1. Z. Ghassemlooy, S Rajbhandari and M Angelova
Signal Detection and Adaptive Equalization Using Discrete Wavelet Transform - Artificial Neural Network for OOK Indoor Optical Wireless Links
Z. Ghassemlooy, S Rajbhandari and M Angelova
School of Computing, Engineering & Information Sciences, University of Northumbria, 
Newcastle upon Tyne, UK

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

3. 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)

4. Digital Signal Detection - The Classical Approach
The discrete-time impulse response of the cascaded system
optical channel (ceiling bounce)

5. Digital Signal Detection - The Classical Approach
OOK - the average probability of error:
the probability of error for the penultimate bit in ai: .
where opt is the optimum threshold level, set to the midway value of RPave (Tb)0.5

6. Digital Signal Detection - The Classical Approach
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.

7. Digital Signal Detection - The Classical Approach
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 problem
1- J. M. Kahn and J. R. Barry, Proceedings of IEEE, 85 (2), pp , 1997
2- G. W. Marsh and J. M. Kahn, IEEE Photonics Technology letters, 6(10), pp , 1994
3- D. C. Lee and J. M. Kahn, IEEE Transaction on Communication, 47(2), pp , 1999

8. 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

9. 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
2- C. Ching-Haur, et al , Signal Processing,vol. 47, no. 2, pp
3- S. Haykin, Communications Magazine, IEEE , vol.38, no.12, pp , Dec. 2000
4- D. Cariolaro et al, IEEE Intern. Conf. on Communications, New York, NY, USA, pp , 2000.

10. Receiver - Classification Based
Optical
Signal
Optical Receiver
Feature Extraction
Pattern Classification
Post-Processing
Wavelet Transform
Neural Network
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 , 2005.

11. Feature Extraction Tools
Time-Frequencies Mapping
Fourier Transform
Short-time Fourier Transform
Wavelet Transform
No time-frequency localization
Fixed time-frequency resolution: Uncertainty problem
No resolution problem: ultimate transform

12. CWT vs. DWT CWT DWT - Infinite scale - but with redundant coefficients
- 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

13. Discrete Wavelet Transform
Level 1
DWT
coefficients
Level 2
DWT
coefficients
Down-
sampling
Filtering
cD1
h[n] 2
cD2
Signal
h[n] 2
x[n]
cA1
. . .
g[n] 2
cA2
g[n] 2
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

14. 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
Denoised coefficient are applied to ANN
ANN is trained to classify signal into two binary classed based on DWT coefficients

15. 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

16. Simulation Parameters
Value
Data rate Rb
155 Mbps
Channel RMS delay spread Drms
10 ns
No. of samples per bit 8
Mother wavelet
Discrete Meyer
ANN type
Feedforward back propagation
No. of neural layers 2
No. of neurons in 1st layer 4
No. of neurons in 2nd layer 1
ANN activation function
log-sigmoid, tan-sigmoid
ANN training algorithm
Scaled conjugate gradient algorithm
ANN training sequence
400 bits
Minimum error
1-30
Minimum gradient
DWT levels 3

17. 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

18. Results - BER for OOK @ 150 & 200 Mb/s5 10 15 20 25 -5 -4 -3 -2 -1
SNR (dB)
BER
ANN(155Mbps, W=3)
Unequalized 155Mbps
Linear Equalizer(200Mbps)
ANN(155Mbps, W=1)
Linear Equalizer(155Mbps)
ANN(200Mbps, W=3)
ANN(155Mbps, W=5)
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
Figure: The BER performance of OOK linear and DWT-ANN base receiver at 155 and 200 Mbps for diffused channel with Drms of 10ns

19. 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.

20. Thank you!
Questions?