relatÓrio de progresso · os relatórios de progresso, apresentados no final de cada ano civil,...

União Europeia – Fundos Estruturais Governo da República Portuguesa

PROJECTOS DE INVESTIGAÇÃO CIENTÍFICA E DESENVOLVIMENTO TECNOLÓGICO

RELATÓRIO DE PROGRESSO

Relatório de Execução Material Relatório de Execução Financeira

REFERÊNCIA DO PROJECTO Nº __ POS_C/EEA-CPS/59401/2004

RELATÓRIO REFERENTE AO ___1__º ANO DE EXECUÇÃO


NORMAS PARA A ELABORAÇÃO DO RELATÓRIO DE PROGRESSO

Os relatórios de progresso, apresentados no final de cada ano civil, fazem o ponto da situação sobre o andamento dos trabalhos e devem conter todos os dados que se mostrem necessários à apreciação e avaliação da execução do projecto. Os relatórios de progresso são compostos por duas partes: 1. A parte referente à EXECUÇÃO MATERIAL descreve de forma pormenorizada (incluindo

tabelas, quadros ou mapas) a execução dos trabalhos do projecto ao longo do período considerado, de acordo com a programação e calendarização constante na proposta aprovada, bem como uma análise dos desvios verificados face ao programado, a fim de permitir a avaliação dos trabalhos de investigação desenvolvidos. Deve igualmente incluir cópia das publicações ou de outras formas de divulgação efectuadas no âmbito do projecto, preferencialmente apresentadas em CD-ROM.

2. A parte referente à EXECUÇÃO FINANCEIRA discrimina a forma como foram aplicados os

quantitativos atribuídos ao projecto aprovado, independentemente de já terem sido objecto de pedidos de pagamento. Para tal deve-se proceder ao preenchimento dos quadros constantes neste formulário.

Com vista a uma sistematização de procedimentos relativamente à elaboração do relatório de execução financeira, as despesas efectuadas no âmbito do projecto devem ser apresentadas por rubricas e discriminadas nos quadros em anexo. Os documentos comprovativos das despesas efectuadas apenas deverão ser enviados em casos excepcionais em que não tenham sido anexados aos respectivos pedidos de pagamento apresentados à FCT. Devem ser rigorosamente observadas as cláusulas do Regulamento para atribuição de financiamento a projectos de investigação científica e as Normas de execução financeira em vigor na FCT.

SPP

2004-01-26


Identificação da instituição proponente

Nome ou designação social Instituto de Engenharia de Sistemas e Computadores, Investigação e

Desenvolvimento em Lisboa (INESC-ID)

Morada R. Alves Redol, 9

LocalidadeLisboa Código postal 1000-029

Telefone 213100300 Fax 213145843 Email [email protected]

Unidade responsável pela execução do projecto

Nome Sistemas de Processamento de Sinal

Morada R. Alves Redol, 9

LocalidadeLisboa Código postal 1000-029


Identificação do investigador responsável

Nome José António Beltran Gerald


Data de Entrada_____________________ Data de Verificação__________________ Nº de Registo ______________________ Assinatura ________________________

Espaço reservado à Fundação para a Ciência e a Tecnologia

Referência do projecto: POSC/_EEA-CPS/_59401/_2004__

Título do projecto: Sistema de Comunicação OFDM Adaptativo na Rede de

Distribuição de Energia Eléctrica

Data de Início do Projecto: __1__/___Abril______/__2005__

Duração: _24___ Meses


Instituições que participam no projecto (preencher só em caso de haver alterações) DESIGNAÇÃO

Instituição 1

Instituição 2

Instituição 3

Instituição 4

Equipa de investigação (preencher só em caso de haver alterações)

NOME CARGO/FUNÇÃO TAREFAS %TEMPO

Esforço global do projecto, expresso na unidade pessoa*mês

(referente ao ____1º____ ano de execução)

Unidade: em número

Instituição Proponente 8,25

Instituição 1 2

Instituição 2

Instituição 3

Instituição 4


Resumo dos trabalhos desenvolvidos No período aqui relatado, decorreram as Tarefa 1 - "Power Line Model Validation" (de 1de Abril 31 de Dezembro de 2005), Tarefa 2 - "Comparative study of Coding Schemes and Digital Modulation Techniques" (de 1 de Outubro a 31 de Dezembro de 2005) e Tarefa 3 - "Adaptive Communication Techniques" (de 1 de Outubro a 31 de Dezembro de 2005). Os trabalhos visaram os objectivos das respectivas tarefas, especialmente a de validação do modelo a adoptar para a linha de distribuição de energia. Também, foi iniciado a realização de um sistema de simulação em computador para estudo das técnicas OFDM, necessário à execução das restantes 2 tarefas. Tarefa 1: No referente à primeira tarefa (esta tarefa tem 9 meses de execução e vai continuar), foi realizado um novo sistema de interface em hardware para acoplamento à linha de distribuição de energia eléctrica. Este sistema permite acoplamento com isolamento galvânico, tem protecções a sobrecargas na linha, dispõe de um interface para o utilizador (ainda em desenvolvimento) e serve para testar a linha e comunicar em OFDM (ainda em desenvolvimento). Foi melhorado o sistema base, mediante uma caracterização completa do sistema de interface e implementação de hardware dedicado à facilidade de manuseamento do sistema, nomeadamente para interface com PC. Foram realizadas experiências com a linha de 220 V. As experiências já realizadas confirmaram o perfil de ruído típico das linhas de distribuição de energia eléctrica, a característica de impedância destas e a variação da atenuação com a distância e com as fases escolhidas. Esta tarefa produziu 1 protótipo (par de interfaces). Tarefa 2: No referente à Tarefa 2 (esta tem 3 meses de execução e vai continuar), foi começado a desenvolver um sistema base de simulação em computador (utilizando o programa Matlab com Simulink) de comunicação na linha de distribuição de energia eléctrica usando OFDM. Foi assim produzida uma aplicação computacional. A parte já desenvolvida do programa de simulação representa as tarefas base da comunicação em OFDM com um canal fornecido pelo operador, exceptuando as tarefas respeitantes ao sincronismo do receptor e codificação. Já se encontra implementado um versão clássica de repartição dos bits pelas subportadoras, de acordo com uma estimativa do canal em termos de relação sinal-ruído. Foi Também realizado um estudo teórico (que ainda continua) respeitante às técnicas de sincronismo do receptor. Tarefa 3: No referente à Tarefa 3 (esta tem 3 meses de execução e vai continuar), esta depende muito das 2 tarefas precedentes, com especial relevo para o programa de simulação em desenvolvimento. Assim, foram iniciados os estudos teóricos respeitantes às técnicas adaptativas clássicas para optimizar a comunicação com OFDM, não exclusivamente em linhas de distribuição de energia eléctrica, mas também em comunicação em RF via espaço livre.


Indicadores de realização física

(Referente ao _1º____ ano de execução)

Unidade: em número

A- Publicações

Livros

Artigos em revistas internacionais

Artigos em revistas nacionais

B- Comunicações

Em congressos científicos internacionais

Em congressos científicos nacionais

C- Relatórios

D- Organização de seminários e conferências

E- Formação Avançada

Teses de Doutoramento

Teses de Mestrado

Outra 3

F- Modelos

G- Aplicações computacionais 1

H- Instalações Piloto

I- Protótipos laboratoriais 1

J- Patentes

L- Outros (discriminar)


Publicações (listar as publicações com origem no projecto)

AS REFERÊNCIAS BIBLIOGRÁFICAS DEVEM CONTER OS SEGUINTES ELEMENTOS ESSENCIAIS: LIVROS: Autor(es); Título; Número e/ou identificação da edição; Número do volume; Lugar da publicação; Ano da publicação; Número de páginas. TRABALHOS ORIGINAIS PUBLICADOS EM REVISTAS CIENTÍFICAS E TRABALHOS DE REVISÃO E/OU PUBLICAÇÃO: Autor(es); Título do artigo; Título da Revista; Lugar da publicação; Número do volume ou ano; Número da primeira e última página; Ano de publicação. ABSTRACTS DE COMUNICAÇÕES CIENTÍFICAS OU OUTRAS PARTICIPAÇÕES DE ÍNDOLE CIENTÍFICA EM CONGRESSOS NACIONAIS OU INTERNACIONAIS: Autor(es); Título da comunicação; Nome da publicação; Volume; Número de páginas; Ano. Nos trabalhos aceites para publicação deve ser mencionada a revista e a data de aceitação.


RELATÓRIO DE EXECUÇÃO MATERIAL

(incluir o relatório de execução material elaborado de acordo com as normas)

Authors: José A. B. Gerald

Gonçalo N. G. Tavares Paulo A. C. Lopes


Relatório de Execução Material ( in english)

Objectives (as stated in the proposal): The main objective of this research project is the study and simulation of a digital communication system over power lines using OFDM-like multicarrier technology, and operating with data-rates above 1 Mbps. The tasks to be performed in this project will lead to a deep understanding of the power line transmission medium. The characterization of the transmission medium will also provide a mathematical model for the communication channel. The identification of digital modulation schemes for OFDM subcarrier modulation, which best suit the specific problems in PLC is also one key objective of this project. Another objective is the development of new OFDM precoding techniques that will effectively mitigate the adverse effect of the channel. These techniques will allow reliable transmission even in the presence of deep spectral nulls in the channel transfer function and will provide a blind channel identification algorithm. The development of a custom, user-friendly and versatile software simulation tool, specific tailored to the PLC environment, is also an important goal of this project. Task 1 - Power Line Model Validation (01-04-2005 to 31-03-2006) To find the theoretical models that best fit the experimental results already available by the project team and some yet to be obtained.

Results at month 9: The work in this task began by implementing a hardware system to interface with the power lines. The system was implemented (almost all) and experimental results are being executed. Until recently, most home’s and building’s automation was realized through systems which need a special transmission medium, such as, pair of twisted wires, coaxial cable or optical fiber. Recent technological developments led to power line medium equipments which send and receive information with some reliability, [1]. The main advantage of a PLC system is that the physical medium is already installed, making it an attractive alternative in all buildings without pre-routed data infrastructure, like historical buildings or brief local data networks, [2]. The implementation of a PLC system has some advantages when compared with others, since additional costs in a data network installation are avoided. However, although the transmission can be easily executed, the reception needs complex decoding and forward error correction algorithms. Due to this, a complex decoding algorithm, like OFDM (Orthogonal Frequency Division Multiplexing) or SS (Spread Spectrum) is required, [3] [4] [5]. Also, in order to implement a PLC system is necessary to study the communication channel characteristics, because the choice of the system’s architecture depends on these results. The system adopts a mixed solution between analog and digital circuitry. While the digital circuits were used for control and digital processing purposes, the analog focused on coupling, filtering and signal amplification of the emitted and received signal.


The interface system’s architecture is shown in Figure 1.

Figure 1 – PLC Interface System Architecture.

This system is composed by coupling and (analog and digital) signal processing circuits, and can be subdivided in three blocks: (i) AFE (Analog Front End), composed by the analog signal processing circuits (from the coupling to the AD/DA converter’s input); (ii) Analog-to-Digital (ADC) and Digital-to-Analog (DAC) Converters; (iii) Modem, which includes the digital signal processing for the control, modulation and demodulation operations.

1. AFE (Analog Front End) In PLC systems, where the transmission medium is the electrical power network, it is necessary to have a galvanic isolation between the transmission circuits and the power line. Thus the coupling was realized through a transformer with a bandwidth of 1MHz to 30MHz. Its purpose, besides the galvanic isolation, is to drop off the high voltage of the power line (with a frequency of 50 Hz, in this case). The coupling to the mains is accomplished by means of two essential elements: the transformer and the filters. The purposes of these circuits are:

1. Adaptation between the transmitted signals and the transmission channel; 2. Galvanic insulation; 3. Reduction of parasitic noise, outside the used bandwidth, (realized through

the transformer ‘s bandwidth and the filters cut off frequencies); 4. Circuit’s protection by the limitation of the maximum signal excursion.

Transformer The transformer is an extremely important element, since the circuit performance and maximum rate transmission depend on its characteristics [6]. Its manufacture and characterization is essential to develop, produce and implement a high quality AFE. In this system, the transformer was design in order to operate in the 1 MHz to 30 MHz frequency bandwidth. The transformer representation is illustrated in Figure 2. The corresponding Steinmetz concentrated parameters model is illustrated in Figure 3. Using this architecture, a computational model was implemented in order to characterize and optimize the transfer function.


Figure 2 – Transformer

representation.

Figure 3 – Steinmetz model.

As the Steinmetz’s model parameter values can not be directly determined, they were calculated through impedance measurements, according to the following method:

1. Impedance measurement of each coil, separately, in order to determine their inductances (L11 and L22), loss resistances (Rc, R1 and R2) and the coil capacitances (C1 and C2).

2. Inductance measurement of the two coils when coupled in series (Ls). 3. Inductance measurement of the two coils when coupled in anti-series (Las).

Analyzing the transformer equivalent models with coils in series and anti-series, represented in Figures 4 and 5, respectively, it is possible to conclude that the equivalent inductance for both coils is:

2

11 22

2

11 22

( 1)

( 1)

s M

as M

nL L L Ln

nL L L Ln

+= + +

−= + +

(1)

(2)

Z22Z11

VG

V2nV2

I-I/nn:1

Figure 4 – Transformer’s equivalent

model with both coils in series.

Z22Z11

VG

V2nV2

II/nn:1

Figure 5 – Transformer’s equivalent model with both coils in anti-series.

Note that, the coil and intercoil capacitances were disregarded since their value is small (approximately 1pF). This approach was later confirmed by the experimental results. From (1) and (2) and solving in order to LM, the magnetizing inductance is given by,

( )14M s asL L L= − (3)

Also, the coupling coefficient k and the L11 e L22 inductances are given by:

1 2 1 2

14

s asM L LLkL L L L

−= =

(4)

(5)


11 1

22 21

M

M

L L nL

L L Ln

= −

= −

(6)

Finally, these values were slightly adjusted so that the obtained model could represent the measured transfer function of the transformer, with the smallest error possible for the considered bandwidth.

Power Line Filter and Protection Circuits In order to suppress the power line high energy signal (with 50 Hz frequency and 2 ×220 V of peak value), besides the transformer own attenuation, a first order high-pass filter was implemented by means of the two capacitors Cline, in the primary of the transformer, introducing a low frequency zero and isolating both terminals from the power line (see Figure 6). Once found the equivalent transformer parameters, Steinmetz model, and known its impedance when loaded with the AFE circuit, the only unknown is the capacitor value. This allows one to calculate the first order filter components to eliminate the power supply harmful high energy signal.

1lineC

2lineC

Figure 6 – Power line filter.

Additionally, to protect the sensitive AFE circuits from power line spikes, it was implemented an additional circuit using fast response diodes ( 1D and 2D ) to clamp these spikes (see Figure 6). Designating VD as the forward biasing diode voltage, the maximum voltage on the secondary will be given by:

EE D AFE CC DV V V V V− ≤ ≤ + (7)

Emitter Circuit The emitter can be described by the block diagram of Figure 7.

Figure 7 –Emitter block diagram circuit.


Next, each block will be presented and explained. The system was designed in a way that the emission signal, injected in the power line, is digitally created and controlled. This solution is intended to increase the system’s flexibility, making it possible to test several digital signal codifications, transmission schemes and techniques. The two most used transmission techniques in power line communications are SS (Spread Spectrum) and OFDM (Orthogonal Frequency Division Multiplexing). Since the DAC’s output is in current, a simple current to voltage circuit was implemented using an operational amplifier and some additional components (Current to Voltage Converter block). To help to reduce the abrupt signal level transitions of the DAC’s output, a second order Sallen&Key low pass filter was built (LP filter block). Also, other first order filters with cut off frequency around 30 MHz, were implemented along the emitter circuits in order to reduce the high frequency harmonics generated in the DAC’s output, thus improving the SNR (Signal to Noise Ratio). At last, in the output stage, the signal’s power fed into the coupling transformer is increased through a push-pull class AB driver. Figures 8 and 9 show the final transfer function of the emitter circuit obtained by simulation when the transformer is loaded with a 47Ω resistor (rough approximation to the power line impedance used to check the circuit’s transfer function).

10,00kHz 100,0kHz 1,000MHz 10,00MHz 100,0MHzFrequency (Hz)

(dB)

10,00

0,000

-10,00

-20,00

-30,00

-40,00

-50,00

-60,00

-70,00

dB(out/ input_lp)

Figure 8 – Amplitude characteristic of the emitter’s transfer function (simulated).


(Deg

)

0,000

-100,0

-200,0

-300,0

-400,0

-500,0

-600,0

-700,0

-800,0

PHASE(out)

Figure 9 – Phase characteristic of the emitter’s transfer function (simulated).

Receiver Circuit The implemented receiver block diagram is represented in Figure 10.

Figure 10 – Receiver’s Block Diagram.

Next, each block will be presented and explained. Although the transformer behaves like a band pass filter, conditioning the out of band noise, a Sallen&Key band pass filter was implemented in order to decrease the out of


band noise signals (BP block). As the AGC maximum gain is high, 48 dB, it is essential to reduce the noise in order to avoid pour SNR signal in the ADC converter. The automatic gain control is essential, as it prevents the signal at the ADC’s inputs to saturate, keeping it at appropriate levels. The power line characterization showed that the signal’s attenuation is closely related with the distance between the emitter and the receiver, making it necessary to implement an AGC circuit capable of responding to the channel’s characteristics changes. Finally, in a similar way to the emitter circuit, the decoding of the received signal is accomplished through digital processing of the converted analog to digital signal furnished by the ADC. Figures 11 and 12 show the final transfer function of the receiver circuit obtained by simulation when the AGC gain is set to one.


(dB)

50,00

25,00

0,000

-25,00

-50,00

-75,00

-100,0

-125,0

-150,0

dB(out_r/ in)

Figure 11 – Amplitude characteristic of the receiver’s transfer function

(simulated).


(Deg

)

0,000k

-0,250k

-0,500k

-0,750k

-1,000k

-1,250k

-1,500k

PHASE(out_r)

Figure 12 – Phase characteristic of the receiver’s transfer function (simulated).

2. Analog-to-Digital and Digital-to-Analog Converters The Analog-to-Digital converter (ADC) and the Digital-to-Analog converter (DAC) were chosen according to their performance and availability. The ADC used is the IC ADS826, which is a 10-bit ADC that operates till 60 MHz. The DAC used is the IC DAC900, which is a 10-bit DAC that achieves 165 MSPS.

3. Modem/PC Interface The signal processing, coding and decoding, makes use of digital techniques, using for such purpose an FPGA, an ADC and a DAC. This solution enables the use of a simple FPGA for digital processing or an advanced integrated PLC modem available in the market, which might have a higher hardware interface like JTAG and/or MII. If one chooses to use this type of modems, there are also integrated solutions that convert MII to USB interface, allowing a high level control and communication using a PC to achieve high binary rates. An example of this inter-connections and high level approach can be seen on Figure 13.


Figure 13 –Example of a system inter-connection between the AFE and the PC. Due to the level of complexity in developing the USB interface, the control (including coding and decoding) was made on a FPGA Spartan 200. Using the FPGA’s resources, it was implemented the receiver digital circuit represented in Figure 14.

Figure 14 – FPGA emitter block diagram.

The main principle of the emitter consists on placing the coded wave forms (used on the channel’s coding scheme) and data in the FPGA’s memory. The memory access (by the emitter control) is made in a synchronous way with the clock, preventing oscillations on the binary data fed into the DAC in the AFE board. The coding and decoding of an OFDM signal will be considered later due to its high level of complexity and small relevance for the design and test of the AFE board. So, in order to test the system, another transmission method, simpler, was adopted: a narrow band FSK signal using non-coherent detection, as represented in Figure 15.


Figure 15 – Narrow band non-coherent receiver’s decoding mechanist block diagram using a counter.

In this technique, Figure 15, the received signal is digitalized and used to create a counter’s enable/reset signal. Since the clock frequency is much higher then the one used for carriers (Nyquist theorem), the signal decoding is possible by using only a counter, enabled on the positive arcades and cleared on the negative ones. With this method, the transmitted data is decoded and directly given by the counter’s final value, as is represented by the receiver’s waveforms of Figure 16.

Figure 16 – Decoding receiver’s waveforms representation.

4. Experimental Results

The transmission medium (the power line) does not present constant characteristics and parameters, depending on the quantity and type of equipment connected to it. So, these characteristics, noise, channel impedance and attenuation, vary not only with the location, but also over time, allowing the establishment of a time relation with the day period. Thus, the PLC interface system must be capable of adapting to inconstant power line characteristics and of achieving the higher transmission rate possible in such conditions. Although other models and power line evaluation have been presented by several authors, [7] [8] [9], in order to better characterize the transmission channel, the power line impedance, the observed noise and the line attenuation were studied over time. The experimental results were taken in a scientific laboratory located on a residential area. A 15 miliwatts mean power signal was used in the experiments. However, the system was designed not only to have the flexibility to adapt to future regulation of spectrum and power usage, [10] [11], but also to have the capability of changing of modulation schemes.


For the purpose of testing and validation, a simple narrow band FSK modulation scheme was used achieving a maximum rate of about 1 Mbit/s. However, if a different and more complex modulation technique were employed, OFDM for example, one can expect to achieve higher transmission rates, [12]. From the impedance measurement results, illustrated in Figure 17, one verifies that it hardly varies over time ( 10%≅ of maximum punctual variation), so it may be considered constant for future calculations. These values have high reliability for the 500kHz to 21MHz frequency bandwidth. As all experiments began at 9am, the following temporal correspondence, between the day and graphical hours, must be done:

hourday = hourgraphic + 9 [hours] (8) In what concerns the noise spectrum, the experimental results up to 30 MHz are illustrated in Figures 18 and 19. For frequencies up to 145 kHz (where it assumes the higher values), the noise is essentially due to:

1. Coloured background noise (produced by electrical motors, microwave ovens and light dimmers);

2. Narrowband noise (caused by radio AM broadcast signals ingress and TVs horizontal synchronism frequency);

3. Impulsive noise (produced by on and off switching events). The observation of the recorded temporal evolution values in Figures 18 and 19 confirm these assumptions, as the highest noise levels in low frequency occur around 9 pm, when the greater number of televisions, microwave ovens and light dimmers are turned on, as well as others on/off electrical switching events.

Figure 17 – PLC impedance throughout 48

hours.


Figure 18 – PLC channel noise throughout 48 hours.

Figure 19 -PLC channel noise throughout 48 hours.

Due to the electrical characteristics of the power line, this can be considered as bifilar transmission line (pair of parallel wires) or pair of twisted wires. This way, according to the general line transmission theory, for low frequencies the attenuation is close related with the distance between the emitter and the receiver, as illustrated in Figure 20. In high frequencies, due to reflections by mismatched impedances, the signal attenuation in the medium is almost not dependent on the distance between the emitter and the receiver (Figure 20). The attenuation between different network phases is similar to the verified for the same phase for a distance of 30 meters (Figure 21). This fact can be justified not only by the parallel wires transmission line concentrated parameters model, mainly the capacitance C between the conductors that produce coupling, but also by the electromagnetically radiation produced at these frequencies.

Figure 20 – Attenuation dependence with the distance between the emitter and the

receiver.

Figure 21 – Attenuation between the emitter and the receiver, when

connected to different network phases. Another interesting topic for the interested reader is the reference [13], where other problems with these high frequency systems are discussed, related with signal reach and loss. This work continues now with more experiences with the power lines, in order to characterize their transfer function as a channel and with the goal of optimize the overall interface system, namely, introducing OFDM schemes and improving the system interaction with the user.

Task 1 References

[1] Developments in high frequency communications using the low voltage power distribution network, http://www.metering.com


[2] Niovi Pavlidou et al., “Power Line Communications: State of the Art and Future Trends”, IEEE Communications Magazine, Abril 2003.E. Biglieri, “Coding and Modulation for a Horrible Channel”, IEEE Communications Magazine, Maio 2003.

[3] Savo Glisic, Branka Vucetic, “Spread Spectrum CDMA Systems for Wireless Communications”, Artech House Publishers, Boston London, 1997.

[4] “OFDM – technical note”, http://www.magnadesignnet.com/technote/ofdm [5] M. Speth, “OFDM Receivers for Broadband-Transmission”,

http://www.iss.rwthaachen.de/Projekte/Theo/OFDM/www_ofdm.html. [6] RF Transformers, http://www.minicircuits.com [7] F. J. Cañete et al., “Modeling and Evaluation of the Indoor Power Line

Transmission Medium”, IEEE Communications Magazine, Abril 2003. [8] M. Sellars, D. Kostas, “Comparison of QPSK/QAM OFDM and Spread Spectrum

for the 2-11GHz PMP BWAS”, IEEE 802.16.3.c-00/23, Setembro 2000. [9] Manfred Zimmermann e Klaus Dostert, “A Multipath Model for the Powerline

Channel”, IEEE Transactions on Communications, vol.50, No. 4, Abril 2002. [10] Gerald Schickhuber, Oliver McCarthy, “Power Line Communication in Europe”,

University of Limerick, Limerick, Ireland. [11] Power Line Communication, http://www.geocities.com/luisferm/pdf/ [12] E. Biglieri, “Coding and Modulation for a Horrible Channel”, IEEE

Communications Magazine, Maio 2003. [13] Jose Abad et al., “Extending the Power Line LAN Up to the Neighborhood

Transformer”, IEEE communications Magazine, Abril 2003.

Task 2 – Comparative Study of Coding Schemes and Digital Modulation Techniques (01-10-2005 to 30-09-2006) To study and compare the different coding strategies that best suits the communication over power lines. Also, to compare the different digital modulation techniques that can be used to modulate OFDM subcarriers.

Results at month 3:

1. Matlab Simulink Simulation of a MODEM for high speed Power Line Communications

As proposed a power line communication (PLC) system simulation is being developed. The system is being constructed in Matlab with Simulink in order to take advantage of the large number of tools that this platform offers while still maintaining a high degree of flexibility and ease of use. The MODEM implemented is an adaptive OFDM MODEM. The proposed modem has a variable bit rate which adapts to the signal to noise ratio in each sub-carrier. We define a bit block as the groping of all the bits for all the subcarriers in the OFDM system. A packet can be formed by one or more of such blocks. This implies that the block size and packed size will be variable in length. This causes some problems simulink, since usually one would implement the processing one block at a time, and this implies that the signal carrying bus in


simulink must be variable in length. Since the signal carrying bus sizes are setup when the simulation starts this implies that the block size and the number of bits per carrier must be set before the start of the simulation. This is accomplished by using two different simulink systems to implement the MODEM. One system implements channel estimation and channel signal to noise assessment. In this system, the number of bits and the power that will be allocated to each sub-carrier is determined and the block length is determined. The other system implements the main PLC modem using the block length and bit distribution previously calculated.

Channel Estimation and Signal to Noise Ratio Assessment

The channel estimation and signal to noise ratio assessment system is formed by three blocks, as shown in the figure bellow. The modulator block (MODEM1), the channel model block and the demodulator block (MODEM2).

OFDM PLC MODEM

PulseGenerator1

click to open PLC_sim

PLC_sim

Rx_Signal

CE

MODEM2

Tx_Signal

MODEM1

0

Display

12:34

Digital Clock

In1 Out1

Channel

double

double

double (c) [288x1] double (c) [288x1]

Figure 2 – Channel estimation and signal to noise assessment system. The modulator is presented bellow.

1

Tx_Signal

U U(E)

Selector

In1 Out1

IFFT

ToFrame

Frame Status Conversion1

training_seq

DSPConstant1

double (c) [256x1]double (c) [288x1] double (c) [288x1]

[288x1]

double (c) [32x1]

[32x1]

[256x1]

[256x1]

double (c) [256x1]

Figure 3 - Modulator block

1Out1

IFFT -K-

Gain

ToSample


1In1

double (c) [256x1]double (c) [256x1] double (c) [256x1] double (c) [256x1]

Figure 4 – IFFT block The channel estimation is made using a training sequence. This sequence is generated by the training_seq block bellow. The sequence used is a random signal which resembles white noise, being fairly spread over time and frequency. This is better than a more obvious choice of a training sequence which is constant and equal to one for all bins, because this would result in a periodic impulse train after the IFFT operation, which would be hard to implement due to its very high peak to mean power ratio. The use of pseudo random sequences optimized for the given FFT length should give the


best peak to mean power ratio while still maintaining a flat spectrum. The FFT of the random sequence was then calculated and normalized to have an equal to one, constant, amplitude for all bins, while still maintaining a more or less random phase so that the signal would spread in time. After the training sequence block is the IFFT block. This block is essential in any OFDM system. It maps the signal bits into the time domain symbols that they correspond. This block is followed by the blocks that add the circular prefix. The circular prefix is a copy of the end of the block that is added before the beginning of the same block. Since all the symbols in an OFDM system have a period that is a fraction of the block length this is equivalent to prolong the symbols backward in time for some length. After passing throw a linear time invariant channel the sinusoidal symbols of the OFDM system will be modified by a transitory and forced response. The forced response of the channel will be compensated by the channel equalization at the reception. The transitory response will affect mainly the circular prefix, so by removing this prefix at the reception inter-symbolic interference can be totally eliminated. Finally there is a To Frame block that indicates that the signal vector should be treated as a time domain signal.

U U(E)

Selector

In1

CE

FFT&CE

2 CE

1Rx_Signal

double

double (c) [256x1]double (c) [288x1]

Figure 5 – Demodulator block The demodulator represented in Figure 5. It is composed by the selector block, that removes the circular prefix, and the FFT&CE block that implements the FFT and channel estimate operations. The FFT&CE block is presented in Figure 6. The FFT operation is followed by a N gain that guarantees that the signal is properly normalized. The channel estimate block is an enabled block. It is only enabled after passing the time correspondent to one block. This assures that the signal emitted by the modulator block has reached the demodulator. In an actual implementation some packet detection technique should be used do determine the arrival of the packet.


-K-

Gain

FFT

In1

CE1

2

CE

1

In1

double (c) [256x1] double (c) [256x1] double (c) [256x1]

[256x1]

double

Figure 6 – FFT&CE block The actual channel estimation is done by the block in Figure 7. The block generates two global variables in the matlab workspace: channel_estimate and signal_noise_ratio. The variables correspond as suggested to the channel estimate and the signal to noise ratio of the channel. MATLAB Fnc1, Fnc2 and Fnc3 are simple plotting commands that show the state of the simulation, namely the current channel estimate, received signal and training signal to noise estimate. The channel estimate is simply obtained by dividing the received signal by the training sequence at the input of the channel and averaging for several periods (namely 20 blocks). One should remember that after removing of the circular prefix only the forced response of the channel remains, that is characterized by an amplitude gain and phase for each OFDM symbol, or subcarrier. The averaging operation is a simple average as in,

1

][

ˆ 0

+

=∑=

Mt

ny

H

M

n i

i

i , (1)

where [ ]nyi is the input signal for bin i at time n , it is the training sequence complex value at bin i and M is the number of averages taken. However, this average is calculated interactively by the mean block, namely one has

1/][

1)1(ˆ)(ˆ

++

+−=

ntny

nnnHnH ii

ii , (2)

with 0)1(ˆ =−iH and ii HMH =)(ˆ . This is done by the mean block represented in Figure 8. The matlab function block implements a 1)/u-(u operation. In the right side of the figure are the blocks that calculate the value of n , which is stored in the delay block. At the left side of the figure are the blocks that update the value of )(ˆ nH i based on the new input sample.


signal_noise_ratio

To Workspace2

channel_estimate To Workspace

Product1

Product

Media

Média1

Media

Média

1

u

MathFunction3

|u|2MathFunction2 |u|2Math

Function1

|u|2

MathFunction

1

u

MahFunction4

MATLABFunction

MATLAB Fcn3

MATLABFunction

MATLAB Fcn2

MATLABFunction

MATLAB Fcn1

training_seq DSPConstant1

1e-9

DSPConstant

Enable

1In1

[256x1]

[256x1][256x1][256x1]

[256x1]

[256x1]

[256x1][256x1]

[256x1]

[256x1]

[256x1][256x1]

[256x1]

[256x1]

[256x1]

[256x1]

[256x1]

[256x1]

[256x1]

[256x1][256x1]

[256x1]

[256x1]

[256x1]

[256x1][256x1]

[256x1][256x1]

Figure 7 – Channel estimate and signal to noise ratio determination block.

1 Out1

z

1

Unit Delay1

Product2

Product1

1

uMath

Function

MATLABFunction

MATLAB Fcn

1 Constantz

1

Chanel Estimate

1 In1

[256x1]

[256x1]

[256x1]

[256x1]

[256x1]

[256x1][256x1]

[256x1]

[256x1]

[256x1]

Figure 8 – Iterative mean calculation block The signal to noise ratio (SNR) is given by, [ ] [ ]22 )(/E)(E nrny where [ ]ny is the received signal and [ ]nr is the noise at the receptor. This should be calculated for a given power value at each bin in the emitter. Since the power line communications signal is essentially limited by the radiation emitted by the signal for electromagnetic compatibility reasons, it is not limited by the total signal power, but by maximum values for the power spectral density, or the power allocated to each bin. This means


that each bin will always run at maximum or no power, to achieve the best signal to noise ratio. So by setting the power of the training sequence to this value the signal to noise ratio measured using the training sequence will be the same as in normal working conditions. The division by the training sequence at the left of the block will affect the signal and noise in the same way, and thus will not change the signal to noise ratio. This means that the blocks that were used to calculate the channel estimate can be used to calculate the signal power, and that the input signal can be assumed to be equal to one. So the signal power at each bin will be 2ˆ

ii HS = . Since the input signal is constant, then the noise power can be calculated simply by the variance of the received signal. This will be given by

[ ] [ ] [ ] 2222 ˆEEE iiiii HyyyN −=−= . The calculations are carried out by the Media1, Math Function1 and sum block in Figure 7. Finally the signal to noise ratio is calculated and stored in the signal_noise_ratio global variable.

Main PLC MODEM System In Figure 9 is the system for simulation of the main PLC MODEM. Once more it is composed of a modulator, the channel and the demodulator. The transmitted and received bits are compared in the “Error rate calculation block” to determine the bit error probability of the system. The received bits signal is delay of exactly one block relatively to the transmitted bits signal.

OFDM PLC MODEM

click to open channel_estimate

channel_estimate

Rx_Signal Rx_Bits

MODEM2

Tx_Bits Tx_Signal

MODEM1

[Rx_Bits][Tx_Bits]

[Rx_Bits]

[Tx_Bits] Error Rate

Calculation

Tx

Rx

0

Display

12:34

Digital Clock

in_bits

DSPConstant1

In1 Out1

Channel

0

[2020x1]

3[2020x1]

[2020x1]

[288x1][288x1][2020x1][2020x1]

[2020x1]

Figure 9 – Main PLC MODEM simulation

Channel Block

In Figure 10 is presented the channel block of the system. The “Fir Interpolation” implements the reconstruction filter at the output of the DSP board.

1Out1

In1 Out1

Modulator

x[n/4]

FIRInterpolation

x[4n]

FIRDecimation1

DF FIR

Digital Filter

In1 Out1

DesModulator1

In1

Calculate Power1

In1

Calculate Power

AWGN1In1

[288x1][288x1] [288x1][288x1][288x1]

[288x1]

[288x1] [288x1][288x1]

[288x1]

[288x1]

Figure 10 - Channel block

The in the Modulator block the base band complex signal is modulated around a carrier frequency FO.


1Out1

DSP

Sine Wave2DSP

Sine Wave1

Product1

Product

Re(u)Im(u)

Complex toReal-Imag

1In1

[288x1]

[288x1]

[288x1]

[288x1]

[288x1][288x1]

[288x1] [288x1]

[288x1]

[288x1][288x1]

[288x1]

Figure 11 - Modulator block

The modulator block is followed by the channel filter block that implements the actual channel impulse response using a FIR filter. The filter frequency response is represented in Figure 12 and the filter impulse response is presented in Figure 13.

0 0.5 1 1.5 2

x 107

-80

-70

-60

-50

-40

-30

-20

f (Hz) Figure 12 – Frequency the response of the Power Line Channel

0 1 2 3 4

x 10-6

-0.01

0

0.01

0.02

0.03

0.04

0.05

Figure 13 – Impulse response of the Power Line Channel

Following the digital filter block is the demodulator block, presented in Figure 14. The received signal is multiplied by the output of a complex oscillator, shifting the signal back to base band, and then lowpass filtered by the anti-aliasing filter at the input of the receiver.


1Out1

DSPSine Wave2

DSPSine Wave1

Re

Im

Real-Imag toComplex

Product

1In1

Figure 14 – Demodulator block

Finally is the additive white noise block to add noise at the receiver of the channel.

Emitter Block (MODEM1) In Figure 15 is represented the emitter block. It starts with a QAM Modulator block that implements a bank of QAM modulators with different constellation one for each FFT bin. The block is implemented as an “m” function. The bits at the input of the modulator are distributed to each simple QAM modulator according to the number of bits attributed to each bin by the bit loading technique, calculated after the channel estimation and signal to noise ratio assessment phase. The bits are assumed to be Gray coded. The block in fact implements a Gray to binary conversion, followed by a binary to decimal conversion. The calculation is done simultaneously for all input bits using Matlab vector processing. This is much faster than doing each calculation independently. Also the output of each QAM modulator is scaled so that the output power is constant for all input bins.

1

Tx_Signal

U U(E)

SelectorMATLABFunction

QAM Modulator

In1 Out1

IFFT

ToFrame


ToSample

Frame Status Conversion

1

Tx_Bits

Figure 15 - Emitter block

Table 1 – QAM Modulator code After the QAM Modulator is the IFFT block that creates the OFDM symbols based on the symbols amplitudes. This is followed circular prefix insertion as described in “Channel estimation and signal to noise ratio assessment” section.

function y = qam_modulator(in); global n_bitsPAM bit_ind max_bits max_value k_normalisation k_normalisation_inverse; M=length(n_bitsPAM); bits_raw = zeros(M, max_bits); bits_raw(bit_ind) = in; % cada bin passa a corresponder a duas linhas: real e imag value = bi2de(gray2bi(bits_raw),'left-msb')-max_value; value_cplx = value(1:2:M)+value(2:2:M)*j; y = value_cplx .* k_normalisation;


Receiver Block (MODEM2) The receiver block is represented in Figure 16. It starts with a selector block that removes the circular prefix. This is followed by FFT and channel equalization (FFT&CE) block presented in Figure 17.

1Rx_Bits

U U(E)

Selector

MATLABFunction

QAM DeModulator

ToFrame


ToSample

Frame Status Conversion

In1 Out1

FFT&CE

1Rx_Signal

[256x1] [256x1] 2018 [2018x1][256x1][288x1]

Figure 16 – Receiver block

The FFT&CE block implements the FFT operation, followed a normalization gain. After this channel equalization takes place by multiplying the output of each bin by the inverses of the channel estimate for that frequency.

1

Out1

A

D

ScaleColumns

A*D

MatrixScaling

-K-

Gain

FFT

channel_estimate_inverse

DSPConstant

1

In1 [256x1]

[256x1] [256x1] [256x1]

[1x256]

[1x256]

Figure 17 – FFT and channel equalization block

After this is the QAM demodulator block, implemented by an “m” file function. The operations effectuated are the inverse of the ones of the QAM modulator block. Namely a decimal to binary conversion is followed by a binary to Gray code conversion. The processing is once more done simultaneously for all subcarriers using Matlab vector processing. Some care must be taken to avoid overflows in the conversion.

Table 1 – QAM Demodulator code

This concludes the tour of the MODEM Implementation.

function bits = qam_demodulator(in); global n_bitsPAM bit_ind max_bits max_value k_normalisation k_normalisation_inverse; M=length(n_bitsPAM); in = in.*k_normalisation_inverse; value=zeros(M,1); value(1:2:M) = real(in); value(2:2:M) = imag(in); I = find(value>max_value); value(I)=max_value(I); value = value + max_value; value(find(value<0))=0; value=round(value); bits_raw = bi2gray(de2bi(value,max_bits,'left-msb')); bits = bits_raw(bit_ind);


Some Results The MODEM was simulated using the described channel and with a signal to noise ratio at the receiver of 20dB. In Figure 18 is presented, in linear scale, the estimated signal to noise ratio for each frequency bin. In Figure 19 the correspondent number of bits allocated for each frequency bin. This is calculated at the end of channel estimate and signal to noise ratio assessment so that the probability of error is lower than 310− .

0 50 100 150 200 250 3000

50

100

150Signal/Noise

Figure 18 – Signal to Noise Ratio for each frequency bin.

0 50 100 150 200 250

0

1

2

3

4

5

Figure 19 - Number of bits allocated for each bin based on the signal to noise ratio.

In Figure 20 is presented the estimated channel, amplitude and phase, for each frequency bin. The sampling frequency of the MODEM was of 10MHz, and the carrier frequency was of 10MHz. This means that the transmitted signal occupied the band from 5MHz to 15MHz. The channel viewed by the MODEM will be the 5MHz to 15MHz band of Figure 11. The reader can confirm that this in fact corresponds to Figure 20. The simulation was run and a global error probability of 4103 −× was obtained. Figure 21 represent the combined constellations for all output bins grouped together. One can see the 64-QAM constellation for the bins with 4 bits and the 4-QAM constellation for the bins with two bits. The figure was obtained with a very low noise level in the channel. It can be seen there is almost none inter symbolic interference.


0 50 100 150 200 250 3000

2

4x 10

-3 channel estimate

0 50 100 150 200 250 300-5

0

5channel estimate

Figure 20 - Channel estimate

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Constelation

Figure 21 – Constellation for all output bins grouped together with a very low noise

level. The improving of the simulator continues with the adding of complementary missing blocks, as for instance the synchronization processing.

2. Frequency offset Estimation in the OFDM Receiver One important disadvantage of OFDM transmission systems is its relatively high sensitivity to carrier frequency offsets which arise from small differences between transmitter and receiver oscillator frequencies and also from oscillator instabilities. The presence of frequency offset destroys the inherent orthogonality of the OFDM subcarriers and leads to reduced system performance. There are a significant number of carrier frequency offset estimators proposed to operate eith OFDM signals namely the algorithms of Schmidl and Cox [1], Morelli and Mengali [2] and Zhao, Zhang, Zhou, Liu and Gao [3]. The algorithm adopted in this project is the one proposed by one proposed by Morelli and Mengali [2].


An efficient algorithm for OFDM frequency offset estimation has been proposed by Schmidl and Cox [1] (Schmidl and Cox Algorithm, SCA). It uses one pilot OFDM symbol divided into two halves. The algorithm of Morelli and Mengali [2], is an extension of the SCA wherein the pilot symbol is divided in 2L > identical parts. It achieves both an accuracy and estimation range increase. Lets consider an OFDM signal which uses QPSK modulation in each subcarrier and is generated by means of and inverse fast Fourier transform IFFT applied to a vector of N QPSK symbols ic . The useful part of the OFDM symbol has duration T and is preceded by a cyclic prefix (CP) which, to avoid intersymbol interference (ISI) has duration superior to the channel impulse response. In the receiver, the signal ( )x t is sampled with a sampling period sT T N= , where N is the IFFT length. The normalized frequency offset (relative to the OFDM symbol frequency 1 T , is denoted v . The received signal samples may then be written: ( ) ( ) ( )2j vk Nx k e s k n kπ= + (1)

where ( )n k is the additive Gaussian noise with zero mean and variance

( ) 22n E n kσ = and ( )s k is the signal component of ( )x t . Assuming there are

2 1uN + subcarriers the signal component may be written

( ) 21 ,u

n s

u

Nj f kT

n nn N

s k c eT

π

=−

= Γ∑ 0 1k N≤ ≤ − (2)

where nf stand for the frequency of the n th subcarrier and nΓ is the channel response at frequency nf . The signal-to-noise ratio (SNR) is 2 2SNR s nσ σ , with

( ) 22s E s kσ .

The estimation of v is based on an observed OFDM pilot symbol with L identical parts. These symbols are composed of a pseudo-noise sequence with symbols at multiple frequencies of L T (in the implementation in this project we used the QPSK

symbols ( ) ( )1 2 1 2j+ and ( ) ( )1 2 1 2j− + − placed alternately. The other

part of the pilot symbol is composed of zero-symbols. The estimation method explores the correlation of the received signal samples, computing the sample correlation

( ) ( ) ( )1

*1 ,N

k mMR m x k x k mM

N mM

−

=

= −− ∑ 0 m H≤ ≤ (3)

where M N L= is the lengths in sampling periods of each section of the pilot symbol and H an implementation parameter less than or equal to 1L − . Inserting (1) in (3) yields


( ) ( ) ( )2 1j mv LR m e D m mπ γ= + (4) where ( )D m is defined as

( ) ( )1 21 N

k mM

D m s kN mM

−

=− ∑ (5)

After some calculations 1.5.5 may be written

( ) ( ) ( ) ( ) ( ) ( ) ( )1

* * *1 N

k mMD m s k n k mM s k mM n k n k n k mM

N mM

−

=

− + − + − − ∑ (6)

where ( ) ( ) 2j vk Nn k n k e π is a noise process statistically equivalent to ( )n k . To grasp the idea behind the estimation strategy lets consider the angles ( ) ( ) ( )

2arg arg 1 ,m R m R m

πϕ − − 1 m H≤ ≤ (7) where [ ]2

xπ

represents the modulo- 2π operation ( x is reduced to the interval

[ ],π π− ) and ( ) arg R m represents the argument of ( )R m . As we shall see, for high SNR and for values of v satisfying

2Lv ≤ (8)

information about the carrier frequency can be reliable extracted from the sample autocorrelation. For SNR 1 the envelope of ( )n k is, with high probability, much less than the

envelope of ( )s k and therefore the term ( ) ( )*n k n k mM− is negligible. Also we

may assume that the real and imaginary components of ( )mγ , ( )R mγ and ( )I mγ respectively, have envelope much less than unity. Therefore we may write

( ) ( )2

arg 2 IR m mv L mπ

π γ≈ + (9) Substituting (9) in (7) and applying (10) yields [ ] [ ] [ ]2 2 22x y x y

π π ππ − = − (10) ( ) ( ) ( )

22 1 ,I Im v L m m

πϕ π γ γ≈ + − − 1 m H≤ ≤ (11) When ( )i mγ and ( )1I mγ − are small and (8) is verified the operation modulo- 2π is immaterial and ( ) ( ) ( )2 1 ,I Im v L m mϕ π γ γ≈ + − − 1 m H≤ ≤ (12)


From (12) we see that ( )mγ has a deterministic component, 2 v Lπ , proportional to v . Using (12) we may resort to the Best Linear Unbiased Estimator (BLUE) for the estimation of v as a function of the observations ( ) mϕ . The BLUE is defined as

( ) ( )1

1ˆ2

H

mv m m

Lω ϕ

π =

= ∑ (13)

which is the frequency offset estimate used in this project. In (13), the weights ( )mω are the elements of the vector

1

1

11 1T

CCϕ

ϕ

ω−

−= (14)

In this equation Cϕ is the covariance matrix of ( ) ( ) ( ) ( )1 , 2 ,...,

Tm Hϕ ϕ ϕ ϕ and

[ ]1 1,1,...,1 T is a column vector of length H . The BLUE provides estimates with variance

( )2 1

1 1ˆvar1 12 Tv

CL ϕπ −= (15)

After computing the covariance matrix, it may be shown that

( ) ( )( ) ( )( )2 2

13

4 6 3 1L m L m H L H

mH H LH L

ω− − + − −

=− + −

(16)

and

( )( )

12

2 2 2

3 SNR1ˆvar4 4 6 3 1

Lv

MH H LH Lπ

−

=− + −

(17)

Analyzing (17) it is easy to show that ˆvar v attains a minimum for 2H L= , which is given by

( ) 1

2

2

3 SNR1ˆvar12 1

vN

Lπ

−

= −

(18)

If 2L = e 1H = in (13) the algorithm becomes the previously defined SCA with frequency estimate given by

( )1ˆ 1v ϕπ

= (19)

with variance

( ) 1

2

2 SNRˆvar v

Nπ

−

= (20)


After this study we describe some of the characteristics of the adopted algorithm and its comparison with the SCA. Equation (13) may be viewed as an extension of (19), and for this reason the algorithm is considered an extension of the SCA and is named Extended Schmidl and Cox Algorithm (ESCA).

• If SNR 1 and 2v L≤ ,then the ESCA is the BLUE estimator.

• From the analysis of (16) it is seen that the weights ( )mω are independent of the channel transfer function and therefore the ESCA is the BLUE for any channel.

• Comparing (18) with (20) it is seen that with the ESCA lower variances are attained than with the SCA. For example, for 8L = the ESCA variance is about 1.2 dB lower.

• The ESCA is approximately unbiased, [ ]ˆE v v≈ . • The estimation range increases with L and can be made wide enough. • The better variance of the ESCA is paid by a higher algorithm complexity.

While the ESCA requires computing H angles ( )mϕ the SCA requires only

( )1ϕ . The ESCA is currently under simulation assessment and will be incorporated in the synchronization circuits of the OFDM receiver being developed in the context of this project.

3. Bit Loading and water filling in OFDM systems An OFDM system can be interpreted as a multicarrier system composed of several subcarriers, one for each bin of the DFT operation. For each subcarrier the system behaves as simple QAM modulation system. In order to achieve maximum performance the number of bits and the signal level in each subcarrier can be made dependent on the signal to noise for that subcarrier. Here are derived the equations for doing this job [4]-[6].

Bit Loading The FFT operation at the receiver in fact implements a bank of matched filters for all signals in all subcarriers. The received signal for one subcarrier is:

)()()()()( IIRR0 twtsbtwtsatr +++= (3)

Where ka and kb are the real and imaginary coefficients for the M-QAM constellation (for M power of 4, namely 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc), witch take the values 2/d 7 5, 3, 1, 1,- 3,- 5,- 7,- min…… , with mind representing the minimum distance between points of the constellation. The variables )(R ts and

)(I ts are the truncated cosine and sine symbols respectively; )(R tw and )(twI are the real and imaginary noise terms of a Gaussian white noise process with variance σ and zero mean. Note that the noise variance can be obtained from WN 0

2 =σ , where

0N is half of the power spectral density of the noise and W is the bandwidth of the


system. After the matched filters, that is, at the output of the FFT operation and disregarding the noise terms, and since )(R ts and )(I ts are orthogonal, the sampling of the output signals at time 0=t results in,

Irrr IR )0()0()0(1 += with dttsarR ∫+∞

∞

=-

2R )()0( and dttsbrI ∫

+∞

∞

=-

2I )()0( . (4)

Defining dttsdtts ∫∫+∞

∞

+∞

∞

==-

2I

-

2R )()(Es results in,

Es)0( arR = and Es)0( brI = . (5)

Now the power of the received signal is given by, [ ] [ ] [ ] [ ] 22222

I2

R2

1 EsEEsE)0()0(E)0(E barrrS +=+== . (6)

If all point in the constellation are equally probable then,

[ ] [ ] ( )

( ) ( ) 2min

2min

22

min

21

21

2

2min

2222222222

d12

12/d3

1/2/d)2(

2/d 7 ,5 ,3 ,1 ,(-1) ,(-3) ,(-5) ,(-7)EE

−=

−==

……==

∑

∑−

+−=

MNNi

Nba

N

Ni

, (7)

where 2NM = . So for M-QAM the received signal power is given by,

22min Esd

61−

=MS . (8)

The noise power is given by [ ] 222 2E σ=+ IR ww , 22σ=N . (9)

Now we proceed to calculate the probability of error. The probability that a Gaussian noise variable exceeds half of the distance between adjacent constellation points is,

=

σ2Es

Q minX

dP , (10)

where )Q(x ,

( ) dxexx

x

∫∞

−= 2

2

21Qπ

. (11)

The probability of a symbol error is equal to: the probability of a wrong decision for the real component of the signal, or, for the imaginary component. The probability of error in a given direction (real or imaginary) is equal to the probability of error of an


N-PAM ( 2NM = ) signal. This error probability is equal to X2P for the 2−N inner points and to XP for the two outer points so the average probability of error is given by,

−

=σ2

EsQ)1(2 minPAM

dN

NP , (12)

and the probability of symbol error is given by, PAMe 2PP = ,

−

=σ2

EsQ)1(4 mine

dN

NP . (13)

Note that for Gray coding the bit error probability is equal to the symbol error probability per dimension, so 2/_ eerrorbit PP = . Now one can define, the SNR gap, Γ , as

2

2min

2

4Es

3σd

=Γ (14)

which result in,

( ) ( )Γ≤Γ−

= 3Q43Q)1(4e N

NP , (15)

and,

3

14Q

2e1

−=Γ

−

NNP

or (16)

( )

34/Q 2

e1 P−

=Γ (17)

From the formula for the M-QAM signal power, S , one can obtain,

22

min

2

22min Esd

261Esd

612 σNSSMb +=+== (18)

where b is the number of bits per QAM symbol, and,

Γ+=

NSb /1log2 , (19)

so Γ actually represents the gap in the signal no noise ratio that separates the bit rate from the maximum achievable capacity given by the Shannon's formula, ( )NSb /1log2 += . (20)


Note the error probability is for encoded signals, adding error correcting codes will decrease the error rate. In fact he capacity gap is equal to,

( )

dBdBdB3

4/QCm

2e

1

γγ −+

=Γ

− P (21)

where mγ is the margin, which is the amount to extra performance that is required to ensure adequate performance in the presence of unforeseen channel impairments ( dB6 for ADSL); and mγ is the coding gain of the code. The following table represents the value for the capacity gap for the encoded case with no margin in function of the bit error probability, or error probability per dimension:

2/eP Γ )(log10 10 Γ (dB)

710− 9.458 9.76 dB

510− 6.503 8.13 dB

310− 3.609 5.57 dB

Table 1 - Capacity gap

Water Filling

The number of bits transmitted in each subcarrier the can be calculated using (19) so the total number of bits transmitted per block is equal to,

∑∑

Γ+==

= i

iiL

ii

NSbB

/1log2

1

. (22)

where L is the number of subcarriers or FFT bins. Notice that Γ is taken to be independent of the subcarrier, which is only true if we take the upper bond on the probability of error in (15). Defining the channel SNR function as,

)()(

)(2

fNfH

f =γ . (23)

The SNR at the output of the matched filter is given by,

)()()(

)()(/

2

ffPfN

fHfPNS γ== . (24)

So the total number of bits transmitted is,


∑

Γ+=

i

iii NPB

/1log2

γ. (25)

Maximizing this quantity subject to the constrain of maximum total output power (which may not be the best criterion for Power Line Communications…), namely, T

ii PP <∑ , (26)

using the Lagrange multipliers method results in the following power distribution:

+

Γ−=

)(iPi γ

µ . (27)

where µ is selected so that Ti

i PP =∑ , and []*. is a function that clamps negative

values to zero. This adaptive power distribution is called “spectral water filling”.

Task 2 References [1] Timothy M. Schmidl and Donald C. Cox, “Robust Frequency and Timing

Synchronization for OFDM”, IEEE Transactions on Communications, Vol. 45, No. 12, Dec. 1997, pp. 1613-1621.

[2] Michele Morelli and Umberto Mengali, “An Improved Frequency Offset Estimator for OFDM Applications”, IEEE Communications Letters, Vol. 3, No. 3, Mar. 1999, pp. 75-77.

[3] Zhongshan Zhang, Ming Zhao, Haiyan Zhou, Yuanan Liu and Jinchun Gao, “Robust Frequency Offset Estimation Algorithm with Low Complexity in OFDM Systems”, Revision to CL2003-0971.

[4] Juha Heiskala and Jonh Terry, “OFDM Wireless LANs: A theoretical and Practical Guide”, Sams Publishing 2002.

[5] John M. Cioffi, “A Multicarrier Primer”, http://www-isl.stanford.edu/people/cioffi/pdf/multicarrier.pdf

[6] G. David Forney and Gottfried Ungerboeck, “Modulation and Coding for Linear Gaussian Channels”, IEEE Transactions on Information Theory, Vol. 44, No. 6, October 1998

Task 3 – Adaptive Communication Techniques (01-10-2005 to 31-03-2007) To compare the different adaptive OFDM techiques already available for transmission over media other than power lines (for instance, bit rate reduction, precoding, OFDM subcarrier supression), and assess their suitability for PLC communication. To develop new adaptive schemes that take in consideration the specific nature of the power line transmission medium.


Results at month 3: This last task is the main task of the project, the one that is expected to produce the most relevant results. It depends on the previous tasks results. This task can only produce results of its own after the power line be characterized and the simulation system be fully operational. So, it depends on Task 1 conclusions (where the power line is characterized as a transmission channel) and of Task 2 software results (where the simulation system model is now under development). Meanwhile, a research on the available adaptive techniques has started.


RELATÓRIO DE EXECUÇÃO FINANCEIRA

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Financiamento Recebido

Unidade: Euros

FONTES DE FINANCIAMENTO

1º ANO 2º ANO 3º ANO Total

FCT

AUTO-FINANCIAMENTO

OUTRO

TOTAL

Lista do equipamento adquirido (Equipamento de valor superior a 500 Euros) (indicar a marca e modelo ou referência do equipamento adquirido)

DESCRIÇÃO Nº RECIBO DATA FORNECEDOR OBS.


Termo de responsabilidade

Instituição Proponente

Nome Instituto de Engenharia de Sistemas e Computadores, Investigação e Desenvolvimento em Lisboa

Data 30 de Janeiro de 2006

Assinatura (com carimbo ou selo branco)

Investigador Responsável

Nome José António Beltran Gerald


Assinatura

Instituição 1

Nome Escola Superior de Tecnologia e Gestão


Assinatura (com carimbo ou selo branco)

Investigador Responsável da Instituição 1

Nome Luis Miguel Gomes Tavares


Assinatura

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