IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, …

1 IEEE TRANSACTIONS ON POWER delivery , VOL. 20, NO. 3, JULY 20051879 Home network POWER - line communication SignalProcessing based on Wavelet Packet AnalysisHaibo He, Student Member, IEEE, Shijie Cheng, Senior Member, IEEE, Youbing Zhang, and J. NguimbisAbstract Recent advances in signal processing methodologieshave spawned the way for a high-speed home network POWER -linecommunication (PLC) system. In this paper, a novel signal pro-cessing method based on wavelet packet analysis is proposed tocombat the adverse communication environment over POWER comparison research between wavelet transform and waveletpacket transform is presented. Since wavelet packet decomposi-tion can provide more precise frequency resolution than waveletdecomposition, this paper proposes to use the wavelet packet anal-ysis to deal with the highly polluted PLC communication hardware structure for the PLC system is presented as an ex-perimental platform for sampling an actual communication results based on these kinds of actual communicationsignals show the effectiveness of the proposed Terms Noise, POWER - line communication , signal pro-cessing, wavelet packet transform, wavelet INTRODUCTIONTHIS PAPER aims to develop a novel home networkpower- line communication (PLC) signal processingmethod based on wavelet packet analysis .

2 The PLC system isbecoming a hot research topic and has attracted more attentionrecently; however, it is still challenging for high-quality signaltransmission over such systems. The major drawbacks for thePLC signal transmission include noise influence [1] [3], signalattenuation [3], [4], and multipath and reflection [5] [7].How to overcome the above mentioned deficiencies by ad-vanced signal processing methods is one of the most importantresearch aspects in the PLC system. Reference [8] proposed aneffective solution for the PLC system based on the advancedsignal processing techniques. In this system, the multicar-rier code-division multiple-access (MC-CDMA) systems areemployed for data transmission, and multiuser detection andturbo decoding are used for data detection.

3 It is reported thatthe proposed system achieves nice performance to combat thedeficiencies of time-varying channel attenuation, multipath fre-quency-selective fading, and impulse noise. Recent advancesin wavelet analysis have spawned the way for PLC signalprocessing. Paper [5] proposed to use the complex wavelettransform to deal with the signal reflection problem in PLCM anuscript received November 26, 2003; revised April 13, 2004. Paper He is with the Department of Electrical Engineering, School of ElectricalEngineering and Computer Science, Ohio University, Athens, OH 45701 USA(e-mail: Cheng, Y. Zhang, and J. Nguimbis are with the Department of ElectricalEngineering, Huazhong University of Science and Technology (HUST), Wuhan430074, China (e-mail: Object Identifier It is presented that by the use of phase informa-tion obtained by complex wavelet transform, one can pick upthe useful information from the received signal .))

4 In reference[9], a novel scheme for PLC signal processing is scheme combined the using of wavelet transform andthe Wigner Ville distribution (WVD) to analyze the noisyPLC signal . This method is a powerful investigation tool fortime-frequency localization and signal readability. It can beused to detect the desired communication paper proposed an effective method for using the waveletpacket transform to analyze the PLC signal . Since the wavelettransform only decomposes the approximations at each reso-lution level to yield the approximation and detail informationat a higher level, it has the limitations in application to thehighly polluted PLC signal . However, in wavelet packet trans-form, both the approximation and details at a certain resolutionlevel are further decomposed into the next level, which meansthe wavelet packet transform can provide a more precise fre-quency resolution than the wavelet transform.

5 Simulation re-sults and comparison research based on the actual POWER -linecommunication signals show the effectiveness of the rest of this paper is organized as follows: Section II pro-vides the brief background for wavelet transform analysis . Sec-tion III presents the multiresolution analysis used in this paper;theoretical comparison of the wavelet transform and waveletpacket transform are discussed in this part. In Section IV, theexperimental platform for the PLC system is given. This willprovide the actual communication data for the later analysisin Section V. In Section V, simulation results of the proposedmethod are given based on the sampled data from the experi-mental system in Section IV. Comparison of the results with thewavelet transform is discussed to show the effectiveness of theproposed method.

6 Finally, the conclusion is given in Section WAVELETTRANSFORMU nlike the short-time Fourier transform (STFT) with a fixedwindow function, the wavelet transform involves a variedtime-frequency window and can provide good localizationproperty in both the time and frequency domain, which pro-vides nice performance in analyzing highly polluted , a wavelet is a functionwith a zeroaverage(1)0885-8977/$ 2005 IEEE1880 IEEE TRANSACTIONS ON POWER delivery , VOL. 20, NO. 3, JULY 2005 Fig. 1. (a) Time-frequency window of STFT. (b) Time-frequency window continuous wavelet transform (CWT) of a signalisthen defined as(2)whereis called the mother wavelet, the asterisk denotescomplex conjugate, andand() are the scaling(dilation) and translation parameters, respectively.

7 The scaleparameterwill decide the oscillatory frequency and thelength of the wavelet; the translation parameterwill decideits shifting show the advantages of the wavelet transform, Fig. 1(a)and (b) gives the time-frequency characteristic of STFT andwavelet transform, respectively. From Fig. 1(a), we can see thatthe STFT has afixed time-frequency window (and),which means it is lackingflexibility. However, the wavelet trans-form can provide varied time-frequency windows at differentscales [Fig. 1(b)]. This enables users to choose a proper windowto see signals at different resolutions. In addition, waveletsare highly localized in both time-frequency domains. These arethe main advantages of wavelet transforms compared with practical application, we will use the discrete wavelet trans-form (DWT) instead of CWT.

8 This is implemented by using dis-crete values of the scaling parameterand translation parameter. To do so, setand(), and we get(3)For a signal ,wehave(4)The DWT transform is given by(5)Generally, we can chooseand. This choice willprovide a dyadic-orthonormal wavelet transform and providethe basis for multiresolution analysis , which will be discussedin detail in Section III and used in the later simulation MULTIRESOLUTIONANALYSIS:WAVELETANDWAVELE TPACKETA. Wavelet Multiresolution AnalysisThe multiresolution analysis is a sequence of closed linearsubspacesthat satisfied the following conditions [10]:1)withand;2);3), for all;4)is an orthonormal basis in, whereis the translates of, the then calleda scaling function every,defineto be the orthogonal complementofin, thenandBased on this, for any, we have the following equation:(6)where all subspacesare on the multiresolution analysis , any time seriescan be completely decomposed in terms of the approximations,provided by scaling functionsand the details, provided bythe wavelets.

9 The scaling function is associated with thelow-passfilters withfilter coefficientsand the waveletfunction is associated with the high-passfilters withfilter coeffi-cients. The approximations are the low-frequency com-ponents of the time series and the details are the analysis leads to a hierarchical and fastscheme. This can be implemented by a set of successivefilterbanks as shown in Fig. 2, whereandare the low-passand high-passfilters, the down samplingwith a factor of 2. Considering thefilter bank implementationin Fig. 2, the relationship of the approximations and detailsbetween two adjacent levels are given as [11](7)(8)whereandrepresent the approximation and detailcoefficients of the signal at level, al.: HOME network POWER - line communication signal PROCESSING1881 Fig.

10 2. Waveletfilter bank 3. Wavelet packetfilter bank decomposition.(a)(b)Fig. 4. (a) Wavelet decomposition. (b) Wavelet packet Wavelet Packet AnalysisThe wavelet packet was introduced by Coifman and Wicker-hauser [12] by generalizing the link between multiresolution ap-proximation and wavelets. Simply speaking, the wavelet packettransform is a generalization of the structure of the wavelettransform to a full decomposition. Different from Fig. 2 forwavelet multiresolution analysis , Fig. 3 gives the wavelet packetfilter bank decomposition on the above analysis , Fig. 4(a) and (b) give thecomparison of a three-level wavelet decomposition and waveletpacket decomposition. It can be seen in Fig. 4(a) that in waveletanalysis only the approximations (represented by capital A inthefigure) at each resolution level are decomposed to yieldapproximation and detail information (represented by capital Din thefigure) at a higher level.