
Am
plit
ud
e
Denoised signal for LOS links
Received signal
Denoised Signal(Threshold approach)
Denoised SignalCoeff. Removal Approach
Non-LOS LinksNon-LOS Links
0 2 4 6 8 10-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Normalized TimeA
mp
litu
de
Denoised signal for non-LOS links
Denoising (Threshold Approach)
Denoised Signal(Coeff. Removal Approach)
Received Signal
•Denoising effectively removes high frequency component.•Equalization is necessary for non-LOS links•Identical performance for both de-noising approaches.
21Artificial Neural Network : Pattern Classifier
Artificial Neural Network can be trained to differentiate the interference from signal plus interference.
DWT are fed to ANN. ANN is first trained to classify by providing
examples. ANN can be utilized both as a pattern
classifier and equalizer.
Results
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The Coefficient removal approach (CRA) of denoising gives the best result. Easier to train ANN using CRA as the DWT coefficients are removed by 8 folds if 3 level of DWT is taken. Effective for detection and equalization.
Figure: The Performance of On-off Keying at 150Mbps for diffused channel with a Drms of 10ns
Comparison with traditional methods
•Maximum performance of 8.6dBcompared to linear equalizer• performance depends on the mother wavelets.• Discrete Meyer gives the best performance and Haar the worst performance among studied mother wavelet
Conclusion
Digital signal detection can be reformulated as feature extraction and pattern classification.
Discrete wavelet transform is used for feature extraction.
Artificial Neural Network is trained for pattern classification.
Performance can further be enhance by denoising the signal before classifying it.
Sujan Rajbhandari
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25
Thank You
Discussions