data communication over the smart grid
DESCRIPTION
smart grids ieeeTRANSCRIPT
Abstract—The emerging smart grid system requires high speed
sensing of data from all the sensors on the system within a few
power-cycles. The Advanced Metering Infrastructure is a simple
example of such a system where all the meters on a certain grid
must be able to provide the necessary information to the master
head end within a very short duration (fraction of a second for
real time load control). Wireless solutions for the smart grid
systems have been implemented, but cannot access all grid
locations, especially enclosed ones. In this paper, we present an
interactive, OFDMA based communication system optimized for
operation over the low voltage power lines in the CENELEC
bands A and B. A channel model representing statistical time-
varying, and frequency selective powergrid channels and noise is
presented. Using this model, an OFDMA based transceiver is
developed that is capable of providing smart grid like access
capacity to the head end connected to multiple meters. The
transceiver is optimized based on the channel model and the
characteristics derived from the structure of the grid. Keywords—Smart grid, channel modelling, OFDMA, sub-band
allocation
I. INTRODUCTION
HE efficiency, safety and reliability of the electricity
transmission and distribution system can be improved by
transforming the current electricity grids into an interactive
(customers/operators) service network or the smart grid [11].
Advanced Metering Infrastructure (AMI) provides consumers
with the ability to use electricity more efficiently and provides
utilities with the ability to monitor and repair their network in
real time. Smart grid communication technologies must allow
the powergrid control center to access each meter connected to
it interactively several times in a second, offering dynamic
visibility into the power system. Some implementations exist
of this infrastructure using wireless technologies. In this paper
we explore the use of the existing infrastructure; i.e. the low
voltage power-lines for high speed, reliable simultaneous two-
way communication between the head end (i.e. the nearest
powergrid communication hub) and meters located on
different parts of the network. Data communication through
the power grid offers several advantages in that new
infrastructure is not required, and in principle even enclosed
sensors not accessible by wireless technologies can be read.
This Multi-user communication over the low-voltage power-
lines must deal with several issues such as, large number of
sensors, time varying circuit behaviour, high
background/impulsive noise and varying grid topologies.
In the first part of this paper, we present a channel model
representing statistical time-varying, and frequency selective
powergrid channels. The model views the current grid
configuration as a MIMO/MISO (Multiple Input
Multiple/Single Output) channel. In the second part of the
paper, we use this channel information to develop an OFDMA
based transceiver. For multi-access, the sub-band based carrier
allocation is made based on the uplink channel seen by each
meter. The nature of the uplink channel changes depending
upon location of the meter with respect to the head end and
this adaptation allows us to construct a system that can provide
reliable and fair communication between the meters and the
head end, irrespective of the meter’s location.
Our work extends previous work on integrated meters by Choi
et. al [16] and others by tightly integrating a statistical channel
model with the design of the multi-access physical layer. We
extend Barmada et al [5]’s analysis to include statistical
correlated variations in the channel as seen by the meters in a
smart grid. Compared to multi-access schemes in low voltage
powerline network in the frequency range of 1-20 MHz [15],
we consider the CENELEC bands A and B,. While we
primarily discuss meter reading, our approach actually treats
fundamental communication issues (channel responses,
correlations amongst responses between different transmitter-
receiver pairs, aggregate and minimal capacity) in
implementing ubiquitous sensing in a smart grid.
The paper has been organized as follows. Section II discusses
the MIMO nature of the channel and the correlation between
frequency responses seen by various meters. Section III
analyzes a representative channel in detail. Section IV presents
the OFDMA based transceiver that utilizes the channel
information for sub-band allocation to individual meter.
Section V and VI discuss the simulation environment and
results, followed by conclusions in section VII.
Data Communication over the Smart Grid
G. N. Srinivasa Prasanna1, Amrita Lakshmi
2, Sumanth. S
1, Vijaya Simha
1, Jyotsna Bapat
1 , and
George Koomullil2
1Department of Information Technology, IIITB, Electronics City, Bangalore, India.
2Corporate Innovation & Technology, NXP Semiconductors India Pvt Ltd, Nagawara, Bangalore, India
T
978-1-4244-3790-0/09/$25.00 ©2009 IEEE 273
II. CHANNEL MODEL
Figure 1 depicts the key challenge in simultaneous data
communication over the grid. A grid bus is shown with time
varying loads Z1(t), Z2(t), and Z3(t). The time-variation of
these loads represent primarily the complex frequency
dependent, switching behavior in the CENELEC bands of
residential and commercial powered equipment.
Fig. 1. Time Varying Grid Bus – Only Vertical Impedances Named
For the analysis, these time varying loads are modeled as
random variables. It is assumed that meters/sensors exist at
these same loads, and their (typically large) impedance is
subsumed in the impedances presented by these loads.
Communication has to be simultaneously established between
the meters and the head end located at say, a step down
transformer. The analysis determines the channel responses to
A, HA(f), to B, HB(f), and to C, HC(f), and shows that they are
correlated and time-varying, exhibiting in general non-
Rayleigh fading behaviour. This extends the work of Barmada
et al, [5] where bounds on time-varying channel responses
using wavelets are presented, but correlations are not
discussed.
We shall analyze this MISO channel based on transmission
line theory. Our analysis treats MISO communication between
the root and the leaves of a tree structured bus with branches.
Now, any node in a tree can be treated as the root. Hence the
same analysis is applicable to the MIMO channel - when
meters/sensors talk to each other simultaneously. The signal is
additionally impacted by colored background noise and
impulse noises in time and frequency domains. Details of these
models are discussed next.
A. Channel Frequency Selectivity
From transmission line theory, the propagation of the
incident and reflected waves is governed by the matrix
equations relating the sending and receiving end voltages and
currents Vs, Is and VL, IL, as [7]
cosh( ) sinh( )0
1 sinh( ) cosh( )
0
l Z lVV
SLl lI IZL S
γ γ
γ γ
−
= −
(1)
( )( )R j l G j C jγ ω ω α β= + + = +
where α is the propagation constant and β is the phase constant
and fπω 2= where f is the frequency. The input impedance
is given by
cosh( ) sinh( )
00 cosh( ) sinh( )
0
Z l Z lLZ Zin
Z l Z lL
γ γ
γ γ
+=
+
(2)
Propagation in tree networks (Figure 2) can be analyzed using
this matrix equation to recursive propagate the leaf
impedances to the source, and the signals to the leaves from
the source using voltage/current division (Equation 4 below).
Given the wide variety of power-grid topologies, the channel
responses are variable, and details are presented in Section II
and III. Given LT grid dimensions of a few kilometers
between transformers and the load, multiple nulls can be
expected in the CENELEC band stretching to 125KHz.
Impulse responses ranging to 0.5 milliseconds or more can
occur. Signal attenuations can be easily 60+ dB. The
transceiver system has to robust to these impairments.
B. Channel Statistical Behavior and Dynamics
Not only is the channel frequency selective, but the
switching on/off of loads causes fading. This fading is
however, unlike the classical Rayleigh fading, since it is due to
time-varying circuit elements. Strictly speaking, time-varying
loads cause nonlinear behaviour, and Fourier analysis is not
directly applicable. However, if the nonlinearity changes
slowly relative to the frequencies of interest, then we can use a
quasi-static approximation, and use Fourier analysis, with
time-varying and stochastic impedances. Our analysis below is
based on this quasi-static approximation.
Figure 2 shows signal propagation through the ith node (load
and meter) (i=0,1,2, …) of a tree branch. Using Equations 1,
and 2, the complex transfer function Hi(f) from the head-end
to the ith node, and equivalent impedance Z
ieq(f,t), can be
calculated.
Figure 2 Recursive Analysis of a Tree Branch, H(i)(f) is the transfer function
from the source to node i at frequency f. All impedances are time-varying.
Using the relations between voltage and current at node i,
( ) ( ) ( ),i i i
V f Z f t I fL= (3)
Hi(f) can be calculated. We have explicitly indicated the
time varying and frequency-dependent nature of the impedance
Z1(f) Z
i+1eq(f)
Head
End
ZLi+1
(f) ZL(f)
Z ieq(f)
ZLi (f)
H(i)(f)
Z1(t) Z2(t) Z3(t)
A B C
Head
end
Hi+1(f)
274
as ( )1,
iZ f t
L
+above. Under quasi-static assumptions, the
impedance will be modeled as a sample of a time-invariant
impedance ensemble, drawn from an appropriate distribution.
We shall denote this random variable (which is a function of
frequency), as ( )1iZ f
L
+. Using equations 1, 2, and 3, it is
easy to show that, Hi(f) is given recursively (voltage division
in Equation 1) in terms of transfer function to the (i-1)th node,
Hi-1
(f) as
( )( )
( )
( ) ( ) ( ) ( )( )
( )( )
( ) ( ) ( )( )
1* ( ) * ( )
0
1* ( ) * ( )
0
1
cosh sinh0
/
iZ f Cosh l Z Sinh l
eqiZ f
in iZ Cosh l Z f Sinh l
eq
i i i iZ f Z Z f Z f Z f
eq L in L in
iZ f
eqi iH f H
iZ f l Z l
eq
γ γ
γ γ
γ γ
++
=+
+
= +
−=
+
(4)
where ( )1i
eqZ f+ is the equivalent impedance seen towards
the leaves at the (i+1)th node (Figure 2). The impedances are
calculated in the backward recursion, and the transfer
functions in the forward direction. We reiterate that our
analysis is a quasi-static approximation, since all the
impedances in Equations 3 and 4 are time-varying.
Since the impedances in Equation 4 are random, so is the
transfer function. Furthermore, due to the recursion, the
channel response at different meters is correlated, and exhibits
complex fading dynamics. The correlation is also frequency
dependent. It should be noted that the same equation can be
used for branched structures. The correct statistical behaviour
of the equivalent impedance at each branch point has to be
determined, and the recursion executed. If two branches are
statistically similar, they each lose 3dB in signal, and hence 1
bps/Hz in the maximal (Shannon) capacity.
Equations 3 and 4 can be numerically solved to determine the
joint probability distribution of the (complex) transfer function
at some or all points. Alternatively, Monte-Carlo simulations
can be used to estimate various parameters of interest (mean,
correlations, etc - our work has used this approach).
Additionally, under special cases of the probability distribution
of the loads, ranging from a 2-state Markov process (on-off
loads) to a uniform load, closed-form solutions are possible for
single stage networks. If the load is 2-state Markov, so is the
transfer function, but in other cases, the p.d.f of the transfer
function differs from that of the load. Details are skipped for
brevity. These equations are used in Section III to get
theoretical insight into the communication potential of the grid
in the CENELEC band.
C. Channel Noise
Noise measurements on power lines Hooijen [3] have shown
that the background noise in power line channels is colored,
with the noise power spectral density (PSD) decreasing with
increasing frequency. The PSD of the background noise can be
approximated as in [3],
kHzWfN HzfxK /10)( )/1095.3( 5−−= (5)
where, K follows a Gaussian distribution with mean µ = -5.4
and standard deviation, σ = 0.5. This is used to model the
colored noise in the simulations.
D. System Capacity Estimation
Based on the channel responses to different nodes as per
equation (4), the noise as per equation (5) and a given transmit
power, the received SNR at each node, and hence the
(frequency dependent) limiting channel capacity can be
calculated as per Shannon’s formula. These results are used to
evaluate the actual implementation of our OFDMA system
with respect to the theoretical bounds.
III. MODEL RESULTS
Equations 1 through 4 characterize the performance of the
system of multiple nodes (meters) communicating to a head-
end over the power-grid. We reiterate that while the equations
have been written for a single branch, the recursive
decomposition of a tree structure enables them to be used for
arbitrary trees. Since any tree node can be treated as the root,
the same can be used, for estimating channel performance
between any two points, in either direction. Hence Equations 1
through 4 represent a general MIMO channel, where the
impedances at the ith
node are computed from a leaf node to
the node chosen as the root.
For analyzing the fundamental properties of this channel, a
representative structure has to be chosen. We chose to analyze
a section with 10 meters, corresponding to the longest branch
in the structure used in Section IV (corrections for transmit
power at each branch are 3dB, as already mentioned). We
assume that the transmitter uses 1 Watt of power over the
entire CENELEC band, corresponding to a per channel power
of 0 dBm in our 1024 channel OFDMA system described later.
The noise is as per Equation 5 from [3]. Equations 3 and 4 are
used in a Monte Carlo simulation for channel analysis. Loads
are randomly selected from a uniform distribution, with a
maximum up to ten times the characteristic impedance.
Statistical parameters like min/mean/max of the transfer
function, Shannon capacity, etc are estimated from the
simulation. We also estimate the minimum simultaneous rate
of transmission between all the meters and the head-end, by
allocating larger spectrum to meters with high
attenuation/poorer SNR.
275
A. Channel Dynamics: Mean Attenuation & Capacity
Figure 3: Transfer function bounds (min, average, max) as a function of
frequency for 10 meter section
Figure 4. Received SNR and spectral density (Bps/Hz) in CENELEC band
Figure 3 shows the minimum, average, and maximum of the
transfer function as a function of frequency in the CENELEC
band,. Figure 3 shows that while the mean attenuation for the
1st meter is less than 10 dB, the maximum attenuation can go
as high as 50 dB. For the last meter in the span, attenuation
ranges from 25 dB to 80 dB at the lower band edge, and from
40 to 140 dB at 125 KHz. Note that these are the limits of
channel responses, and do not necessarily correspond to any
specific channel. Indeed resonant loads can cause the response
to increase with frequency, and this will be shown in Section
IV. Figure 3 shows that attenuation can be excessive in bad
cases, for spans 10 meters or more deep. Mesh architectures
may have to be used in these cases.
Figure 4, which plots average system spectral density
(bps/Hz) shows that the close by meters can reach very high
spectral densities of 15 Bps/Hz at the higher band edge, while
far off meters can manage 1-2 bps/Hz at the lower band only.
Figure 5 shows aggregate system capacity. It shows that the
aggregate capacity can be as high as 1 Mbps+ for the closest
meter, decreasing to less than 20 Kbps for the last meter, if the
entire CENELEC band is allocated to the respective meter.
The cumulative capacity over all 10 meters is about 5 Mbps.
Figure 6 shows minimum rate available over all meters,
decreases from 1 Mbps+ to about 7 Kbps if 10 meters are
transmitting simultaneously. If even more meters communicate
simultaneously, capacity drops dramatically. These results
indicate that powergrid with sections composed of more than
about 10-15 meters have to adopt mesh architectures, with
multi-hop communication.
Figure 5: Available Total Capacity at each Meter While we have discussed a sample grid configuration, clearly
the approach using the recursive equations is valid for general
structures.
Figure 6: Minimum rate (Kbps) at which all meters can simultaneously
transmit, as a function of number of meters simultaneously transmitting.
B) Channel Correlations
From the classical results of Foschini et al [6], MIMO
channels are characterized by the correlation between the
transfer functions of different channels. Since the signal
propagates sequentially down the grid, the transfer function to
different taps is correlated, impacting MIMO performance. We
can compute the covariance coefficient to different taps as
( )( ) ( )( )( ) ( ) ( )( )( )
( )( ) ( )( )
*i i j j
ij i j
H f E H f H f E H fK f E
Var H f Var H f
− −
=
Monte-Carlo simulations based on Equations 3 and 4, using
random impedances, are used to determine Kij(f). The results
276
indicate that correlation is high between different nodes at low
frequency (9 KHz), where the correlation coefficient is close
to unity everywhere. At such a low frequency, the entire
network behaves like a resistive system. Correlation
progressively decreases as frequency increases (125 KHz),
with a minimum less than 40%. Details are skipped for brevity.
IV. OFDMA SYSTEM
Orthogonal frequency division multiple access (OFDMA)
systems have been in use for various wireless systems
including WiMax and 3GPP systems for optimizing the
simultaneous use of available bandwidth for data transmission
from mobile stations to the base station. A unique subset
(referred to as a sub-band) of the available subcarriers is
assigned to each user in an OFDMA system for the
simultaneous transmission of data. The most prominently used
allocation schemes are interleaved OFDMA and sub-band
based OFDMA. Though the interleaved assignment benefits
from frequency diversity, it is shown to be more sensitive to
errors in frequency offset estimation [12]. The sub-band based
assignment divides the available bandwidth into a number of
sub-bands and assigns them to different users. This scheme
may see performance degradation when any of the sub-bands
sees a long, deep null.
We propose an OFDMA system (Fig. 7) for the smart grid
with multiple meters, which uses an allocation algorithm based
on the SNR seen by each meter in individual sub-bands during
channel estimation and aims to maximize the data rate of all
meters fairly and uniformly. It should be noted that the goal of
the algorithm is uniform access capability for all meters and
not maximizing the overall data rate.
The performance metric to be maximized for sub-band
allocation attempts to simultaneously increase SNR, as well as
reduce differences between SNR seen by different meters. One
possible metric achieving this can be defined as:
21 SNR
SNR
σ
µ
+=Γ (6)
smSNRSNR
N
i
jim
SNR
jNjj
NjNiQE
QN
QE
QQQQ
m
mNm
,...,1,,...,1],)[(
1)(
,........,,
22
1
ˆ,
,,2,1^^
2
^
1
==−=
==
=
∑=
µσ
µ
where Nm denotes the number of meters in the grid, Ns denotes
the number of available sub-bands . The average SNR for ith
meter in jth
sub-band is denoted as SNRij. For each meter i, the
best possible sub-band of index j is selected with effective
SNR ofji
Q ˆ,. µSNR is the average of the effective SNRs seen by
each meter over its assigned sub-band of operation.
Maximizing Γ is a balance between high average SNR, and
low variance between quality of communication link seen by
different meters on the grid irrespective of their distance from
the head end.
SNR based sub-band allocation algorithm:
The sub-band allocation function allocates sub-band j to
user i such that the metric Γ is maximized. For simplicity, it is
assumed that sm NN = or one sub-band is available per meter.
Xij is the SNR seen by meter i in subband j.
1) Initialization
},...,1{ mNI = , },...,1{ sNJ = , Xij = zeros(Nm,Ns)
ijij SNRX = , JjIi ∈∀∈∀ ,
2) For: mNi ,...,1=
∑=
=sN
j
ijtotali XX
1
3) while ≠I Ø, J ≠ Ø
)(minminˆ
totaliii
XP =
min min
max ( )ˆ ˆ ˆ,Q Xji j i j
=
}ˆ{
}ˆ{ min
jJJ
iII
−=
−=
The algorithm first selects the meter with lowest total SNR
across all sub-bands and assigns the sub-band with highest
SNR to that meter. The meter and the sub-band thus assigned
to it are removed from the set of meters and sub-bands and the
process continues till all the meters are assigned a sub-band.
Faraway meters experiencing hostile channel characteristics
are allowed to choose first and are allocated best sub-bands for
the channel they are facing, thereby achieving the goal of best
possible connectivity for all meters, irrespective of their
physical location.
Figure 7. Block diagram of an OFDMA system for simultaneous transmission
of data from meters to the head-end
277
V. A SAMPLE GRID
The configuration of the power line grid used in the current
study is given in Figure 8, with meter Mi having (resistive)
impedance Zi. For clarity, we label the meter by its impedance
only.
Zs
Z1
T1 T10T7T5T3T2 T18T14 T15 Z20
Z14
Z11
Z8
Z3
Z4
Z15
Z17
T16Z6
Z5
T6
T17 Z16
T8Z7
T12
T11 Z10
Z12
T13 Z13
T19Z18
Z19T9 Z9
277m
333m
452m224m
Z2
321m
481m
448m
293m
485m
208m
122m
454m
399m
197m
150m
398m
122m
155m
219m
411m
257m
367m338m
148m
368m 334m
137m
123m
417m
142m
372m
104m
442m
453m
106m
120m
412m
T4
135m
T --- Taps
Z --- Meter Impedances
Z1 - 141
Z2 - 493Z3 - 300
Z4 - 142
Z5 - 654
Z6 - 554Z7 - 428
Z8 - 255
Z9 - 410
Z10 - 443Z11 - 655
Z12 - 647
Z13 - 549
Z14 - 528Z15 - 690
Z16 - 638
Z17 - 335
Z18 - 224Z19 - 562
Z20 - 133
Figure 8. The grid configuration used in the current study.
This sample powergrid consists of 20 meters downstream of
a transformer Zs. The available frequency band from 9 kHz to
125 kHz has been divided into 1024 channels, with channels
width of 113.28 Hz. Of the 1024 channels, 800 channels are
used for upstream data transmission by 20 meters (from which
sub-bands consisting of 40 distinct carriers each are assigned
to each meter). Two preamble OFDM symbols are used for
channel estimation and carrier acquisition. With inclusions of a
cyclic prefix of 256 samples, the total transmission time per
burst with two preamble symbols and two OFDM symbols is
approximately 44 ms. It should be noted that the difference in
propagation time from different meters is in microseconds and
is considered negligible in comparison to the RMS delay
spread due to signals reflections of multipath channels.
The responses of the channels from each meter placed on
the leaf node of the grid configuration to the concentrator are
estimated using Equations 3 and 4 in Section III. The impulse
and frequency responses of these channels are plotted in
Figures 9 and 10.
Figure 9. Impulse responses of all channels obtained for the grid
configuration.
Figure 10. Frequency responses of all channels obtained for the grid
configuration.
VI. SIMULATION RESULTS
Simulations were conducted using Matlab with the
parameters of the OFDMA system as discussed in previous
section. A sub-band of 40 adjacent subcarriers, is assigned to
each meter using two types of sub-band allocation techniques.
The first technique uses the sub-band allocation algorithm
discussed in section IV to allocate appropriate sub-bands to
the meters. The second one allocates the sub-band randomly.
Background colored noise, as discussed in [3] is used in the
simulations.
The minimal bit rate achieved at a BER of 10-3
is about 2
Kbps/meter, which is 30% of the predicted bound of 7Kbps
from our model in Figure 6. The total available capacity
(entire band) at each meter (Mi with impedance Zi from Figure
8) is about 1Mbps at the first meter, consistent with Figure 5.
This shows that even simple systems like the one proposed can
perform reasonably well.
The BER performance for each meter using both mappings
are plotted versus the transmit power for each meter in figures
11 and 12. The figures show a more consistent BER
performance for each meter using the sub-band allocation
technique. The metric for SNR-based allocation algorithm was
found as 1.7489 and for the random allocation as 0.0980.
These results are consistent with the goal of the system, which
is uniform and fair access for all the meters, rather than high
overall bit rate. Further improvements can be achieved by
uneven sub-band allocation to the meters and powerful error
correction codes such as LDPC [14]. It should be noted that
current results are for un-coded BPSK data, coding techniques
yield even better results.
VII. CONCLUSIONS
We have investigated the potential of Low Voltage Power
Lines for real time communication, satisfying the requirements
of a smart grid monitoring system. A statistical time-varying
channel model has been developed, and using which, a
multiple access scheme in the form of OFDMA with
appropriate sub-band allocations has been proposed.
Appropriate sub-band allocation has been shown to be of
278
paramount importance in gaining access to all the meters
simultaneously. Channel capacity bounds have been evaluated
using the model, and the transceiver performance is shown to
approach those bounds. For realistic channel topologies,
minimal capacities of a few Kbps per second per meter can be
achieved with 20 meters simultaneously transmitting at a total
channel power of 1 W. Further improvements using
sophisticated bit loading techniques and FEC codes are
currently under investigation. Our analysis yields insight into
the general MIMO problem, encountered when ubiquitous grid
sensors communicate with each other.
-10 -5 0 5 10 15 20 2510
-4
10-3
10-2
10-1
Transmit power(dBm)
BE
R
Performance of 20 meters using OFDMA with SNR-based sub-band allocation
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
Figure 11. Performance of 20 meters with SNR-based sub-band allocation.
-10 -5 0 5 10 15 20 25 30 35
10-3
10-2
10-1
100
Transmit power(dBm)
BE
R
Performance of 20 meters using OFDMA with random sub-band allocation
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
Figure 12. Performance of 20 meters with random sub-band allocation
REFERENCES
[1] D. Cooper and T. Jeans, “Narrowband, low data rate communications
on the low-voltage mains in the CENELEC frequencies-part I: noise and
attenuation,” IEEE Tr. Power Delivery, vol. 17, no. 3, July 2002.
[2] M. Zimmerman, K. Dostert, “A Multipath Signal Propagation Model for
the Power Line Channel in the High Frequency Range”, Proc. of 3rd
Int’l Symp. Power Line Comm. and its Applications, 1999, pp. 45-51.
[3] O. G. Hooijen, “A channel model for the residential power circuit used
as a digital communications medium,” IEEE Tr. Electromagnetic
Compatibility, vol. 40, no. 4, pp. 331-336, November 1998.
[4] “Signalling on low-voltage electrical installations in the frequency range
3 kHz-148.5kHz, BS Standard EN50065-1:1992, 1992.
[5] Bramada, et al, “Innovative Model for Time-Varying Power Line
Communication Channel Response Evaluation”, IEEE JSAC, July 2006,
pp1317-1326
[6] G.J.Foschini and M.J. Gans,"On Limits of Wireless Communications in
a Fading Environment when Using Multiple Antennas", Wireless
Personal Communications, vol.6,pp.311-335, 1998.
[7] Edward C. Jordan, Keith G. Balmain, Electromagnetic Waves and
Radiating Systems, Prentice Hall, 2005
[8] Z. Mingyue, “Channel Measurements and Channel Characteristics of
LV Power Line Communications Networks in China”, Proc. IEEE-
ISPLC2006 Orlando, FL.
[9] Guerrini et. al. “Homeplug AV system and DLC bit loading algorithm
over Opera power line channels with impulsive noise”, ISPLC 2008.
[10] Bausch et. al. “Characteristics of indoor power line channels in the
frequency range 50-500 kHz”, ISPLC 2006, pp. 86-91.
[11] “The Smart Grid: an Introduction”, prepared for the U.S. Department of
Energy by Litos Strategic Communication
[12] Z. Cao, U. Tureli, Y. Yao, “Deterministic Multiuser Carrier-Frequency
Offset Estimation for Interleaved OFDMA Uplink”, IEEE Transactions
on Communications, Vol. 52, No. 9, Spetember 2004.
[13] J.M. Choi, J.H. Lee, “Sounding subband allocation algorithm for
proportional fair scheduling in OFDMA/FDD uplink”, Electronics Letters 26
th April 2007, Vol. 43, No. 9.
[14] Andreadou, N. Assimakopoulos, C. Pavlidou, F.-N, “Performance
Evaluation of LDPC Codes on PLC Channel Compared to Other Coding
Schemes”, Proc. ISPLC 2007, Pisa.
[15] S. Gault, P. Ciblat, W. Hachem, “An OFDMA based modem for power
line communications over the low voltage distribution network”, ISPLC
2005.
[16] M. Choi, S. Jui, Y. Lim, "Design of integrated meter reading system
based on powerline communication”, ISPLC 2008.
279