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 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)

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

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.

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. 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

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.

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.

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

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

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

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

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

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

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 5 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

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.

Thank you! Questions?