Performance of Discrete Wavelet Transform – Artificial Neural Network Based Signal Detector/Equalizer for Digital Pulse Interval Modulation in Practical Indoor Optical Wireless Links Z. Ghassemlooy, S. Rajbhandari and M. Angelova School of Computing, Engineering & Information Sciences, University of Northumbria, Newcastle upon Tyne, UK

Outline  Optical wireless – introduction  Modulation Techniques- Overview  Mutipath induces ISI  Unequalized power penalty  Wavelet-ANN receiver  Final comments

What Optical Wireless Offers ?  Abundance bandwidth  Free from electromagnetic interference  High data rate  No multipath fading  High Directivity.  Secure data transmission  Spatial confinement.  Low cost of deployment  License free operation  Quick to deploy  Compatible with optical fibre  Simple transceiver design.  Small size, low cost component and low power consumptions. 3

Modulation Techniques  On-off keying (OOK): the most basic, simple to implement but requires a high average optical power.  Pulse position modulation (PPM): The most power efficient but require high bandwidth, susceptible to the multipath induced intersymbol interference (ISI).  Differential PPM (DPPM) and digital pulse interval modulation (DPIM): Variable symbol length, built-in symbol synchronization; improved throughputs and efficient utilization of the available bandwidth compared to PPM.  Dual header pulse interval modulation (DH-PIM): Variable symbol length, built-in symbol synchronization; the most efficient utilization of channel capacity compared to OOK, PPM and DPIM. 4

Baseband Modulation Techniques

Normalized Power and Bandwidth Requirement  PPM the most power efficient while requires the largest bandwidth.  DH-PIM 2 is the most bandwidth efficient.  DH-PIM and DPIM shows almost identical bandwidth requirement and power requirement.  There is always a trade-off between power and bandwidth Bit resolution, M Normalized bandwidth requirement PPM DH-PIM 1 DPIM DH-PIM 2 OOK Bit Resolution, M Normalized Power Requirement (dB) DH-PIM 2 PPM DH-PIM 1 DPIM

Indoor Optical Wireless Links  The key issues are: -The eye safety -shift to a higher wavelength of 1550 nm where the eye retina is less sensitive to optical radiation -power efficient modulation techniques. -Mobility and blocking -Use diffuse configuration instead of line of sight, but at cost of -reduced data rate -increased path loss -multipath induced inter-symbol-interference (ISI) -High noise at receiver due to artificial light.

Effect of Artificial Light  Dominant noise source at low data rate.  Interference produce by fluorescent lamp driven by electronic ballasts can cause serious performance degradation at low data rate.  The effect of artificial light is minimised at the receiver using combination of the optical band pass filter and electrical low pass filter.  At the high data rate, the ISI is the limiting factor in the performance of the system instead of artificial light. 2 1 Figure : Optical power spectra of common ambient infrared sources. Spectra have been scaled to have the same maximum value. 1 J. M. Kahn and J. R. Barry, Proceedings of IEEE, vol. 85, pp , A. J. C. Moreira, R. T. Valadas, and A. M. d. O. Duarte, IEE Proceedings -Optoelectronics, vol. 143, pp , 1996.

Intersymbol Interference (ISI)  Limiting factor in achieving high data rate in diffuse links.  ISI is due to broadening of pulse.  Diffuse links are characterised by RMS delay spread.  The impulse response in Ceiling bounce model is given by 1 : 9 LOS Diffuse Diffuse shadowed LOS shadowed where u(t) is the unit step function 1- J. B. Carruthers and J. M. Kahn, IEEE Transaction on Communication, vol. 45, pp , Normalized Time Amplitude Received signal for non-LOS Links

Unequalized Performance  The discrete-time impulse response of the cascaded system is  In non-LOS links, c k contains a zero tap, a single precursor tap (with the largest magnitude) and possibly multiple postcursor taps.  The optimum sampling point is at the end of each slot period T s for LOS link.  On dispersive channels, the optimum sampling point changes as the severity of ISI changes.

Unequalized Performance  For the LOS channel, the slot error probability P se of DPIM is given by: where R is the photodetector responsivity, η is the noise spectral density, P avg is the average transmitted optical signal power, R b is the bit rate, M is bit resolution and L = 2 M.  In a multipath channel, the P se is calculated by summing the error probabilities in all possible sequences. where b i is the m-slot DPIM(NGB) sequence and where  opt is the optimum threshold level, set to the midway value of RP ave (T b ) 0.5.

Unequalized Power Penalty  There is exponential growth in power penalty with increasing delay spread for all orders of DPIM.  The average optical power required to achieve a desirable error performance is impractical for normalized delay spread grater than 0.1.  To mitigate the ISI the solution is to incorporate an equalizer at the receiver. 12

Equalization  Maximum likelihood sequence detector : Though the optimum solution, not suitable for variable symbol length modulation schemes like DPIM since symbol boundaries are not known.  Hence sub-optimum solutions based on finite impulse response filters would be the preferred option.  But equalization based on the finite impulse response (FIR) filter suffers from severe performance degradation in time varying and non-linear channels. 1  The equalization problem can be formulated as classification problem and hence artificial neural network can be used to reduce the effect of ISI. 2,3 1- A. Hussain, J. J. Soraghan, and T. S. Durrani, IEEE Transactions on Communications, vol. 45, pp , J. C. Patra and N. R. N. Pal, Signal Processing, vol. 43, pp , L. Hanzo, C. H. Wong, and M. S. Yee, Adaptive wireless transceivers: Wiley-IEEE Press, 2002, pp

Equalization: A Classification Problem  Classification capability of FIR filter equalizer is limited to a linear decision boundary, which is a non-optimum classification strategy 1.  FIR base equalizers suffer from severe performance degradation in time varying and non-linear channel 2.  The optimum strategy would be to have a nonlinear decision boundary for classification.  ANN is employed for equalization because of its capability to form complex nonlinear decision regions. - In fact both the linear and DFE are a class of ANN 3.  Wavelet based equalization L.Hanzo, et al, Adaptive wireless transceivers: Wiley-IEEE Press, 2002, pp C. Ching-Haur, et al, Signal Processing,vol. 47, no. 2, pp S. Haykin, Communications Magazine, IEEE, vol.38, no.12, pp , Dec D. Cariolaro et al, IEEE Intern. Conf. on Communications, New York, NY, USA, pp , 2000.

Wavelet Transform Neural Network Block Diagram of Receiver Based on Classification Optical Receiver Feature Extraction Pattern Classification Post- Processing Optical Signal  For efficient classification, feature extraction tools are incorporated in the receiver.  The receiver is made modular by having separate block for : (a) Feature extraction (wavelet transform) and (b) pattern classification (ANN).  WT-ANN based receiver outperforms the traditional equalizers R. J. Dickenson and Z. Ghassemlooy, International Journal of Communications Systems, Vol. 18, No. 3, pp , 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  Infinite scale in CWT, having highly redundant coefficients.  Redundancy in CWT can be removed by utilizing the DWT.  The DWT is easier to implement using filter bank of high pass and low pass filters.  Reduced computational time compared CWT.  Possibility of denoising of signal by thresholding the wavelet coefficient in DWT. 17

Discrete Wavelet Transform x[n] h[n] 2 g[n] 2 cD 1 cA 1 h[n] 2 g[n] 2 cD 2 cA 2 Level 1 DWT coefficients Level 2 DWT coefficients... Signal Filtering Down- sampling  DWT coefficient can efficiently be obtained by successive filtering and down sampling.  Signal is decomposed using high pass h[n] and a low pass g[n] filters and down sampled by 2.  The two filter are related to each other and are known as a quadrature mirror filter.

Denoising Signal using DWT  Denoising is performed by hard/soft thresholding of the detail coefficients. - Hard thresholding - Soft thresholding - The threshold level  for universal threshold scheme : : the variance of the wavelet coefficient.  Denoised signal where is the inverse WT.

WT-ANN Based Receiver Model  The receiver incorporates a feature extractor (DWT) and a pattern classifier (ANN).  16-samples per bit.  Signal is decimated into W-bits discrete sliding window. (i.e. each window contains a total of 16W discrete samples ).  Information content of the window is changed by one bit.  3-level DWT of each window is calculated.  DWT coefficients are denoised by: a) Thresholding : A threshold is set and ‘soft’ or ‘hard’ thresholding are used for detail coefficients. b) Discarding coefficients: detail coefficients are completely discarded.  The denoised coefficient are fed to ANN.  ANN is trained to classify signal into two binary classed based on the DWT coefficients.

Simulation Parameters 21 ParametersValue Data rate R b 200 Mbps Channel RMS delay spread D rms 1-10 ns No. of samples per bit16 Mother waveletDiscrete Meyer ANN typeFeedforward back propagation No. of neural layers2 No. of neurons in 1 st layer4 No. of neurons in 2 nd layer1 ANN activation functionlog-sigmoid, tan-sigmoid ANN training algorithmScaled conjugate gradient algorithm ANN training sequence100 symbols Minimum error1 -30 Minimum gradient1 -30 DWT levels3

Simulation Flowchart 22

Results  Unequalized DPIM- worst error performance.  The unequalized error performance is not practically acceptable for highly diffuse channel like channels with D rms > 5ns.  Both linear and DWT-ANN equalizers show improve error performance compared to unequalized cases.  The DWT-ANN based receiver showed a significant improvement in SER performance compared to linear equalizer.  The SNR gain with DWT-ANN at the SER of is ~ 8.6 dB compared to linear equalizer.  Performance of DWT-ANN also depends on selection of mother wavelet, with discrete Meyer wavelet showing the best performance.  Further improvement in SER performance can be achieved by using error control coding. 23 Figure : The SER performance against the SNR for unequalized, Linearly equalized and a DWT-ANN based receiver at data rate of 200 Mbps for diffuse links with D rms of 1, 5 and 10 ns.

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.  ANN is trained for classify received signal into binary classes.  DWT-ANN equalizers performance offers an SNR gain of almost 8 dB at SER of at data rate of 200 Mbps for all values of channel delay spread.  The rapid increase in the processing time of electronic devices can make the system practically feasible.  Practical implementation of the proposed system in the process of being carried out at the photonics Lab, Northumbria University.

Acknowledgement  Northumbria University for supporting the research.  OCRG and IML lab for providing require software for simulation. 25

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