relatório de progresso - INESC-ID
Transcrição
relatório de progresso - INESC-ID
PROJECTOS DE INVESTIGAÇÃO CIENTÍFICA E DESENVOLVIMENTO TECNOLÓGICO RELATÓRIO DE PROGRESSO Relatório de Execução Material Relatório de Execução Financeira REFERÊNCIA DO PROJECTO Nº __ POSC/EEA-CPS/59401/2004 RELATÓRIO REFERENTE AO ___2__º ANO DE EXECUÇÃO União Europeia – Fundos Estruturais Governo da República Portuguesa Data de Entrada_____________________ Nº de Registo ______________________ Data de Verificação__________________ 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 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 Telefone 213100300 Código postal 1000-029 Fax 213145843 Email [email protected] Unidade responsável pela execução do projecto Nome Sistemas de Processamento de Sinal Morada R. Alves Redol, 9 LocalidadeLisboa Telefone 213100300 Código postal 1000-029 Fax 213145843 Email [email protected] Identificação do investigador responsável Nome José António Beltran Gerald Telefone 213100368 Fax 213145843 União Europeia – Fundos Estruturais Email [email protected] Governo da República Portuguesa 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 ____2º____ ano de execução) Unidade: em número Instituição Proponente 17,1 Instituição 1 5,2 Instituição 2 Instituição 3 Instituição 4 União Europeia – Fundos Estruturais Governo da República Portuguesa Resumo dos trabalhos desenvolvidos No período aqui relatado, decorreram as Tarefa 1 - "Power Line Model Validation" (de 1de Janeiro a 31 de Março de 2006), Tarefa 2 - "Comparative study of Coding Schemes and Digital Modulation Techniques" (de 1 de Janeiro a 31 de Dezembro de 2006) e Tarefa 3 - "Adaptive Communication Techniques" (de 1 de Janeiro a 31 de Dezembro de 2006). Os trabalhos visaram os objectivos das respectivas tarefas, especialmente a de validação do modelo a adoptar para a linha de distribuição de energia, objectivo que se tem revelado bastante mais difícil de concretizar devido ao complexo hardware necessário. Também, foi continuada 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, foi realizado um novo modem PLC em hardware para acoplamento à linha de distribuição de energia eléctrica. Este novo modem-protótipo tem a vantagem, sobre o circuito inicialmente utilizado, de ser modular, permitindo uma relativa independência entre os módulos Interface de Linha (AFE- Analog Front End), Processamento de Sinal (DPB - Data Processing Board) e Fontes de Alimentação (PSB - Power Supply Board) (o que se requer num circuito para desenvolvimento e teste de soluções), para além do modem poder ser ligado a um utilizador externo via USB. Foram realizadas experiências com a linha de 220 V. As experiências realizadas não foram contudo suficientes para caracterização completa da linha. Desta forma, esta tarefa não está completamente encerrada. Dos resultados obtidos nesta tarefa foi submetida uma comunicação em conferência internacional (ISCAS'07). Tarefa 2: No referente à Tarefa 2 (esta tarefa deveria ter terminado a 30 de Setembro de 2006 mas ainda continua, em parte devido à interrupção que ocorreu na bolsa de iniciação à investigação, por desistência do primeiro bolseiro), foi continuado a ser desenvolvido um sistema base de simulação em computador (utilizando o programa Matlab com Simulink) de comunicação na linha de distribuição de energia eléctrica usando OFDM, tendo sido acrescentado uma parte de recuperação de sincronismo no receptor. Também, foi recentemente acrescentada uma parte do simulador correspondente à codificação do sinal OFDM, nomeadamente no que se refere à utilização de Turbo Codes ou Low-Density Parity-Check Codes. Foi assim continuado o desenvolvimento da aplicação computacional. Tarefa 3: No referente à Tarefa 3, foi continuado o desenvolvimento de técnicas adaptativas para melhorar a comunicação com OFDM. Foram desenvolvidos novos algoritmos adaptativos (o Kalman LMS e suas simplificações) e um novo equalizador adaptativo com cancelamento de ruído cruzado entre as sub-bandas de OFDM. Dos resultados obtidos nesta tarefa foram submetidas 2 comunicações em conferências internacionais (ICASSP'07 e ISCAS'07). União Europeia – Fundos Estruturais Governo da República Portuguesa Indicadores de realização física (Referente ao _2º____ ano de execução) Unidade: em número A- Publicações Livros Artigos em revistas internacionais Artigos em revistas nacionais B- Comunicações Em congressos científicos internacionais 2 Em congressos científicos nacionais C- Relatórios D- Organização de seminários e conferências 1 E- Formação Avançada Teses de Doutoramento Teses de Mestrado Outra F- Modelos G- Aplicações computacionais 1 H- Instalações Piloto I- Protótipos laboratoriais 1 J- Patentes L- Outros (discriminar) Relatório de Bolsa de Investigação União Europeia – Fundos Estruturais 1 Governo da República Portuguesa Publicações (listar as publicações com origem no projecto) PUBLICAÇÕES [1] PAULO LOPES, GONÇALO TAVARES, JOSÉ GERALD, “A New Type of Normalized LMS Algorithm Based on the Kalman Filter”, submitted to ICASSP’07. [2] PAULO LOPES, JOSÉ GERALD, “New Normalized LMS Algorithms Based on the Kalman Filter”, submitted to ISCAS’07. [3] PAULO LOPES, “Survey of Adaptive OFDM and Application to the Power Line Channel”, INESC-ID Seminar, October 2006. [4] ANTÓNIO NUNES, “Power Line Communication System using Adaptive OFDM",Relatório da parte realizada da bolsa de iniciação à investigação científica no âmbito do projecto POS_C/EEA-CPS/59401/2004 – Power Line Communication System using Adaptive OFDM, Dezembro de 2006. União Europeia – Fundos Estruturais Governo da República Portuguesa 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 Luis Miguel G. Tavares Paulo A. C. Lopes José Vaz União Europeia – Fundos Estruturais Governo da República Portuguesa 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 suits the specific problems in PLC is also one of the key objective of this project. Another objective is the development of new OFDM coding 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 31-032006) 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 12: 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 were obtained. Results obtained till month 9 were already presented in 1st year report. Next a new PLC modem development and new results obtained with this improved version are presented. 1.1 PLC modem – Version II In this work we improved the PLC Modem for domestic communication, including software for easy handling, using the adequate modulation for data power line communication. The idea of a PLC communication is to add a broadband signal to the 50 Hz signal of the power line. This modulated signal does not affect in any way the normal União Europeia – Fundos Estruturais Governo da República Portuguesa work of the domestic electric/electronic devices or industrial machines since the signal power is insignificant. The normal indoor power line layout, with its several plugs and domestic devices that may be connected to them, cause a lot of interference in this communication channel. Therefore, the use of a modulation which manages the noise elimination in an effective manner is required. For this purpose we tried to implement an adequate modulation such as OFDM. Unfortunately, there was no time to obtain full experimental results with OFDM and the power line. The work towards the final PLC modem prototype still goes on. The previous PLC modem circuitry already performs the 220 V network coupling and A/D and D/A transmitted data conversion. The expected channel bandwidth goes from 1 MHz to 20 MHz. The bottom frequency is due to the generated noise by other appliances, which is not filtered by any kind of device in the network, and the top frequency is due to either the electric network frequency response or the transformer bandwidth. The present work consists in implementing the modem control system and OFDM modulator/demodulator and a Universal Serial Bus (USB) interface with the user. For simplicity it will be used USB 1.1 specification. The transmission rate should be no less than 1 Mbps. The emitted OFDM signal center frequency of 4 MHz was chosen after some experiences with the AFE. Some attention was paid to the emitted signal power: It does not go over 30 µV/m in a 30 m distance above 3.5 MHz, which correspond to a -86dBW (-56dBm) level (according to the US FCC Part 15 standards, also used in Europe) [1]. For data processing implementation it was chosen a Field-Programmable Gate Array (FPGA) instead of a Reduced Instruction Set (RISC) processor, because the former is faster. The chosen FPGA was considered for its capability of executing FFT/IFFT very fast. Fig. 1.1 shows the PLC modem architecture. Power Modem USB Memory FPGA AFE Extra: communication plugs and buttons Fig. 1.1 – PLC Modem architecture simplified diagram. Along with the required modem circuitry, other facilities were implemented with the goal of creating a "demoboard", suitable for testing other modem alternatives. So, this FPGA has in fact more outputs then those strictly needed, and União Europeia – Fundos Estruturais Governo da República Portuguesa the board has a Series protocol DB9 connector and a parallel protocol DB25 connector. The FPGA is connected to a 4 Mb Xilinx memory through a JTAG connection in order to keep its firmware. This data processing unit is dedicated to modulate/demodulate the data and connect to the user by means of an 8-bit USB circuit (for its simplicity). With the implemented circuit the transmission rate is up to 8 Mbps. Fig. 1.2 shows the signal path (AFE excluded) in the considered OFDM PLC transmission. Except for the Line path, all the signal processing is performed in the FPGA board. Input QPSK Modulation Series/Parallel IFFT Parallel/Series Carrier Multiplication Echos Carrier Multiplication Noise Line = Unknown channel Output Series/Parallel FFT Demodulation Parallel/Series Fig. 1.2 – Signal path in the OFDM PLC transmission. Next the modem main units are presented, i.e., the Analog Front End (AFE), the Data Processing Board (DPB), and the Power Supply Board (PSB). A) Analog Front End (AFE) Starting with the AFE Board, which connects to the Data Processing Board through a 26 pin socket and flat cable. The AFE block diagram and AFE board are shown in Fig. 1.3 and Fig. 1.4, respectively. The AFE is composed by: • Analog-to-Digital Converter (ADC) • Digital-to-Analog Converter (DAC) • Lowpass Filters • Automatic Gain Control (AGC) • Bandpass Fiters • Line Drivers • Coupling Circuitry União Europeia – Fundos Estruturais Governo da República Portuguesa I/O Gate (26 pins) ADC 10bit AGC DAC LPF BPF Driver Transformer Fig. 1.3 – AFE block diagram. Output stage Transistors 50Hz Filtering Capacitors Transformer 1:1 DAC Filters ICs Connector (26 pins) AGC Fig. 1.4 – AFE board. As shown in Fig. 1.3, the 26-pin connector is used for a 10-bit data bidirectional bus, a clock signal, an emission signaling bit (connected to a LED), a reception signaling bit (connected to a LED) and 3 gain control signal bits for the AGC. All communication between the AFE and the Data Processing Board is synchronized by the FPGA, with the help of a crystal oscillator implemented in the Data Processing Board. União Europeia – Fundos Estruturais Governo da República Portuguesa B) Data Processing Board (DPB) In the Data Processing Board one can find the following components: • FPGA Xilinx Spartan 3 XC3S1000 • Xilinx XC18v04 memory • 120MHz oscillator • USB circuit FTDI FT245BM • Microchip memory 93LC46 • 6 MHz crystal for the USB FTDI • Transceiver RS232 MAXIM M3386E and DB9 connector for series interface • Transceiver Philips 74ALVC16245 and DB25 connector for parallel interface • 8 LEDs (red) • 8 Dipswitches • 5 pressure buttons Xilinx advises the XC18v04 memory for programming the 1000 kgates FPGA. Pressure buttons serve for FPGA testing, by choosing input debug bits, as well as the red LEDs connected to the FPGA outputs. The parallel connection may serve for slow communication (in both directions) using the transceiver direction control bit. Fig. 1.5 shows the Data Processing Board. RS232 Parallel Connector Oscillator USB Transceiver FPGA JTAG Memory Pressure Buttons Dipswitches Leds AFE Connector Fig. 1.5 – Data Processing Board of the PLC modem. União Europeia – Fundos Estruturais Governo da República Portuguesa The FPGA is the DPB main processing unit, and it interacts with all the circuits around. Fig. 1.6 illustrates the FPGA connections. One can see in Fig. 1.6 that there is no direct communication among the surrounding circuits. All communication is established through the FPGA. The communication between the digital gates and the AFE is controlled by the FPGA firmware. The 120 MHz signal from the crystal oscillator is used as clock, for instance for the FPGA and for the AFE converters. The only exception is the USB circuit, which has its own clock. Note that the flash memory connected to the FPGA, where its firmware is stored, can also be used for storing program data, depending on the implemented program. JTAG EEPROM USB AFE Connector (26 Pins) FPGA Series Connector Clock Parallel Connector Figura 1.6 – FPGA connections block diagram. Table 1.1 illustrates the connection among all the ICs' pins. The USB circuit was implemented with the FTDI FT245BM circuit. The USB unit schematic and functional blocks can be seen in Fig. 1.7 and Fig. 1.8, respectively. It has an 8-bit input/output bus and several control bits. Fig. 1.9 and Fig. 1.10 show the connections between the other circuits of the USB unit. The series connection is implemented by the Maxim MAX3386E transceiver and the 9-pin DB9 socket, which connect to the input and output transmission signal pins. It were used the T3 and R1 signal lines (which correspond to pins 9-15 and 1114, respectively). União Europeia – Fundos Estruturais Governo da República Portuguesa Transceiver USB D0 D1 D2 D3 D4 D5 D6 D7 RD# WR TXE# RXF# SI/WU PWREN# FPGA A4 A3 B1 C1 D1 E1 G1 H1 J1 K1 M1 N1 P1 R1 Pressure Buttons S1 S2 S3 S4 S5 Dipswitches DS0 DS1 DS2 DS3 DS4 DS5 DS6 DS7 FPGA LEDs FPGA T5 R4 T4 R3 T3 LD1 LD2 LD3 LD4 LD5 LD6 LD7 LD8 RS232 TX RX J16 K15 K16 L15 M16 N16 P15 P16 R6 T7 R7 T8 T9 R9 T10 R10 Parallel Connector D0 D1 D2 D3 D4 D5 D6 D7 FPGA AFE FPGA H16 G16 G15 E16 E15 D16 D15 C16 OSCILATOR A8 D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 CLK TX_EN RX_EN GAIN_A0 GAIN_A1 GAIN_A2 T12 R13 R11 N15 M15 B14 B13 A14 A13 A10 B16 A12 A9 R16 R12 T14 A5 A7 Table 1.1 – FPGA pin-out. União Europeia – Fundos Estruturais Governo da República Portuguesa Figura 1.8 – USB chip functional blocks Fig. 1.7– Schematic Fig. 1.9– Connection to the USB chip memory Fig. 1.10–USB and Power socket connections Fig. 1.11 shows the usual connection of the MAX3386E circuit, with the required capacities for the RS-232 transmission line adaptation. União Europeia – Fundos Estruturais Governo da República Portuguesa Fig. 1.11– RS232 transceiver connection. C) Power Supply Board (PSB) In order to make the PLC modem the most modular possible, the power supply circuitry was implemented in a separate board. In this board all the required voltages will be generated from the 220 V AC signal. The AFE board needs +5V, -5V, and +3,3V; the DPB needs +1,2V, +2,5V and +3,3V. First the 220V AC signal must be converted in a DC low voltage one. This is accomplished with the help of a transformer plus a rectifier bridge and some capacitors, as shown in Fig. 1.12 (TP6 and TP7 inputs are connected to the mains). 1 TP7 MAIN2 5 TP6 MAIN1 6 7 10 9 T1 TRANS5 DGND -9V AC2 C8 10uF + DGND D1 BRIDGE AC2 AC1 V- C9 2200uF DGND V+ +9V AC1 + + C10 2200uF DGND C11 10uF DGND Fig. 1.12–AC/DC Converter circuit. União Europeia – Fundos Estruturais Governo da República Portuguesa In order to generate the +5V and the -5V it were used the LM317 and LM337 voltage regulators, respectively, as shown in Fig. 1.13. U6 +9V IN VDD_+5V 2 OUT ADJ 3 1 + C19 100uF C21 100nF R11 240R LM317T R9 240R + C23 10uF R10 240R + C24 10uF C25 100nF DGND U5 2 1 C26 100nF C22 100nF Vin ADJ + C20 100uF R12 240R Vout 3 LM337T -9V VDD_-5V Fig. 1.13 – Power source (+5V, -5V) circuit. The positive voltage circuit (+5 V) functioning is as follows: C19 and C21 capacitors are used to eliminate some residual signal fluctuations. The LM317 circuit has a 1.25 V reference signal, which allows to obtain at its output a DC signal with amplitude given by R VDD + 5V = 1.251 + 9 R11 (1.1) The negative voltage circuit has a similar functioning. Although the negative voltage signal follows right after to the AFE board, the positive voltage signal is still used as reference for the lower voltage regulators of this board. The 3.3V is obtained with the circuit shown in Fig. 1.14, which uses the LT1761ES5-BYP IC. The 2.5V and 1.2V are obtained with similar circuitry. TP1 PROBE TEK DPO T2 VDD_3V3 7 BD139 U2 2 1 10uH 60MHz U1 LT1761ES5-BYP IN OUT C1 10uF GND BYP ADJ 6 5 3 3 R3 C2 10nF R1 2K7 4 R21 330R DGND 2K C3 3.3uF AD797AR + C4 10uF DGND R4 + C7 100R 10uF 4 L1 2 +5V C6 100nF C5 100nF DGND R2 47K DGND Fig. 1.14 Power source (+3.3V) circuit. Once again the output voltage for the 3.3V circuit is given by União Europeia – Fundos Estruturais Governo da República Portuguesa R1 VDD 3V 3 = 0.661 + R2 (1.2) It was necessary to use a feedback architecture for these power supplies because the maximum output current for the regulators is about 100 mA, which has revealed not to be enough for the AFE and the DPB all together. To note that the R21 resistor is extremely important, because the regulator must have always some output current to ground. Also, R3, C3, C4 and C5 serve for filtering purpose only, attenuating the high-frequency components at the amplifier input. This amplifier has a very low output noise (0.9nV/√Hz) and low distortion (120 dB of THD at 20 kHz), and its purpose is only to function as a voltage follower, being the BD139 transistor the one responsible for all the output current required. The 1.2V circuit was implemented with the TPS72201 circuit from Texas Instruments. Fig. 1.15 shows the Power Supply Board with its main blocks identification. Transformer Other Voltage Regulators Rectifier bridge +5V and -5V Regulators Output Transistors Fig. 1.15– Power Supply Board. Experimental Results The required VHDL code for implementing the OFDM data processing and AFE control was introduced in the FPGA. Some experimental results were obtained in order to confirm the modem performance. União Europeia – Fundos Estruturais Governo da República Portuguesa The transmitted OFDM signal in time can be observed in Fig. 1.16. In this figure one can differentiate the OFDM amplitude signal variation, which is typical in this type of modulation. A detail of this figure can be observed in Fig. 1.17, where one can better see the signal transitions. The OFDM signal is centered at 3.7675 MHz, as expected, as can be confirmed in Fig. 1. 18. This figure shows the OFDM transmitted signal spectrum. Fig. 1.16– OFDM transmitted signal in time. Fig. 1.17 – Detail of the OFDM transmitted signal in time. União Europeia – Fundos Estruturais Governo da República Portuguesa Fig. 1.18 – OFDM transmitted signal spectrum In these experiences the carrier had peak-to-peak maximum amplitude of 16 mV and the modulating signal had peak-to-peak maximum amplitude of 8 mV. One can also observe that the SNR at the Channel is high (although it was not measured). Other experiences were made with the test pressure buttons and the red LEDs, which confirmed the DPB good functioning, especially in what concerned the USB circuitry. Next, some relevant results from the ModelSim compilation report obtained in the FPGA programming task are presented in Table 1.2. In those results one can see the Spartan 3S1000 ft256 FPGA is far from being full, remaining much space for more data processing implementation. For instance, with 64-points IFFT and no USB communication, the occupied portion rounds the 15% of its full capacity. Although not yet accomplished, we believe that there is enough capacity in the FPGA for implementing the full emitter/receiver plus the USB communication. Timing Summary: Speed Grade: -5 Minimum period: 9.593ns (Maximum Frequency: 104.239MHz) Device utilization summary: Selected Device : 3s1000ft256-5 Number of Slices: União Europeia – Fundos Estruturais 555 out of 7680 7% Governo da República Portuguesa Number of Slice Flip Flops: 809 out of 15360 5% Number of 4 input LUTs: 942 out of 15360 6% 27 out of 173 15% Number of BRAMs: 3 out of 24 12% Number of MULT18X18s: 5 out of 24 20% Number of GCLKs: 2 out of 8 25% Number used as logic: 864 Number used as Shift registers: 78 Number of bonded IOBs: IOB Flip Flops: 1 Table 1.2 - ModelSim report detail for the FPGA programming. Fig. 1.19 shows the full PLC modem, already assembled in 3 boards. Data Processing Board Connection plug Power Supply Board AFE Board Plug for 230V 50Hz Fig. 1.19 – Full Modem 1.2. Line Model A general description and characterization of the power line communications (PLC) channel is not feasible due to the variety of lines and cable types presented in a home network. Despite this general agreed difficulty, several studies have attempted to achieve a simulation model characterization of the power line. The main parameters affecting the power line characterization are the channel impedance, signal attenuation and interferences and noise. Channel Impedance varies from place to place due to lines and cable characteristics and also the network topology, as also with the loads connected at each União Europeia – Fundos Estruturais Governo da República Portuguesa time to the network. This issue causes multipath signal propagation, thus degrading communication performance. The Signal Attenuation is caused by the signal loss along the channel, increasing with the frequency and distance between devices connected. Interferences and Noise, having different causes whether in an indoor or outdoor environment. For indoor communications, the main causes for interference and noise are the equipments/appliances connected to the power line. It is commonly accepted that five classes of noise are present in the power line: colored background noise; narrow-band noise; periodic impulsive noise asynchronous to the mains frequency; periodic impulsive noise synchronous to the mains frequency and asynchronous impulsive noise. Although natural the appearance of any of the above classes of noise, asynchronous impulsive noise raises from the switching on and off of appliances connected to the network, causing severe system degradation. The PLC channel model is far from being standardized, and there is no widely accepted model as is the case with other communications environments, namely telephone or mobile channels. Studies on this issue are based on measurements taken directly from the network, or using the knowledge of topology and characteristics of the network elements (wiring, cable type, distances, loads). These models will have a specific scope, and are valid for the local network being used. Models based on topology knowledge are available in the literature, e.g. [2-5] but are considered as unfeasible to use in a general context due to the inherent need of determining all the network parameters. A power line model of the transfer function, based on extended measures was given by Zimmermann and Dostert [6] in 2002, using multipath signal propagation, with several paths and different delays and attenuations. The model is given as: H (f ) = N ∑ i =1 gi N weighting factor ( ) − a +a f k d 0 1 i − j 2π f τ i . e . e attenuation factor delay factor (1.3) Where N is the number of paths between emitter and receiver; i is the path number; a0 and a1 are attenuation parameters; k is factor typically varying between 0.5 and 1; gi is the weighting factor for path i; di is the length of path i; and τi is the delay for path I ( τ i = di / v p , di is the length of path I and vp is the signal propagation velocity). The above model is obtained by analyzing a multipath signal propagation with just one tap on the line, and then combined by superposition for the complete network. The attenuation factor given was obtained as a simplification of the initial form given in [6] by extensive analysis of real measured attenuation results. Comparison results for this model where given in [6] and, although the complexity inherent to the model is high (namely the numerous parameters needed to estimate for an accurate matching of the channel model), it gives accurate results for a large signal bandwidth. Fig. 1.20 shows the results for a measurement in a 110 meter link containing 6 branches of about 15 meters, together with the simulated model (N=44 in this case): Although, for practical use, the model complexity is very high, it can be simplified, reducing the total number of branches (N) still giving good results. In this case, as N is reduced, the model will start to give poor agreement on the deep notches present in the transfer function (see Fig. 1.21). União Europeia – Fundos Estruturais Governo da República Portuguesa Fig. 1.20 – Model with 44 paths. (a) Amplitude response. (b) Phase details. (c) Impulse response. (From [6]). Fig. 1.21 – Model with 15 paths. (a) Amplitude response. (b) Phase details. (c) Impulse response. (From [6]). União Europeia – Fundos Estruturais Governo da República Portuguesa Task 1 References [1] AMERICAN RADIO RELAY LEAGUE, “ARRL, the National Association for Amateur Radio“(http://www.arrl.org) [2] J. BARNES, “A physical multi-path model for power distribution network propagation,” in Proc. 1998 Int. Symp. Powerline Communications and its Applications, Tokyo, Japan, Mar. 1998. [3] A. DALBY, “Signal transmission on powerlines – Analysis of powerline circuits,” in Proc. 1997 Int. Symp. Powerline Communications and its Applications, Essen, Germany, April 1997. [4] H MENG, S. CHENG et al, “Modeling of Transfer Characteristics for the Broadband Power Line Communication Channel,” IEEE Transactions on Power Delivery, Vol. 19, No. 3, July 2004. [5] S. GALLI, T. C. BANWELL, “A deterministic Frequency-Domain Model for the Indoor Power Line Transfer Function,” IEEE Journal on Selected Areas in Communications, Vol. 24, No. 7, July 2006. [6] M. ZIMMERMAN, K. DOSTERT, “A Multipath Model for the Powerline Channel,” IEEE Transactions on Communications, Vol. 50, No. 4, April 2002. União Europeia – Fundos Estruturais Governo da República Portuguesa Task 2 – Comparative Study of Coding Schemes and Digital Modulation Techniques (01-10-2005 to present) 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 15: 2. Matlab Simulink Simulation of a MODEM for high speed Power Line Communications with Error Correction Codes The proposed power line communication (PLC) system simulation development has continued. Synchronization at the receiver and other main blocks (as for instance other type of channels and new equalizer) were added. More recently, some blocks concerning correction codes were implemented. This process is still in the beginning, and both Turbo codes and Low-Density Parity-Check (LDPC) codes are under evaluation. Since the PLC channel is a very noisy environment (usually a mix of time-varying erasure and fading channels), the usual trade-off in decrease the error rate is to increase transmission power or reduce data rate. Since these two standard approaches run against the original goal of low-complexity hardware and high data rates, another route must be taken. Hence, in order to maintain data integrity across the PLC channel while providing high data rates, it is essential to consider the use of error-correction coding constructs. [See appendix A2.1 for a comparison of relevant ECC methods]. The current (2006) most efficient ECC schemes used are Turbo Codes and Low Density Parity Check codes (LDPC). The following ECC's are scheduled to be implemented and tested: Low Density Parity Check codes (LDPC) and Turbo Codes. See Appendix A2.1 for a quick comparison. 2.1. Linear Block Codes The structure of a linear block code is completely described by the generator matrix G or the parity check matrix H. The capacity of correcting symbol errors in a codeword is determined by the minimum distance (dmin). For a (7,4) Hamming Code with generator matrix H [ ] 1 1 1 0 1 0 0 H= 1 1 0 1 0 1 0 1 0 1 1 0 0 1 dmin is the least number of columns in H that sum up to 0. 2.2 Low Density Parity Check União Europeia – Fundos Estruturais Governo da República Portuguesa While LDPC [1], [2] and other error correcting codes cannot guarantee perfect transmission, the probability of lost information can be made as small as desired. As of 2001 codes have been built within 0.0045 dB of the Shannon Limit [3]. As with other linear codes, a LDPC code is completely described by it's the generator or parity check matrix, although LDPC matrices have special properties such as z H is sparse c Very few 1’s in each row and column. c Expected large minimum distance z Regular LDPC codes c H contains exactly Wc 1’s per column and exactly Wr=Wc(n=m) 1’s per row, where Wc m. z If the number of 1’s per column or row is not constant, the code is an irregular LDPC code, which usually (with adequate construction) outperforms regular LDPC codes. The encoding, as with other linear block codes, can be described by the relationship C=XG. Unfortunately, there are some issues with this algebraic implementation such as G being very large (10000,5000), and not sparse (as opposed to H). An alternative approach to simplified encoding is to design the LDPC code via graph methods. The general decoding of linear block codes follows the relationship CHT=0 only if C is a valid codeword. The used decode does not use this relationship, since its full implementation is very inefficient. A sum-product algorithm and message passing algorithm are being evaluated for decoding purposes 2.3. Methodology For modelling the full ECC system, an incremental design philosophy was chosen, and building upon previously achieved results. The following table shows the channel and ECC combination matrix, and expected implementation complexity. Channel ECC Class Complexity Class Complexity BER low regular LDPC low AWGN low irregular LDPC high BER+AWGN moderate turbo moderate PLC moderate turbo + interleaver high Table 2.1: List of expected channel and ECC's combinations (16) expected to be tested. Currently, the channels being modelled are BER and AWGN. The codes being tested are regular LDPC, and irregular LDPC. União Europeia – Fundos Estruturais Governo da República Portuguesa The current modelling architecture is shown in the next figure: Fig. 2.1 Modeling architecture. The original data (source block) is error-encoded and sent through the channel. After an iterative decoding, in order to correct transmission errors, the data is delivered to the receiver. An observer module (ECC performance evaluation) monitors and signals error rates. z The Channel block can be any of the following: c Average White Gaussian Noise (AWGN) c Binary Erasure (BER c Power Line (PLC) c any mix of the above channels z The ECC encoder/decoders can be either be of following codes c Low Density Parity Check c Turbo Codes z Modulator and Demodulator currently implement Binary Phase Shift Key (BPSK), but future work will evaluate other modulation blocks. 2.4. Preliminary Results The usual LDPC code is a regular one (i.e. all columns have the same weight). It has been shown in [4] that irregular codes (with different weights per column) with cycles removed, outperform regular ones. Cycles are a pattern or sequence of zeros or ones (in the parity check matrix) that repeats itself in different columns. The existence of cycles degrades the performance of the code. The following figure shows the performance difference of regular code and code with all cycles of size 4 removed. União Europeia – Fundos Estruturais Governo da República Portuguesa Fig. 2.2 - BER for regular and 4-cycle removed. 2.5. Conclusions and Short Term Work The current work stage, is focused in the topmost four tasks of table 2, which means the current effort is centred in LDPC codes. Some preliminary results show the adequacy of LDPC codes as a effective choice for ECC. As stated in the two previous sections, a more thorough comparison between Turbo Codes and LDPC parameters will have to be carried out. The following are a list of the (expected) remaining tasks: Tasks Reasoning LDPC cycle removal Assure current algorithm for cycle removal is optimal LDPC parameters Select appropriate LDPC parameters n, k, r for optimal code performance LDPC decoding algorithm Must selected between MAP and sum-product decoding LDPC + channel modeling Must develop a larger test result bank, for AWGN and BER channels LDPC modeling PLC channel Full suite of results for evaluation LDPC as selected ECC Turbo code encoder/decoder Create turbo encoder/decoder implementation Modulation schemes Test the overall performance of the system, while using modulation schemes, other than BPSK TC + PLC channel modeling Full suite of results for evaluation Turbo Codes as selected ECC Final data analysis, and end report Table 2.2 - List of expected tasks. Appendices A2.1 ECC methods and features quick reference A2.1.1 Turbo Codes Pros: z z close to approaching the Shannon limit well research (since 1993) Cons: z z high encoding/decoding complexity patent encumbered União Europeia – Fundos Estruturais Governo da República Portuguesa A2.1.1 LDPC Pros: z z z z suitable parallel encoding/decoding linear decoding complexity in time lowest error rate floor (minimum distance is proportional to code length) as close as desired to Shannon limit Cons: z z cycles within the code internal structure degrade decoding performance (see preliminary results) “worst” than turbo codes for short code block lengths A2.2 Timeline of significant ECC discoveries and events 1949 Claude E. Shannon publishes his landmark paper Communication in the Presence of Noise, defining a bound on the maximum amount of error-free digital data (that is, information) that can be transmitted over such a communication link with a specified bandwidth in the presence of the noise interference, under the assumption that the signal power is bounded and the Gaussian noise process is characterized by a known power or power spectral density. 1950 Richard Hamming introduces Hamming codes for forward error correction (FEC - a type of ECC whereby the sender adds redundant data to its messages), which allows the receiver to detect and correct errors (within some bound) without the need to ask the sender for additional data. 1955 Peter Elias introduces convolutional codes 1960 Irving S. Reed and Gustave Solomon propose Reed-Solomon codes 1960 Robert G. Gallager proposes Low-density parity-check codes; they are unused for 30 years due to technical limitations. 1967 Andrew Viterbi presents the Viterbi algorithm, making decoding of convolutional codes practicable. 1993 Claude Berrou, Alain Glavieux and Punya Thitimajshima introduce Turbo codes 1998/9 Richardson, Urbanke, and MacKay, rediscover LDPC Task 2 References [1] [2] [3] [4] D. MACKAY, "Good Error-Correcting Codes Based on Very Sparse Matrices," IEEE Transactions on Information Theory, vol. 45, no. 2, March 1999 D. MACKAY, R.M. NEAL, “Near Shannon limit performance of low density parity check codes”, Electronic Letters, vo1.32, No.18, pp.1645-1646, August 1996 SAE-YOUNG CHUNG, G. D. FORNEY, T. J. RICHARDSON and R. URBANK, "On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit," IEEE Communications Letters, vol. 5, no. 2, February 2001 J. MCGOWAN, R. WILIAMSON, "Removing Loops from LDPC Codes," Australian Communication Theory Workshop Proceedings, 2003 União Europeia – Fundos Estruturais Governo da República Portuguesa Task 3 – Adaptive Communication Techniques (01-10-2005 to 31-032007) To compare the different adaptive OFDM techniques 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 15: In this Task, adaptive techniques have been developed and added to the communication system program developed in Task 2. A new equalizer, which performs the crossing information of the noise channel between adjacent sub-bands have been developed and tested. Also, a new adaptive algorithm - the Kalman LMS have been developed and tested. 3.1 The KLMS Algorithm and It Simplification SIKLMS The Least Mean Squares (LMS) algorithm for adaptive filters has bean extensively studied and tested in a broad range of applications [1–4]. In [1] and in [5] a relation between the Recursive Least Squares (RLS) and the Kalman filter [6] algorithm is determined, and in [1] the tracking convergence of the LMS, RLS and extended RLS algorithms, based on the Kalman filter, are compared. However, there is no link established between the Kalman filter and the LMS algorithm. The classical adaptive filtering problem can be stated in the following manner. Given an input signal u(n) and a desired signal d(n) determine the filter, w, that minimizes the error, e(n), between the output of the filter, y(n), and the desired signal, d(n). An algorithm that solves this problem is the well known LMS, which for the case of Finite Impulse Response (FIR) Transversal filters, is given by, w(n + 1) = w(n) + m u(n)* e(n) (1) This equation updates the vector of the filter coefficients w(n).The output of the filter is y(n) = wT(n) u(n) with u(n) =[u(n)… u(n-N+1)] were N is the filter length, and e(n) = d(n) - y(n). It is known that the LMS algorithm is only stable if the step size is limited, namely it should be inversely proportional to the power of the reference signal [1]. This leads to the normalized LMS algorithm (NLMS). It is shown in [1] that this algorithm is stable as long as the step size a be restricted to 0 <a < 2 and of course, u(n)T u(n)* ≠0. In order to prevent this last possibility, in practice, the algorithm is usually modified to w(n + 1) = w(n) + α União Europeia – Fundos Estruturais u (n)* e(n) uT (n) u (n)* + q (2) Governo da República Portuguesa where q is selected to be small enough when compared with uT(n) u(n)*. This is usually chosen in an ad doc fashion. Techniques to select this value based on the proposed algorithm are presented later. The Kalman filter can be used in adaptive filtering by making a number of correspondences. The adaptive filtering problem is reformulated as a state estimation problem, were the state vector corresponds to the filter coefficients vector. Since the state estimate is the state that minimizes the square of the error at each coefficient, it will also minimize the output error of the filter [6]. The optimal filter variation in time is modeled as a Markov model with white noise input, n(n), and state transition matrix, F(n) = λI with λ close to one. The measured signal d(n) is related to the state through the reference signal vector u(n) plus an additional measurement noise v(n). The resulting algorithm is then, α (n) = d (n) − uT (n) w(n) w(n + 1) = w(n) + λ ∑ w (n + 1) = λ 2 ∑ w (n) − λ 2 (3) ∑ w (n)u (n)α (n) u (n) ∑ w (n)u (n) + qv (n) T ∑ w (n)u (n)uT (n) ∑ w (n) + Qnn (n) uT (n) ∑ w (n)u (n) + qv (n) (4) (5) The variance matrix ∑ w (n) can be made diagonal by carefully selecting the state noise autocorrelation matrix Qnn(n) at each iteration. More, this can be done without changing the state noise total power, tr{Qnn(n)}, were tr{} stands for the trace of the matrix. To do this one simply makes ∑ w (n) = σ w2 (n) I and tr{Qnn(n)} = N qn(n) and apply the trace operator to (5). The resulting algorithm is the Kalman based LMS algorithm (KLMS) and is represented in table 3.1. Note that tr{u(n) uT(n)}= uT(n)u(n). The actual algorithm presented in table 3.1 has been modified to allow complex signals. Namely, in the calculation of the power and in the coefficients update, u(n)*, the conjugate of u(n), is used in its place. Initialize w(0)=0 σ w2 (0) = σ w2 0 (6) (7) Iterate from n=0 to … P=uT(n)u(n)* (8) α(n)=d(n)-uT(n)w(n) (9) União Europeia – Fundos Estruturais Governo da República Portuguesa w(n + 1) = w(n) + σ w2 (n + 1) = σ w2 (n) 1 − u (n)*α (n) P(n) + qv (n) / σ w2 (n) (10) P ( n) / N + qn (n) 2 P (n) + qv (n) / σ w (n) (11) Table 3.1 - Normalized LMS algorithm based on the Kalman filter - KLMS algorithm. The model for the state variation is, w j (n + 1) = λ w j (n) + n j (n) (12) Each coefficient corresponds to a low frequency signal, with time constant given by τ = T / ln(λ) were T is the sampling period. This can be approximated by τ = T /(1 - λ) if λ is close to one. So one has, λ ≈ (1-T/τ). The variance of each coefficient is easily calculated as, σ w2 = qn 1− λ2 (13) This should be equal to the value chosen to initialize the algorithm σ w2 = σ w2 0 . This results that the state noise can be chosen as, qn = σ w2 0 (1 − λ 2) ≈ 2σ w2 0 T (14) τ where the last approximation is valid for large τ , where τ is the time constant of the underlaying model, as previously discussed. The use of the NLMS algorithm can lead to amplification of the measurement noise in low order filters when the reference signal power takes low values. This can be seen by assuming d(n) = uT(n)wop(n) + v(n) and rearranging the NLMS algorithm to, w(n + 1) = ( I − Γ) w(n) + Γwop (n) + v ( n) u (n)u* (n) + q T (15) where Γ is a matrix given Γ =α União Europeia – Fundos Estruturais u* (n)uT (n) uT (n)u* (n) + q (16) Governo da República Portuguesa Equation (15) may be made diagonal to represent a bank of lowpass first order IIR filters with added noise, the last term in the equation. For low reference signal power this term will assume high values, resulting in poor performance of the algorithm. The KLMS solves this problem by carefully selection of the value of q. Simulation results are presented for the case of a one coefficient complex filter and a ten real coefficient filter. Comparisons are made with the LMS and NLMS algorithm. The one-coefficient complex filter is typically used in orthogonal frequency division multiplexing (OFDM) [7] channel equalization. In this application equalization is done in the frequency domain resulting in one-coefficient filters. Also, due to the presence of nulls in the channel frequency response and due to the low pass characteristics of many channels, the input signal power varies considerably. The measurement noise, which is a prior to the algorithm, can be considered constant, resulting in a large variation of the signal-to-noise ratio. This fits nicely to the KLMS formulation while the NLMS is more suitable for a fixed signal to noise ratio, since the α parameter is related to it. Also, the NLMS will perform poorly when the input signal power takes low values, as shown in the simulations. 1.2 Kalman LMS NLMS LMS Mean Square Error 1 0.8 0.6 0.4 0.2 0 20 40 60 Iterations 80 100 Fig. 3.1 - Mean Square error convergence of the KLMS, NLMS and LMS algorithm. The parameters off all the algorithms were optimized for best performance Fig. 3.1 presents the convergence curves of the mean square error between the output of the adaptive filter and the desired signal for the case of a one coefficient complex filter. The reference signal was uniform distributed with power of one, and the measurement error had a standard deviation or root mean square value (RMS) of 0.3. This results in a signal to noise ratio of 10.4 dB that is enough to allow fairly low bit error rate in QPSK communication. The measurement noise power of the KLMS has set to, qv = (0.3)2, the optimal value, and the state noise to zero. The step size of the LMS and NLMS were optimized to achieve a similar residual noise. The curves are the result of the ensemble average of 100 trials. It can be seen that the KLMS has the best performance. In the case of the NLMS, due to the low filter order, occasional low values of the reference signal power União Europeia – Fundos Estruturais Governo da República Portuguesa result in very high values of the residual error. The LMS has slower initial convergence. 1.2 Kalman LMS NLMS LMS Mean Square Error 1 0.8 0.6 0.4 0.2 0 20 40 60 Iterations 80 100 Fig. 3.2. Mean Square error convergence of the KLMS, NLMS and LMS algorithm, with a 3 times higher reference signal level than in Fig. 1 but with the same algorithms parameters. In Fig. 3.2 the reference signal level was amplified three times, while the parameters of all the algorithms were kept constant. It can be seen that the LMS algorithm gets unstable. The NLMS has fewer problems, but it still suffers from measurement noise amplification occasionally. The KLMS still performs accurately. In addition, the KLMS has faster convergence than the NLMS. Fig. 3.3 provides a comparison of the convergence of the mean square error of the KLMS, and NLMS. Kalman LMS NLMS Mean Square Error 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 20 40 60 Iterations 80 100 Fig. 3.3. Mean Square error convergence of the KLMS, NLMS and LMS algorithm, for a 10 real coefficient filter. União Europeia – Fundos Estruturais Governo da República Portuguesa The desired signal was equal to the reference signal filtered by a sinusoidal bandpass filter, with unit gain at the center frequency. The reference signal had unit power and the RMS of the measurement error was 0.3. Some care had to be taken in the initial stages, when the filter buffer was not full. The NLMS buffer was initially filled with ones to prevent the step size to increase to much at the initial stages. In the case of the KLMS the buffer can be left at zero, as long as care is taken in choosing the prior standard deviation of the filter coefficient, σ w2 0 . Both algorithms have similar performance. Simplification of the Algorithm If one is not interested in the initial convergence, then the algorithm in Table 3.1 can be simplified. The coefficients estimation error standard deviation σ w2 (n) converges to a steady state value, resulting that qv(n)/ σ w2 (n) converges to, qv (∞) / σ w2 (∞) = 4qv P ( −1 + 1 + ) 2 NPqn (3.17) This can be used in place of qv ( n) / σ w2 (n) . The value of the state noise can be calculated as in (3.14). Another approximation can be made if, the state noise is low or zero. In this case equation 3.5 can be written as, Σ −w1 (n + 1) = Σ −w1 (n) + u (n)uT (n) qv (3.18) The matrix Σ −w1 ( n + 1) can be approximated by a diagonal matrix if the reference signal autocorrelation is narrow. Doing this and applying the trace operator results, σ w−2 (n + 1) = σ w−2 (n) + P ( n) Nqv (n) (3.19) by defining the total power up to (but not counting) time n, PT (n) , by the equation, PT (n + 1) = PT (n) + P(n) (3.20) one can prove by finite induction that σ w−2 (n) = União Europeia – Fundos Estruturais PT (n) + X Nqv (3.21) Governo da República Portuguesa as long as X = Nqv / σ w2 0 and PT (0) = 0 (3.22) resulting in the algorithm presented in Table 3.2. Note that this algorithm is equivalent to the KLMS for the case N = 1. Initialize w(0)=0 PT (0) =0 (3.23) (3.24) Iterate from n=0 to … P=uH(n)u(n) (3.25) α(n)=d(n)-uT(n)w(n) (3.26) w(n + 1) = w(n) + u (n)*α (n) P (n) + PT (n) / N + qv (n) / σ w2 0 PT(n+1)=PT(n)+P(n) (3.27) (3.28) Table 3.2 - Information Form Kalman Based LMS - IKLMS - algorithm The algorithm also suggests further simplification where the time varying quantity PT(n+1) is replaced by an estimate of its value at time M, resulting in, w(n + 1) = w(n) + u (n)*α (n) N + M −1 H 2 u (n) u (n) + qv / σ w0 N (3.29) We call this algorithm the Simplified Information Form Kalman LMS SIKLMS. In the next simulation results, the reference signal is the output of the channel and the desired signal is the input of the channel. The input of the channel was a QAM64 signal with a power of one. A noise signal with standard deviation of 0.25 was added at the output of the channel. This means that the channel is driven with a capacity gap of 3 dB. The measurement noise power of the KLMS has set to, qv = (0.25)2, the optimal value. The step size of the LMS and NLMS and the N of the SIKLMS were optimized to maximize the convergence rate of the algorithms, resulting in the values of 0.5, 0.5 and 2.0. The curves are the result of the ensemble average of 100 trials. União Europeia – Fundos Estruturais Governo da República Portuguesa Fig. 3.4 presents the convergence curves of the mean square error between the output of the adaptive filter and the desired signal for the case of a one coefficient complex filter for channel equalization and tracking. The step of the NLMS and LMS algorithm was set to 0.5 and the M parameter of the SIKLMS was set to 2.0. It can be seen that the KLMS has the best performance. In the case of the NLMS, due to the low filter order, occasional low values of the reference signal power result in very high values of the residual error. The LMS and SIKLMS both have good results. Fig. 3.4. Mean-square error convergence of the NLMS, KLMS and SIKLMS algorithms. The parameters of the LMS and NLMS were optimized for maximum convergence. In Fig. 3.5, the reference signal level was amplified by 40%, while the parameters of all the algorithms were kept constant. It can be seen that the LMS algorithm gets unstable. The NLMS has fewer problems, but it still suffers from measurement noise amplification occasionally. The KLMS and SIKLMS still give good results. To note that in the conditions of Figures 3.4 and 3.5, namely N=1, the IKLMS results in the KLMS. União Europeia – Fundos Estruturais Governo da República Portuguesa Fig. 3.5. Mean Square error convergence of the LMS, NLMS, KLMS and SIKLMS algorithms, with a 3 times higher reference signal level than in Fig. 3.4 but with the same algorithms parameters. Fig. 3.6 provides a comparison of the convergence of the mean square error of the IKLMS, Kalman Filter, KLMS, and NLMS for a 10 real coefficient filter. The desired signal was equal to the reference signal filtered by a bandpass filter, with unit gain at the center frequency. The reference signal had unit power and the RMS of the measurement error was 0.03. The adaptive algorithms were only started after ten iterations, when the input buffer was full. The step size of the NLMS was optimized for best performance while in the KLMS, the algorithm’s parameters were chosen naturally. As one can see, the performance of the Kalman filter is the best, but at the expenses of a much heavier computational effort. All the others have a similar performance. The SIKLMS, although not shown in this figure, present a behavior similar to that of the KLMS. As a conclusion, new versions of the NLMS algorithm based on the Kalman filter (the KLMS, the IKLMS and the SIKLMS) were derived. The new algorithms are stable since they were derived from the Kalman filter. They allows faster convergence and much higher noise immunity when the reference signal vector norm takes low values, namely in the case of low order filters (like in OFDM systems). In the NLMS algorithm, q, prevents division by zero. In the new algorithms accurate formulas for q give it good noise immunity properties. The simplified versions of the KLMS, namely the IKLMS and the SIKLMS, although provide a slightly worse performance as the original KLMS, they require a lighter computational effort, being good performancecomplexity compromises. União Europeia – Fundos Estruturais Governo da República Portuguesa Root Mean Square Error KLMS IKLMS NLMS Kalman Filter 0.5 0.4 0.3 0.2 0.1 0 10 20 30 Iterations 40 50 Fig. 3.6. Mean Square error convergence of the Kalman Filter, KLMS, IKLMS and NLMS algorithm, for a 10 real coefficient filter. The NLMS step was hand optimized. From the results obtained with this Task two papers have been submitted: one to the ISCASSP'07 [8] and other to the ISCAS´07 [9]. 3.2 The Crossing Information Adaptive Equalizer The PLC channel is a time-variable response channel, susceptible to high noise levels, due to the very different kinds of loads connected to the power grid. The model used was proposed by Gotz, Rapp and Dostert [10]. Figures 3.7, 3.8 and 3.9 show its amplitude response, phase response and impulse response, respectively. The full system, simulated in MATLAB Simulink, has the architecture represented in Fig. 3.10. From left to right, (top to bottom), the data in the system flows from a random data source, arrives at the transmitter modem, where it is encoded, modulated and sent through the PLC channel. At the receiver modem, after demodulation and decoding the data is recovered. The remaining bottom blocks implement performance monitoring. União Europeia – Fundos Estruturais Governo da República Portuguesa Modulus (dB) Phase (rad) Fig. 3.7. PLC channel amplitude response. Fig. 3.8. PLC channel phase response. União Europeia – Fundos Estruturais Governo da República Portuguesa Amplitude Fig. 3.9. PLC channel impulse response. União Europeia – Fundos Estruturais Governo da República Portuguesa União Europeia – Fundos Estruturais Governo da República Portuguesa A more detailed functional block-level representation is presented in Fig 3.11. Fig. 3.11. PLC system block-level architecture. Simulation Results Two of the constraints that were expected to greatly impact the outcome system performance were channel equalization, and frequency offset between the transmitter and receiver. Channel equalization allows the receiver to compensate for some attenuation in specific frequencies PLC channel, effectively trying to invert the PLC channel timevarying transfer function. Three different simulations results for channel equalization are shown in Fig. 3.12. Blue line depicts the results for no-equalizer and no-PLC channel scenario. Red line depicts the results for equalizer without PLC channel scenario. Finally, green line depicts the results for equalizer and PLC channel scenario. For both no-PLC channel scenarios, the symbol probability error is always lower when the equalizer is used. Both lines converge to probability 0.75, which is the intrinsic system symbol probability error, for very high noise levels. For the PLC channel scenario and since the line noise is larger, the equalization process convergence is worst, and the symbol probability error is higher. Frequency offset between transmitter and receiver can cause degradation in the symbol decoding process and in severe cases no synchronization between transmitter and receiver. Figures 3.13 and 3.14 depict two different scenarios, with probability of symbol error (symbol error rate) of 10-2 and 10-4, respectively. The offset (X axis) is measured in symbols length. The type of channel used is AWGN. An important detail from both figures, is that they both show a bias (static error), when compared to the ideal channel (Fig. 3.13). União Europeia – Fundos Estruturais Governo da República Portuguesa OFDM carrier frequency desviation Fig. 3.12. Performance evaluation of the equalizer. OFDM carrier frequency desviation Fig. 3.13. Symbol error rate with ideal channel. União Europeia – Fundos Estruturais Governo da República Portuguesa OFDM carrier frequency desviation Fig. 3.14. Performance evaluation for a symbol error rate of 10-2. OFDM carrier frequency desviation Fig. 3.15. Performance evaluation for a symbol error rate of 10-4. União Europeia – Fundos Estruturais Governo da República Portuguesa From both figures, one can conclude that there must be a correlation between high frequency offsets and high SNRs at the channel, in order to have low probability of symbol error. As a conclusion, according to the so far obtained results in the OFDM simulated PLC system, the following recommendations were confirmed: z It would be advantageous to implement an adaptive OFDM control in the transmitter to detect and avoid the channel frequencies that lead to more errors, in order to reduce the error probability of the transmitted signal; z Some sort of forward error correction (FEC) coding should be implemented, in order to attempt extracting the most possible information of a received sequence, instead of just discarding it, with the added benefit of increasing the transmission bit rate. Task 3 References [1] [2] S. HAYKIN, Adaptive Filter Theory. Prentice-Hall, Inc., 1996. J. HOMER, “Quantifying the convergence speed of LMS adaptive FIR filter with autoregressive inputs,” Electronics Letters, vol. 36, no. 6, pp. 585–586, March 2000. [3] Y. GU, K. TANG, H. CUI, and W. DU, “Modifier formula on mean square convergence of LMS algorithm,” Electronics Letters, vol. 38, no. 19, pp.1147 – 1148, September 2002. [4] M. CHAKRABORTY and H. SAKAI, “Convergence analysis of a complex LMS algorithm with tonal reference signals,” IEEE Trans. Speech Audio Process., vol. 13, no. 2, pp. 286 – 292, March 2005. [5] A. SAYED and T. KAILATH, “A state-space approach to adaptive RLS filtering,” IEEE Signal Process. Mag., vol. 11, no. 3, pp. 18 – 60, July 1994. [6] B. D. O. ANDERSON, Optimal Filtering. Dover Publications, 2005. [7 J. A. C. BINGHAM, “Multicarrier modulation for data transmission: an idea whose time has come,” IEEE Commun. Mag., vol. 28, no. 5, pp. 5–14, May 1990. [8] P. LOPES, G. TAVARES, J. GERALD, “A New Type of Normalized LMS Algorithm Based on the Kalman Filter”, ICASSP’07. [9] P. LOPES, J. GERALD, “New Normalized LMS Algorithms Based on the Kalman Filter”, ISCAS’07. [10] M. GOTZ, M RAPP and K. DOSTERT, “Power Line Channel Characteristics and Their Effect on Communication System Design”, IEEE Communications Magazine, pp. 0163-6804, Apr. 2004; União Europeia – Fundos Estruturais Governo da República Portuguesa RELATÓRIO DE EXECUÇÃO FINANCEIRA Segue em separado União Europeia – Fundos Estruturais Governo da República Portuguesa Financiamento Recebido FONTES DE FINANCIAMENTO FCT 1º ANO 2º ANO 3º ANO Unidade: Euros Total 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 União Europeia – Fundos Estruturais OBS. 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