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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 7, JULY 2006
1267
A Mathematical Model of Noise in Narrowband
Power Line Communication Systems
Masaaki Katayama, Senior Member, IEEE, Takaya Yamazato, Member, IEEE, and Hiraku Okada, Member, IEEE
Abstract—This manuscript introduces a mathematically
tractable and accurate model of narrowband power line noise
based on experimental measurements. In this paper, the noise is
expressed as a Gaussian process whose instantaneous variance is a
periodic time function. With this assumption and representation,
the cyclostationary features of power line noise can be described
in close form. The periodic function that represents the variance
is then approximated with a small number of parameters. The
noise waveform generated with this model shows good agreement
with that of actually measured noise. Noise waveforms generated
by different models are also compared with that of the proposed
model.
Index Terms—Colored noise, impulsive noise, narrowband
power line communication (PLC), noise measurement, noise
model, nonstationary noise.
I. INTRODUCTION
P
OWER-LINE COMMUNICATIONS (PLCs) can be classified on the basis of their frequency bandwidth: PLCs can
be either wideband (broadband), or narrowband systems. Wideband PLC systems are recently calling attention for high-speed
Internet access. The systems of this class use high-frequency
(HF) band, or up to the low-end of very high-frequency (VHF)
band. Because of this very wide frequency band, the wideband/
broadband PLC systems achieve 10–100 Mb/s without any new
communication wiring effort. Though the use of the HF/VHF
has advantageous features, it also contains difficulties. In HF
band, there are many radio users listening very weak signals,
such as shortwave broadcasting listeners, radio amateurs, receivers for emergency calls, and radio-astronomers [1]. Because
of the strong concern about interference from PLC systems,
many countries do not allow the use of the HF band for PLC
systems.
Narrowband systems use low or medium frequencies, between 3 and 148.5 kHz in Europe under CENELEC and below
450 kHz in Japan. The systems of this class have been used
for many years, and there is no difficulty concerning the regulations. Though the allowed frequency range is relatively narrower than in wideband PLC systems, the range is still wide
enough for some applications such as controls. For example,
Manuscript received April 18, 2005; revised January 15, 2006 and February
21, 2006. This paper was presented in part at the International Symposium on
Power Line Communications, Vancouver, BC, Canada, 2005.
M. Katayama and T. Yamazato are with the Division of Information and
Communication Sciences, Ecotopia Science Institute, Nagoya University,
Chikusa Nagoya 464-8603, Japan (e-mail: [email protected];
[email protected]).
H. Okada is with the Center for Transdisciplinary Research, Niigata University, Niigata 950-2181, Japan (e-mail: [email protected]).
Digital Object Identifier 10.1109/JSAC.2006.874408
ECHONET consortium [2], which was established in 1977, has
defined specifications for narrowband PLC for control and monitor of home appliances. The control of power-grid systems is
another important application, which can be realized by PLC
systems with relatively low speeds [3], [4]. In addition to PLC
on mains power lines, there have been many applications with
relatively low speeds on variety of power lines. The control
of ground-lights of airport runways through 0.4–6 kV current
loops [5] and communications of control data with 40 kb/s in
streetcar/subway systems on 750 V DC networks [6] are interesting examples of them.
Although narrowband PLC systems have often been used for
low-speed applications, they have been considered unreliable
because of the higher noise levels present at lower frequencies. However, the low speed and low quality of narrowband
PLC systems are not an ineluctable destiny. The reason of the
insufficient performance of the conventional narrowband PLC
systems is that they simply introduce relatively old-fashioned
signaling schemes developed for an environment very different
from power lines. Therefore, the employment of sophisticated
schemes may result in much higher performance.
For the introduction of sophisticated communication schemes
in narrowband PLC systems, the environment of power lines as
communication channels should be known. One of the most peculiar features of power lines is strong and time-varying nonwhite noise. The power line noise at an outlet is the sum of
noise waveforms produced and emitted to the lines from the
appliances connected to the power line network. In the design
and the analysis of conventional communication systems, stationary additive white Gaussian noise (AWGN) is often used as
a model of noise. In PLC systems, however, the statistical behavior of this man-made noise is quite different from that of
stationary AWGN. The non-Gaussian features of the noise are
often believed to be the cause of the low quality of PLC systems.
Actually, the fact that Gaussian distribution has the largest entropy implies that the communications under the non-Gaussian
noise may achieve better performance than under AWGN, if the
system is designed to adapt the noise statistics [7]. Thus, narrowband PLC systems still retain much capacity for performance
improvement if the behavior of the noise is clarified and taken
into account in the system design.
In order to study communications in a man-made impulsive
noise environment, a simple model that expresses the noise
behavior in closed-form equations is necessary. One of the
most popular and important models of non-Gaussian noise is
the probability density function (PDF) proposed by Middleton
[8]. According to this model, the PDF of impulsive noise can
be expressed as a sum of Gaussian functions with different
variances. With this model, various classes of impulsive noise
0733-8716/$20.00 © 2006 IEEE
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 7, JULY 2006
Fig. 2. Noise waveform by an inverter driven fluorescent lamp (30 W).
Fig. 1. Noise waveform by a CRT color TV.
can be expressed by a simple function with a small number
of parameters. The disadvantage of this model is that the
model does not define time-domain features. The PDF does not
describe whether the noise waveform is peaky (impulsive) or
smooth in the time-domain.
The power line noise is not white and it has a complicated
power density spectrum (PDS). In [9], the bandwidth is divided
into several subbands, and noise voltages are sampled at each
subband to define a PDF by a histogram of noise voltages. The
noise waveform is then generated using the set of PDFs of all
the subbands. In [10], the same concept is applied, and PDF
for each subband is approximated by Nakagami-m distribution.
With this model, the colored noise can be expressed by a set of
closed form functions.
In many studies about power line noise, including those referred to above, it is assumed that the noise is stationary and,
therefore, only the time averaged power spectrum densities and
the time-independent intensity distributions are taken into account. The characteristics of the noise in power lines, however,
are not stationary.
It is known that the power line noise has periodic features,
which are synchronous to the mains voltage. This is because
many appliances generate noise synchronously to the instantaneous value of the mains voltage. Some switching devices turn
on and off at a certain voltage of AC, and these switching operations also cause impulses synchronous to the mains voltage.
Therefore, a model, which can describe the statistics of the instantaneous value of the noise, is still needed. Examples of snapshots of noise from individual appliances are shown in Figs. 1–3,
which are taken at the same outlet where the appliances are conis 1/2 of the mains cycle duration,
nected. In the figures,
which is 1/120 s in Nagoya, or western part of Japan. In addition
to the behaviors of appliances, channel characteristics between
the noise sources and a receiver may vary synchronously to the
mains voltage [11]. This channel fluctuation also causes in the
periodic features of the noise.
The frequency of the periodic features of the noise is the same
or twice the mains frequency. This is relatively slow compared
with the data/packet rate of high-speed wideband systems. In the
case of narrowband PLC systems, however, the symbol duration
and thus packet length tend to be long because of the relatively
narrow bandwidth, and thus the periodic features of noise cannot
Fig. 3. Noise waveform by a vacuum cleaner with brush motor (600 W).
be ignored. Furthermore, these features can be used by communication systems to find/estimate time slots with low-noise
level for adaptive signal transmission and maximum a posteriori probability (MAP) detection with reliability of data based
on the noise.
In [12], the power line noise is divided into four classes, i.e.,
(A) continuous colored noise; (B) continuous tone jammers;
(C) Periodic impulses synchronous to mains; and (D) impulsive
noise asynchronous to mains. In [13], Zimmermann and Dostert
represent the time variant features of noise with a partitioned
Markov chain with multiple states. This model represents the
last class, (D), of noise for wideband PLC systems.
In narrowband PLC systems, however, the continuous noise
in classes (A) and (B) are dominant, together with periodic
impulses of (C). For this reason, the authors have first proposed
a mathematical model which represents the continuous noise
with the periodic features [15]. In addition, in [16], the model
that includes stationary and impulsive components is proposed.
Further considerations are made in [18]. Based on these former
studies, this paper proposes a mathematical model of the power
line noise that can represent its nonstationary and nonwhite
features by a simple PDF function with a small number of
parameters.
In Section II, the setup to measure the power line noise at
outlets is described and an example of measured noise waveform is represented. Using this measurement as an example,
Section III describes the proposed model of power line noise.
The model defines power line noise as the Gaussian process
whose variance is a time and frequency dependent function.
Then, a simple approximation to express the variance function
KATAYAMA et al.: A MATHEMATICAL MODEL OF NOISE IN NARROWBAND PLC SYSTEMS
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Fig. 5. Pickup circuit.
TABLE I
CIRCUIT ELEMENTS
Fig. 4. Measurement system.
is proposed. Section IV describes the procedure to find the parameters of the model from the measured noise waveform, and
Section V illustrates an example waveform of noise generated
by the model. In Section VI, another approximation for the variance function is provided, and statistical comparisons are made.
The final section concludes this paper with future problems.
II. NOISE MEASUREMENT
A. Measurement Setup
In many measurement reports on power line noise, spectrum
analyzers are often used to show average or peak values of
power line noise in the frequency domain. Some reports focus
on noise waveforms in the time domain, but only for short time
period. In contrast, in this study, the discussion is based on the
measurement of the whole noise waveforms in a long observation time.
The system for the noise measurement is shown in Fig. 4. The
system consists of a pickup circuit followed by an A/D converter
(ADC) and a computer (PC), and the injection circuit with a
waveform generator. The pickup and injection circuits are connected to an outlet and no other electrical appliance shares the
outlet. The measurements are made in university laboratories,
apartments, individual houses. Since the measured waveforms
at different locations have similar features, a waveform taken at
the laboratory of the authors is used as an example of discussion
in this paper.
The pickup circuit is shown in Fig. 5. In this figure, the mains
alternating current (AC) component is attenuated by the capacitors, common-mode noise component is removed by a radio-frequency transformer, and balance-to-unbalance transform of the
circuit is performed by a balun. The noise component is obtained
at the terminal labeled “noise” in the figure. In order to eliminate
aliasing effect, low-pass filter (0–1.9 MHz) is inserted before the
ADC. ADC then samples the waveform with 10 M [samples/s]
and passes the data to the computer. As described in the following sections, the rest of processing is executed with digital
signal processing programs in the PC.
The pickup circuit also outputs a down-transformed AC
waveform with the peak-to-peak voltages of 2 [V] at the terminals labeled “AC.” This AC voltage waveform is used as
a trigger to start the ADC. The circuit elements are shown in
Table I.
In power line communication systems, line impedance is
not stationary. It often fluctuates along with the mains AC
voltage [11]. This fluctuation of line impedance often causes
the impedance mismatch between lines and a receiver, which
decreases both the received noise and signal levels. In order
to monitor and compensate the effects of the impedance mismatch, we introduce a reference tone, which is injected into the
power lines from the same outlet where pickup circuit is connected. The injection circuit and the pickup circuit for “noise
component” have the same configuration and parameters.
B. Normalization of Noise Waveforms
The input to the ch.1 of the ADC can be expressed as
, where
denotes the reference tone, while
is the noise component. According to the results of authors’ experiments in several locations, in wideband (broadband) PLC,
which uses whole HF band, the frequency dependence of lineimpedance as a time function cannot be ignored. Thus, we have
to use a multitone signal as a reference. In narrowband PLC,
however, the fluctuation of line-impedance is almost frequency
independent. In other words, the ratio of the voltage of reference
signals with different frequencies is time independent. For this
reason, the measurements described in this paper use a single
kHz as the reference.
tone with the frequency
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 7, JULY 2006
Let us assume that the power of the reference tone is constant
. The reference tone for
for a short duration
this time duration can be denoted as
(1)
where
kHz and are the frequency and the phase of
the reference tone. The power
is calculated by
(2)
Fig. 6. A snapshot of a measured noise waveform (normalized).
is sampled with the sampling rate
In the measurement,
MHz . The sample at
is
. The train of the samples is stored in PC and the reference tone and noise components are extracted by narrowband
(bandpass and band-rejection) filters of the center frequency ,
which are realized by onboard digital signal processing. After
and
components, the power of
the extraction of
is calculated as
the reference tone in the vicinity of
(3)
where
. In the numerical example shown in this man10 s , and thus
.
uscript,
In order to compensate the fluctuation of noise level caused
due to mismatch between fluctuating line-impedance and
is divided by the
pickup circuit, each noise sample
instantaneous level of the measured reference tone component
. The resultant normalized noise level,
is obtained as follows:
(4)
Let us have
samples in the duration of cycles of the
, where
is the mains
mains AC voltage, i.e.
cycle duration. In Nagoya, or in western Japan, the mains fre10 . The integer
quency is 60 Hz and
is the largest integer no greater than
. Then, the
is calculated as
time-averaged variance of
(5)
With this value
III. NOISE MODEL
A. Cyclostationary Gaussian Model
Fig. 7 shows an example of the cumulative probability distribution functions of a measured noise waveform [16]. In the
figure, solid lines indicate the distribution of the noise level (absolute voltage) and dotted lines show Gaussian distribution of
the same power. Since the noise in power lines has periodic
, in (A), we calculate the
features with the frequency
cumulative probability distribution of the noise level sampled
, at the instance when the mains AC
with this frequency
voltage crosses zero. The distribution of the noise level taken
at the peaks of the mains absolute voltage is shown in (B). For
comparison, the distribution of the noise level taken at random
phase is also given in (C).
From (C), we can find that the distribution function of the amplitude of the noise in power lines is larger than that of Gaussian
when amplitude is small, though the Gaussian has larger values
of distribution function at larger amplitude region in all figures.
This is the typical feature of the impulsive noise. In other words,
it can be concluded that the noise in power lines is impulsive if
the samples are taken at random.
On the contrary, in (A) and (B) of the figure, in which the
, the amplitude
noise is observed periodically at every
distributions can be assumed as Gaussian. The authors have
confirmed that this Gaussian distribution of periodically sampled noise can be observed at any phase of the mains and in
many other power line noise waveforms. Considering this interesting feature, the authors have proposed a model of power line
noise [16], which assumes that the noise is cyclostationary (periodically stationary) [17] additive Gaussian noise whose mean
is zero and the variance is synchronous to the AC voltage of
mains. With this assumption, the PDF of the noise at the incan be expressed as
stance
is normalized to have unity variance as
(6)
Fig. 6 shows an example of the normalized noise waveform
. From this figure, we can observe that the noise has the
periodic features with the frequency of
Hz .
(7)
In this equation,
is the instantaneous varidenotes ensemble average. Since
ance of the noise, where
the variance
is a periodic time function of the freqency
KATAYAMA et al.: A MATHEMATICAL MODEL OF NOISE IN NARROWBAND PLC SYSTEMS
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Fig. 8. Example of cyclic average of measured noise variance.
of Middleton [8], which expresses the noise PDF as a sum of
Gaussian distribution functions with different variances. This
is because, the noise of the proposed model has different variances at different phases of the AC voltage. In other words,
Middleton PDF in PLC channel is thedescription of power line
noise without the consideration of time depending (periodic)
features, which can be expressed by the proposed model.
B. Simple Expression of the Instantaneous Variance
Based on the assumption that
is a periodic
function, let us replace the ensemble average by the average of
instanteneous power of the normalized noise waveform taken at
s. Then, for
, we have instantaevery
neous power (variance) of
as
(8)
Fig. 7. Amplitude probability distribution of noise. [16]. (a) Noise at same
phase of AC voltage (0, 180, 360, 1 1 1). (b) Noise at same phase of AC voltage
(90, 270, 450, 1 1 1). (c) Noise at ramdom phase over the observed duration.
, the PDF (7) is also a periodic function:
for any integer .
The importance of this expression is that the time dependent
or nonstationary features of noise are represented mathematically in the closed form of PDF.
It is noteworthy that if the noise described by this proposed
model is sampled at random timing without the synchronization to the AC voltage, the resultant samples follow the PDF
which is shown in Fig. 8, using 2
10 sam10 samples/s. Note that
ples with the sampling rate 10
.
If the noise has cyclostationary characteristics, we can expect
. The results of our experiments
show that
, i.e. observation of about one second,
.
is enough for the convergence of
Then, the next problem is to approximate this time function
by a simple function with a small number of parameters. For this
purpose, the model employs the following periodic function to
:
approximate
(9)
where a set of
parameters
, , and
for
denotes the characteristics of the noise.
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 7, JULY 2006
component, and the parameters and are not needed, i.e.,
is zero and can be an arbitrary value. The second term is used
to express continuous periodic features of noise and the last term
for periodic impulsive noise. As a result, seven parameters are
needed for (9) plus an additional one that describes the feature
of noise in the frequency domain as discussed in the previous
section.
A. Parameters for PDF
Fig. 9. Example of power spectrum density of power line noise.
Note that the following equation should stand to keep the
unity, i.e.,
time-average power of
There may be various ways to assign values for the parameters of (9) from measurement results. As an example, we employ
the following intuitive method.
, which describe periodic
1) The parameters of the term
impulsive noise, are first calculated as follows.
and assign the
a) Find the maximum value of
.
value as
be given at
, then we have
b) Let the
(13)
(10)
. Note that
and
represent the same waveform of (9).
be
c) Let the 3 dB-width of the pulse centered at
. Then,
is calculated by solving the equation
where
The proposed model is based on the central limit theorem,
which is robust in many types of communication systems. Any
power line noise produced by a collection of independent noise
sources (appliances), which are stationary or cyclostationary,
can be captured by this model. According to the authors’ experience of measurements, in almost all locations this assumption
stands. Exception is the case if a small number of appliances
near the measured outlet dominate the noise waveform. If we
use larger , larger set of parameters, more complex behavior
of the noise can be expressed. Note that the does not represent
the number of noise sources but number of noise classes.
In the preceding discussion, noise statistics in the frequency
domain are not considered, but it is not difficult to introduce the
nonflat spectrum of the noise in the model. Fig. 9 shows an example of PDS of the measured noise waveform shown in Fig. 6,
10 samples with 10 [M samcalculated with 2
ples/s]. From this figure, we can confirm that the noise in power
line is nonwhite. In addition, the noise power is time function
as is discussed in the previous section. For this reason, the proposed noise model denotes the variance of power line noise at
on the frequency as
(11)
where
is the PDS denoted as
(12)
IV. PARAMETER ESTIMATION
In order to express the detailed features of noise by (9), large
is needed; however, often
is enough. In this case, the
first term is used to represent the constant (or background) noise
(14)
The obtained
makes the 3 dB-width of
identical to that of the
.
pulse of
of the term
, which describes time
2) The parameter
invariant noise, is then calculated as the average of the least
.
10% samples of
) term, which
3) The parameters of the second (i.e.,
describe the periodic continuous noise, are derived by
, , and
, which
searching a set of parameters,
and
of (9)
minimize the difference of
defined as
(15)
In finding the parameters for
, we use the method of
steepest descent, several times with different initial values,
has many local minsince the function
imum points. In order to eliminate the influence of the impulsive component, summation in (15) excludes the samples in the 3 dB-width in the time domain around the impulse component, which is defined in preceding step for the
term.
third
Table II shows the parameters obtained by the above procedure for the waveform in Fig. 8. Note that is represented in dedescribed by these
gree. In Fig. 10, the variance function
parameters is shown to be compared with Fig. 8.
KATAYAMA et al.: A MATHEMATICAL MODEL OF NOISE IN NARROWBAND PLC SYSTEMS
1273
TABLE II
PARAMETERS FOR (t) OF FIG. 10
Fig. 11. Power distribution of power line noise in subbands.
Fig. 10. Example of approximated noise variance.
B. Parameters for PDS
Note that the (12) becomes a linear function with a negative
inclination in the domain of positive frequency if the power is
plotted in logarithm scale as
(16)
where is a constant. Thus, the parameter can be estimated
by least-squares method. In the calculation of , we have used
averaged noise power in subbands of width 50 kHz, as shown in
Fig. 11, instead of raw data of noise spectrum in Fig. 9. For an
10 from Fig. 11.
example, is estimated
Since the inverse Fourier transform of PDS is autocorrelation,
the following equation denotes the correlations of noise samples
taken at two different time instances:
Fig. 12. Convergence of the derived parameters [18].
.) The vertical axis represents the difference of the parameters
periods,
derived by the samples in periods and those in
i.e.,
(18)
where
is a parameter estimated by -periods of samples.
From this figure, all parameters converge at about
cycles of the mains voltage, which means less than 1 s. We
have confirmed the same conclusion by the experiments in other
locations.
(17)
V. GENERATION OF NOISE WAVEFORM
Note that this equation implies that the noise samples at different time instances have significant correlation only for small
. For example, if
s , the correlation of two
samples is less than 10%.
C. Necessary Observation Duration
In the parameter estimation procedure, we expect that variand thus the parameters derived
ance as a time function
from the function converge to constant values when is enough
large. Fig. 12 shows an example of the convergence of the derived parameters [18] with sampling rate 10 10 . (The phase
parameters are omitted from the figure as they are insensitive to
Using the mathematical model discussed above, we can generate simulated waveforms of power line noise as follows.
.
1) Determine a set of parameters for
.
2) Generate Gaussian noise with instantaneous variance
3) Pass the noise to the filter with the frequency response
. Parameter is needed.
In the previous sections, we have derived parameters from
the noise shown in Fig. 6 and obtained a set of parameters for
in Table II and the parameter in frequency domain as
10 . Fig. 13 shows an example of a simulated noise
waveform generated by these parameters using the procedure
shown above. Comparing Fig. 13 and Fig. 6, we can confirm
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TABLE III
PARAMETERS FOR (t) OF FIG. 15
Fig. 13. Computer simulated power line noise.
Fig. 15. Instantaneous variance with Fourier series approximation.
where
(20)
(21)
Fig. 14. Difference of parameters used in noise-generation and determined by
the generated noise [18].
that the features of cyclostationary power line noise are well
represented by the computer generated noise.
In order to confirm reliability of above parameter-determination procedure, in [18], we compare the parameters determined
by computer-generated noise with the parameters used to generate the noise. Fig. 14 shows the difference between the parameters used in the noise generation and the parameters derived
from the generated noise. From this figure, we can confirm the
agreement of both parameters if observation duration exceeds
40 50 cycles of the mains voltage.
VI. COMPARATIVE DISCUSSION
In the proposed model, the noise is assumed as a time-variant
Gaussian process defined by (7). The instantaneous variance of
is estimated by the meathe noise as a periodic function
defined as
surement of noise, and then approximated by
(9). This equation for the approximation is derived by the rule of
thumb, and there could be other strategies of the approximation.
is a periodic function, Fourier series expansion
Since
(19)
could be a candidate of the approximation. Benefit of Fourier
series expansion is that the parameter estimation is easy and
straightforward. In addition, the approximation
asymptotwith the increase of .
ically approaches to
Table III shows the parameters obtained for the above Fourier
, which has the
expansion on the waveform in Fig. 8 up to
same number of parameters as in Table II for
. The approxdefined by these parameters is
imated variance function
shown in Fig. 15, which has large difference from the original
function in Fig. 8. The sharp impulse in original variance function disappears in the approximated function. This is because
abrupt changes cannot be expressed by low harmonic terms of
Fourier series. In other words, the Fourier series approximation
with truncated sum is not suitable to express the variance of the
power line noise, which has periodic impulsive components.
Fig. 16 is an example of noise waveform generated from this
and (12), where
10 . It is interesting
variance
that the generated noise waveform is similar to that of the original noise, whose snapshot is shown in Fig. 6. Of course, the
results of the comparison of noise waveforms do not have large
significance, as the noise waveforms are stochastic processes.
If we observe the noise waveforms for long duration and calculate the expectation of the noise power sampled synchronous to
mains, then we have agreement to that of measured noise with
, as in Fig. 10, and disagreement with
, as in Fig. 15.
If we ignore the periodic features of the noise and sample the
noise at random timing asynchronously to the mains voltage
KATAYAMA et al.: A MATHEMATICAL MODEL OF NOISE IN NARROWBAND PLC SYSTEMS
1275
VII. CONCLUSION
Fig. 16. Noise waveform by Fourier series approximation.
In this manuscript, a simple mathematical representation of
the noise in narrowband power line communication systems is
introduced. This model can express time variant and nonwhite
features of the noise in power lines with a small number of parameters. The meaning of the noise model and also the procedure to generate noise waveform from given parameters are described, and a set of parameters derived from the noise waveforms recently measured is provided.
The proposed model provides a benchmark for design and
evaluation of communication systems under the time variant
colored power line noise environment, which cannot be represented by conventional noise models. However, the importance
of the proposed model lies not only in the definition of a useful
tool for the performance evaluation of PLC systems, but also in
the definition of a powerful tool for the study of time-variant
man-made noise itself. In fact, various types of measured noise
can be easily described with the proposed model.
The measurement and parameter determination of noise
waveforms at many locations, the construction of a database
of power line noise, and the establishment of a standard set of
parameters represent important future areas of investigation.
ACKNOWLEDGMENT
Fig. 17. Probability density functions (linear scale).
The authors would like to thank A. Kawaguti, O. Ohno,
S. Itou, and all the other students of Katayama Laboratory,
Nagoya University, for their kind support and their efforts
to prepare the figures for this manuscript. They also express
their appreciation to Chubu Electric Power Corporation for
their valuable support. Last but not least, they express their
sincere gratitude to anonymous reviewers and the Co-Guest
Editor Dr. Galli for their valuable comments and suggestions to
improve the manuscript.
REFERENCES
Fig. 18. Probability density functions (logarithmic scale).
as for (C) of Fig. 7, then we have non-Gaussian PDF of the
noise density. In Figs. 17 and 18, the PDFs of measured noise
of
waveform, and two generated noise waveforms by
as in Fig. 15 are compared with PDF of
Fig. 10 and
Gaussian distribution with the same averaged variance. From
the figures, it can be confirmed that the noise generated by
the proposed model and the original measured noise have
almost the same PDF, which has large difference from that
of stationary Gaussian process. This result implies that the
distribution of the noise voltage generated by the proposed
model has the robustness against estimation/approximation
errors in the variance function.
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Masaaki Katayama (M’86–SM’05) was born in
Kyoto, Japan, in 1959. He received the B.S., M.S.,
and Ph.D. degrees from Osaka University, Osaka,
Japan, in 1981, 1983, and 1986, respectively, all in
communication engineering.
He was an Assistant Professor at the Toyohashi
University of Technology from 1986 to 1989, and a
Lecturer at Osaka University from 1989 to 1992. In
1992, he joined Nagoya University as an Associate
Professor, and has been a Professor since July 2001.
He is now a Professor at the Division of Information
and Communication Sciences, EcoTopia Science Institute, Nagoya University.
He was with the College of Engineering, University of Michigan, from 1995 to
1996, as a Visiting Scholar. His current research interests are on the physical
and media-access layers of radio communication systems. His current research
projects include software defined radio systems, reliable robust radio control
systems with multidimensional coding and signal processing, power line communication systems, and satellite communication systems.
Dr. Katayama received the Institute of Electrical, Information, and Communication Engineers (IEICE) (was IECE) Shinohara Memorial Young Engineer
Award in 1986. He is a member of SITA, IEICE, and the Reliablility Engineering
Association of Japan.
Takaya Yamazato (S’90–M’92) was born in
Okinawa, Japan, in 1964. He received the B.S.
and M.S. degrees in electrical engineering from
Shinshu University, Nagano, Japan, in 1988 and
1990, respectively, and the Ph.D. degree from Keio
University, Yokohama, Japan, in 1993.
From 1993 to 1998, he was an Assistant Professor
in the Department of Information Electronics,
Nagoya University, Nagoya, Japan. From 1997 to
1998, he was a Visiting Researcher with the Research Group for RF Communications, Department
of Electrical Engineering and Information Technology, University of Kaiserslautern. From 1998 to 2004, he was an Associate Professor in the Center
for Information Media Studies, Nagoya University. Since 2004, he has been
with the EcoTopia Science Institute, Nagoya Univeristy. His research interests
include sensor networks, satellite and mobile communication systems, CDMA,
and joint source-channel coding.
Dr. Yamazato received the Institute of Electrical, Information, and Communication Engineers (IEICE) Young Engineer Award in 1995. He is a member of
IEICE and SITA.
Hiraku Okada (S’95–M’00) received the B.S.,
M.S., and Ph.D. degrees in information electronics
engineering from Nagoya University, Nagoya, Japan,
in 1995, 1997, and 1999, respectively.
From 1997 to 2000, he was a Research Fellow
with the Japan Society for the Promotion of Science.
In 1999, he was a Visiting Researcher in the Department of Electronics and Electrical Engineering,
University of Edinburgh. From 2000 to 2006, he was
an Assistant Professor at Nagoya University, Japan.
Since 2006, he has been an Associate Professor
in the Center for Transdisciplinary Research, Niigata University, Japan. His
current research interests include the packet radio communications, multimedia
traffic, wireless multihop/multicell networks, and CDMA technologies.
Dr. Okada received the Inose Science Award in 1996, and the Institute of
Electrical, Information, and Communication Engineers (IEICE) Young Engineer Award in 1998. He is a member of IEICE and SITA.