Communication System over Power Line
WU DAN
Master of Science Thesis Stockholm, Sweden 2013
Communication System over Power Line
WU DAN
Master of Science Thesis performed at the Radio Communication Systems Group, KTH.
May 2013
Examiner: Ben Slimane
Radio Communication Systems (RCS) TRITA-ICT-EX-2013:99
⃝ Wu Dan, May 2013c Tryck: Universitetsservice AB
Improvements for LDPC coded OFDM Communication system over Power Line
Wu Dan
Master’s Thesis at COS Department, KTH Supervisor: Fuliang Yin, Zhe Chen
Examiner: Prof. Ben Slimane
March 2013
Abstract
Power line communication has been around in past decades and gained renewed attention thanks to the demand of high‐speed Internet access. With the significant advantages of existing infrastructure and accessibility to even remote areas, power grid has become one of the promising competitors for multi‐media transmission in household. However, the power line was not oriented for data transmission providing a rather hash environment. To overcome the difficulties, advanced modulation and channel coding schemes should be employed.
In the thesis low density parity check code (LDPC) is employed to reduce the loss caused by various kinds of effects in the channel especially the noise since its performance approaches to Shannon capacity limit. Moreover, OFDM multi‐carrier transmission technique is involved which could decrease the inter‐symbol interference and frequency selective fading. Nevertheless, LDPC decoding process was designed specifically for the common Gaussian white noise condition, combined with OFDM modulation the system still could not provide satisfying and practicable performance so improvements are needed for the system.
The main works of the thesis are as follows. Set up an environment of power line transmission investigating and simulating the channel characteristics; employ multi‐path channel model and Class‐A noise model for further developing the improvement algorithms to deal with the selective fading and impulse noise. Two algorithms proposed here are from different perspectives: the first one is modifying initial posterior information for LDPC decoding and the second one aims at suppressing the impulse noise after demodulation. Finally, a few simulations are performed to reveal the effectiveness of proposed methods. As a result, the improved scheme shows a great superiority improving the performance by no less than 5dB compared to traditional system.
KEY WORDS: low‐voltage power line communication (LV‐PLC), LDPC, OFDM, impulse noise suppression, Class‐A noise
Catalogue
Chapter 1 Background ... 1
1.1 Background and significance of the project ... 2
1.2 Power line communications for Internet access ... 2
1.3 Appliances and standards for PLC... 4
1.3.1 HomePlug Power‐Line Alliance ... 4
1.3.2 Products in the field ... 5
1.3.3 Other organizations ... 5
1.4 Low Density Parity Check codes theory ... 5
1.4.1 LDPC codes development... 5
1.4.2 Advantages of LDPC codes ... 6
1.5 Thesis structure outline and main work... 7
Chapter 2 Power line channel characterization ... 9
2.1 Overview ... 10
2.2 PLC channel modeling ... 11
2.2.1 Introduction ... 11
2.2.2 Zimmermann and Dostert model ... 12
2.3 Noise for PLC channel ... 13
2.3.1 Brief introduction ... 14
2.3.2 Noise modeling techniques for PLC ... 15
2.3.3 Middleton Class A noise ... 15
Chapter 3 Key techniques of power line communications ... 19
3.1 OFDM modulation fundamental ... 20
3.2 OFDM realization with DFT/IDFT ... 22
3.3 OFDM techniques ... 24
Chapter 4 Low Density Parity Check Codes ... 26
4.1 Basic concept of LDPC ... 27
4.1.1 Tanner graph of LDPC codes ... 27
4.1.2 Regular and irregular LDPC codes ... 29
4.1.3 Cycle and minimum distance in LDPC codes ... 30
4.2 LDPC check matrix construction ... 31
4.2.1 Regular LDPC codes construction by Gallager ... 31
4.2.2 Regular LDPC by MacKay and Neal ... 32
4.2.3 Quasi‐Cyclic LDPC construction ... 33
4.2.4 Deterministic LDPC construction ... 33
4.3 LDPC encoding scheme ... 34
4.4 LDPC decoding scheme ... 36
4.4.1 Message passing ... 36
4.4.2 Belief propagation in probability domain ... 37
4.4.3 Belief propagation in log domain ... 42
4.4.4 Min‐Sum decoding scheme ... 44
4.4.5 Bit‐flipping decoding scheme ... 45
Chapter 5 Noise suppression and modified decoding for PLC system ... 48
5.1 Algorithms for performance improvement in terms of impulsive noise ... 49
5.2 Robust decoding of LDPC codes in the presence of impulsive noise ... 50
5.2.1 Motivation and formulation for robust decoding ... 50
5.2.2 Implementation ... 52
5.3 Impulsive noise suppression in LDPC coded OFDM system... 53
5.3.1 Motivation ... 53
5.3.2 Principle and implementation process ... 55
Chapter 6 Performance of improved PLC system... 57
6.1 LDPC coded OFDM system with impulse noise ... 58
6.2 Performance of modified LDPC over PLC ... 60
6.3 Performance of impulse noise suppression over PLC... 62
6.4 Performance of improved system over PLC ... 65
6.4.1 Integrated improvement scheme ... 65
6.4.2 Performance of integrated scheme in more realistic scenario ... 67
6.5 Conclusion ... 68
Chapter 7 Conclusion and future work ... 70
7.1 Conclusion for the thesis ... 71
7.2 Future work ... 71
Reference ... 73
Chapter 1 Background
1.1 Background and significance of the project
In informational society, Internet has become an indispensable part of our daily lives, especially the mushroom growth of high speed Internet, multi‐media and power line communications (PLC), lead to people’s higher expectation and demand for a convenient and fast way to get access to the Internet.
As a new access mode PLC has already been paid more attentions, which employs the low voltage line of power distribution networks for multi‐media service such as VOD (video‐on‐demand) and voice conference [1]. Thanks to the existing power grid, subscribers can access the high‐speed and high‐capacity backbone networks with a satisfactory quality of service (Qos). With the significant advantages of existing infrastructure and accessibility to even remote areas, power network has become one of the promising competitors for multi‐media transmission in household.
Unfortunately, since the power line was specifically oriented and designed for power conveyance, it provides a rather harsh environment when used for multi‐media transmission such as the instable quality, considerable attenuation and also networking security, etc. Moreover, the noise from loads and interference introduced by radio broadcast are also severe enough to make a bad influence on the communication channels and thus have to be considered seriously. For instance, the turn‐on and turn‐off actions to the loads cause the fluctuation of the current flow on the network, leading to the generation of electromagnetic wave around power lines and making troubles when transmitting data. The quality of communication basically depends on the situation of channel, on which the noise presented is the main factor to some extent. On this occasion, signals are apt to corrupt by high‐frequency impulse noise, especially over the period of peak demand, leading to the instability [2]. Moreover, the impulse noise on the PLC channel has characteristics of transient, high power and wide coverage and cause severe effect on the transmitted signals, making it hard to make decision and correction on the receiving end.
To overcome the above‐mentioned difficulties and make assurance for Qos, advanced techniques have to be adopted. Typically, noise suppression is necessary and moreover channel coding is an excellent means of improving the PLC transmission quality. Among all kinds of channel coding schemes, low density parity check (LDPC) codes has drawn renewed attention due to its outstanding performance‐very close to Shannon limit [3]. Compared to Turbo codes, LDPC is more flexible and easier for hardware realization. Besides interleaver is not necessary on account that LDPC codes has resistance to burst errors by itself. Since it has been ignored for several decades few of the standards in practice employs this kind of codes even though with such excellent characteristics. So in this thesis, LDPC coding scheme is studied and employed to deal with impulse noise presented on the PLC channel. By improving LDPC decoding particularly against the channel characteristics and applying OFDM modulation techniques, a considerable enhance in performance would be expected.
1.2 Power line communications for Internet access
Generally, PLC technique can be categorized into three classes: high‐voltage PLC (≥
35kv), medium‐voltage PLC (10‐30kv) and low‐voltage PLC (380v/220v). High‐voltage power line is mainly used for long distance transmission with the frequency below 150 kHz while medium‐voltage and low‐voltage can be employed for both narrow‐band carrier communication and broad‐band data transmission. Considering the latter, it is the popular application for power line networks which is also called high speed PLC technique.
While the PLC of medium‐voltage is mainly used as transmission links, providing access for backbone network and electric distribution network automation, etc., the low‐voltage is deployed commonly for Internet access, household local area networks, remote recording and smart grid. Herein, low‐voltage PLC is the task which will be focused and discussed in details.
For low‐voltage power line communications, the market for Internet access is two‐folded: the “last mile access” which means network to the home and the “last inch access” referring the in‐home networking. [2]
According to some research, power line communications does not show any superiority to other “last mile access” ways including cable modem, digital subscriber lines (xDSL) and broadband wireless. While as for “last inch access”, it is considered to be an optimum scheme compared with other technologies such as cable, wireless or phone line networking [2]. Figure 1‐1 illustrates the concept of “last inch”.
adapter
electric meter
router
Backbone networks
power line
Internet
adapter
modem
Figure 1‐1 “Last inch” access in home
The Internet access in household this way is achieved by employing power line as a transmission medium. PLC adapters should be applied, extending the original power distribution networks into power line communication networks and the power socket into plug‐in socket for Internet. The first PLC adapter connected to modem or LAN port of router is necessary for spreading Internet signal into power lines, and then for any other electric devices in the house willing to get access to the Internet, it just has to be connected with any other outlet through another PLC adapter. In this way power line communication network is built and users are able to get access to the Internet wherever there are power outlets.
One of the insightful advantages for power line access lies in that it could excellently handle the situation in which deploying wire is hard or expensive and also for the situation where wireless signal cannot completely cover or the blind spots exist such as big apartment or villadom, in which case both wireless and power line can be employed working together to provide best Internet access for the whole space.
1.3 Appliances and standards for PLC
1.3.1 HomePlug Power‐Line Alliance
HomePlug Powerline Alliance was set up in the year 2000 with more than 70 members all through the world. As a leading open standard organization for developing power line communication protocol, it has set a series of specifications and standards for PLC technology forming a complete system which basically includes all the application fields for PLC. By cooperating with international standard organizations like IEEE, HomePlug Powerline Alliance has been devoted into spreading PLC techniques and applications. Considering the harsh environment provided by power line for data transmitting, many efforts have been made with regard to error correction in the protocols.
(1)HomePlug 1.0
HomePlug 1.0 is the first standard in HomePlug approved in the year 2001 with the theoretical maximum speed 14Mbps. In 2004, HomePlug 1.0 Turbo was proposed with the maximum speed 85Mbps. HomePlug 1.0 appoints Burst mode OFDM as the basic transmission techniques, for which each independent sub‐carrier can employ different modulation schemes. Physical layer takes up the bandwidth between 4.5 and 21MHz with a total of 84 sub‐carriers. In respect of error control, concatenate Viterbi, Reed Solomon (RS) and interleave techniques is applied in the standard.
In the past few years millions of PLC products based on HomePlug 1.0 standard have been sold out, proving the feasibility of the technique as well as standard. However, those products on basis of HomePlug 1.0 proved to be easily corrupted by the influence of other devices, for example, the speed for Internet suffering could suddenly drop from 2Mbps down to 64kbps or even lower due to the open action of television. In order to make up the deficiencies HomePlug appliance proposed the substitute of HomePlug 1.0 in August of 2005, and that is HomePlug AV.
(2)HomePlug AV
HomePlug AV aims at providing satisfying performance for digital multi‐media transmission in family and high‐speed Internet access with the practical transmission rate up to 70‐100Mbps. Moreover, the new standard concerns the QoS technology which guarantees the transmission for 128 bit AES coded audio and video and the security for HomePlug AV is much better than early one. The new standard adopts OFDM modulation with windowing and Turbo convolutional code (TCC) enhancing the reliability. It has been proved that HomePlug AV provides satisfying performance even tested with old power line networks and in more than 80% percent cases the
data rate is no less than 50‐55 Mbps.
(3)HomePlug C&C and BPL
HomePlug C&C is a set of low speed sensing and monitoring networks employing original power lines for support of smart grid and family automation. And HomePlug BPL targets the realization of connection between family and exterior networks.
(4)G.hn
G.hn is a collection of home network technology of standards developed by the International Telecommunication Union’s Telecommunication standardization sector (ITU‐T) [5]. The specification aims at making rules for the unified next generation of Home Networking Transceiver over power lines, telephone lines and coaxial cables in terms of MAC and PHY layer.
The recommendation G.9960 received approval on October, 2009 which specifies the physical layer and architecture of G.hn. It specifies the FFT realization of OFDM modulation and LDPC codes as the forward error correction mechanism.
1.3.2 Products in the field
IN5200 is a type of PLC integrated circuit (IC) from Intellon based on the standard HomePlug 1.0 with maximum speed up to 14Mbps. Then in September 2004, a new chipset INT 5500 was issued by the same company with a higher speed up to 85Mbps, providing services of high‐definition television (HDTV) and television (IPTV), etc. After that the first PLC chip set on the basis of HomePlug AV INT6300 came into the market and it is regarded as the best suitable for multi‐media streaming applications. In the current market most of the PLC related products is based on the standards of HomePlug Alliance.
1.3.3 Other organizations
There are some other research groups working in the field of PLC and the standardization, for example, European Telecommunications Standards Institute power‐line telecommunications aims at providing standards for voice and data service over power line and IEEE are due to the IEEE BPL study group.
1.4 Low Density Parity Check codes theory
1.4.1 LDPC codes development
As one of the most important people who made great contributions to modern communication theory, Shannon, an American mathematician put forward channel capacity in 1948. In his paper, he figured out that channel capacity refers to the maximum transmission rate for a specific channel, which means when the
transmission rate is equal or lower than this maximum rate, reliable communication can be achieved for any bit error rate. In contrast, with a higher transmission rate the quality of transmission cannot be guaranteed in spite of what kind of transceivers is used. This theory is also called Shannon theorem.
Since Shannon theorem had been put forward various kinds of channel coding schemes were developed including block code and convolutional code, etc. However, the characteristic of these coding schemes were limited, far from channel capacity.
Thus, Shannon theorem was considered to be an unpractical limit that cannot be achieved, providing only theoretical significance. In 1993, a French academic C.Berrou raised parallel concatenated convolutional code (PCCC, also called Turbo code) based on the exchange of extrinsic information and iterative decoding method, of which the characteristic is rather close to Shannon limit. After that, iteration‐based decoding scheme became the target of research and investigations and different kinds of coding method appeared including Turbo convolutional code (TCC) and Turbo product code (TPC), etc.
During this time, Mackay and Neal found out a kind of linear block code, which was based on belief propagation decoding scheme of graph theory and very close to Shannon limit. It has been found that this kind of code scheme was just the same as the one put forward by Gallager as low density parity check (LDPC) in 1962 [6]. In his paper for PhD degree, Gallager proposed a decoding scheme on basis of probability domain iteration and proved this kind of scheme was rather close to Shannon limit.
However, due to the limitation of computer signal processing level, it was rather hard to put this code scheme into practice. Moreover, people’s deep belief and general acceptance for the combination of linear block code and convolutional code made it harder for LDPC to be noticed and adopted in the later 30 years until Mackay and Neal raised it again. Later, Luby came up with irregular LDPC on basis of the simple binary regular code scheme, and Davey extended the scheme into Galois field (GF), proposing multi‐nary LDPC [7]. Then Richardson raised probability density estimation (DE) scheme, providing an explanation for belief propagation iteration decoding method as well as theory foundation for LDPC method being close to Shannon theorem. Irregular LDPC codes based on this theory has only 0.0045dB away from the limit, having rather good performance. What is more, M.Chiain evaluated the performance of LDPC under the condition of memory fading channel, based on which B.Myher put forward a coding scheme with self‐adapted rate applied in slow‐varying flat fading channel. The scheme can also be used for FEC‐ARQ systems.
1.4.2 Advantages of LDPC codes
Comprising with another Shannon limit codes, e.g. Turbo codes, LDPC has the following advantages.
(1) The decoding scheme of LDPC codes is an iterative process based on sparse matrix with low computation complexity, besides the parallel structure makes it easier to be implemented on hardware.
(2) Since code rate for LDPC is easy to be adjusted, it is feasible for realizing system optimization with a flexible and self‐adapted coding scheme. Compared to Turbo codes LDPC performs better when it comes to high‐speed data transmission or high‐performance system.
(3) Low error floor is another advantage of LDPC, which makes it possible work in application with low bit error rate (BER), such as wire communication, deep space communication and disk storage industry, etc.
(4) LDPC was raised in 1960s, of which the theory and concept is clear and open to the public without any troubles on intellectual property and patents, providing convenience and good chances for those countries and companies which stepped late into communication fields.
(5) LDPC has the characteristic of resistance to burst error since when bits far from each other involved in the same check equation in a long symbol burst error could hardly have influence on the performance. As a result, interleaver is not necessary in the course of encoding so that the time delay by interleave is successfully avoided.
In summary, LDPC has superiority in the field of high capacity communication. At present, LDPC codes has been adopted in some standards since it is free of patent fees, for example next generation of Digital Video Broadcasting standards DVB‐S2 has taken LDPC as the coding scheme and in the wireless transmission standard 802.11n LDPC is also used as the optional coding scheme substituting Turbo codes in the previous standards 802.11g. However, since it came late onto the stage, the practical use of LDPC in the industry field has not been that common yet and still has a huge space to develop.
As can be seen from the previous section, LDPC codes has not been widely employed in the field of PLC since few of early standards for power line communications choose LDPC as its code scheme. In December 2008, the protocol G.9960 of Home Networking also assigned QC‐LDPC as its code scheme in the standards. It is not hard to find that LDPC is a tendency for various broadband standards nowadays. Thus LDPC codes will be focused and employed for improving the performance in power line communication in the thesis.
1.5 Thesis structure outline and main work
The main work for the thesis is to research on the performance of power line communication with LDPC codes, simulating the communication system as a whole including transmitter and receiver. To test on the performance and provide an accurate testing environment, suitable channel models and characteristics have to be investigated and involved in the simulation. Finally, improvements for this particular system will be proposed in respect of decoding schemes and noise mitigation and simulation results of those improved methods will be shown and compared. Here the PLC transmission system is refined and simplified with only the main procedures in the thesis as in Figure 1‐1.
Figure 1‐2 LDPC coded OFDM system block diagram Structure of the thesis is arranged as follows:
Chapter 1
Introduce the background and significance of the thesis, briefly explaining the application and advantages of power line communication and why LDPC code is a promising choice in this case.
Chapter 2
Research on the characteristics of the power line channel including attenuation and noise character and investigate feasible models to characterize the power line environment. Introduce Zimmermann and Dostert channel model and Class A noise models.
Chapter 3
Introduce OFDM modulation and the related key techniques.
Chapter 4
Describe the principle and process of LDPC codes and look deeply into its soft iterative decoding schemes.
Chapter 5
Firstly, analyze and simulate the performance of system with channel attenuation, noise influence and OFDM modulation. In order to obtain better performance under the case of serious impulse noise, improvements need to be made on the system.
Motivation and detailed methods will be described.
Chapter 6
Performance of improvements are simulated and compared for both theoretical and practical situations.
Chapter 7
Make conclusions on the work. Indicate deficiencies and further work.
Chapter 2 Power line channel characterization
2.1 Overview
Power lines were initially set up for electric power transmission in the frequency range between 50 and 60 Hz and data transmission through power line was first launched by power distribution system to protect sections in case of faults. Since the Internet has developed rapidly in last decades due to the very large scale integration and digital signal processing achievements, power line communication is once more concentrated attentions as one of the best candidates for Internet access.
Researchers have made a large amount of investigations into this field and figured out the power line channel has enough bandwidth for high‐speed data transmission (above 2Mbps). The dominant advantage of PLC lies in the general deployment of power grid in household which makes it feasible to get access to Internet wherever by exploiting existent power delivery infrastructure even for rural or remote areas.
However, it could be a really tough work confronted with a number of problems.
Generally, power line carrier provides a harsh environment for data transmission due to three main issues:
(1) Transmission attenuation
The attenuation for power line has two main aspects: coupling attenuation and line attenuation. The cause for coupling attenuation lies in the mismatch of line input impedance and communication modules, which can be enhanced by adjusting the communication module output impedance.
As for line attenuation, since power line is generally made of aluminum or other kinds of good conductors of which the resistance are rather small and steady for signals with various frequencies, the main factor for this kind of attenuation rests on the complexity of electric network infrastructure rather than the resistance of the lines and thus has a time‐varying characteristics brought by plugging in and pulling out the electric appliances. Hence, attenuation of power line transmission significantly depends on line attenuation when the internal impedance of coupler is made small.
Moreover, there are large attenuations between three‐phase power line channels (about 10‐30dB). Generally, carrier signal can be only transmitted along power line with single phase, however, out‐phase signals can be received when communication distance is short. Different ways of coupling determines the attenuation for PLC signals and cross‐phase coupling attenuation is about 10dB larger than in‐phase coupling.
(2) Impedance mismatching
The impedance characteristic for power line is rather important when employed as communication medium since it concerns the efficiency of transmitter and receiver.
Due to the random actions of plug‐in and pull‐out of the electric loads, the input impedance tends to vary in a large degree in both time and position making it hard for the receiver to have a matching output impedance and serious reflection is brought in as a result. Reflection spots lead to the repeated reflections and multipath transmission, in which the phase of signals from multipath of a certain frequency can
be deviated just 180 degrees and thus counteracted. As a consequence, deep fading happens on some certain frequencies and causes the frequency‐selective characteristics for power line communication.
(3) Noise effect
The main kind of noise in power line channels is not additive Gaussian white noise;
instead it is likely to vary rapidly in a short period caused by all kinds of electric appliances in power networks which may have a disastrous effect for data transmission. In general, noise appear in power line communication includes colored background noise and impulse noise which can be further classified into five categories and will be illustrated further in the subsequent session.
As in most occasions, power line channel should also be expressed by the combination of a channel model and noise. And in the later session, those two parts will be discussed in detail respectively.
Figure 2‐1 Basic communication system model
2.2 PLC channel modeling
2.2.1 Introduction
Channel model is of paramount importance for any communication system since the design and optimization of systems have to be matched to particular channel characteristics. Generally, performance analysis and investigations of a certain transmission environment depend on the availability of accurate channel models that are commonly recognized. Since power line provides harsh and noisy environment for data transmission, models which effectively describing channel characteristics are required and have been widely investigated in the recent decades among which two approaches are top‐down and bottom‐up approach.
The top‐down approach treats the PLC channels a black box, using echo models for multi‐path transmission and retrieves the corresponding parameters from the measurements. The method is easy to implement and requires little computation;
moreover, it is suitable and simple for computer simulation. However, the practical applicability of this approach depends on the empirical accuracy like paramount
fitting methods. Furthermore, modeling channel is not capable of describing and reflecting the practical topology and the influence of loads, etc [8]. Researchers have done a lot of investigations in both time domain [9] [10] and frequency domain [11].
As for the bottom‐up approach, channel modeling starts from obtaining parameters by theoretically computation according to network components including lines and branches, which clearly describes the relationship between network behavior and model parameters. Besides, the bottom‐up approach is more versatile and flexible with regard to the changes in network topology by making modifications to the formulated parameters in the channel model. The disadvantage is much more computation is required compared to top‐down approach and it is also limited to theoretical analysis. For the mechanism of obtaining transfer function, either network matrix [12] approach or theory of transmission line (TL) [13] can be adopted.
2.2.2 Zimmermann and Dostert model
As mentioned above, since power grid has been developed into a multipurpose medium instead of a pure energy distribution network, power line communication has drawn much attention again. In particular, modeling of PLC channel is in the focus of various research activities. In contrast with several modeling proposals which were impractical using bottom‐up approach with limited frequency range, Zimmermann and Dostert put forward a top‐down channel model in the year 2002 in the paper “A multipath model for the powerline channel” [14] and caused a sensation. In this approach, channel is described by the transfer function H(f) with a frequency range of 500kHz to 20MHz and limited parameters, which is an analytic model suitable for computer simulation.
At first, frequency response is expressed as:
2 1
( ) N i ( , )i j f i
i
H f g A f d e
(2‐1)
Herein, N is the number of dominant path to reasonably approximates the infinite number of paths, gi is the weighting factor (a product of transmission and reflection factors), A(f, di) indicates the attenuation by cables which increases with length and frequency and i stands for the delay of a single path:
0
i r i
i
d d
c v
(c0 is the speed of light, di is the length of cables and r is the dielectric constant). Then by simplifying the propagation constant
0 1
( )
( , ) ( )f d fk di
A f d e e (2‐2) The final version of the frequency response is given as:
0 1 2 ( / )
( )
1
( ) N i fk di j f d vi p
i
H f g e e
(2‐3)
There are three parts in total representing weighting factor, attenuation portion and
delay portion respectively. To obtain the parameters in the formula, certain strategies are used for the estimation and finally the accuracy has been verified in the measurement. Parameters for four‐path and fifteen‐path of the network are given in the paper. [14]
Table I parameters of the four‐path model
Attenuation parameters k = 1 a0 = 0 a1 = 7.8*10‐10s/m
Path‐parameters
i gi di/m i gi di/m
1 0.64 200 3 ‐0.15 244.8
2 0.38 222.4 4 0.05 267.5
The simulation result of 4‐path channel response is shown in the following according to this modeling approach:
Figure 2‐2(a) Frequency response of channel modeling Figure2‐2 (b) Impulse response Thanks to the simplification and applicability of this channel model, it will be used for further research on the PLC system improvement under impulse noise in later chapters. The frequency range is 0‐25Mhz. Parameters and simulation results are also given in their paper for larger numbers of path modeling, which are more precise, presenting deep notches in certain spots, but to simplify N=4 is chosen for the simulation.
Moreover, there are some literatures attempting to make improvement on the basis of this modeling method which make parameters related to the reflections be random according to certain statistics [15]. For example, let the weighting factor be a product of a random sign flip and uniform distributed random variable with a range of (0,1].
2.3 Noise for PLC channel
2.3.1 Brief introduction
Since the fact that noise in the power lines has rarely similar characteristics with the common additive white Gaussian noise and is difficult to analyze, a large quantity of studies have been conducted in this field including noise classification, the impulse duration distribution, amplitude distribution and inter arrival time (IAT).
Typical sources of noise presented at PLC channel can be either internal (inside the power grid) such as fluorescents and brush motors or external (outside the power grid) such as switching power supplies or dimmer switches. A detailed classification of noise is described in the following [17].
(a) Colored background noise: caused by the summation of various noise sources with rather low power. It has a relatively low power spectrum density (PSD) and varies with frequency (decreases with increasing frequency). Regarding time, it varies slowly over time, remaining constant in terms of minutes or even hours.
(b) Narrow‐band noise: mostly consists of amplitude modulated sinusoidal signals caused by short and medium wave interference from broadcast station. The interference level varies during different times of the day.
(c) Periodic impulse noise asynchronous to the mains frequency: caused by switching power supplies on the network. The repetition rate is between 50 and 200 kHz.
(d) Periodic impulse noise synchronous to the mains frequency: mainly caused by switching actions of rectifier diodes found in many electrical appliances.
(e) Asynchronous impulse noise: caused by the transient in the power grid and occurs randomly. This type of noise can be up to 105 times stronger than the background noise.
noise Colored background noise
Narrow‐band noise Periodic impulse noise asynchronous to the mains frequency
Periodic impulse noise synchronous to the mains
frequency
Asynchronous impulse noise
channel +
Figure 2‐3 Noise classification in power line channel
Generally, as for the first two types of noise, since the root mean square (RMS) amplitudes vary slowly with time (minutes or hours), so that they can be summarized as background noise. While for the latter three types, they can be categorized as impulse noise due to the rapid changing amplitude (microseconds or milliseconds).
2.3.2 Noise modeling techniques for PLC
Since noise is hard to be modeling and characterized from theory analysis, most of the existing noise modeling methods are based on empirical measurements. Noise modeling can be divided into time‐domain and frequency‐domain approaches according to measuring technique. Frequency‐domain approach is the measurement in terms of noise frequency spectrum while time‐domain approach measures the noise real value over time.
For background noise, frequency‐domain approach is usually employed. To obtain both average noise spectrum and the corresponding randomness at each particular frequency, background noise variation should be represented as probability density function (PDF) with statistical method after fitting PSD of the measured noise into some certain functions of frequency [18]. Proposed PDFs for promoted noise model includes “sum of two Rayleigh” distribution, log‐normal distribution and Gaussian distribution [19].
On the other hand, impulse noise is modeling completely by measurement. In time‐domain impulse can be characterized with three parameters: amplitude, impulse duration and IAT. From literatures noise models in time‐domain are based on statistical characteristics of these three parameters, of which the probability distribution are gained from measurement in most cases. Some researchers proposed to characterize distributions for those parameters with partitioned Markov chain, in which the transition probability metrics are derived from measurement [20].
Besides, some researchers came up with the cyclo‐stationary noise model to characterize the summation of background noise and impulse noise. However, this model is based on the assumption that most noise in power line channel change with synchronization of half cycles of the supplying power. Furthermore, several other researchers directly employ the “Class A” noise raised by Middleton to depict the impulse noise in terms of amplitude and interval distribution [21].
2.3.3 Middleton Class A noise
In paper [21], Middleton put forward a canonical formula for noise representative of both natural electromagnetic (EM) and man‐made interference hugely distinctive from Gaussian behavior. The deviation of models is rather mathematically complicated and based on a series of work by others. Parameters of the model are obtained from experimental data and agreement between theory and experiment inclusive of different types of noise has revealed the availability of this model.
Owing to the fact that this noise model is not specifically set up for power line channel, its accuracy for modeling noise presented in power line is still inconclusive to some extent. However, being a classic model employed in real‐world EM interference over the years, it is still applicable characterizing noise in power line.
Hence, this noise model is selected for characterizing PLC environment together with
the channel model described in the last section considering the manageable and canonical characteristics. And since power line channels belong to the Class A type, expression and parameters are described as follows. The phase character has been proved to be uniformly distributed in(0, 2 ) . For envelope of the noise, the probability density function should be as follows:
2/2 2 0 2
( ) !
m z m
A
m m
A z e p z e
m
,0 z (2‐4)
The total power of noise 2G2I2is the sum of Gaussian noise power and impulse noise power and herein 2 2 /
m 1
m A
. The noise model can be treat as impulse sources of Poison distribution eAAm/ !m with the background noise of Gaussian behavior when m=0. There are three parameters as follows.
(a) Overlap index A: defined as the product of the average number of impulses per second and the mean duration of that emission. With a small A, the instantaneous noise characters mainly depend each individual event presenting impulsive behavior, while for the noise with a large A value its properties includes more statistic factors [21].
(b) “Gaussian factor” G2/I2: with G2and 2 Arepresenting the mean power of Gaussian component and impulse component of the input interference respectively, Gaussian factor expresses the ratio between them. When both A and are small, i.e. A being 0( 1, 2) and being 0( 1/2), the dominant component should be the impulse part.
(c) I2: intensity of the “non‐Gaussian” impulsive interference.
According to the conception above and formula (2‐4), the probability density for noise envelop is as follows. The parameters employed here are A=0.35, 5 104 [21].
The factor Am / !m makes each term
2 2
2
/ 2
!
m z
A m
m
A z e
e m
decreases rapidly with the
increasing m. Terms should be summed until Am/ !m is not larger than the error tolerance providing an accurate approximation. As can be seen in the following, since terms with m>3 contributes very little to the whole probability density function curve, m=3 is enough for most situations with a rather small value of A [22].
Figure 2‐4 Normalized PDF terms with m=0‐4 Figure 2‐5 Normalized PDF for Class A noise For better understanding of the noise model simulations with various parameters are performed and compared in the Figure 2‐6(a) and (b).
Figure 2‐6(a) Class A noise of various A Figure 2‐6(b) Class A noise of various For Figure 2‐6(a), the value ofis set as 0.01 and value of A varies from 1 to 3. As mentioned previous the parameter A can be treated as an indicator of the level of
“Gaussianness” for the noise distribution. When taking a small value, such as A=1 in this case, the chances of high power noise emerging is small and the noise is more dependent on those impulse which are difficult to handle. While with a larger A, such as 3, high power impulse is more usual and behaves closer to Gaussian noise.
For Figure 2‐6(b), the overlap index A is settled as 0.35 and the noise power radio differentiates among 0.001, 0.01 and 0.1. Since presents the power ratio between Gaussian noise and impulsive noise, with a largethe total power is more concentrated in Gaussian part while when is small, only a small portion of energy
is attributed to Gaussian section.
Chapter 3 Key techniques of power line communications
For power line communication systems, the most serious problems that affect the transmission quality are multipath fading and impulsive noise. Fading influence can be disposed easily for signals with narrow band, but for those having rather broad band inter‐symbol interference (ISI) occur as a consequence of frequency selective fading and lead to the rapid increase in bit error rate. Hence, channel self‐adaption equalization measures have to be adopted, of which the complexity increases with the high demanding transmission rate. Fortunately, channel interference elimination could also turn to a more advanced multi‐carrier modulation scheme‐OFDM, which has been widely used in standards and practice.
In the presence of impulse noise, OFDM modulation also provides an advantage since the energy of impulse noise is evenly spread among sub‐carriers thus decreasing the bit error rate. In the thesis, OFDM modulation is employed working together with channel coding to provide good performance.
3.1 OFDM modulation fundamental
The traditional ways for multi‐carrier transmission generally take advantage of the non‐overlapping frequency division modulation (FDM), in which guard bands (fg) are added between adjacent carriers so as to reduce interference between them.
However, the guard band reduces the available frequency source and leads to a waste. Hence OFDM modulation scheme has been put forward and significantly improved the utilization efficiency of frequency spectrum by exploiting multiple orthogonal carries, of which the spectrum can be overlapped each other.
As for OFDM modulation system with N sub‐carriers, each sub‐channel has multi‐path fading respectively. However, the bit rate for each sub‐carrier is just the 1/N of that for single carrier with the same transmission rate, extending the symbol period to N times larger than before. As a consequence, high‐rate transmission can be achieved with satisfied transmission quality since the extended symbol period is probably larger than the channel maximum time delay and thus reduces the ISI and system equalization complexity. Besides, in order to remove the influence of multi‐path, guard intervals (GI) are inserted in between each OFDM symbol for the sake of ISI by being made larger than the maximum channel time delay.
Unfortunately, the insertion of GI may introduce inter channel interference (ICI), thus in order to keep the orthogonality between sub‐channels, cyclic prefix (CP) should be bought in as the GI. In this way, channels become independent without the influence of ICI or ISI, which can be seen as non‐frequency selective respectively though the whole channel is a selective one. At the receiver side, simple frequency equalizers are capable of eliminating the effect of selective fading.
The mechanism of OFDM is illustrated in the following picture:
