Applications of Wavelet Transform and Artificial Neural Network in ...

cracklegulleyAI and Robotics

Oct 19, 2013 (3 years and 7 months ago)

76 views


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 Angelova

Prof. 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

1

1

0

0

0

1

1

0

1


Links

Sujan Rajbhandari

4

Non
-
LOS









Multipath Propagation


Intersymbol interference (
ISI
)


Difficult to achieve high data
rate if ISI is not mitigated.

Rx

Tx



LOS

LOS








No multipath propagation


Noise and device speed
are limiting factors


Possibility of blocking

Tx

Rx

Received Signal

Sujan Rajbhandari

5

Non
-
LOS

LOS

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

6

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








Sujan Rajbhandari

Receiver
from

the

Viewpoint of Statistics

9


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

Optical

Receiver

Wavelet

Transform

Artificial

Neural Network

Threshold

Detector

Feature

Extraction

Pattern

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
.

Sujan Rajbhandari

11


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




Sujan Rajbhandari

12

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

13

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.

CWT of Signal
f
(
t
) and reconstruction is given by

Discrete Wavelet Transform



Dyadic

scales and positions



DWT coefficient can efficiently be obtained by
filtering

and
down sampling
1

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

16

b

w
n

y

x
1


f
(
.
)



w
1

Output

x
n


.


.


.



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

Sujan Rajbhandari

17

Feature Extraction:

Discrete Wavelet Transform

Sujan Rajbhandari

18

DWT of Interference only

DWT of signal +Interference




Significant difference in approximation coefficient ,a
3
.



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

19

De
-
noised Signal

Sujan Rajbhandari

20

LOS Links

Non
-
LOS Links


Denoising effectively removes high frequency component.


Equalization is necessary for non
-
LOS links


Identical performance for both de
-
noising approaches.

21

Artificial 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

Sujan Rajbhandari

22



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
D
rms

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

24

25

Thank You


Discussions