Z. Ghassemlooy, S. Rajbhandari and M. Angelova

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. AngelovaSchool of Computing, Engineering & Information Sciences,

University of Northumbria, Newcastle upon Tyne, UKhttp://soe.unn.ac.uk/ocr/

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-PIM2 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.

2 3 4 5 6 7 80

2

4

6

8

10

12

14

16

18

20

Bit resolution, M

Nor

mal

ized

ban

dwid

th re

quire

men

t

PPM

DH-PIM 1

DPIM

DH-PIM 2

OOK

2 3 4 5 6 7 8-16

-14

-12

-10

-8

-6

-4

-2

0

Bit Resolution, M

Nor

mal

ized

Pow

er R

equi

rem

ent (

dB)

DH-PIM2

PPM

DH-PIM1

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

1Figure : Optical power spectra of common ambient infrared sources. Spectra have been scaled to have the same maximum value.

1J. M. Kahn and J. R. Barry, Proceedings of IEEE, vol. 85, pp. 265-298, 1997.2A. J. C. Moreira, R. T. Valadas, and A. M. d. O. Duarte, IEE Proceedings -Optoelectronics, vol. 143, pp. 339-346, 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 by1 :

9

)(1.06

)( 7

6

1.0tu

t

Dth

rms

rms

D

LOS

DiffuseDiffuse 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. 1260-1268, 1997. 0 2 4 6 8 10-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Normalized Time

Am

plitu

de

Received signal for non-LOS Links

Unequalized Performance

The discrete-time impulse response of the cascaded system is

In non-LOS links, ck 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 Ts for LOS link.

On dispersive channels, the optimum sampling point changes as the severity of ISI changes.

bkTttrthtpkc )()()(

Transmitter filterp(t)

Multipathchannel

h(t)

LavgPavg n(t)

OutputBits,

Inputbits, ai

sample

Unit energy filter r(t)

(matched to p(t))

R

Transmitter ReceiverChannel

X(t) S(t) Z(t) yiiaDPIM

encoder

y(t)

Unequalized Performance For the LOS channel, the slot error probability Pse of DPIM is given by:

where R is the photodetector responsivity, η is the noise spectral density, Pavg is

the average transmitted optical signal power, Rb is the bit rate, M is bit resolution and L = 2M.

In a multipath channel, the Pse is calculated by summing the error probabilities in all possible sequences.

where bi is the m-slot DPIM(NGB) sequence and

0 if5.0)05.0(

1 if5.0)05.0(

iaN

iyoptQ

iaN

optiyQ

i

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

.

bRavgRP

LMQseP2

1

ii ibPDPIMseP all

)(,

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

10-2

10-1

100

0

1

2

3

4

5

RMS delay spread / slot duration

Ave

rage

opt

ical

pow

er p

enalt

y (d

B)

L = 4 L = 8 L = 16L = 32

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. 1358-1362, 1997.2- J. C. Patra and N. R. N. Pal, Signal Processing, vol. 43, pp. 81 - 195, 1995.3- L. Hanzo, C. H. Wong, and M. S. Yee, Adaptive wireless transceivers: Wiley-IEEE Press, 2002, pp. 299-383.

Equalization: A Classification Problem

Classification capability of FIR filter equalizer is limited to a linear decision boundary, which is a non-optimum classification strategy1.

FIR base equalizers suffer from severe performance degradation in time varying and non-linear channel2.

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 ANN3 .

Wavelet based equalization4. 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. 20004- D. Cariolaro et al, IEEE Intern. Conf. on Communications, New York, NY, USA, pp. 74-78, 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 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

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.

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Discrete Wavelet Transform

x[n]

h[n]

g[n]

h[n]

g[n]

Level 1 DWT coefficients

Level 2 DWT coefficients

. . .

Signal

FilteringDown-

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.

n

l nkgnXky ]2[][: cD n

h nkhnXky ]2[][:cA

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 .

k

kk HT if1

if0)(

))(sgn()( kkk ST

])[((][ 1 nXnX d 1

Nlog2

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.

DWT ANN

Threshold detector

Z(t)

Tb/n

Zj jbFeature extractor & pattern classifier

jZ

Bit to decode

3 bit window The denoised coefficient are fed to ANN. ANN is trained to classify signal into two binary classed based on the DWT

coefficients.

Simulation Parameters21

Parameters ValueData rate Rb 200 MbpsChannel RMS delay spread Drms 1-10 ns

No. of samples per bit 16Mother 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 100 symbolsMinimum error 1-30

Minimum gradient 1-30

DWT levels 3

Simulation Flowchart22

Results Unequalized DPIM- worst error

performance. The unequalized error performance is not

practically acceptable for highly diffuse channel like channels with Drms > 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 10-5 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.

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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 Drms 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 10-5 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.

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Questions/Suggestions/Comments

Thank you!