ICEE08, Tehran, Iran Signal Detection and Adaptive Equalization Using Discrete Wavelet Transform -...

ICEE08, Tehran, Iran

Signal Detection and Adaptive Equalization Using Discrete Wavelet Transform - Artificial

Neural Network for OOK Indoor Optical Wireless Links

Z. Ghassemlooy, S Rajbhandari and M AngelovaSchool of Computing, Engineering & Information Sciences, University of

Northumbria, Newcastle upon Tyne, UK

http://soe.unn.ac.uk/ocr/


Outline

Optical Wireless – Key issues Digital Signal Detection Equalization Wavelet ANN Based Receiver Results and Conclusion


Indoor Optical Wireless Links

The key issues:

- Eye safety- shift from 900 nm to 1550 nm - eye retina is less

sensitive to optical radiation- power efficient modulation techniques

- Mobility and blocking- diffuse configuration instead of line of sight, but at

cost of: - reduced data rate- increased path loss- multipath induced inter-symbol-interference (ISI)


Digital Signal Detection - The Classical Approach

The discrete-time impulse response of the cascaded system

optical channel (ceiling bounce)

Transmitter filterp(t)

Multipathchannel

h(t)

2Pavg n(t)

OutputBits,

Inputbits, ai

sample

Unit energy filter r(t)

(matched to p(t))

R

Transmitter Receiver Channel X(t)

S(t) Z(t) Zj

ia

bkTttrthtp

kc )()()(

)(7)1.0(

6)1.0(6)( tu

rmsDt

rmsD

th



OOK - the average probability of error:

the probability of error for the penultimate bit in ai:

m

iimOOKbite

P2

12

1,,

0 if5.0)

05.0(

1 if5.0)

05.0(

ia

N

iy

optQ

ia

N

optiy

Q

i

where opt is the

optimum threshold level, set to the midway value of RPave (Tb)0.5

.



Matched filter is difficult to realized when channel is time varying.

Maximising the SNR based on the assumption that noise statistics is known.

SNR is sensitive to the sampling instants. - In non-dispersive channel, the optimum sampling point is at the end of each

bit period. - In dispersive channel, the optimum sampling point changes as the severity

of ISI changes.



For higher values of normalized delay spread (> 0.52)- bit error rate cannot be improved simply by increasing the

transmitter power

To mitigate the ISI, optimum solutions are: - Maximum likelihood sequence detector- Equalizers1-3 - A practical solution

(i) Inverse filter problem- The frequency response of the equalizing filter is the

inverse of the channel response.- Adaptive equalization is preferred if the channel

conditions are not known in advance.- Two classes : linear and decision feedback equalizer.

(ii) Classification problem1- J. M. Kahn and J. R. Barry, Proceedings of IEEE, 85 (2), pp. 265-298, 1997 2- G. W. Marsh and J. M. Kahn, IEEE Photonics Technology letters, 6(10), pp. 1268 - 1270, 19943- D. C. Lee and J. M. Kahn, IEEE Transaction on Communication, 47(2), pp. 255-260, 1999


Equalization - A Classification Problem

Dispersion induced by channel is nonlinear in nature

Received signal at each sampling instant may be considered as a nonlinear function of the past values of the transmitted symbols

Channel is non-stationary - overall channel response becomes a nonlinear

dynamic mapping


Equalization: A Classification Problem

Classification capability of FIR filter equalizer is limited to a linear decision boundary (a non-optimum classification1)

FIR bases equalizers suffer from severe performance degradation in time varying and non-linear channels2

The optimum strategy - to have a nonlinear decision boundary for classification- ANN

- with capability to form complex nonlinear decision regions

- In fact both the linear and DFE are a class of ANN3 .

- Wavelet4

1- L.Hanzo, et al, Adaptive wireless transceivers: Wiley-IEEE Press, 2002, pp. 299-383.

2- C. Ching-Haur, et al , Signal Processing,vol. 47, no. 2, pp. 145 - 158 1995.

3- S. Haykin, Communications Magazine, IEEE , vol.38, no.12, pp. 106-114, Dec. 2000

4- D. Cariolaro et al, IEEE Intern. Conf. on Communications, New York, NY, USA, pp. 74-78, 2000.


Wavelet Transform

Neural Network

Receiver - Classification Based

Optical Receiver

Feature Extraction

Pattern Classification

Post-Processing

Optical Signal

Modular based receiver: Feature extraction (wavelet transform) - for efficient classification Pattern classification (ANN).

WT-ANN based receiver outperforms the traditional equalizers1.

1- R. J. Dickenson and Z. Ghassemlooy, International Journal of Communications Systems, Vol. 18, No. 3, pp. 247-266, 2005.


Fourier Transform

Wavelet Transform

Feature Extraction Tools

Time-Frequencies Mapping

Short-time Fourier Transform

No time-frequency

localization

Fixed time-frequency resolution:

Uncertainty problem

No resolution problem: ultimate

transform


CWT vs. DWT

CWT- Infinite scale

- but with redundant coefficients

DWT- no redundancy as in CWT

- easier to implement using filter banks (high pass and low pass)

- reduced computational time

- possibility signal denoising by thresholding the wavelet coefficient


Discrete Wavelet Transform

x[n]

h[n]

g[n]

h[n]

g[n]

Level 1 DWT

coefficientsLevel 2

DWT coefficients

. . .

Signal

FilteringDown-

sampling

DWT coefficient - obtained by successive filtering and down sampling

Signal is decomposed: - using high pass h[n] and a low pass g[n] filters

• filters are related to each other and are known as the quadrature mirror filter.

- down sampling by 2

n

l nkgnXky ]2[][: cD n

h nkhnXky ]2[][:cA

cD1

cA1

cD2

cA2


WT- ANN Based Receiver Model

8-sample per bit Signal is decimated into W-bit discrete

sliding window. (i.e. each window contains a total of 8W-bit discrete samples )

Information content of the window is changed by one bit

3-level DWT for each window is determined

DWT coefficients are denoised by: i) Thresholding : A threshold is set and

‘soft’ or ‘hard’ thresholding are used for detail coefficients

ii) Discarding coefficients: detail coefficients are completely discarded

DWT ANN

Threshold detector

Z(t)

Tb/n

Zj jbFeature extractor & pattern classifier

jZ

Bit to decode

3 bit window Denoised coefficient are applied to ANN ANN is trained to classify signal into two binary classed based on DWT

coefficients


Denoising Signal using DWT

Hard thresholding

Soft thresholding

The threshold level for universal threshold scheme:: variance of the wavelet coefficient

Denoised signal

where -1 is the inverse WT

k

kk

HT if1

if0)(

))(sgn()( kkkST

])[((][ 1 nXnX d

Nlog2


Simulation Parameters16

Parameters ValueData rate Rb 155 MbpsChannel RMS delay spread Drms 10 ns

No. of samples per bit 8Mother wavelet Discrete MeyerANN type Feedforward back propagationNo. of neural layers 2No. of neurons in 1st layer 4No. of neurons in 2nd layer 1ANN activation function log-sigmoid, tan-sigmoid ANN training algorithm Scaled conjugate gradient algorithm

ANN training sequence 400 bitsMinimum error 1-30

Minimum gradient 1-30

DWT levels 3


Results – BER for OOK @ 150 Mb/s

Maximum performance of ~6 dB compared to linear equalizer.

Performance depends on the mother wavelets.

Discrete Meyer gives the best performance and Haar the worst performance among studied mother wavelet.

Figure: The Performance of OOK at 150Mbps for diffused channel with Drms of 10ns


Results - BER for OOK @ 150 & 200 Mb/s

The DWT-ANN based receiver showed a significant improvement compared to linear equalizer

SNR gain of ~6 dB at BER of 10-5 for W = 3

3-bit window is the optimum Reduced complexity

compared to CWT based receiver without any degradation in performance

0 5 10 15 20 2510

-5

10-4

10-3

10-2

10-1

100

SNR (dB)

BE

R

ANN(155Mbps, W=3)

Unequalized 155MbpsLinear Equalizer(200M

bps)

AN

N(155M

bps, W=1)

Linear Equalizer(155Mbps)

AN

N(200M

bps, W=3)

ANN(155Mbps, W=5)

Figure: The BER performance of OOK linear and DWT-ANN base receiver at 155 and 200 Mbps for diffused

channel with Drms of 10ns

Conclusions

The traditional tool for signal detection and equalization is inadequate in time-varying non-linear channel.

Digital signal detection can be reformulated as feature extraction and pattern classification.

Both discrete and continuous wavelet transform is used for feature extraction.

Artificial Neural Network is trained for classify received signal into binary classes.

3-bit window size is adequate for feature extraction. Enhance performance compared to the traditional FIR equalizer

( a gain of ~ 6dB at BER of 10-5. Reduced complexity using DWT compared to CWT based

receiver with identical perfromance.


Questions?Questions?

Thank you!Thank you!

ICEE08, Tehran, Iran Signal Detection and Adaptive Equalization Using Discrete Wavelet Transform -...

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