indoor power-line communications channel

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1402 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 3, JULY 2008 Indoor Power-Line Communications Channel Characterization up to 100 MHz—Part II: Time-Frequency Analysis Mohamed Tlich, Member, IEEE, Ahmed Zeddam, Fabienne Moulin, and Frederic Gauthier Abstract—Estimations of coherence bandwidth and time-delay parameters from wideband channel sounding measurements made in the 30 kHz–100 MHz band in several indoor environments are described in [1] and taken back in this paper. Powerline commu- nications (PLC) modems rather see a channel which starts almost from 2 MHz [2]. A comparison between coherence bandwidth and time-delay parameters estimated in both frequency bands 30 kHz–100 MHz and 2 MHz–100 MHz is elaborated in this paper. Results are intended for applications in high-capacity in- door power-line networks. The investigation is aimed to show that the PLC channel studies in a band starting from a frequency lower than 2 MHz distorts the real values that an implementer should take, as the PLC modem see only the frequencies from 2 MHz. The coherence bandwidth and the time delay parameters are estimated from measurements of the complex transfer functions of the PLC channels. For the 30 kHz–100 MHz frequency band, the 90th percentile of the estimated coherence bandwidth at 0.9 correlation level stay above 65.5 kHz and below 691.5 kHz. It was observed to have a minimum value of 32.5 kHz. The maximum excess delay spread results show that 80% of the channels exhibit values between 0.6 s and 6.45 s. And a mean rms delay spread of 0.413 s is obtained. The passage to the 2 MHz–100 MHz frequency band induced an increase of the coherence bandwidth, whose min value is brought back to 43.5 kHz, and an important reduction of the time delay parameters: The min, max, mean, and standard deviation values of the maximum excess delay are almost divided by 2. For the twice frequency bands, this paper studies, also, the variability of the coherence bandwidth and time-delay spread parameters with the channel class [10], and thus with the location of the receiver with respect to the transmitter, and finally relates the rms delay spread to the coherence bandwidth. Index Terms—Coherence bandwidth, first-arrival delay, max- imum excess delay, mean-excess delay, power-line communications (PLC), RMS delay spread. I. INTRODUCTION P OWER-LINE COMMUNICATIONS (PLC) earmarked for future wideband wireline services in the 2–30 MHz frequency band envisage data transmission rates up to 200 Mb/s [2]. Generally, effective data rates do not exceed 70 Mb/s [3]. In order to much further increase the data rates, many equipment Manuscript received May 11, 2007. Paper no. TPWRD-00282-2007. M. Tlich is with the INNOVAS Society, Lannion 22300, France (e-mail: mo- [email protected]). A. Zeddam, F. Moulin, and F. Gauthier are with the France Télécom Division R&D, Lannion 22300, France (e-mail: [email protected]; [email protected]; frederic.gauthier@orange-ftgroup. com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2007.916095 suppliers are studying the possibility of extending the PLC frequency band up to 100 MHz. The successful implementa- tion of this solution requires a detailed knowledge of signal propagation modes inside this enlarged frequency band. Extensive characterizations of power-line channels have been reported in [6]–[8], and [9]. However, these studies are mainly focused on frequencies up to 30 MHz. The coherence bandwidth is a key parameter whose value relative to the bandwidth of the transmitted signal, subsequently determines the need for employing channel protection tech- niques (e.g., equalization or coding to overcome the dispersive effects of multipath [4], [5]). The impulse response of trans- mission channels can be characterized by various parameters. The average delay is derived from the first moment of the delay power spectrum and is a measure of the mean delay of signals. The delay spread is derived from the second moment of the delay power spectrum and describes the dispersion in the time domain due to multipath transmission. For PLC channels, and for the 1–30 MHz frequency band, thorough studies were undertaken in [6], [7]. It was observed that 99% of the studied channels have an rms delay spread below 0.5 s. In [6], the coherence bandwidth at 0.9 correlation level was observed to have an average value of 1 MHz. Also, in [8], it was indicated that for signals in the 0.5–15 MHz frequency band, the maximum excess delay was below 3 s, and the minimum estimated value of B was 25 kHz. In [9] and for the frequency range up to 30 MHz, it has been found that, for 95% of the channels, the mean-delay spread is between 160 ns and 3.2 s. And 95% of the channels exhibit a delay spread between 240 ns and 2.5 s. In this paper, coherence bandwidth and time-delay parame- ters studies are extended up to 100 MHz frequency band. For this purpose wideband propagation measurements were under- taken in the 30 kHz–100 MHz and 2 MHz–100 MHz bands in various indoor channel environments (country and urban, new and old, apartments and houses) as shown in Table I. The measurements obtained using a swept frequency channel sounder yielded sufficient statistical data from which frequency correlation functions were derived. These results were used to obtain the coherence bandwidth of the PLC channels investi- gated and their impulse responses, obtained by applying the in- verse Fourier transform to the estimated frequency response [5]. The PLC transfer functions study presented hereby relates to seven measurement sites and a total of 144 transfer functions. For each site, the transfer function is measured between a prin- cipal outlet (most probable to receive a PLC module) and the 0885-8977/$25.00 © 2008 IEEE

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Estimations of coherence bandwidth and time-delay parameters from wideband channel sounding measurements madein the 30 kHz–100 MHz band in several indoor environments

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  • 1402 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 3, JULY 2008

    Indoor Power-Line Communications ChannelCharacterization up to 100 MHzPart II:

    Time-Frequency AnalysisMohamed Tlich, Member, IEEE, Ahmed Zeddam, Fabienne Moulin, and Frederic Gauthier

    AbstractEstimations of coherence bandwidth and time-delayparameters from wideband channel sounding measurements madein the 30 kHz100 MHz band in several indoor environments aredescribed in [1] and taken back in this paper. Powerline commu-nications (PLC) modems rather see a channel which starts almostfrom 2 MHz [2]. A comparison between coherence bandwidthand time-delay parameters estimated in both frequency bands30 kHz100 MHz and 2 MHz100 MHz is elaborated in thispaper. Results are intended for applications in high-capacity in-door power-line networks. The investigation is aimed to show thatthe PLC channel studies in a band starting from a frequency lowerthan 2 MHz distorts the real values that an implementer shouldtake, as the PLC modem see only the frequencies from 2 MHz.The coherence bandwidth and the time delay parameters areestimated from measurements of the complex transfer functionsof the PLC channels. For the 30 kHz100 MHz frequency band,the 90th percentile of the estimated coherence bandwidth at 0.9correlation level stay above 65.5 kHz and below 691.5 kHz. It wasobserved to have a minimum value of 32.5 kHz. The maximumexcess delay spread results show that 80% of the channels exhibitvalues between 0.6 s and 6.45 s. And a mean rms delay spreadof 0.413 s is obtained. The passage to the 2 MHz100 MHzfrequency band induced an increase of the coherence bandwidth,whose min value is brought back to 43.5 kHz, and an importantreduction of the time delay parameters: The min, max, mean, andstandard deviation values of the maximum excess delay are almostdivided by 2. For the twice frequency bands, this paper studies,also, the variability of the coherence bandwidth and time-delayspread parameters with the channel class [10], and thus with thelocation of the receiver with respect to the transmitter, and finallyrelates the rms delay spread to the coherence bandwidth.

    Index TermsCoherence bandwidth, first-arrival delay, max-imum excess delay, mean-excess delay, power-line communications(PLC), RMS delay spread.

    I. INTRODUCTION

    POWER-LINE COMMUNICATIONS (PLC) earmarkedfor future wideband wireline services in the 230 MHzfrequency band envisage data transmission rates up to 200 Mb/s[2]. Generally, effective data rates do not exceed 70 Mb/s [3]. Inorder to much further increase the data rates, many equipment

    Manuscript received May 11, 2007. Paper no. TPWRD-00282-2007.M. Tlich is with the INNOVAS Society, Lannion 22300, France (e-mail: mo-

    [email protected]).A. Zeddam, F. Moulin, and F. Gauthier are with the France Tlcom Division

    R&D, Lannion 22300, France (e-mail: [email protected];[email protected]; [email protected]).

    Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

    Digital Object Identifier 10.1109/TPWRD.2007.916095

    suppliers are studying the possibility of extending the PLCfrequency band up to 100 MHz. The successful implementa-tion of this solution requires a detailed knowledge of signalpropagation modes inside this enlarged frequency band.

    Extensive characterizations of power-line channels have beenreported in [6][8], and [9]. However, these studies are mainlyfocused on frequencies up to 30 MHz.

    The coherence bandwidth is a key parameter whose valuerelative to the bandwidth of the transmitted signal, subsequentlydetermines the need for employing channel protection tech-niques (e.g., equalization or coding to overcome the dispersiveeffects of multipath [4], [5]). The impulse response of trans-mission channels can be characterized by various parameters.The average delay is derived from the first moment of the delaypower spectrum and is a measure of the mean delay of signals.The delay spread is derived from the second moment of thedelay power spectrum and describes the dispersion in the timedomain due to multipath transmission.

    For PLC channels, and for the 130 MHz frequency band,thorough studies were undertaken in [6], [7]. It was observedthat 99% of the studied channels have an rms delay spread below0.5 s. In [6], the coherence bandwidth at 0.9 correlation levelwas observed to have an average value of 1 MHz.

    Also, in [8], it was indicated that for signals in the 0.515 MHzfrequency band, the maximum excess delay was below 3 s, andthe minimum estimated value of B was 25 kHz.

    In [9] and for the frequency range up to 30 MHz, it has beenfound that, for 95% of the channels, the mean-delay spread isbetween 160 ns and 3.2 s. And 95% of the channels exhibit adelay spread between 240 ns and 2.5 s.

    In this paper, coherence bandwidth and time-delay parame-ters studies are extended up to 100 MHz frequency band. Forthis purpose wideband propagation measurements were under-taken in the 30 kHz100 MHz and 2 MHz100 MHz bands invarious indoor channel environments (country and urban, newand old, apartments and houses) as shown in Table I.

    The measurements obtained using a swept frequency channelsounder yielded sufficient statistical data from which frequencycorrelation functions were derived. These results were used toobtain the coherence bandwidth of the PLC channels investi-gated and their impulse responses, obtained by applying the in-verse Fourier transform to the estimated frequency response [5].

    The PLC transfer functions study presented hereby relates toseven measurement sites and a total of 144 transfer functions.For each site, the transfer function is measured between a prin-cipal outlet (most probable to receive a PLC module) and the

    0885-8977/$25.00 2008 IEEE

  • TLICH et al.: INDOOR POWER-LINE COMMUNICATIONS CHANNEL CHARACTERIZATION UP TO 100 MHZPART II 1403

    TABLE IDISTRIBUTION OF TRANSFER FUNCTIONS BY SITE

    Fig. 1. Average transfer function magnitude by class.

    whole other outlets (except improbable outlets such as refriger-ator outlets ). The distribution of the transfer functions by siteand the characteristics of each site are given in Table I.

    Because calculating distances separating transmitters fromreceivers was impossible, the PLC channels were classified into9 classes per ascending order of their capacities (according tothe Shannons capacity formula and for a same reference noiseand PSD emission mask).

    In [10] and as shown Fig. 1, we have demonstrated that thechannels of each class have a transfer functions with a sameaverage magnitude. Thus, a class 9 channel will, for example,be supposed to have a shorter transmitterreceiver distance thana class 28 channel, and so on.

    II. CHANNEL SOUNDER HARDWARE

    This section outlines the swept frequency channel sounderdesign, its calibration, and the devices used in the measure-ments.

    Transfer function measurements were carried out in the fre-quency domain, by means of a vectorial network analyzer, asshown in the block diagram of Fig. 2

    The coupler box plugging into the ac wall outlet behaves likea high-pass filter, with the 3 dB cutoff at 30 kHz. The probingsignal passes through the coupler and the ac power line networkand exits through a similar coupler plugged in a different outlet.A direct coupler to coupler connection is used to calibrate thetest setup.

    Fig. 2. Power-line channel measurement system.

    Two overvoltage limiting devices with a dB and dBlosses, respectively, are used in front of the entry port of thevectorial network analyzer 8753ES and its exit port, which canserve as an entry port, to protect it from over-voltages producedby the impulse noises of the ac power line.

    A computer is connected to the network analyzer through aGPIB bus. This allows it to record data and control the networkanalyzer with INTUILINK software [13].

    The network analyzer and the computer are isolated from thepower-line network using a filtered extension. This extension issystematically connected to an outlet unlikely to be connectedto a PLC modem, such as washing machine outlet. These pre-cautions are taken in order to minimize the influence of the mea-surement devices on the measured transfer functions.

    III. WIDEBAND PROPAGATION PARAMETERS

    Characterization of wideband channel performance subject tomultipath can be usefully described using the coherence band-width and delay spread parameters.

    A. Coherence Bandwidth

    The frequency-selective behavior of the channel can be de-scribed in terms of the auto-correlation function for a wide sensestationary uncorrelated scattering (WSSUS) channel. Equation(1) gives , the frequency correlation function (FCF)

    (1)

    where is the complex transfer function of the channel,is the frequency shift, and denotes the complex conjugate.

    is a measure of the magnitude of correlation betweenthe channel response at two spaced frequencies. The coherencebandwidth is a statistical measure of the range of frequenciesover which the FCF can be considered flat (i.e., a channelpasses all spectral components with approximately equal gainand linear phase).

    In other words, coherence bandwidth is the range of frequen-cies over which two frequency components have a strong po-tential for amplitude correlation. It is a frequency-domain pa-rameter that is useful for assessing the performances of variousmodulation techniques [11]. No single definitive value of corre-lation has emerged for the specification of coherence bandwidth.Hence, coherence bandwidths for generally accepted values of

  • 1404 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 3, JULY 2008

    Fig. 3. Illustration of a typical power-delay profile and the definition of thedelay parameters.

    correlations coefficient equal to 0.5, 0.7, and 0.9 were evaluatedfrom each FCF, and these are referred to as and ,respectively.

    B. Time-Delay Parameters

    Random and complicated PLC propagation channels can becharacterized using the impulse response approach. Here, thechannel is a linear filter with impulse response . The power-delay profile provides an indication of the dispersion or distri-bution of transmitted power over various paths in a multipathmodel for propagation. The power-delay profile of the channelis calculated by taking the spatial average of . It can bethought of as a density function, of the form

    (2)

    The rms delay spread is the square root of the second centralmoment of a power-delay profile. It is the standard deviationabout the mean excess delay, and is expressed as

    (3)

    where is the first-arrival delay, a time delay corresponding tothe arrival of the first transmitted signal at the receiver; andis the mean excess delay, the first moment of the power-delayprofile with respect to the first arrival delay

    (4)

    The rms delay spread is a good measure of the multipathspread. It gives an indication of the nature of the inter-symbolinterference (ISI). Strong echoes (relative to the shortest path)with long delays contribute significantly to .

    A fourth time-delay parameter is the maximum excess delay. This is measured with respect to a specific power level,

    which is characterized as the threshold of the signal. When thesignal level is lower than the threshold, it is processed as noise.For example, the maximum excess delay spread can be specifiedas the excess delay for which falls below dBwith respect to its peak value, as shown in Fig. 3.

    A typical plot of the time delay parameters is presented inFig. 3.

    Fig. 4. Frequency correlation functions of the measured channels. (i) class 9;(ii) class 6; and (iii) class 3.

    TABLE IICOHERENCE BANDWIDTH VALUES IN KHZ FOR 0.5, 0.7, AND 0.9

    CORRELATION LEVELS FOR THE CURVES OF FIG. 4

    IV. ANALYSIS OF RESULTS

    In this section, an analysis of the measured results, estimationof coherence bandwidth, its variability and interrelationshipwith rms delay spread, and analysis of time-delay spread pa-rameters are outlined for the both frequency bands 30 kHz100MHz and 2 MHz100 MHz referred to as and ,respectively.

    A. Coherence Bandwidth Results

    For the both frequency bands, Fig. 4 shows the frequency cor-relation functions (FCFs) obtained for three transmitter receiverscenarios: a class 9 channel (curves (i)), which can be assumedto have the least multipath contributions. Curves (ii) and (iii)correspond to the FCFs obtained from a class 6 and class 3 chan-nels, respectively.

    The degradation of the frequency correlation functions cor-responding to class 6 and class 3 channels with respect to theclass 9 channel can be seen in Fig. 4. Rapid decrease of the fre-quency correlation function with respect to the frequency sepa-ration and also as the class number decreases can be observed.The decrease in frequency correlation function is not mono-tonic, and this is due to the presence of multipath echoes in thePLC channel.

    Concerning frequency bands comparison, a first result can bealready released: the FCFs associated to each frequency bandare juxtaposed for the class 9 and class 6 cases (dotted linesand dashed lines curves respectively). Nevertheless, a signifi-cant difference tags the class 3 case (bold lines curves).

    From the shape of the FCFs, an estimation of the coherencebandwidth corresponding to a correlation coefficient of 0.5 can

  • TLICH et al.: INDOOR POWER-LINE COMMUNICATIONS CHANNEL CHARACTERIZATION UP TO 100 MHZPART II 1405

    TABLE IIISTATISTICS OF THE COHERENCE BANDWIDTH FUNCTION FOR 0.5, 0.7, AND 0.9 CORRELATION LEVELS IN KILOHERTZ

    be obtained. In Fig. 4, this is almost 2.1 MHz for curves (ii) and18.8 MHz for curves (iii). In general, the smallest frequencyseparation value is normally chosen to estimate the coherencebandwidth. This is in agreement with observations made in [12]that coherence bandwidth characterization using spaced tones[11] is not satisfactory unless measurements are taken over alarge number of points.

    Coherence bandwidth values for 0.5, 0.7, and 0.9 correlationlevels for the curves of Fig. 4 are given in Table II, and statisticsof the coherence bandwidth function for 0.5, 0.7 and 0.9 correla-tion levels for all channel measurements are shown in Table III.

    For the 0.9 coherence level and the frequency band FB ,the coherence bandwidth was observed to have a mean of291.97 kHZ, minimum coherence bandwidth of 32.5 kHz, and334.36 kHz standard deviation (Std). For 90% of the time,the value of obtained was below 691.5 kHz and above65.5 kHz. If we focus on the frequency band FB values, wesee that they are greater than the FB values. The minimumcoherence bandwidth becomes 43.5 kHz, and 90% of the PLCchannels have values greater than 89.5 kHz.

    For the 0.7 coherence level and the frequency band FB , amean coherence bandwidth of 833.9 kHz was obtained. Here,the minimum value emerged as 98.5 kHz and the standard devi-ation as 1.063 MHz. The FB values are very close to the FBones.

    In the 0.5 coherence level, 80% of the channel measurementshave a values below 13.376 MHz and above 423.5 kHz.Like the 0.9 and 0.7 coherence levels, the FB mean value of

    (4.801 MHz) is greater than the FB1 one (4.539 MHz).But, the min and max values are lower in the FB case.

    In what follows, we will focus our study only on . Inorder to characterize the channels most prone to the variationof when we replace FB by the frequency band FB reallyseen by the PLC modem, we will study in the next paragraphthe behavior of with the channel classes.

    B. Coherence Bandwidth Versus Channel Class

    The minimum and mean values of coherence bandwidth func-tion for 0.9 correlation level as a function of the channel class isgiven in Fig. 5. It can be observed that the coherence bandwidthis highly variable with the location of the receiver with respectto the transmitter.

    To investigate the reasons for the fluctuations of the coher-ence bandwidth values, magnitude curves of the complex fre-quency responses are shown. Fig. 6 represents the channel fre-quency response for the case where the coherence bandwidthwas estimated at 1.859 MHz in FB . Fig. 6 clearly shows that the

    Fig. 5. Min and Mean values of coherence bandwidth for 0.9 correlation levelas a function of channel class.

    channel frequency response presents few notches, large peaks,and is relatively flat over the 100 MHz bandwidth. Not surpris-ingly therefore, the coherence bandwidth assumed a relativelyhigh value.

    Next, the least value of the coherence bandwidth (32.5 kHz)in FB was investigated. Fig. 7 shows the magnitude responsein this case which shows significant frequency selective fadingof the channel, resulting in deep fades at several frequenciesand narrow peaks. The presence of this significant frequencyselective fading explains the relatively small value of coherencebandwidth observed. Both of these cases demonstrate that thePLC indoor channel is considerably affected by multipath, andthat the coherence bandwidth value decreases with frequencyselective fading.

    Fig. 5 demonstrates also that the mean values of areunaffected by the frequency band choice for the channels ofthe classes 5 to 9. Nevertheless, for the 2nd, 3rd, and 4th class,the mean values of are greater in FB than in FB . Thisis due to the fact that, in the frequency band 30 kHz2 MHz,the transfer function fluctuations are more significant for thechannels of low numbered classes rather than those of high-numbered classes.

    Concerning the min values of , the most important resultis that the smaller values pertain to the FB case.

    From an implementation point of view, the highly fluctuatingcoherence bandwidth means that the system designer can relyonly on the lowest value of this parameter in such an environ-ment. From Table III and Fig. 5, this is 43.5 kHz (in FB ) andnot 32.5 kHz of FB . Thus, considering the FB frequency band

  • 1406 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 3, JULY 2008

    Fig. 6. Measured transfer function envelope of the maximum B value.

    Fig. 7. Measured transfer function envelope of the minimum B value.

    values of coherence bandwidth distorts its real value that an im-plementer should take.

    The coherence bandwidth, determined from (1) is calculatedfrom the complex frequency response of the channel, in whichthe phase changes instantaneously and significantly over anychange on the state of an electrical device. The coherence band-width thus determined is more appropriately termed the instan-taneous coherence bandwidth. To study the time dispersive na-ture of the PLC channel, its more suitable to focus on the time-delay spread parameters.

    C. Time-Delay Parameters Results

    By means of an inverse Fourier transform the impulsive re-sponse can be derived from the absolute value and thephase of a measured transfer function. For the frequency bands30 kHz100 MHz (FB ) and 2 MHz100 MHz (FB ), the am-plitudes of the impulse responses of the channels of Figs. 6 and7 are depicted in Figs. 8 and 9, respectively.

    As the maximum excess delay is specified as the excessdelay for which falls below dB with respect to itspeak value, the lower signal levels are processed as noise. Con-sequently, it is more suitable to calculate the mean excess delay

    Fig. 8. Impulse response of Fig. 6 channel.

    Fig. 9. Impulse response of Fig. 7 channel.

    and the rms delay spread on the basis of channeltime coefficients lower than .

    The impulse responses of Figs. 8 and 9 show some peakswhich confirm the multipath characteristics of PLC channels.For the frequency band FB , the impulse response of Fig. 8 ex-hibits a maximum peak at a delay , a mean excessdelay s, an rms delay spread s,and a maximum excess delay s for whichfalls below dB with respect to its peak value.

    The same parameters of the impulse response of Fig. 9 ares, s, s, and

    s. This is quite foreseeable as the impulse response ofFig. 8 is associated to a shorter PLC channel and much lessaffected by multipath.

    More interesting are the reduced delays of the impulse re-sponses of Figs. 8 and 9 when the frequency band FB is con-sidered. Mean excess delay, rms delay spread, and maximumexcess delay parameters become s,

    s, and s for Fig. 8 impulse response. ForFig. 9 impulse response, the effect is more undeniable. In fact,time delay parameters fall spectacularly until s,

    s, s, and s.

  • TLICH et al.: INDOOR POWER-LINE COMMUNICATIONS CHANNEL CHARACTERIZATION UP TO 100 MHZPART II 1407

    TABLE IVSTATISTICS OF TIME DELAY PARAMETERS IN MICROSECONDS

    TABLE VSTATISTICS OF THE TIME-DELAY SPREAD PARAMETERS IN MICROSECONDS AS A FUNCTION OF THE CHANNEL CLASS

    Statistics of time-delay spread parameters for all measuredPLC channels are given in Table IV. In the frequency bandFB , the first-arrival delay was observed to have a mean of0.17 s, minimum of 0.01 s, and 0.11 s standard deviation.For 90% of the time, the value of obtained was below 0.31 sand above 0.05 s. Compared to the frequency band FB case,there is not a great difference to note for this parameter.

    For the mean-excess delay parameter and the FB case, amean value of 0.25 s was obtained. Here, the minimum valueemerged as 1 ns and the standard deviation as 0.23 s. Con-cerning the maximum-excess delay, 80% of the channel mea-surements have values of between 0.6 s and 6.45 s. 80%of the channels exhibit an rms delay spread between 0.06 s and0.78 s. The measured channels have a mean rms delay spreadof 0.413 s.

    The passage to FB induced an important reduction of themaximum excess delay, whose min, max, mean, and standarddeviation values were almost divided by 2.

    D. Time-Delay Parameters Versus Channel Class

    The mean values of first-arrival delay, mean-excess delay,rms-delay spread, and maximum-excess delay as a function ofthe channel class are given, for the twice frequency bands FBand FB , in Table V. It can be observed that these parametersare highly variable with the class number.

    Generally speaking, the four considered time parametersdecrease with the class number in both frequency bands. In fact,the high-numbered classes are those whose channels are shorterand less affected by multipath. The transmitted signal arrives to

    Fig. 10. Maximum excess delay as a function of the class number.

    its destination more quickly; furthermore, the number of echoesand their delay excess are less than those of low-numberedclasses.

    Because, in the frequency band 30 kHz2 MHz, the transferfunction fluctuations are more significant for the channels oflow numbered classes, the delay differences between FB andFB cases in Table V are more important for the low-numberedclasses. This is especially visible on the maximum excess delayparameter as a function of the class number and the frequencyband, also reported in Fig. 10.

  • 1408 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 3, JULY 2008

    Fig. 11. Scatter plot of coherence bandwidth against rms delay spread.

    E. Coherence Bandwidth Versus RMS Delay Spread

    Fig. 11 shows a scatter plot of the rms delay spread against thecoherence bandwidth of the PLC channel measures for the twicefrequency bands FB and FB . The scatter plot shows a highconcentration of points in the range 0.1 s-0.9 s at which thecoherence bandwidth is almost under 500 kHz and over 50 kHz.Higher values of coherence bandwidth are observed for rmsdelay spread values less than 0.1 s. In system design terms,higher coherence bandwidth translates to faster symbol trans-mission rates [11].

    For both frequency bands, Fig. 11 depicts a same and clearrelation between the values of B and estimated in theoverall set of measured channels, and which can be approxi-mated by

    (5)

    In Fig. 11, the relation (5) is represented by the red-circles curve.

    V. CONCLUSION

    Based on measurements in different environments, the paperincludes analysis of both coherence bandwidth and time delayspread parameters for inhouse power-line channels in the fre-quency range up to 100 MHz.

    A comparison between these parameters in both frequencybands 30 kHz100 MHz and 2 MHz100 MHz, which is thefrequency band really seen by PLC modems, was elaborated.

    Rapid increase of the coherence bandwidth and decrease ofthe time delay parameters with respect to frequency band andalso as the channel class increases was observed.

    For the first frequency band, the 90th percentile of the esti-mated coherence bandwidth at 0.9 correlation level stayedabove 65.5 kHz. Also, 90% of estimated values of B werebelow 691.5 kHz. B was observed to have a minimum valueof 32.5 kHz.

    The maximum excess delay spread results showed that 80%of the channels exhibit values between 0.6 s and 6.45 s. A

    mean rms delay spread of 0.413 s was obtained, and 80% of thechannels had an rms delay spread between 0.06 s and 0.78 s.

    Using the second frequency band (2 MHz100 MHz) inducedan increase of the coherence bandwidth and an important reduc-tion of the time delay parameters.

    The min value of was brought back to 43.5 kHz, thereally value that a system designer should rely on. The min, max,mean, and standard deviation values of the maximum excessdelay were almost divided by 2.

    Finally, a relationship between the rms delay spread and thecoherence bandwidth was determined.

    REFERENCES

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    [11] L. H.-J. Lampe and J. B. Huber, Bandwidth efficient power line com-munications based on OFDM, Int. J. Electron., Jan. 2000.

    [12] D. C. Cox and R. P. Leck, Correlation bandwidth and delay spreadmultipath propagation statistics for 910-mHz urban mobile radio chan-nels, IEEE Trans. Commun., vol. COM-23, no. 11, pp. 12711280,Nov. 1975.

    [13] IntuiLink Connectivity Software. [Online]. Available: http://www.home.agilent.com/agilent/product.jspx?nid=-536902427.536882050.00&cc=CA&lc=fre.

    Mohamed Tlich (M04) was born on May 22, 1979,in El Alia, Tunisia. He received the Ph.D. degreein electrical engineering from the Ecole NationaleSuprieure des Tlcommunications de Paris (ENSTParis) and France Tlcom Division R&D (OrangeLabs), Lannion, France, in 2006.

    His research interests include information theory,communication theory, and digital signal processing.His current research focuses on the applicationof multiuser communication theory to xDSL andincreasing the quality of service (QoS) and through-

    puts of PLC systems.Dr. Tlichs Ph.D. dissertation was awarded as being one of the three best

    France Tlcom R&D Ph.D. dissertations in 2005.

  • TLICH et al.: INDOOR POWER-LINE COMMUNICATIONS CHANNEL CHARACTERIZATION UP TO 100 MHZPART II 1409

    Ahmed Zeddam was born on April 9, 1952. He re-ceived the Ph.D. degree in electromagnetics from theUniversity of Lille, Lille, France.

    From 1979 to 1982, he was an Assistant Professorof Electronics at Lille I University. Since 1982, hehas been with the Research and Development Divi-sion of France Telecom, Lannion, where he is Headof a research-and-development unit that deals withelectromagnetic compatibility. He is the author andco-author of many scientific papers, published in re-viewed journals and international conferences.

    Dr. Zeddam is a member of several technical committees of internationalstandardization bodies dealing with electromagnetic compatibility (ITU-T, IEC,CENELEC) and is involved in Commission E "Electromagnetic Noise and In-terference" of the International Union of Radio Science (URSI). He is a memberof many scientific committees of national and international symposia on EMC.

    Fabienne Moulin received the Ph.D degree from the INSA Rennes, Rennes,France, in 2001.

    Currently, she is with France Telecom R&D, Lannion, France. Her researchdeals with increasing the quality of service (QoS) of the xDSL and PLT audioand video services.

    Frederic Gauthier received the Ph.D. degree fromthe University Pierre et Marie Curie, Paris, France,in 1989.

    He joined France Telecom R&D, Lannion, France,in 1989. His research deals with the characterizationand modelling of the PLT and xDSL channel.