Angelova, Maia

Ghassemlooy, Zabih

Rajbhandari, Sujan

English

Northumbria Research Link

Signal Detection and Adaptive Equalization Using a Discrete WaveletTransform - Artificial Neural Network for OOK Indoor OpticalWireless LinksAbstract: The paper presents an alternative approachfor signal detection and equalization using the discretewavelet transform (DWT) and the artificial neuralnetwork (ANN) in diffuse indoor optical wireless links.The received noisy signal is sampled at multiple ratesand the DWT is used for feature extraction while thefeedforward backpropagation ANN is used for thepattern classification (i.e. equalization). Differentwindow lengths are investigated and a window of 3-bitis being used for signal classification (i.e. equalization).The simulation results show that for a highly dispersivechannel the proposed receiver/equalizer outperformsthe traditional equalizer by offering SNR gain of morethan 6 dB at the data rate of 155 Mpbs.Keywords: Adaptive equalization, indoor opticalwireless, neural network, discrete wavelettransform.1. IntroductionThe future communication system with multipleapplications requires a huge bandwidth per userthat radio and microwave frequencies currently areunable to provide. The last mile problem isbecoming more acute, therefore the need foralternative link schemes. Dropping fibre to homesis one solution but costly at the present time, whichwill reduce over the next decade or so. There is analternative and complementary solution based onthe optical wireless (OW) link that is capable ofproviding bandwidth in excess of 150 Mbps forboth indoor and outdoor applications, and canreadily be linked to the high-speed fibre backbone[1, 2]. Compared with the RF links, OW offers anumber of advantages including a huge bandwidthat a single wavelength, no need for the frequencyreuse, rapid installation, security, well defined cellpattern, offering different traffic using multiplewavelengths in a single cell, and being protocoltransparent.The key issues in the indoor OW communicationlinks are the eye safety, mobility, blocking andmultipath induced inter-symbol-interference (ISI)in non-line-of-site (non-LOS) links [3, 4]. Eyesafety could be overcome by shifting to a higherwavelength of 1550 nm where the eye retina is lesssensitive to optical radiation [5] or by adoptingmore power efficient modulation techniques likepulse position modulation. Lack of mobility andblocking is an issue in LOS links, thus limiting itsapplication to a specific environment. Whereas indiffuse (non-LOS) links, blocking, and to a certaindegree mobility, is overcome at the cost of reduceddata rate, increased path loss and ISI [4], thusmaking it more appropriate for portable indoorapplications. Reduced data rate and increased ISIis compensated by employing equalizationtechniques at the receiving end as outlined in [3, 6,7].The classical approach of digital signal detection isbased on the matched filter, which maximized thesignal-to-noise (SNR) when the signal is corruptedS. Rajbhandari1 , Prof. Z. Ghassemlooy 1 and Prof. Maia Angelova 21 Optical Communication Research Group2 Intelligent Modelling LabSchool of Computing, Engineering and Information Sciences, Northumbria University, Newcastleupon Tyne, UKby the adaptive white Gaussian noise (AWGN) [8].However, not all physical channels and signals areGaussian in nature [9], and the maximum SNR issusceptible to the exact position of samplinginstants. Additionally, the traditional equalizationbased on the finite impulse response (FIR) filtersuffers from severe performance degradation intime varying and non-linear channels [10, 11]. In[12] signal detection in a non-stationaryenvironment has been formulated as one of patternclassification problem, thus offering the possibilityof applying neural network based classifier at thereceiver to improve the performance.In [18, 19] the concept has be taken further byemploying the continuous wavelet transform(CWT) for the feature extraction and ANN for thepattern classification at the receiver. Wavelet basedequalization has also been adopted to combat theproblem of channel induced distortion, a majordifficulty in diffuse OW systems [13, 14]. TheANN is an adaptive system with learningcapabilities under a supervised environment. Thelearning process can further be enhanced (i.e.faster convergence) by removing the noise fromthe training signal and reducing the number ofinput (if possible). Furthermore feature extractioncould also be improved by removing the redundantcoefficients in the CWT. In this paper we proposesignal detection and channel equalization based onthe DWT and ANN, which offer reducedcomplexity compared to the CWT-ANN basedreceiver and improved performance compared tothe equalizers based on the FIR digital filters.Furthermore in CWT with a large number ofcoefficients, to find the best scales extensive searchis a requirement, whereas in DWT this can readilybe realized using the digital filters [15].The paper is organised as follows: the bit erroranalysis of OOK in diffuse channel is presented inSection 2 and DWT is discussed in Section 3. Theproposed receiver based on the DWT and ANN isoutlined in Section 4, followed by the BERperformance results in Section 5. Finally, theconclusion is given in Section 6.2. Unequalized On-Off KeyingThe simplest and the most common modulationtechnique for intensity modulated and directdetection (IM/DD) is the well known on-off keying(OOK) scheme. It offers bandwidth efficiency andresilience to multipath induced ISI, but at the costof a high optical average power. The effect of ISIis significant for bit rates above 10 Mbps [16]. Ablock diagram of the unequalized OOK systemunder consideration is shown in Fig. 1. Thediscrete-time impulse response of the cascadedsystem is given as:bkTtk trthtpc  )()()( ,(1)where bit duration Tb = Rb-1, and Rb is the bit rate.The impulse response h(t) of the optical channel inthe ceiling bounce model can be approximated to[16]:,)()1.0()1.0(6)( 76tuDtDthrmsrms (2)where u(t) is the unit step function and Drms is thedelay spread which depends on the size and designof the room.Unless the channel is nondispersive, ck contains azero tap, a single precursor tap (with the largestmagnitude) and possibly multiple postcursor taps.On a non-dispersive channel, the optimumsampling point, i.e. that which minimises theprobability of error, occurs at the end of each bitperiod Tb. However, on dispersive channels, theoptimum sampling point changes as the severity ofISI changes. The receiver filter output yicorresponding to the penultimate bit, in theabsence of noise, is given by:mkkavg ciRPiy  a2 , (3)where R is the photodetector responsivity, Pavg isthe average transmitted optical signal power, ai isthe m-bit sequence,  10,ia is the value of thepenultimate bit in ai, m is the number of taps.Thus, the average probability of error is given by:Transmitterfilterp(t)Multipathchannelh(t)2Pavg n(t)OutputBits,Inputbits, aisampleUnit energyfilter r(t)(matched top(t))RTransmitter ReceiverChannelX(t)S(t) Z(t) ZjiaˆFig.1: Block diagram of the unequalized OOK system.miimOOKbiteP2211,,  , (4)where the probability of error for the penultimatebit in ai is given by:0if)5.0(1if)5.0(5.005.00iioptiiiaNyQaNyQ opt ,(5)where opt is the optimum threshold level, set tothe midway value of bavg TRP .Beyond the normalized delay spread of 0.52, theerror rate becomes irreducible, i.e. the target biterror rate (BER) cannot be achieved simply byincreasing the transmitter power. To mitigate theISI, the optimum solution would be to usemaximum likelihood sequence detector (MLSD),but in a practical system the decision feedbackequalizer (DFE), a suboptimal equalizer, has beenadopted [17]. In [18] it has been reported that thepower penalty in diffuse channel can be reduced by5.7 dB when using a zero-forcing DFE (ZF-DFE)at data rate of 100 Mbps, thus making it practicallyfeasible for implementation. Unlike theunequalized OOK, there is no simple relation topredict the power penalty and the error probabilityin equalized systems. However, the trend of powerpenalty can be approximated by [18]:Power penalty (ZF-DFE) = 3(c0-1-1), (6)where co is the zero tap given in (1), normally dueto LOS path. More recently, equalizers based onthe WT-ANN have been studied [19], showing aBER performance outperforming that of the DFE.3. Discrete Wavelet TransformThe topic of wavelets is multi-faceted and highlymathematical, and a subject that is arguablydominated by researchers with a mathematicalbackground. It was developed to resolve the time-frequency resolution problem of Fourier transform(FT) and short-time Fourier transform (STFT)[20]. The FT does not provide a time-frequencyrepresentation of signal while a STFT causesuncertainty in the time-frequency representation[21]. The WT is the ultimate solution inrepresenting the time-varying signal. It has avariable window, enabling it to provide a moreflexible time and frequency resolution than STFT[20, 21]. The CWT produces coefficients forevery scale up to a scale where one chooses tostop. Unfortunately this can lead to asignificant amount of computational effort andrequires a reasonable amount of‘computational horsepower’.The redundant coefficients in CWT can beremoved by selecting the dyadic (power of 2) scaleand translation, thus leading to the DWT. TheDWT process involves using successive,complementary low-pass g[n] and high-pass h[n]filters to split the signal under analysis into itsapproximation and detail coefficients. With thetraditional digital filtering techniques this wouldleave us with two signals both having the samenumber of sample points as the original signal.However, the DWT process down-samples bothsignals by a factor of two [15]. Figure 2 representsthe wavelet decomposition tree with theapproximation and detail coefficients given as:  nl nkgnXky ]2[][  nh nkhnXky ]2[][(7)(8)The high-pass and low-pass filters are related toeach other and satisfy the condition of quadraturemirror filter, i.e. the sum of the magnituderesponse of high-pass filter and low-pass filter isequal to one for all frequencies. The approximationcoefficients can further be decomposed intodifferent DWT coefficient levels with a maximumlevel of log2L, where L is the signal length.Fig. 2: The 2-level DWT decomposition of a signal.In addition to removing the redundant coefficientsin the CWT, DWT provides another dimension offlexibility compared to the CWT and that is thedenoising of signal corrupted by the AWGN.Denoising is performed by hard/soft thresholdingof the detail coefficients [22]. Let ω(X[n])represent the WT of the discrete signal X[n]. Thedenoised reconstruction of the signal is given by:])[((][ 1 nXnX d  , (9)where 1 is the inverse WT, and  is thethresholding operator defined for the hard and softthresholdings as:kkkHT if1if0)( (10)))(sgn()(  kkkST (11)There are a number of algorithms used to select theoptimum threshold level . For the universalthreshold scheme  is defined as: Nlog2 , (12)where  is the variance of the wavelet coefficientin each level. Different threshold estimations aredescribed further by Donoho [22] .4. WT-ANN Based Receiver ModelThe unit energy filter in Fig. 1 is replaced with afeature extraction and pattern classification modulecomposed of the DWT and ANN units, see Fig. 3.The received signal is decimated into discrete W-bit sample lengths, where the sample informationcontent is changed by one bit. Figure 3(b) showsan example for W = 3, which can be thought of as a3-bit sliding window that can slide by one bit at atime. Each window containing a total of 24discrete samples (8 samples/bit and a 3-bit slidingwindow) is applied to the DWT to extract thewavelet coefficients. These coefficients can eitherbe directly applied to the ANN for signalclassification or they can be further processed toreduce the noise content of the signal prior tosignal classification. The ANN is trained with 400known samples prior to classification of theunknown data, and is set to detect the central bit ofa 3-bit window as the binary ‘1’ or ‘0’.As for denoising, here we have adopted thefollowing two schemes:1. Thresholding: A threshold level for eachdecomposition stage is calculated using (12)before applying them to (10) and (11) todetermine the thresholding operator for the softand hard thresholding respectively.2. Discarding coefficients: With multiple samplestaken per bit, discarding the entire detailcoefficients will not result in the loss ofinformation. Therefore, we only use theapproximation coefficients of high-pass filterfor training and classification.5. Results and DiscussionThe proposed receiver shown in Fig. 3 is simulatedusing Matlab. The simulation parameters areshown in Table 1.Figure 4 shows the BER performance against theSNR for the DWT-ANN based receiver at datarates of 155 Mbps and 200 Mpbs for a channelwith Drms of 10 ns and for different values of W.Also shown are the BER performance ofunequalized (155 Mbps only) and the linearlyequalized OOK, the former showing the worstperformance. The results illustrate that equalizationand denoising based on the DWT-ANN show amarked improvement in the BER performancecompared with the linearly equalized andunequalized cases. Increasing W from 3 to 5 bitsdoes not offer any improvement in the BERperformance while decreasing it to 1 bit leads todegradation in the error performance.jbˆjZˆFig. 3: (a) The block diagram of receiver andequalizer based on the feature extraction andpattern classification: with feature extractor(DWT) and pattern classifier (ANN), and (b) 3-bit sliding window.Table 1: Simulation parametersParameters ValueData rate Rb 155 MbpsChannel RMS delay spreadDrms10 nsNo. of samples per bit 8Mother wavelet Discrete MeyerANN type Feedforwardback propagationNo. of neural layers 2No. of neurons in 1st layer 4No. of neurons in 2nd layer 1ANN activation function log-sigmoid, tan-sigmoidANN training algorithm Scaled conjugategradientalgorithmANN training sequence 400 bitsMinimum error 1-30Minimum gradient 1-30DWT levels 3Compared with the traditional equalizer, the newapproach shows a significant improvement inperformance with the SNR gains of ~6 dB and ~5.8dB at BER of 10-5, W of 3 and 5 and Drms of 10ns for data rates of 155 and 200 Mbps,respectively, showing a close match to the earlierresults [23]. However, compared to [23], anidentical performance is achieved by reducing thenumber of neurons (4 neurons is utilised in firstlayer in comparison to 100 neurons in [23]). Thisreduces the system complexity and computationaltime.6. ConclusionA receiver/equalizer based on the DWT-ANN isproposed and the BER performance of theproposed system is simulated in Matlab. Thereceived noisy signal is sampled at multiple ratesand the DWT is used for feature extraction (i.e.denoising) while the feedforward backpropagationANN is used for the pattern classification (i.e.equalization) based on the DWT coefficients.Different sliding windows are studied and awindow size of 3-bit is shown to be adequate forfeature extraction. The simulation results show thatthe proposed DWT-ANN system outperforms thetraditional equalizer offering a SNR gain of morethan 6 dB at a data rate of 155 Mpbs in a dispersivechannel with Drms of 10 ns. The system shows areduced neural complexity compared to alreadyproposed system based on the WT-ANN.Fig. 4: The BER performance against the SNR of a linear equalizer and a DWT-ANNbased receiver (for different window length) at data rate of 155 Mbps and 200 Mbps ina diffuse link with Drms of 10 ns.References[1] D. A. Rockwell and G. S. Mecherle,"Optical wireless: low-cost, broadband,optical access," SONA CommunicationsCorporation, 2007.[2] A. G. Al-Ghamdi and J. M. H. Elmirghani,"Multiple spot diffusing geometries forindoor optical wireless communicationsystems," International Journal ofCommunication Systems, Vol. 16, No. 10,pp. 909-922, 2006.[3] J. M. Kahn and J. R. Barry, "Wirelessinfrared communications," Proceedings ofIEEE, Vol. 85, No. 2, pp. 265-298, 1997.[4] N. Hayasaka and T. Ito, "Channelmodeling of nondirected wireless infraredindoor diffuse link," Electronics andCommunications in Japan, Vol. 90, No.6,pp. 9-19, 2007.[5] D. A. Rockwell and G. S. 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50-Mb/s diffuse infrared free-space link using onoff keying with decision-feedback equalization,&quot;

A new adaptive functional-link neural-network-based DFE for overcoming co-channel interference,&quot;

A polynomial-perceptron based decision feedback equalizer with a robust learning algorithm,&quot;

BER performance of 166 Mbit/s OOK diffuse indoor IR link employing wavelets and neural networks,&quot;

Channel modeling of nondirected wireless infrared indoor diffuse link,&quot;

Coding and equalization for PPM on wireless infrared channels,&quot;

De-noising by softthresholding,&quot;

Experimental characterization of non-directed indoor infrared channels,&quot;

Introduction to Wavelets and Wavelet transforms: A primer.

Modeling of nondirected wireless Infrared channels,&quot;

Multiple spot diffusing geometries for indoor optical wireless communication systems,&quot;

Neural networks expand SP's horizons,&quot;

Optical wireless: low-cost, broadband, optical access,&quot;

Performance evaluation of experimental 50-Mb/s diffuse infrared wireless link using on-off keying with decisionfeedback equalization,&quot;

Recovery of ISI channels using multiresolution wavelet equalization,&quot;

Signal detection in a nonstationary environment reformulated as an adaptive pattern classification problem.&quot;

Ten Lectures on Wavelets SIAM: Society for Industrial and Applied Mathematics,

Wavelength selection for optical wireless communications systems,&quot;

Wavelet based adaptive equalization algorithm,&quot;

Wavelet-AI equalization and detection for indoor diffuse infrared wireless systems,&quot;

Wireless infrared communications,&quot;

Signal detection and adaptive equalization using a discrete wavelet transform : artificial neural network for OOK indoor optical wireless links

Signal detection and adaptive equalization using a discrete wavelet transform : artificial neural network for OOK indoor optical wireless links

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