Orthogonal Frequency Division Multiplexing OFDM Concept and SystemModeling

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 Introduction

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

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

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

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

Caractéristiques du canal

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

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

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

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

Concept of an OFDM signal Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5 Ch. 6 Ch. 7 Ch. 8 Ch. 9 Conventional multicarrier techniques Ch. 10 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 Implementation and System Model frequency

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

Generating the OFDM signal (1) • 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 Window function xi, k Sub-carrier Im Re

Spectrum of the modulated data symbols • Rectangular Window of duration T 0 • Has a sinc-spectrum with zeros at 1/ T 0 Magnitude T 0 • Other carriers are put in these zeros • sub-carriers are orthogonal Frequency N sub-carriers: resembles IDFT!

Generating the OFDM signal (2) xn serial-toparallel x 0, k x 1, k IDFT (IFFT) x. N-1, k xi, k parallelto-serial sn s. N-1, k N data symbols: (in frequencydomain) s 0, k s 1, k Base-band signal Im (time-domain) Re

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

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). GT Delay OFDM Symbol Delay GT SYM GT GT SYM Delay OFDM Symbol Delay GT SYM

OFDM System Model • Multiplication of data symbols with (complex-valued) channel transferfunction: Introduction

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

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 x(n) Canal h(n) y(n)

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.

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

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

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.

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.

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

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

OFDM Symbol Configuration (1) OFDM System Design

Spectral Shaping by Windowing OFDM System Design

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

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

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

Problems of OFDM (Research Topics) time domain signal (baseband) 0. 2 • Synchronization issues: – Time synchronization • Find start of symbols – Frequency synchr. • Find sub-carrier positions • 0. 1 0 -0. 1 -0. 2 imaginary real 0 20 40 Non-constant power envelope – Linear amplifiers needed • Channel estimation: – To retrieve data – Channel is time-variant OFDM Technology 60 80 100 120 sample nr. 140 160 180 200

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

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

Applications of OFDM • Wireless LAN – IEEE 802. 11 a/g – HYPERLAN • DAB, DVB, etc. – Digital Audio/Video Broadcasting • x. DSL (Digital Subscriber Line) – uses Discrete Multitone (DMT) Summary and Applications

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