Development of a Statistical Model for Powerline Communication Channels

Transcription

1 Development of a Statistical Model for Powerline Communication Channels Holger Philipps Institute for Communications Technology Braunschweig Technical University Schleinitzstr. 22 D Braunschweig, Germany Phone : Fax : philipps@ifn.ing.tu-bs.de Keywords: in-house, channel characteristics, transfer function, impulse response, noise, statistical model 0 Abstract Subject of this paper is the development of a statistical channel model describing transfer and noise characteristics of typical in-house powerline channels in the frequency range up to 30 MHz. The transfer function is described by an echo model, the noise spectrum is described by a combination of disturbances with different characteristics. 1 Introduction The powerline can be used for creating an in-house network or for bridging the last mile between the transformer station and the access point of the end-user. The advantage of this transmission medium is the existing, very extensive infrastructure. Each wall outlet can be used as an access point to this netwo1;k. As the powerline has been designed for distribution of energy and not for transmission of data, there are unfavourable channel characteristics with considerable noise and high attenuation. In addition, there are regulatory restrictions by the CENELEC norm EN ([CEN]) concerning the useable frequency range and the maximtun transmission voltage. These limitations lead to low data rates of up to a few kbitls. In future the regulatory restrictions may change and higher frequencies may be allowed to be used. In order to transmit higher data rates an extended frequency range has to be used. A measurement campaign has been carried out which covered a few hundred powerline channels in the frequency range up to 30 MHz. The campaign comprised the measurement of impedance, transfer function and noise. A statistical analysis of the measurements has been carried out pointing out a lot of characteristic findings. In chapter 2 the measured channel characteristics are described in detail. For understanding the complex characteristics of powerline channels and for developing suited and optimised transmission systems channel models are required. Based on the analysis of the channel characteristics statistical models have been developed which describe transfer characteristics (chapter 3) and noise characteristics (chapter 4) of typical in-house powerline channels. These channel models describe powerline channels by a limited set of parameters in a statistical manner. The models can be used for software and hardware simulations of different transmission techniques. The work has been carried out at the Institute for Communications Technology at the Braunschweig Technical University in co-operation with Siemens AG, Information and Communication Products (ICP), Bocholt. 2 Channel description All measurements have been carried out inside of buildings in residential and commerciayindustria1 environments in the frequency range up to 30 MHz. A basic description of the characteristics of in-house powerline channels can be found in [Phil] and [Phi2]. The impedance of powerline channels is highly varying with frequency, strongly dependent on location and typically in the range of a few Ohm up to a few kilo-ohm. The impedance is influenced by the characteristic

2 impedance of the cable as well as by the topology of the network and the connected electrical loads. The statistical analysis of the measurements shows that nearly in the whole frequency range the average value of the impedance is between 100 Ohm and 150 Ohm. At frequencies below 2 MHz the average value of the impedance tends to drop towards lower values between 30 Ohm and 100 Ohm. Due to the highly varying impedance mismatched coupling in and out and the resulting transmission losses are a common phenomenon. The transfer function of powerline channels has been measured between two wall outlets which may be connected to the same phase or to different phases. The transfer functions of three typical channels of different length (between approximately 16 m and 88 m) are depicted in Fig. 1. The measurements have been carried out by means of a network analyser and represent the insertion transfer function. It can be seen that the attenuation is - i m l 1 l Frequency in MHz Fig. 1 Transfer functions of different channels increasing with increasing transmission length. In addition, there is a slight rise of attenuation with increasing frequency. Deep narrowband notches in the transfer function are distributed over the whole frequency range. The quantity and the depth of these notches is increasing with increasing transmission length, so that the coherence bandwidth is decreasing. The coherence bandwidth is a measure of frequency selectivity of a transmission channel and is derived from the autocorrelation function of the transfer function. At frequencies with deep notches in the transfer function there are discontinuities in the phase characteristics leading to remarkable group delay distortions. There is a multitude of reasons for the characteristics of transfer fupctions of powerline channels. Transmission lines show low-pass characteristics and have increasing attenuation with increasing length. Compared with other reasons of attenuation the influence of this contribution is quite small. There are remarkable frequency-dependent losses due to mismatched impedances at coupling in and at. Powerline networks contain a multitude of branches and connected loads with different impedances. That is why there are a lot of impedance discontinuities at the transmission channel producing reflections and echoes of the transmitted signal. The echoes cause multipath transmission and produce narrowband fading. The statistical analysis of the measurements shows that in the average the attenuation increases in the frequency range from 300 khz to 5 MHz from 30 db to 45 db and in the frequency range from 5 MHz to 30 MHz from 45 db to 50 db. At 90 % of the measured channels the transfer function is within a span of 30 db below the average attenuation and 20 db above the average attenuation. The coherence bandwidth of 95 % of the measured channels is between 200 khz and 8 MHz. The coherence bandwidths of the channels depicted in Fig. 1 are 4.4 MHz (channel I), 590 lchz (channel 2) and 220 khz (channel 3). By means of an inverse Fourier transform the impulse response can be derived from absolute value and phase of a measured transfer function. The amplitude of the impulse response of channel 1 is depicted in Fig. 2. The Fig. 2 Impulse response (of channel 1 in Fig. 1)

3 impulse response shows some peaks which confms the multipath characteristics of powerline channels. It a maximum peak at a delay of approximately 100 ns. The succeeding peaks of this channel have smaller Within a time span of 1 ys approximately 90 % of the power reaches the receiver. The impulse response of transmission channels can be characterised by various parameters. The average delay is derived from the frrst moment of the delay power spectrum and is a measure of the mean delay of signals. For 95 % of the channels this parameter is between 160 ns and 3.2 ps. The average delay of the impulse response in Fig. 2 is 370 ns. 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. 95 % of the channels exhibit a delay spread between 240 ns and 2.5 ys. The given channel has a delay spread of 570 ns. The power gain gives the fraction of the transmitted energy that reaches the receiver. This parameter is in 95 % of the measured channels between - 12 db and -60 db. The power gain of channel 1 is -19 db. ~t the powerline network there is a multitude of noise sources with different characteristics, producing a highly frequency variant noise spectrum. The noise spectrum is predominated by narrowband disturbances. Mediumwave radio signals (MW) in the frequency range up to 3 MHz and short-wave radio signals (SW) in the frequency range from 3 MHz to 30 MHz, which are arranged in frequency bands and distributed over the whole frequency range, are sources of very strong disturbances, which are radiated into the powerline network. There are other sources of narrowband disturbances like switched power supplies, which produce a periodic line spectrum. In addition, there are broadband disturbances, e.g. by universal motors. An example of a noise X $ 10 5 m 0 S E -10 n $ Frequency in Mk Fig. 3 Noise spectrum of measurement I spectrum is depicted in Fig.3. It can be seen that there is an overall decay of the noise level with increasing frequency. The narrowband disturbances from SW-radio signals can be seen very clearly, especially in the frequency range from 5 MHz to 18 MHz. A statistical analysis of all measurements shows that the average noise spectrum is decreasing with increasing frequency from -20 dbpv/hzl" at 3 MHz to -35 dbpv/hz'l2 at 30 MHz. At lower frequencies the slope of the decrease is much steeper. The noise level in frequency bands of SW radio is in the average curve clearly above the surrounding noise level. These findings are focused on residential environments. The results of measurements in commercial and industrial environments show that for most channels the level of broadband disturbances is higher than the level of narrowband disturbances by SW radio. In these environments very often no or only a few narrowband disturbances have been identified as important. The characteristics of powerline channels are varying with changes in the load situation. As these conditions vary within minutes or hours (and not within fractions of a second), the characteristics of powerline channels are quasi-stationary. The channel characteristics, which are important for creating a channel model, can be subdivided into transfer function and additive noise. The development of these parts of the channel model is described in chapter 3 and chapter 4. 3 Modelling the transfer function In [Phi31 different possibilities to describe the transfer characteristics of powerline channels by a limited set of Parameters can be found. One approach describes powerline channels by a cascade of decoupled series resonant circuits. This method is not followed in this paper. A second approach, which will be described in more detail, considers powerline channels as if they were effected by multipath only and is called echo model.

4 When the powerline is characterised by multipath characteristics each transmitted signal reaches the receiver not only on a direct path, but also on several paths, which are delayed and in most cases attenuated. The echoes are caused by reflections at impedance discontinuities. Each path can be described by a delay 7, an amplitude (pl and a phase cp. The impulse response h(~) is the sum of delayed and weighted dirac pulses: For each path a set of 3 parameters has to be defined. Hence, for a channel with N paths 3*N parameters have to be defined. In [Phi31 the set of parameters for a powerline channel is determined by means of an evolutionary algorithm. This method leads to quite a remarkable correspondence - with good correlation coefficient and small root mean square error - between the transfer hction measured and the model. The disadvantage of this method is the quite large computational effort, which is necessary to determine the sets of parameters for a few hundred channels, in order to develop a statistical channel model. Additionally, for the development of a statistical channel model it is not necessary to have an exact, deterministic description of the transfer function with a good optical correspondence between measurement and model for each channel. Hence, another method for defining the parameters has been investigated, which is more suited for developing a statistical channel model. A method with a good trade off between effort and result is the search for significant paths. The impulse responses which are derived from the measured transfer functions are searched for local maxima. A maximum is significant if (a) its amplitude is not below a certain threshold (e.g. 20 db below the global maximum) and (b) the peak rises more than a certain amount (e.g. 3 db) above the level on one or on either sides. A significant path is considered in the discrete impulse response with its delay, amplitude and phase. In Fig. 4 the determination of the parameters of channel 1 (see Fig. 1 and Fig. 2) is depicted. The Fig. 4 Search for significant paths significant paths are marked, whereas maxima below the threshold are disregarded in the discrete impulse response. The impulse response has been derived for all channels evaluated during the measurement campaign. For each channel the number of significant paths and the parameters of each path have been determined by means of the method described above, which means that for all channels the discrete impulse response has been derived. The measured channels are divided into three classes. The separation is performed corresponding to the mean delay of the impulse response of the measured channel, as there is a good correlation between the mean delay and the number of paths, which have to be considered for the discrete impulse response. Channels with a mean delay between 0.45 ps and 1.65 ps are assigned to class 2 (typical). This class contains about 55 % of all measured channels. Channels with a lower mean delay are assigned to class 1 (better than typical) and channels with a larger mean delay to class 3 (worse than typical). These two latter classes contain about 15 % (class 1) and 30 % (class 3) of the channels. For each class a model channel is determined. The number of paths of the model channels are derived from the arithmetic average of the numbers of discrete paths of all channels within the class. The number of discrete paths in the model channels are 7 for class 1, 11 for class 2 and 15 for class 3. For each path of the three model channels delay, amplitude and phase are determined. In order to do this within each class the mean value and the standard deviation of the delay of each path are derived (in view of all channels within this class). The amplitudes of the paths of each channel are normalised to the maximum amplitude of the channel. The scaling factor is the attenuation of the strongest path of a channel and can be viewed as a measure of the mean attenuation of the channel. The scaling factors of the three channels of Fig. 1 are -22 db, -41 db and -65 db

5 which is in good correspondence with the mean attenuation of these channels. For each class a common scaling factor is derived from the average value of the scaling factors of all channels within this class. For the normalised amplitudes of the model channels the mean values and the standard deviations are derived separately for each path. The resulting normalised impulse response of the model channel of class 1 is depicted in Fig. 5 with the mean Fig. 5 Echo model of class 1 value and standard deviation of the amplitude and the mean value of the delay. It can be seen that the delay of the paths is between about 100 ns and 800 ns and the amplitude is decreasing with increasing delay time. The amplitude of the latter paths is about 13 db below the maximum. Compared with the mean value the standard deviation of the amplitude is smallest for the frst path. The discrete impulse responses of the model channels of class 2 and class 3 have larger maximum delays of 1.6 ps and 2.5 ps respectively. For these two classes the strongest path is shifted to delayed paths and the difference between the strongest and the weakest path is decreasing up to 5 db at class 3. The standard deviation of the amplitudes is increasing from class to class. The transfer function of a model channel can be derived by means of a Fourier transform. This has been done for the model channels of the three classes (with each parameter set to the mean value). The resulting transfer functions are depicted in Fig. 6. It can be seen that the average attenuation is increasing from class to class. In , ::-...,.:.... 5: -.. r. ; m im I Frequency in Mtb Fig. 6 Transfer functions of model channels addition the variations with frequency are increasing from class to class, leading to distinct narrowband fading and a decreasing coherence bandwidth. Especially at the channel of class 3 the influence of many paths with nearly the same amplitude gets more noticeable. The channels of Fig. 1 represent channels of class 1 (channel l), class 2 (channel 2) and class 3 (channel 3). Similarities between the measured channels of Fig. 1 and the model channels of Fig. 6 can be seen clearly. 4 Modelling the noise spectrum A method to describe the noise spectrum of powerline channels can be found in [Phi3]. In that paper sources of white noise which are defined separately for adjacent, non-overlapping frequency bands are the basis of the Proposed noise model. In addition sources of narrowband disturbances are added. In order to match the model to

6 a given spectrum, a set of parameters has to be defined and has to be optimised by means of an evolutionary algorithm. In the present paper a different noise model is presented which considers the noise characteristics described in chapter 2. Frequency in Mk Fig. 7 Decomposition of noise spectrum Measurements of the noise spectrum have shown that there are three dominant portions contributing to the disturbances: SW-radio signals, narrowband disturbances and background noise. In Fig. 7 a measured noise spectrum is depicted. In addition the decomposition in different parts of disturbances is shown. The disturbances by SW-radio signals (120 m band to 11 m band) and CB-radio signals are present very often with high amplitudes but restricted to certain frequency bands. Hence, for each of these frequency bands the mean amplitude is derived. In Fig. 7 these disturbances are represented by rectangles with a height corresponding to the mean noise amplitude within the frequency band. Narrowband disturbances, which do not fall into frequency bands of SW-radio signals, are marked with a down triangle. A narrowband interferer is present, if its amplitude rises more than a certain level (e.g. 6 db) above the noise level on either sides. The spectrum which remains after removing the SW-radio and narrowband disturbances is called background noise. In general it shows a decreasing amplitude with increasing frequency. The spectrum of the background noise is interpolated at frequencies which fall into SW-radio bands or which represent a narrowband interferer. For each of the measured noise spectra the parameters of the different parts of disturbances have been determined. This comprises the average amplitude of the disturbances in each SW-radio band and the number of narrowband disturbances at each measurement as well as the amplitude of each narrowband interferer. Measurements have been carried out in two different environments, whose results have been analysed separately: residential and commerciayindustria1 environment. In contrast to residential environments the measurements in commercial and industrial environments show less influence of SW-radio disturbances. Due to strong broadband disturbances by large electrical loads the amplitude of the background noise is higher or in the range of the radiated SW-radio signals. Hence, in this environment the radiated disturbances are not as much remarkable as in residential environments. For both kinds of environments (residential and industrial) a statistical analysis of the parameters has been carried out. For each of the frequency bands of SW radio mean value and standard deviation of the amplitude has been determined. The results for the residential environment are as follows. Below 5 MHz the mean value is at approximately -25 dbpv/hzl". ~etween 5 MHz and 18 MHz the mean value is at higher levels (between -10 d~pv/hz'" and -20 dj3pv/hz1"). At higher frequencies the mean value is smaller at approximately -35 d~pv/hz'" (except the 13 m band at approximately -20 dbpv/hzin). In industrial environments the disturbances in SW-radio bands exhibit nearly the same amplitudes as the background noise. The mean value of the amplitude is decreasing from approximately 0 cll3pv/h~"~ to -30 dbpv/hzl" with increasing frequency. The number of narrowband interfeers in one measurement has been analysed. In residential environments the number of interferers is normal distributed with a mean value of 27 and a standard deviation of 10. In 95 % of the measured channels the value is between 10 and 45. In industrial environments a lognormal distribution with a mean value of about 18 and a standard deviation of 10 fits best. In 95 % of the measured channels in this kind of environment the value is between 5 and 35. The amplitudes of the narrowband disturbances are lognormal distributed in both environments. In residential environments the amplitudes have a mean value of -17

7 d~p~/hz"~ and a standard deviation of 12 db. In 95 % of the measured channels the amplitude is between -30 d~pv/hz'" and 10 dbpv/hzl". In industrial environments the mean value is at -6 dbpv/hzl" and the standard deviation is 17 db. In 95 % of the measurements the amplitude is between -28 dbpv/hzl" and 28 dbpv/hz1". For both environments the narrowband disturbances are equal distributed over the whole frequency range (frequencies of SW radio left out). The background noise is decreasing with increasing frequency. It can be described by an exponential function of fust order. The background disturbances of all channels have been analysed separately for both environments. The mean value of background noise as well as the curves of minimum and maximum background noise have decreasing amplitudes with increasing frequency and can be described by exponential functions, too. The curves of the mean value can be described by: Nresident (f) = e -f [MHz1 NiAst Cf) = e -f rmz for residential environment and for industrial environment. The amplitude of N(f) is given in dbpv/hz'". The frequency has to be inserted in MHz. The noise spectrum of a model channel is assembled of the different parts of noise, which are summed up. For each part the parameters can be set corresponding to the statistical analysis described above. An example of a residential environment, which only consists of background noise and disturbances by SW-radio signals, is Fig. 8 Noise spectrum of model depicted in Fig. 8. The amplitude of the background noise as well as the amplitudes of the SW disturbances are set to the average value of the statistical analysis. It can be seen very clearly that the influence of the radiated disturbances of SW radio is most noticeable in the frequency range between 5 MHz and 22 MHz. 5 Powerline channel model The complete channel model, which comprises of transfer function and additive noise, is depicted in Fig. 9. The parameters of the transfer function, which is determined by N paths, are set corresponding to the descriptions in chapter 3 for modelling different kinds of channels. Depending on the kind of the channel the delay, the amplitude and the phase of each path are set individually. In addition, a common scaling factor can be defined. In the same way the parameters of noise can be set according to the descriptions in chapter 4 in order to model different environments. The amplitude of the SW-radio disturbances as well as number, frequency and amplitude of narrowband disturbances and the curve of the background noise have to be defined. The transfer function can be realised as an FIR filter or as a tapped delay line for software and hardware simulations. The noise spectrum can be realised by sine-wave interferers and white Gaussian noise which is band-pass filtered according to the disturbances by SW-radio signals and background noise.

8 Transfer function, PI X(9 Background noise Namwband disturbances Distuhances by SW-adio Fig. 9 Channel model 6 Conclusions and outlook This paper describes the development of a statistical model for in-house powerline channels in the frequency range up to 30 MHz. Based on a multitude of measurements in different environments a statistical analysis of the channel characteristics has been carried out. The developed model comprises of two parts: transfer function and noise. If the powerline is described by a multipath environment then the transfer function is described by an echo model. Channels of different characteristics are described by different numbers of paths. Each path is defmed by different parameters - delay, amplitude and phase. The model allows a statistical emulation of different powerline channels. It can be realised as FIR filter or as tapped delay line and allows straightforward software and hardware simulations. It has been found that the noise spectrum comprises of different parts of noise: disturbances by short-wave radio signals, narrowband interferences and background noise. These parts have been evaluated for all channels measured. A statistical analysis has been carried out separately for channels in residential environments and for channels in industrial environments. According to the statistics the parameters of the SW-radio disturbances (amplitude), the narrowband disturbances (number, frequency, amplitude) and the background noise (amplitude) can be set in order to describe different kinds of channels. The noise model can be used for software and hardware simulations. At the moment a hardware powerline channel simulator, based on the described channel model, is under development at the Braunschweig Technical University. 7 References [CEN] CENELEC EN 50065, "Signalling on low-voltage electrical installations in the frequency range 3 khz to 148,5 khz", July 1993, Beuth-Verlag, Berlin, 1993 [Phil] Philipps, H., "Performance measurements of powerline channels at high frequenciesc', Proceedings of the 1998 International Symposium on Power-Line Communications and its Applications (ISPLCA '98), Tokyo, Japan, March 1998, p [Phi21 Benjes, I., Philipps, H., "PC-gestiitztes Endgeriit und Zweidraht-Dateniibertragung fir die netziibergreifende Multimedia-Kommunikation", AbschluBbericht fir das MINT-Projekt, Institut fir Nachrichtentechnik der TU Braunschweig, Januar 1999 [Phi31 Philipps, H., "Modelling of powerline communication channelscc, Proceedings of the 1999 ~ntemational Symposium on Power-Lie Communications (ISPLC '99), Lancaster, UK, MarcWApril1999, p