ABSTRACT
This work presents original developed methods, belonging to the soft computing area, that have been applied to solve complex signal processing problems arising in communication systems with “adverse” conditions. The adverse conditions are given by the fact that the considered physical channel is non-linear, non stationary, and the noise is coloured impulsive noise. Modified vector quantization algorithms have been developed for adaptive channel estimation and equalization inside a digital transmission. An unsupervised hierarchical clustering method based on fuzzy partitions has been proposed and application to identification of different noise sources is discussed. The presented soft computing techniques have been developed within the area of digital communication, nevertheless they posses general applicability.
LIST OF PUBLICATIONS
1. Raugi, M.; Tucci, M., "Power-line communications channel estimation and tracking by a competitive neural network,"
Consumer Electronics, IEEE Transactions on , vol.52, no.4,
pp.1213-1219, Nov. 2006
2. Musolino, A.; Raugi, M.; Tucci, M., "Cyclic Short-Time Varying Channel Estimation in OFDM Power-Line Communication," Power
Delivery, IEEE Transactions on , vol.23, no.1, pp.157-163, Jan.
2008
3. Tucci, M.; Raugi, M.; Musolino, A.; Barmada, S., "Blind Channel Estimation for Power-line Communications by a Kohonen Neural Network," Power Line Communications and Its Applications, 2007.
ISPLC '07. IEEE International Symposium on , vol., no., pp.35-40,
26-28 March 2007
4. Tucci, M.; Raugi, M.; Capetta, L.; Tornelli, C.; Napolitano, R., "A Fuzzy-Logic model for impulsive noise in PLC," Power Line
Communications and Its Applications, 2007. ISPLC '07. IEEE International Symposium on , vol., no., pp.87-92, 26-28 March
2007
5. Tucci, M.; Raugi, M.; Musolino, A.; Barmada, S., " Nonlinear Decision Feedback Estimation for Multicarrier Power Line Communication," to be published in Power Line Communications
and Its Applications, 2008. ISPLC '08. IEEE International Symposium on
6. Barmada, S., Gaggelli, A, Musolino, A.; Rizzo, R, .; Raugi, M.; Tucci, M " Design of a PLC system onboard trains: selection and analysis of the PLC channel," to be published in Power Line
Communications and Its Applications, 2008. ISPLC '08. IEEE International Symposium on
CONTENTS
Abstract ... I
List of publications ... III
Contents ...V
Introduction... 1
1 Power line network as a Broadband communication channel.
... 5
1.1 Power line channel modelling ... 6
1.1.1 Channel frequency response simulation, transmission line theory... 7
1.1.2 Example of a realistic indoor apartment power line network ... 10
1.1.3 Experimental model validation ... 13
1.1.4 Cycle-stationary channel... 19
1.2 Impulsive noise in power lines ... 22
1.2.1 Impulsive noise in low voltage power grids... 22
1.2.2 Impulsive noise in MV-HV power grids ... 23
2 Communication system ... 25
2.1 OFDM Transmitter and Receiver ... 25
2.2 OFDM Signal Through Third-Order Nonlinearity ... 27
3 Adaptive algorithms for channel estimation and equalization
... 32
3.1 Nonlinear decision directed estimation ... 32
3.1.1 Basic NDDE algorithm ... 34
3.1.2 Algorithm initialization ... 39
3.1.3 State changes detection ... 40
3.1.4 Adaptive learning rates ... 40
3.1.5 Results ... 42
3.2 Estimation Scheme in presence of HPA nonlinearity... 51
3.2.1 Channel Estimation and Detection Block in the OFDM receiver ... 51
3.2.2 Modified SOM for detecting symbols ... 53
3.2.3 Nonlinear feedback ... 55
3.2.4 Channel estimation and SOM updating ... 56
4 Unsupervised Noise Clustering... 61
4.1 Measuring system... 62
4.2 Clustering of time series data ... 63
4.3 Features extraction ... 65 4.4 Clustering... 68 4.5 Noise model ... 73 4.6 Considerations ... 74
Conclusions ... 76
References ... 77
Publications ... 81
INTRODUCTION
The area of communications is rich of interesting and significant applications, where the imprecise and uncertain nature of the problems makes the use of soft computing techniques an attractive solution strategy.
Power-line communications (PLC) have been rapidly developing in the last years as one of the most promising technology to provide competitive techniques for numerous in-home communication applications, such as fast Internet access, home automation and telephone service. Many marketed devices are capable to reach average transmission speed of about 30 Mbit/sec in residential low voltage electrical installations.
Beyond the significant potential of this technology, some scepticism about the possibility of further increase of the present transmission speeds still exists. These problems concern the increasing demand for "Band" and the real commercial value of the PLC compared with other available technologies (xDSL, Wi-Max, etc.. etc.). Among the technical issues (still under study) that may affect these assessments it could be highlighted the complexity of the transmission channel, which is selective in frequency, time variant and produces stationary and impulsive noise; and the presence of national and international rules that restrict the power of the transmitted signals (electromagnetic compatibility problems).
Nowadays, one of the most promising applications of the PLC technology is its use aboard vehicles. Indeed, in modern transport systems, trains, planes, cars and ships it is increasing the presence of electronic equipment to proper control the handling of the vehicle (for example to control the stability and braking systems of cars, planes and ships) and even for the entertainment of passengers (e.g. video transmissions on board of planes or ships). Currently, the solution used to control these electronic or electromechanical devices is to install a dedicated cable for each of them. In this way there are dozens of cables of hundreds of meters length, located on board of these vehicles. Consequently, the complexity in wiring these heavy and cumbersome cables has become a major problem in design of these vehicles in order to reserve most possible space for passengers.
The use of powerlines to transmit data could thus eliminating this problem, since it would remove all cables for command and control currently used with enormous advantages in terms of simplification of the wiring cables, and save space and weight.
Since all the PLC systems exploit the electrical cables as a communication channel, the issues that their realization meets in different types of electrical installations are similar and they are usually related to the following topics:
1. Identification of circuits capable to couple, in the most efficient way, the signals to be transmitted to the transmission channel;
2. Identification of techniques for the reduction of electromagnetic fields in the surrounding environment;
3. Estimation of changes in the transmission channel in order to have the maximum possible data transfer speed;
4. Classification of noise in the channel; 5. Optimization of bit-loading algorithms. 6. Optimal data modulation.
About the last point that affects all the other ones it can be noted that multicarrier systems have emerged as preferred candidates for a variety of PLC applications, allowing higher symbol rates to become attainable. Amongst various implementation approaches, orthogonal frequency-division multiplexing (OFDM) systems stand out owing to their superior performance over frequency-selective channels, their resilience to inter-symbol interference, and their ease in hardware realization by means of fast Fourier transform (FFT). OFDM is nowadays being selected as the transmission scheme for the majority of new communications systems.
Each of these issues can be associated with one aspect of a PLC system that requires specific skills and dedicated techniques that usually are deeply studied by working groups that have diversified knowledge (circuit theory, identification and classification of the signals, electromagnetic compatibility, etc.).
In this work topic 3 and 4 are mainly addressed.
With regard to topic 3 , the current research motivation is based on the fact that classical linear approaches to channel estimation and equalization reveal their limits in PLC, and the use of soft computing techniques is an emerging tendency [1],[2] The estimation of changes in the channel is related to the problem of tracking the time variation of frequency response. The strong variation in time of the transmission channel can greatly reduce the efficiency of the system because some frequency bands used for the transmission can be randomly unavailable. Then, it is necessary to be able to move some subcarriers from one frequency channel to another in order to maintain the same transmission speed. Some consolidated techniques used for this purpose are based on a periodic sending of "pilot" signals (with known characteristics), and their reception on the basis of which it is possible to rebuild the frequency response by the use of interpolation techniques or the minimum mean squared error-base estimation. However the commonly used equalizer assumes that the channel is time constant in the period
between two different channel estimates; thus, it may be unable to fully compensate the typical time-variant behaviour of the PLC channel. An adaptive, decision-directed estimation procedure is desired to continuously follow the channel alterations. A number of decision-directed estimation techniques have been proposed for wireless OFDM systems, but to the author knowledge a minor effort has been carried out for exporting, analyzing, and optimizing these techniques in the PLC networks’ environment.
In this work neural network based methods for channel identification and tracking are presented [3], [4], [5], [6]. These methods are able to maximize the transmission speed without the use of the "pilot" signals, but working directly on the transmitted useful signals.. In particular two novel algorithms are developed for blind channel estimation and equalization under an OFDM transmission. A first contribution is the development of an adaptive estimation-equalization method, denominated NDDE, where the focus is put on tracking the time variation of the channel. The proposed scheme is a competitive neural network which utilizes the frequency domain data in the receiver performing a decision-directed estimation. This adaptive algorithm is developed for a QPSK OFDM transmission The analysis is focused on the compensation of the distortion caused by the channel variations and by a nonlinearity at the transmitter. Generally nonlinear distortions are introduced by the clipping of the transmitted signal and/or by using the high power amplifier (HPA) near to the saturation where the response is nonlinear. The proposed NDDE algorithm attempt to compensate to the effects of this nonlinearities assuming that their characteristics are unknown to the receiver.
In a second moment the nonlinearity is thought to be a known memory-less distortion at the transmitter side caused by the high power amplifier. A second algorithm is developed for this situation, denominated SANDDE, where the channel tracking is accomplished by a standard LMS (least mean square) estimator, while the nonlinear compensation is delegated to a modified self organizing map (SOM), [7]. In this second algorithm the known nonlinear characteristic of the HPA is used by the equalization algorithm at the receiver, performing an iterative decoding of the received symbols. The algorithm permits the augment of the dimension of the QAM constellation with a minor increase of the computation complexity with respect to the previous method. Proposed algorithms follow a blind approach and do not require the use of pilot tones during the transmission. The performance of the proposed methods has been validated by simulations of the digital transmission using a rigorous PLC model, which is described in the first chapter of this thesis. Publications [3],[4],[5] and [6] report a detailed treatment of the new introduced methods.
The topic 4 concerns the identification and classification of noise present in electrical installations [8] - [10]. Knowledge of this noise is of fundamental
importance to increase the efficiency of the transmission system. Typically the noise existing in a PLC system is non-Gaussian noise and his knowledge and classification can significantly contribute to improve the performance of the system. The various proposed models can be divided into two types: the simplified ones (stationary models) based on a function of probability density like that of Middleton; or the most realistic ones (non-stationary models) which classifies the noise on the basis of its performance in the time domain or on the basis of recent techniques, using the Markov chains or fuzzy-sets.
In this work a fuzzy-logic based model for noise classification is presented [11]. Noise at transient and emergency operation and strong asynchronous impulses are observed in high voltage power lines, but little is known about their frequency characteristics [10],[17]. In this study a first attempt to classify this kind of noises on the basis of their frequency behaviour is accomplished. An unsupervised clustering technique has been developed to identify and classify different kinds of impulsive noise sources affecting the outdoor high voltage power line channel. Clustering of the time domain data is preformed by a feature-based approach and the proposed hierarchical classification procedure is based on the Fuzzy-C means algorithm. Several types of disturbances are recognized, arriving from different kinds of excitation.
1
POWER LINE NETWORK AS A BROADBAND
COMMUNICATION CHANNEL
Broadband over power lines (BPL), also known as power-line Internet or Powerband, is the use of PLC technology to provide broadband Internet access through ordinary power lines. The main technical challenge regarding BPL is the complexity of the power network, which is designed for carrying high power signals at low frequency from few injection points to a high number of receivers, while the communication signals are typically high frequency - low power signals to be carried from point to point. Hence when an indoor power line is used as a communication channel two superimposed voltages are found: a large low frequency signal used for the energy distribution (typically 230V and 50 Hz in Europe) and a small amplitude signal, typically 1-5V, with frequency contents from 0.5 to 30 MHz that (properly modulated) carries the information, as depicted in Fig 1.
In general in standard BPL applications, the power line discontinuities (variable cable section, parallel junctions etc), the presence of transformers and load mismatch create a strong attenuation of the signal. The attenuation rate at the frequencies typical of the most used protocols is generally high and frequency dependent. An additional, yet important, characteristic is that the power network is dynamic: loads can be connected and disconnected, changing the channel characteristics, hence the frequency response of the channel varies with time in a random way. Moreover many common loads are characterized by an impedance variable with the mains voltage, adding another important cause of channel variation. Hence the time-varying behaviour of indoor power-line channels is substantially produced by two causes. The first one is the connection and disconnection of electrical devices at the sockets and determines long-terms variations. The other one is related to the nonlinear behaviour of some electrical devices with respect to the mains voltage and produces short-time variations that are synchronous to the mains [12].
Moreover power lines are inherently a very noisy environment. For instance every time a device turns on or off, it introduces “pops and clicks” into the line, generating single impulses or a burst [13].
Fig 1. The Power line grid as a communication channel
1.1
Power line channel modelling
A link between two points is established by connecting (via a proper coupling network) the transmitter and the receiver at two sockets of the power grid. The link so obtained is time and frequency variant. Despite the short distances usually involved in indoor grids, the attenuation is very high because of the highly branched topology of the power network, which in conjunction with the impedance mismatching, generates a multipath propagation that characterizes a PLC link as a strongly fading channel
Communication systems for BPL need an accurate knowledge of the actual channel they are communicating on, in particular precise and continuously updated information on the frequency response is of vital importance to the health of the communication. Since the power line channel is strong time variant, a continuous real-time frequency channel estimation is needed by the communication devices, which in general are not aware of the network topology, nor of the state of the connected loads. In particular, from the communication system point of view, the power line network is a black box, whose frequency response needs to be identified, and in general this is achieved following two different strategies. The more common one is based on a supervised approach, with the insertion of pilot signals by the transmitter, while recent techniques use an unsupervised approach, estimating the channel directly from the received data. Thus, accurate power line channel models, like the one described in the next paragraphs, are needed only for research and for protocol analysis and development, and they are not to be confused with the internal model that PLC modems needs for an efficient transmission in a power-line channel.
The explicit power-line channel modelling can be performed following two different approaches: either starting from a complete measurement campaign ([13] - [15]) or starting from an analytical approach ([16] - [19]). In the latter case a statistical analysis to take care of the channel variation is also needed.
As clearly stated in [19], it is impossible to have an accurate knowledge of the whole link topology, including the loads. For this reason, it is common practice to construct the channel model (or validate a model based on analytical approaches) by several and accurate measures performed on existing components. The approximate models so obtained are characterized by a certain degree of uncertainty that affects the overall accuracy of the model of the PLC system. As a general matter of fact measurement-based approaches (typically referred to as top-down approaches) cannot be used to predict the transfer function. On the other hand, analytical approaches that are generally based on transmission line theory (bottom-up approaches) are able to predict the transfer function only if detailed knowledge of the whole topology is available. This knowledge can be considered the price to pay to be able to predict channel behavior. Moreover, these bottom-up approaches, whether useful in practice or not, are an important step toward a better understanding of signal propagation along power lines.
In this work a rigorous bottom-up model of the power line frequency response based on the theory of transmission lines is presented and experimentally tested for the numerical simulation of a PLC digital communication system.
1.1.1 Channel frequency response simulation, transmission line theory
Every link of the power line network is considered a transmission line with frequency dependent per-unit-length parameters r
Z
,lZ
,gZ
,cZ
and length L .The well known transmission lines equations in the frequency domain are the following:
( ) ( ) ( ) ( ) V z r j l I z z I z g j c V z z
Z
Z Z
Z
Z Z
w °°w ® w ° °w ¯ , (1)0 ( ) ( ) ( ) ( ) 0 V z r j l V z V z z g j c I z I z I z z
Z
Z Z
Z
Z Z
w § · ¨w ¸ § ·§ ¨ w ¸ ¨¨ ¸¨¸¨ ¨ ¸ © ¹© ¨w ¸ © ¹ M · § · ¸ ¨ ¸ ¸ ¨ ¸ ¹ © ¹ (2)which, for fixed
Z
is a system of first order ordinary differential equations, where the 2X2 complex dynamical matrix Mis implicitly defined in (2). The voltage
V z and the current I z
in (1) and (2) are the phasors of the electrical quantities along the line for a specified frequency.
Given an initial condition for the voltage and the current at the input port of the transmission line
1 1 0 0 V V I I ° ® °¯ ,
the solution of (2) is given by
11 z V z V e I z I § · § · ¨ ¸ ¨ ¸ ¨ ¸ © ¹ © ¹ M (3) If the length of the transmission line is
L
, the voltage and the current at theoutput port of the transmission line are
22 1 L V L V V e I L I I § · § · § · ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ © ¹ © ¹ © ¹ M 1 (4) Considering the ABCD transmission matrix of the two port representation, where
variables at the input port are related to those at the output port:
1 1 2 A B V V C D I I
Z
Z
Z
Z
§ · § · § · ¨ ¨ ¸ ¨ ¨ ¸ © ¹ © ¹© ¹ 2 ¸¸ (5)it is evident that equation (5) can be obtained by inverting equation (4), hence
L A B e C D
Z
Z
Z
Z
§ · ¨ ¸ ¨ ¸ © ¹ M (6) The exponential matrix can be analytically calculated as
cosh( ) sinh( ) sinh( ) / cosh( ) c c L A B L Z e C D L Z L
Z
Z
J Z
Z
J Z
Z
Z
J Z
Z
J Z
§ · § ¨ ¸ ¨ ¨ ¸ ¨ © ¹ © M L · ¸¸ ¹ (7)where the characteristic impedance Zc and the propagation constant
J
are;
c
r
j l
Z
r
j l
g
j c
Z
Z Z
g
j c
Z
J Z
Z
Z Z
Z
Z Z
Z
Z Z
(8)The frequency dependence of the per-unit-length parameters that is considered in this work is based on well known results [20]:
1 ; /
1 2 ; ;
1
2 2 2
r
Z
rZ
lZ
l lZ
gZ
gZ
cS
S
S
Z
c1, (9)where r l l g c1, , ,1 2 1, 1 are constant parameters.
A power-line network (see for instance Fig 3) is interpreted as an interconnection of transmission lines. The frequency response of the channel can be obtained, at each frequency, solving the algebraic linear system of equations obtained from the nodal analysis of the global network circuit. The two port admittance matrix representation of a single line corresponding to (5) is given by
1 1 2 2 1 1 A I V B B I V A V B B § · ¨ ¸ § · § · § · ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ © ¹ © ¹ ¨ ¸© ¹ © ¹ Y 1 2 V (10) obtaining cosh( ) 1
sinh( ) sinh( ) 1 coth( ) csch( )
1 cosh( ) csch( ) coth( ) sinh( ) sinh( ) c c c c c L Z L Z L L L L Z L Z L Z L
J
J
J
J
J
J
J
J
J
§ · ¨ ¸ § · ¨ ¸ ¨ ¸ ¨ ¸ © ¹ ¨ ¸ © ¹ Y LJ
Thus the admittance matrix
Y
is symmetric and with equal diagonal elements, the dependence on the frequency is omitted for simplicity. The self admittance termA
B and the cross admittance term
1
B
are the same at the input and output ports. This is very helpful in writing the node equations. Considering that one wire is grounded for all the two wire transmission lines in the network (all conductors at level in Fig 2 are at the same potential), then from equation (10) only the first equation can be considered. It is straightforward to show that the generic Kirckhoff current law equation at the node , which is connected, by transmission lines, to other nodes, can be written as:
0
y
k N
0 1 1
0
i N N i k k i i i iA
V
V
B
B
§
·
¨
¸
©
¹
¦
¦
(11)Where is the phasor of node voltage of the node , are the node voltages of the nodes that belong to the star centred in k , and ,
0 k
V k Vki
N Ai Bi are
elements of the transmission matrix of the line connecting the node to . In equation (11) all currents are considered out-coming from node .
0 k
V Vki k
Loads terminations are considered as linear impedances with a given frequency dependence. At the nodes connected to lines terminated with a load, the node equation is modified by considering the input admittance Yv of the terminated line:
0 1 1
0
i N N v i k k k i i i iA
V
V
Y
B
B
§
·
¨
¸
©
¹
¦
¦
(12)The source is given by a transmitted voltage phasor VTX 1 V at the node where the transmitter is connected, the TX node. The frequency response of the network
RX TX
V
H
V
Z
can be efficiently obtained by solving the set of node equations,calculating the phasor VRX, for various values of the frequency
Z Z Z
[ min, max]. The frequency range of interest for BPL is in general form 1.8-2 MHz up to 27-30 MHz. As an example in the following a real network is analysed, node equations are obtained, and simulated data is compared to measured data.1.1.2 Example of a realistic indoor apartment power line network The topology of a realistic indoor power-line network is shown in Fig. 3. As stated in the previous section, the wiring can be modelled as a set of interconnected transmission lines that are intrinsically linear under the depicted scenario.
A central node where all the heavy loads (like the electric heaters and oven) are usually connected is easily located. To this node are connected two lines which feed two zones of the apartment. The transmitter and the receivers are connected to the outlets of the grid identified by TX and RX respectively. Other loads are schematised with an impedance that is purely resistive and equal to the characteristic impedance of the transmission lines used to model the cables. The white rectangles are unconnected loads considered as open circuits. Three typical domestic loads are considered connected to the PLC network.
Fig. 3. Topology of a particular apartment indoor power line network
Fig. 4. Typical impedance amplitude of a coffee machine and a fan.
This three devices, a television, a fan and a coffee machine, exhibit a typical frequency dependent impedance, depicted in figure 4, as reported in [21].
The frequency response for the apartment in figure 3 is calculated following the transmission line approach described in the previous section. A complete set of node equations can be written, obtaining 12 equations (11 nodes plus an additional node at the transmitter).
Figure 5 shows the obtained amplitude of the transfer function from TX to RX for the configuration of the loads in the network depicted in Fig 3. The frequency range considered is from 1 MHz to 20 MHz The frequency-selective fading characteristics of the channel can be noticeably seen from Fig. 5. In particular frequencies with an attenuation superior to -40 db are almost certainly not useful as communication carriers. Maintaining the same apartment topology, the state of three matched loads is now changed to open, representing generic disconnections of these loads from the indoor power-line, obtaining the configuration of fig 6.
Fig. 6. Topology of a particular apartment indoor power line network, for a different configuration of the loads. Three loads are changed from matched to open, with respect to the network in Fig 3
Fig. 7. . Amplitude of the frequency response of the channel from TX to RX of the network in Fig 6.
The frequency response from TX to RX of the network of fig 6 with the new configuration of matched-open loads is shown in Fig.7, in particular three terminations are changed from matched to open. With this configurations more frequency notches appear, and the channel of fig 7 is clearly degraded with respect to the channel of fig 5. This is probably due to presence of more open circuit
terminations between the direct path from transmitter and receiver, yielding in this case a more hostile channel because of the greater selective fading.
It is clear that, depending on the state of the loads, the alteration of the transfer function of the same topological network can be very serious.
1.1.3 Experimental model validation
The model for simulation described in has been experimentally validated. Measures of the frequency response of a network of power cables has been made in laboratory. Measures where accomplished by means of a Agilent Vector Network Analyzer, and the simulated channel frequency response, obtained by the method described in 1.1.1, revealed a good accordance with measured data.
Fig 11. Experimental power-line Network
Frequency response measurements
The topology of the PL channel assembled in laboratory is shown in fig 11. Despite the simplicity of the topology, a large number of different responses are observed by varying the three loads
Z Z Z
1,
2,
3. Also cycle-stationary loads (a television and a refrigerator) are plugged and transfer functions from TX to RX are measured at different instants inside a mains cycle. The range of interest is 2MHz-30MHz, where the high pass filter is flat, and all filters have a decoupling circuit. Transmission lines (bold lines with lengths indicated) are two wire conductors of different types. The voltage transfer functions of the channel in Fig. 12 have been experimentally measured by means of a Agilent Vector Network Analyzer. In particular the VNA measures the complex voltage linear gainG
s
21 of the two port equivalent from TX to RX.. The frequency response is then given by21
2
.
Fig 12. Frequency responses of the power-line Network
Per-unit-length parameters measurements and modelling
In order to simulate the frequency response of the PLC channel of fig 11, as described in 1.1.1, the actual per-unit-length parameters need to be evaluated by measurements. Every link in the network of fig. 11 is a cable with different section and length, hence cables have different per-unit-length parameters, which have been determined through reflections measurements performed on each single cable previous to assemble the physical network. By measurements the S-parameter ( ) has been determined, for the 1-port network of the short-circuited and open-circuited transmission line for frequencies up to 40 Mhz, for all the seven cables of the network. The input impedances
11
s
0
Z
(short-circuited) andZ
f (open-circuited) have been evaluated from the S-parameter as0 0 11 0 11 11 11
1
50
1
1
50
1
s
Z
s
s
Z
s
f f f (13)Note that the Agilent VNA uses
50
:
input and output reference impedances, see fig 11. On the basis of these quantities the characteristic impedance and the propagation constant of the cables can been derived as0 0 0
tanh(
)
tanh(
)
arctanh
c c cZ
Z Z
Z
Z
L
Z
Z
L
Z
Z
L
J
J
J
f f f
°
°
®
®
°
°
¯
¯
(14)Fig.13 Characteristic impedance and propagation constant for all links of fig. 11
Fig. 13 shows the results of measured characteristic impedance and the propagation constant, derived from (14). It is worth noting that the characteristic impedance has a typical behaviour: it is almost resistive assuming values around 100 Ohms for frequencies up to 10-15 Mhz. In the same range of frequencies the propagation constant is imaginary and grows linearly with the frequency. At higher frequencies the reflection measurement loose accuracy. Equation (15) is used to obtain the frequency dependent per-unit-length parameters as
Re(
)
Im(
)
Re(
)
Im(
)
c c c c cr
Z
r
j l
Z
l
Z
g
j c
g
Z
r
j l
g
j c
c
Z
J
Z
J Z
Z
J
J
Z
Z
J
Z
°
°
°
®
®
°
°
¯
°
¯
(15)The so obtained per-unit-length parameters shows a frequency dependence that is similar to the theoretical frequency model (9) in a range of frequencies form 2Mhz to 7-8Mhz. In this interval the obtained data for each cable have been approximated by the frequency model (9) here reminded:
, , ,
r l g c
1 ; /1 2 ; ; 1
r r f l l l f g g f c c1.
Hence for each cable a set of five constant parameters have been determined to fit the data (15) through equation (9) in the minimum-square sense. Fig 14 shows the matching between the measured and fitted per-unit-length capacitance and resistance.
1
, , ,
1 2 1,
1r l l g c
, , ,
Fig. 14 Per unit length capacitance and resistance obtained from data (red lines) and fitting model.(black lines)
Frequency response simulation
The frequency response is then simulated as described in 1.1.1. It is assumed the knowledge of the per-unit-length parameters constants of each cable, the cable length and the topology of the connections. From equations (1)-(10) the two-port admittance matrix of each line is obtained. Then the current node equations at the five nodes A, B, C, D, E, are derived. Transmission lines are numbered from 1 to 7 (red numbers in fig. 15), hence subscripts
1
, , ,
1 2 1,
1r l l g c
,
i iA B
,indicate the transmission matrix elements of the i-th line.
1
7
i
!
1 1 1 3 1 1 1 3 1 3 3 5 2 3 5 3 5 7 3 5 7 5 7 7 7 1 1 1 50 50 1 1 0 1 0 1 1 0 1 1 0 50 TX A B v B A v C B v D C E D A V V V B B A A V Y V V 5 7 1 C D E B B B A A V Y V V B B B B A A V Y V B V B B B A V V B B § · ¨ ¸ © ¹ § · ¨ ¸ © ¹ § · ¨ ¸ © ¹ § · ¨ ¸ © ¹ § · ¨ ¸ © ¹ B 3 (16)
Note that from the network scheme of fig 11 the low pass coupling circuit with the mains and the high pass coupling circuit with the VNA have been neglected, because the former can be considered as an open circuit and the latter is a short circuit, for the range of frequencies taken into account (higher than 1 Mhz). The input admittances are calculated by means of the transmission line input admittance relationship, given the output loads impedances
1
,
2,
3 v v vY Y Y
1,
2,
Z Z Z
: 6 3 6 2 1 2 4 2 4 1 2 3 2 1 2 4 2 4 6 3 6; ; .
vC Z
D
vC Z
D
vC Z
D
Y
Y
Y
A Z
B
A Z
B
A Z
B
The transfer function defined as
RX TX
V
H
V
Z
, is obtained takingand and solving the linear system (16) for fixed angular frequency
RX E
V
V
1
TXV
Z
. Notethat
A B
i,
i andY
jv in (16) are functions of the frequencyZ
. By varyingZ
the frequency responseH
Z
is evaluated, for all the frequencies of interest, in magnitude and phase.Fig 16. Two different frequency responses, measured and simulated.
Fig 16 shows two different frequency responses (simulated vs. measured) for two different states of the loads
Z Z Z
1,
2,
3. The response on the top results from open circuited loadsZ
1Z
2Z
3f
, while the response on the bottom is for. The simulation model is close to measured frequency responses for frequencies up to 20-27 Mhz. In particular in this range of frequencies the channel fading (notches) and plateaus of the amplitude response are well reproduced.
1 2
1 ;
3Fig 17 Relative Average Cumulative Frequency Error between model and measured data.
Fig 17 shows the relative average cumulative frequency error between simulated
sim i
H
M
and measuredH
imeasM
responses, evaluated using a large number of measured curves:1
measi
!
N
1 min
min
1
Nmeas f meas simi i meas f i meas i
H
H
E f
d
f
f
N
H
M
M
M
M
¦ ³
Where
f
min10
KHz
is the minimum frequency of the Agilent Vector Network Analyzer. Cumulative error is below 25% up to 15MHz and it grows to 33% from 18MHz to 27Mhz. The relative-cumulative error decreases in the frequency range where per-unit-length parameters have been derived, from 2 to 8 MHz. This results are in accordance with the finding reported in [20], where the model (9) is used to characterize the power-line cables in the frequency range from 0.5 MHz to 30 MHz In the following the performances of the proposed communication schemes will be evaluated by simulating the digital transmission over the rigorous PLC simulation channel here described.1.1.4 Cycle-stationary channel
It is known that several commonly used devices connected to the sockets may exhibit a nonlinear behaviour with respect to the total applied voltage [12]. Namely the large voltage at low frequency can be considered as a bias determining the operating point of various nonlinear devices in the power-line, for instance televisions, ovens, etc. From the small signal point of view, the impedance of the nonlinear device can be characterized by a function of two variablesZ t f( , ).
Common characteristics show that the impedance of nonlinear devices exhibit a gradual variation of 10%-15% over mains cycle with a periodicity of 50Hz.
As a consequence, from the high frequency signal point of view (the Broadband signal) the communication channel is a linear system formed by an interconnection of transmission lines terminated on time varying loads. It was shown that under these circumstances it is possible to consider that, from the high frequency signal point of view, the system is linear but periodically time-varying (LPTV) synchronously with mains [12]. Thus the presence of nonlinear loads produces a cyclic variation of the frequency response of the channel, and this variation is synchronous with the mains,
In the example of the particular apartment of fig 3, consider now that the three devices connected to the network, the coffee machine, the television and the fan, exhibit a cycle-stationary impedance, changing with respect to the mains voltage.
Fig. 8 shows the cloud of the possible impedance curves during a 50Hz cycle for the impedance of a TV [21]. Similar plots are obtained for the impedances of the coffee machine and the fan.
Fig. 9 shows the resultant range of variation of the channel frequency response from the transmitter TX to the receiver RX associated with the cyclic variation of the three nonlinear impedances of the power-line network of fig 3. After a complete period of 50 Hz the channel frequency response has changed within a family of curves that covers the whole strip between the higher and the lower envelops shown in Fig. 9.
Fig. 9. Periodically time variant power-line channel.
Substantially,. the time varying behaviour of indoor power line channels is produced by two causes. The first one is the connection and disconnection of electrical devices at the sockets and determines abrupt, long terms variations. The other one is related to the nonlinear behaviour of some electrical devices with respect to the mains voltage and produces short time variations that are synchronous to the mains. Figure 10 shows the double nature of the possible channel variations. From the example of Fig. 9 it can be noted that the short time cycle-stationary oscillation of the channel frequency response can be large in certain frequency intervals, in this case the channel alteration is relevant for frequencies from 16 to 20 MHz. As a consequence, when a broadband communication signal is transmitted in the power line, this continuous periodical oscillations will produce errors if not suitably followed by the estimation method. Thus the channel need to be continuously estimated, in particular many estimates are needed inside the mains period of 20ms. If the estimation is accomplished by a standard method, that is a linear interpolation of periodically inserted pilot tones, the bandwidth required for channel estimation turn out to be a significant part of the total bandwidth, reducing the transmission rate of useful data. In Chapter 3 it is shown that this problem can be addressed by using blind estimation methods, i.e. decision directed estimation (DDE) methods, that are able to continuously estimate the frequency response without the use of pilot signals.
Fig. 10. Periodically time variant power-line channel for two different configurations of the terminations (open or matched loads in fig 3)
1.2
Impulsive noise in power lines
Noises in a low voltage power grid and in MV or HV power lines arise for different causes and have different behaviours, thought in all cases the noise is described as impulsive noise, as different kinds of impulses and bursts of different duration and repetition frequency are observed in both overhead and indoor power line networks. In this section a description of the physical causes of this impulses is outlined and mathematical models are introduced.
1.2.1 Impulsive noise in low voltage power grids
A number of different devices are connected to the sockets of an indoor power grid. When connected or disconnected from the socket and even during the normal operation, especially in case of switching apparatuses, these devices can generate some noises and cause variations in the frequency response of the PLC channel.
According to [9] the power line noise can be classified into five types: coloured background noise, narrow-band noise, periodic impulsive noise asynchronous to the mains frequency, periodic impulsive noise synchronous to the mains frequency (cyclostationary noise) and asynchronous impulsive noise. The properties of the first three types usually remain stationary over periods of seconds and minutes and may be summarized as background noise
Cyclostationary noise can be related to the short-term variations of the channel due to nonlinear electric devices that are influenced by the mains voltage
Impulsive noise is usually related to start/stop of electrical devices, to topological variation of the grid by connecting or disconnecting of parts of the power network, to switches commutations, included those of electronic switches as those in the switching power supplies. The burst duration connected to impulsive noise is typically on the order of a fraction of microseconds to e few tens of microseconds. The origin of a noise burst can be easily connected to the commutation of a switch. Let us consider the evolution of the power network when only the mains voltage is
active. In the microsecond scale all the voltage and all the currents can be considered as constants. A switch commutation can be approximated as a linear variation of a resistance from a value close to zero to a very high one (or vice versa). As a consequence a transient voltage appears at the switch terminals, propagates on the grid and reaches the receivers.
In order to simulate a PLC channel, the impulsive noise need to be simulated as well, if a rigorous model is required. A classic approach to model impulsive interference is the Middleton Class A noise. This kind of noise model take into account both the background thermal noise and the asynchronous impulsive noise.
The Middleton’s Class A noise probability density function (pdf) of the noise amplitude
z
is given by:2 2 0 1 ( ) exp( ) ! 2 2 A m m m m e A z p z m SV V f
¦
,with 2 2 / 1 m m A V V * * , (17) where A is the impulse index, *V V
g2 I2 is the GIR (Gaussian-to-impulsive noise power ratio) with Gaussian noise powerV
g2 and impulsive noise powerV
I2, andV
2 =V
g2+V
I2 is the total noise power. Signal to noise ratio is usually calculated with respect to the gaussian noise powerV
2. Hence a frequency domain noise with this pdf is usually considered, besides, the noise powersV
2g andV
I2 can change with frequency if noise is coloured.1.2.2 Impulsive noise in MV-HV power grids
The high voltage on overhead transmission lines produces different types of noise what is notable signature of this communication media. Power line noise arising from existing the high voltage can be dividing in two categories
1 .Noise at normal (stationary) operation of the power line. This noise is caused by thermal agitation of conductors, certain static discharges and corona. Noise due to interference with other PLC communication systems and radio stations also belong to this category.
2. Noise at transient and emergency operation. This category comprises noise due to power line faults, circuit breaker and isolator operation, and lightning discharge.
Noises in normal operation are always present at the communication channel and have different values of noise level inside a period of the power frequency. Power-line noise in normal operation dominantly appears due to corona. In the frequency domain, the corona noise [10] has been studied and represented with a power spectral density and with a Gaussian noise voltage with variable root mean
square value in the time domain . Therefore, a power line appears as a noise source by itself due to corona discharges on HV power lines.
Noise at transient and emergency operation and strong asynchronous impulses are also observed in high voltage power lines, but little is known about their frequency characteristics [10]-[17]. The switching operations and faults in power network cause different types of noise, which in general have high amplitude and mostly cause short termination in digital signal communication due to the loss of synchronization and burst errors in digital transmission. In transient operation, power-line noise is dominantly impulsive where background noise appears between pulses that significantly overreach background noise level. While corona noise have a same behaviour over a long time (minutes or hours), the operation of circuit breakers and isolators in the power line networks results in high amplitude impulse noise and duration from milliseconds to few seconds with random occurrence. The power spectral density (PSD) of this type of noise can reach values of more than 50 dB above the background noise. Eventually transmission parameters and noise level are considerably dependent on weather conditions. The power line noise has a dominant influence to communication systems at foul weather conditions. In the following a noise classification system will be introduced and described. A first approach to classify the impulsive noise observed in the overhead power lines by their frequency characteristics has been carried out in [11] by this author. In Chapter XX the proposed procedure is described.
2
COMMUNICATION SYSTEM
Multicarrier systems have emerged as preferred candidates for a variety of PLC applications, allowing higher symbol rates to become attainable. Amongst various implementation approaches, orthogonal frequency division multiplexing (OFDM) based system has received considerable interest in PLC and wireless communications for its advantages in high-bit-rate transmissions over frequency-selective and time-variant channels.
OFDM is a multicarrier communication system where the modulation and the demodulation are implemented by using the Inverse Fast Fourier Transform (IFFT) and the Fast Fourier transform (FFT) respectively [22]. The input data stream is divided into many symbols drawn from a M-QAM constellation and placed in the frequency domain on a number Nof orthogonal subcarriers. The array of subchannel symbols is transformed into a baseband time-domain signal by an IFFT operation. Then the signal is extended cyclically in the time domain to form an OFDM frame to be sent in the channel. This cyclic extension is called the “cyclic prefix” and is inserted by the transmitter in order to remove the intersymbol interference (ISI) and interchannel interference (ICI) that would otherwise cause degradation of the system performance
2.1
OFDM Transmitter and Receiver
Let us first introduce the equivalent block scheme, shown in Fig. 19, of an OFDM system. In each frame interval, a vector of N complex symbols,Akm (belonging to a QAM constellation),k 0,...,N1, is transformed by means of a symmetric IFFT to a vector of 2N real valued channel symbols , inm, n 0,..., 2N1 , which are actually the samples of the baseband OFDM signal. Here, is the generic frame index and
m
N is the number of OFDM subcarrier. The channel symbol stream is suitably modulated to form the OFDM signal with envelope i t
given by
1
0 N m n m n i t i g t nT mNT f f
¦ ¦
(18) where inmis obtained as1 2 1 2 / 2 / 2 0 1
1
2
N N m m jnk N m jnk n k N k k k Ni
A e
A
e
N
S§
·
¨
©
¦
¦
¹
N S¸
(19)Fig 19. OFDM Communication System
m k
A
is the complex conjugate,T is the discrete sampling time (NTis the OFDM frame duration), g tis the pulse shaping adopted for digital to analog conversion. In the following, g t
is a root-raised-cosine function with rolloff
D
and filter gainK
. The impulse response of this commonly used filter is given by2 2 2 cos sinc 4 1 t t T g t K t T T
SD
D
§ · ¨ ¸ § · © ¹ ¨ ¸ © ¹ (20)The voltage signal i t
is inserted by the transmitter in the power line. The power line channel acts as a time variant frequency selective filter and as a noise source. The long impulse response may produce intersymbol interference (ISI). It is assumed that the intersymbol interference between two consecutive OFDM frames is completely cancelled by the insertion of a cycle prefix. The received signal is obtained by a convolution of the transmitted signal
r t
i t and the channel impulse response. Assuming that the power line frequency response is constant throughout the OFDM frame, and that synchronization is perfect, the signal at the receiver after the FFT block is expressed by (21)
m th
m m m
k k k
where
R
km is the received value at the kth subchannel, is the channel complex gain at the frequency of the k -th subcarrier and is complex additive noise produced by a mixture of Gaussian and impulsive noise. In general, in a OFDM system, the transmitted data symbols on each subcarrier are received with a scaling of amplitude and a phase rotation given by the channel complex gain . m kH
th m kW
i
m kH
The number of subcarriers is designed in order that each subchannel will have a narrow bandwidth, and one can say that the fading on each subchannel is approximately flat. In PLC this hypothesis is critical because of the strong fading characteristics of the channel. This problem together with the loss of orthogonality caused by imperfect synchronization and by cyclic short time-variations in the channel is the main reason for investigating better estimation and equalization methods for OFDM.
N
In fact the OFDM standard do not specifies how to accomplish to channel estimation and signal equalization, then the last block in the diagram of Fig 19 is where the research has been focused. Estimation schemes that utilizes neural networks are proposed and analyzed in the following.
2.2
OFDM Signal Through Third-Order Nonlinearity
One of the main disadvantages of the OFDM is the potentially large peak-to-average power ratio (PAPR) characteristic of a multicarrier signal with a large number of subchannels. The conventional solutions to the PAPR problem are to use clipping-filtering method or to back-off the operating point of a nonlinear amplifier. However the transmitter output filter which is required to reduce out-of-band spurii to legal levels has the effect of restoring peak levels that were clipped, so clipping is not an effective way to reduce PAPR. Moroaver It is likely that the HPA may be driven into the nonlinear operating region of its input/output characteristic, in order to be energy efficient. Nevertheless multicarrier transmission systems show a great sensitivity to the nonlinear distortion effects caused by the use of high power amplifiers (HPA) or clipping devices at the transmitter. A theoretical characterization of the distortion effects in OFDM systems caused by a memory-less nonlinearity (AM/AM and AM/PM distortion) is carried out in [23], and a similar analysis for clipped-filtered signals is presented in [24]. In both cases it is shown that under certain hypothesis the distortion effect on the “constellation” of the OFDM signal is simply the combination of a global complex gain (attenuation and phase rotation) equal for all subcarriers, along with the presence of an additive noise (NLD noise). These results apply under the assumption of a large number of subcarriers and certain classes of the D/A pulse
shaping filter and HPA nonlinearities. As a consequence optimum detection of OFDM symbols in the presence of nonlinear distortions is focused on the prediction of the NLD noise [25],[26]. However, these conclusions do not apply directly in cases of circuits with different nonlinearities (i.e. transistors or diodes) [27]. Also to the authors experience it emerge from measurements and simulations that the constellation of an OFDM signals distorted by a nonlinearity exhibits compression and warping, as in the case of single carrier systems.
In this study the HPA is considered as a weakly nonlinear memoryless system, and it is shown that the distortion effects
can be characterized directly in the frequency domain as a nonlinear compression of the amplitude of the QAM symbols at each subcarrier. This results are used in the following to develop a novel algorithm for symbol equalization and detection based on a neural network approach.
Fig 20. OFDM transmitter with HPA nonlinearity
Than a modulated signal i t
, transmitted through a nonlinear memoryless channel, NL, which is described by a third-order polynomial is considered. The theory of weakly nonlinear systems represents a component’s input/output characteristic by a truncated power series around the dc operating point as long as a frequency-independent model is appropriate. On the other hand, if the component’s nonlinearities are not memoryless, Volterra analysis should be used for the representation of the component’s characteristic [26]. The output voltage of the nonlinear circuit is expressed as
3
1 3
u t a i t a i t (22)
where and are the linear gain and third-order nonlinearity coefficient. Commonly, circuit designers make use of third-order intercept point (OIP3). Its dependence on the linear gain is cubic, while it is inversely proportional to :
1
a
a
3 3a
3 1 3 2 OIP3= 3 a aThe amplitude
K
of the transmitter filter g tdefines at what degree the input voltage i t
remains in the linear region or reaches the nonlinear zone of the HPA characteristic. The interest is in the effect of the nonlinear distortion on the signal “constellation” reconstructed from u t
, after HPA block. Real valued discrete time samples , unm n 0,..., 2N1are obtained by filtering u t
with a matched raised cosine filter gR(t) with gain
1/ K
and sampling at instants . By taking them n
t nTmNT
2N FFT of
u
nm the frequency symbols m kZ
k 0,...,N1 are obtained 2 1 2 / 0 N m m jnk k n nZ
u e
S¦
N (23)In [23] it is shown following a theoretical approach that, if g t
is a rectangular pulse shaping filter, and the number of subcarriers tends to infinity, symbols after a memoryless nonlinearity are approximately expressed as
N
0 m m k k m kZ
N
A
D
(24)where is a global complex gain and is an uncorrelated zero mean noise. Fig 21a depicts the obtained
0
N
m kD
m kZ
symbols after the nonlinearity for rectangular pulse shaping,N
4096
, and 64-QAM signalling. Results obtained from simulations confirm the validity of (24) under this conditionsFig 21a. Scatter plot of the transmitted signal at the exit stage of the amplifier, for rectangular pulse shaping and N 4096
On the other hand a more common used filtering approach is raised-cosine pulse shaping. In addition the hypothesis of large , is not considered valid for systems where . In this cases the approximation in (24) may loose accuracy. Figure 21b depicts the constellation of the symbols
N
1024
N
m k
Z for a 64-QAM, where a system with a number N 512subcarriers has been considered.. The digital analog filter is a raised cosine filter with rolloff
D
0.25and filter gain K 2.5,Fig 21b. Scatter plot of the transmitted signal at the exit stage of the amplifier, for raised-cosine filtering
The nonlinearity is given by (22) with a1 1 and a3 0.1, , which is a common characteristic. From figure 21b is evident that (24) is not
accurate. In fact the constellation in fig 21b is not attenuated by a global factor, instead the symbol attenuation seem to be amplitude dependent. Equation (24) may be modified in OIP3 8.24 dBm 0
(
)
m m m k k k m kZ
N
A
A
D
(25)where it is evidenced the dependence of the complex gain from the amplitude of the transmitted symbol, as obtained from extensive numerical simulations. In Figs 21a and 21b symbols at all subcarriers are shown. By examining the symbols at the single subcarriers similar scatter plots are obtained. From this results, as in [23]
the nonlinear gain
N
0 can be considered frequency independent, in both cases of raised cosine and rectangular pulse shaping.The signal at the receiver after the FFT block is expressed by (26)
0
(
)
m m m m m m m m m k k k k k k k k k m kR
H Z
W
H
N
A
A
H D
W
(26)let accurate channel estimates
H
ˆ
km be given so that equalized symbols ER
km are0
ˆ
ˆ
/
(
)
ˆ
ˆ
m m E m m m m k m m m k k k k k m k k k m k kW
W
R
R
H
Z
A
A
D
H
N
H
|
. (27)The constellation of E
R
km depend on that of the distorted transmitted symbols mk
Z
in (25). These results are used in the equalization-estimation procedures by taking into account the effects of the HPA nonlinearity at the receiver.3
ADAPTIVE ALGORITHMS FOR CHANNEL ESTIMATION AND
EQUALIZATION
In this chapter two adaptive equalization algorithm for OFDM communication are introduced and described.
OFDM standard do not specifies how to accomplish to channel estimation and signal equalization. OFDM systems often employ coherent detection that requires accurate information on the channel impulse response (CIR). The CIR can be estimated using predetermined pilot symbols in real time but this reduces the transmission rate. Several pilot-aided channel-estimation schemes for OFDM applications have been investigated as reported in [29], and optimal pilot patterns for time variant, flat channels or time variant and frequency selective channels has been proposed as shown in [30]. The common ground of all these estimation schemes is the representation of the wireless transmission as a multipath propagation in a channel with a frequency response formed by narrowband constant amplitude sub-bands with different phase shifts
Power lines are actually very hostile channels for signal transmission. Indeed, they show significant variations of time and frequency characteristics that can drastically reduce the efficiency of OFDM systems. The commonly used single-tap equalizer assumes that the channel is time constant in the period between two different channel estimates, thus it may be unable to fully compensate the loss of subchannel orthogonality due to the cyclic time-variant behaviour of the PLC channel. A blind, decision-directed estimation procedure is desired to continuously follow the channel alterations. A number of decision-directed estimation techniques have been proposed for wireless OFDM systems [31]-[33], but to the author knowledge a minor effort has been carried out for exporting, analyzing and optimizing these techniques in the environment of PLC networks [1], [34]
3.1
Nonlinear decision directed estimation
In this section a new technique is proposed for blind channel identification and equalization in orthogonal frequency-division multiplexing (OFDM) communication. The proposed scheme is based on a competitive neural network (or Self Organizing Map, SOM ) with one neuron for each QAM symbol, in particular the case of QPSK is considered. Received subcarrier-symbols are presented to a
