Z. Ghassemlooy , S Rajbhandari and M Angelova

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

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 optis 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 :linearand decision feedback equalizer. (ii) Classification problem 1- 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, 1994 3- D. C. Lee and J. M. Kahn, IEEE Transaction on Communication, 47(2), pp. 255-260, 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. 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.

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. 247-266, 2005.

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

12. 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

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

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

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. 0 10 Unequalized 155Mbps -1 10 ANN(155Mbps, W=3) Linear Equalizer(200Mbps) ANN(155Mbps, W=5) -2 10 BER -3 10 Linear Equalizer(155Mbps) ANN(155Mbps, W=1) ANN(200Mbps, W=3) -4 10 -5 10 0 5 10 15 20 25 SNR (dB) 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 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?