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Orthogonal Frequency Division Multiplexing (OFDM): Concept and System-Modeling

Orthogonal Frequency Division Multiplexing (OFDM): Concept and System-Modeling. Klaus Witrisal Signal Processing and Speech Communication Lab Technical University Graz, Austria VL: Mobile Radio Systems, Ch. 5: “Wideband Systems” 24-Nov-05. Outline. Introduction What is OFDM?

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Orthogonal Frequency Division Multiplexing (OFDM): Concept and System-Modeling

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  1. Orthogonal Frequency Division Multiplexing (OFDM): Concept and System-Modeling Klaus Witrisal Signal Processing and Speech Communication Lab Technical University Graz, Austria VL: Mobile Radio Systems, Ch. 5: “Wideband Systems” 24-Nov-05

  2. Outline • Introduction • What is OFDM? • Multipath fading radio-channel • Principle of OFDM • OFDM Implementation and System Model • Advantages and Disadvantages • OFDM in Practice • Summary

  3. PSD PSD f f * -fc fc Radio- channel e.g. Audio 0110 01101101 Receiver: Source decoding Decoding / deinter-leaving OFDM de-modulation Down-converter, I/Q-demod. Info Sink I/Q RF What is OFDM? • Modulation technique • Requires channel coding • Solves multipath problems Transmitter: I/Q RF OFDM modulation Source coding Channel coding / interleaving I/Q-mod., up- converter Info Source

  4. Reflections from walls, etc. Time dispersive channel Impulse response: Problem with high rate data transmission: inter-symbol-interference t p ( ) (PDP) t [ns] Multipath Propagation Multipath Radio Channel

  5. Transmitted signal: Received Signals: Line-of-sight: Reflected: The symbols add up on the channel  Distortion! Inter-Symbol-Interference Delays Multipath Radio Channel

  6. Caractéristiques du canal

  7. Outline • Introduction • What is OFDM? • Multipath fading radio-channel • Principle of OFDM • OFDM Implementation and System Model • Advantages and Disadvantages • OFDM in Practice • Summary

  8. Time 1 Channel (serial) Channels are transmitted at different frequencies (sub-carriers) 2 Channels 8 Channels In practice: 50 … 8000 Channels (sub-carriers) Concept of parallel transmission (1) Channel impulse response OFDM Technology

  9. Power response [dB] 20 15 10 5 0 -5 -10 Frequency The Frequency-Selective Radio Channel • Interference of reflected (and LOS) radio waves • Frequency-dependent fading Multipath Radio Channel

  10. Signal is “broadband” 2 Channels Frequency 8 Channels Frequency Channels are “narrowband” Concept of parallel transmission (2) Channel transfer function Channel impulse response Frequency Time 1 Channel (serial) Frequency OFDM Technology

  11. Concept of an OFDM signal Ch.1 Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10 Conventional multicarrier techniques frequency Ch.2 Ch.4 Ch.6 Ch.8 Ch.10 Ch.1 Ch.3 Ch.5 Ch.7 Ch.9 Saving of bandwidth 50% bandwidth saving Orthogonal multicarrier techniques frequency Implementation and System Model

  12. Outline • Introduction • What is OFDM? • Multipath fading radio-channel • Principle of OFDM • OFDM Implementation and System Model • Advantages and Disadvantages • OFDM in Practice • Summary

  13. Symbol (QPSK) of sub-carrier i at time k Other symbol-alphabets can be used as well (BPSK, m-QAM) Baseband signal is generated by DSP xi,k Im Re Window function Sub-carrier Generating the OFDM signal (1)

  14. Rectangular Window of duration T0 Has a sinc-spectrum with zeros at 1/ T0 Other carriers are put in these zeros  sub-carriers are orthogonal T0 N sub-carriers: resembles IDFT! Spectrum of the modulated data symbols Magnitude Frequency

  15. xi,k Im Re Generating the OFDM signal (2) x0,k s0,k serial-to-parallel x1,k IDFT (IFFT) s1,k parallel-to-serial xn sn xN-1,k sN-1,k N data symbols: (in frequency- domain) Base-band signal (time-domain)

  16. Idea of Guard Interval (GI) Insertion of guard interval (cyclic prefix): 1 OFDM symbol FFT-part time Channel impulse response (shorter than GI): t Cyclicconvolution of transmitted signal with channel impulse response  multiplication in frequency-domain Introduction

  17. Delay Delay GT OFDM Symbol GT OFDM Symbol Delay Delay Delay Delay GT SYM GT SYM GT SYM GT SYM Amélioration OFDM Une communication « normale » aurait besoin de répéter l’intervalle de garde après chaque symbole alors qu’en OFDM, cet intervalle n’est ajouté qu’après un symbole OFDM (des milliers de symboles d’information).

  18. OFDM System Model • Multiplication of data symbols with (complex-valued) channel transfer-function: Introduction

  19. I/Q I/Q Channel coding / interleaving Symbol mapping (modulation) OFDM modulation (IFFT) Guard interval 0110 010101001 1 OFDM symbol N symbols Receiver FFT-part Decoding / deinter-leaving symbol de-mapping (detection) OFDM demod. (FFT) Guard interval removal time I/Q I/Q Channel impulse response: Channel est. Time sync. OFDM Block Diagram Transmitter Introduction

  20. x(n) y(n) Canal h(n) Interprétation de l’OFDM Considérons un système de transmission mono-antenne sur un canal multi-trajets : La réponse impulsionnelle du canal s’étend sur L+1 symboles: 0, 1, …, L

  21. La mise en matrice Maintenant imaginer que nous avion ajouté un préfix cyclique au vecteur d’entrée, c’est-à-dire que les On a donc ajouté L points (taille du filtre – 1) au début de la séquence.

  22. Re-écriture matricielle Matrice circulante Propriété: Soit h une matrice circulante, W matrice de la FFT et WH la matrice de IFFT. WhWH est une matrice diagonale avec des éléments sur le diagonal étant la FFT de la première ligne de la matrice h.

  23. Pré-codage Exploitons cette propriété pour dé-convoluer le signal et le canal. Imaginez que le vecteur de symboles d’information X de taille N (ou M+1) est à envoyer sur un canal multi-trajets. On applique une IFFT avant d’envoyer sur le canal, puis on ajoute un préfixe cyclique. La taille du vecteur à envoyer est maintenant N+Ng où Ng<L. Les N derniers échantillons reçus forme le vecteur y. On peut écrire

  24. En réception On applique un FFT sur le signal reçu x(n) y(n) Alors OFDM n’est qu’un précodage qui permet de diagonaliser un canal multi-trajets.

  25. N canaux parallèles indépendants La capacité équivalent est la somme des capacités individuelles. Water-Filling peut être utilisé en émission si on connaît le canal en émission.

  26. Outline • Introduction • Principle of OFDM • OFDM Implementation and System Model • Advantages and Disadvantages • OFDM System Design • Parameter selection • Implementation Issues • Summary and Applications

  27. Data rate; modulation order Guard interval length FFT symbol length Channel impulse response x(4 … 10) Nr. of carriers Channel Parameters are needed • Other constraints: • Nr. of carriers should match FFT size • and data packet length • considering coding and modulation schemes Design of an OFDM System Introduction

  28. OFDM Symbol Configuration (1) OFDM System Design

  29. Spectral Shaping by Windowing OFDM System Design

  30. OFDM Symbol Configuration (2) • Not all FFT-points can be used for data carriers • Lowpass filters for AD- and DA-conversion • oversampling required • DC offsets; carrier feedtrough; etc. Design of an OFDM System

  31. Outline • Introduction • What is OFDM? • Multipath fading radio-channel • Principle of OFDM • OFDM Implementation and System Model • Advantages and Disadvantages • OFDM in Practice • Summary

  32. Advantages of OFDM • Solves the multipath-propagation problem • Simple equalization at receiver • Computationally efficient • For broadband systems more efficient than SC • Supports several multiple access schemes • TDMA, FDMA, MC-CDMA, etc. • Supports various modulation schemes • Adaptability to SNR of sub-carriers is possible • Elegant framework for MIMO-systems • All interference among symbols is removed

  33. time domain signal (baseband) 0.2 0.1 0 -0.1 imaginary real -0.2 0 20 40 60 80 100 120 140 160 180 200 sample nr. Problems of OFDM (Research Topics) • Synchronization issues: • Time synchronization • Find start of symbols • Frequency synchr. • Find sub-carrier positions • Non-constant power envelope • Linear amplifiers needed • Channel estimation: • To retrieve data • Channel is time-variant OFDM Technology

  34. ... conj. … (M times) conj. ...  Correlation-based Frequency-sync. • Correlation of duplicated parts of OFDM signal • e.g.: Cyclic prefix (Guard interval - GI): Guard interval (M samples) FFT-part (L samples) si: • Peak at optimum position • Phase  frequency-offset • Received signal with f-offset: • Constant phase offset between samples spaced by L Introduction

  35. Outline • Introduction • What is OFDM? • Multipath fading radio-channel • Principle of OFDM • OFDM Implementation and System Model • Advantages and Disadvantages • OFDM in Practice • Summary

  36. Applications of OFDM • Wireless LAN • IEEE802.11a/g • HYPERLAN • DAB, DVB, etc. • Digital Audio/Video Broadcasting • xDSL (Digital Subscriber Line) • uses Discrete Multitone (DMT) Summary and Applications

  37. Summary – Essential “Ingredients” • IFFT & FFT • For efficient implementation • Guard interval insertion • Obtaining simple equalization • Removing all IS- & IC-interferences • Error correction coding • To restore bits that are lost on weak sub-carriers

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