Introduction to Orthogonal Frequency Division Multiplexing

TL;DR: In this article, the principles of QAM-OFDM Modulation by DFT Transmission via Bandlimited Channels are discussed. And the implementation of cyclic OFDM Symbol Extension and decision-directed adaptive channel equalisation of OFDM Bandwidth Efficiency is discussed.

Abstract: This chapter contains sections titled: Introduction Principles of QAM-OFDM Modulation by DFT Transmission via Bandlimited Channels Basic OFDM Modem Implementations Cyclic OFDM Symbol Extension Decision-Directed Adaptive Channel Equalisation OFDM Bandwidth Efficiency Chapter Summary and Conclusion

Summary

TRANSMITTED SIGNAL PERIODIC WHICH PLAYS A DECISIVE ROLL IN AVOIDING INTERSYMBOL AND INTERCARRIER

• INTERFERENCE ; = 4HIS IS EXPLAINED LATER IN THIS SECTION !LTHOUGH THE CYCLIC PREçX INTRODUCES A LOSS IN SIGNAL TO NOISE RATIO 3.2 IT IS USUALLY A SMALL PRICE TO PAY TO MITIGATE INTERFERENCE !.
• DIGITAL IMPLEMENTATION OF A BASEBAND /&$- SYSTEM Ú#0Ú AND Ú#0Úb DENOTE THE INSERTION AND DELETION OF THE CYCLIC PREçX RESPECTIVELY &OR THIS SYSTEM WE EMPLOY THE FOLLOWING ASSUMPTIONS q !the authors.

WHERE G

• K #%3 F K IS THE FREQUENCY RESPONSE OF THE CHANNEL 4HUS WE HAVE OBTAINED THE SAME TYPE OF PARALLEL 'AUSSIAN CHANNELS AS FOR THE CONTINUOUS TIME MODEL 4HE ONLY DIdERENCE IS THAT THE CHANNEL ATTENUATIONS G K ARE GIVEN BY THE - POINT $&4 OF THE DISCRETE TIME CHANNEL INSTEAD OF THE SAMPLED FREQUENCY RESPONSE AS IN !the authors.
• TIME FREQUENCY INTERPRETATION 4HE MODELS DESCRIBED ABOVE ARE TWO CLASSICAL MODELS OF /&$- WITH A CYCLIC PREçX !.

OF SIGNALS FROM ALL MOBILE TERMINALS

• RESPECTIVELY !LL THREE HAVE BEEN PROPOSED IN ; = AND &$-!.
• THOROUGH DESCRIPTION OF THE TRANSFER FUNCTION OF COPPER WIRES AND NOISE SOURCES IS GIVEN BY 7ERNER IN ; = &OR $3,S USING A LARGE FREQUENCY RANGE SEVERAL -(Z OR HIGHER THE ATTENUATION FUNCTION CAN THEN BE APPROXIMATED AS J' E C J D`CJ O E.

6$3, AND ($3, SYSTEMS ARE ANALYZED ; =

• .OISE AND CROSSTALK 4HE MOST IMPORTANT NOISE SOURCES IN THE SUBSCRIBER LINE ENVIRONMENT ARE CROSSTALK FROM OTHER WIRE PAIRS IN THE SAME CABLE RADIO FREQUENCY 2& NOISE FROM NEARBY RADIO TRANSMITTERS AND IMPULSE NOISE FROM RELAYS SWITCHES ELECTRICAL MACHINES ETC !7'.
• IS GENERALLY NOT A LIMITING FACTOR IN DIGITAL SUBSCRIBER LINES FOR SHORT CABLES BUT BECOMES MORE IMPORTANT WITH INCREASING.

WHERE /

• GREAT DEAL OF ATTENTION IS GIVEN TO SYMBOL SYNCHRONIZATION IN /&$- SYSTEMS (OWEVER BY USING A CYCLIC PREçX THE TIMING REQUIREMENTS ARE RELAXED SOMEWHAT 4HE OBJECTIVE IS TO KNOW WHEN THE SYMBOL STARTS 4HE IMPACT OF TIMING ERRORS HAS BEEN ANALYZED IN ; = !.
• NALYSIS OF THE IMPACT OF PHASE NOISE IN CODED SYSTEMS HAS BEEN DONE IN ; = 3AMPLING FREQUENCY SYNCHRONIZATION 4HE RECEIVED CONTINUOUS.

AT A VERY LOW DECODER COMPLEXITY ; = 4HE CODE USED IS A ONE DIMENSIONAL STATE CODE WITH

• LEVEL UNIFORM PULSE AMPLITUDE MODULATION 0!- 4HE 0!- OUTPUT SYMBOLS ARE THEN COMBINED TO A SYMBOL QUADRATURE AMPLITUDE MODULATION 1!- CONSTELLATION.
• AND INTER LEAVED TO BREAK UP CHANNEL MEMORY )N THE RECEIVER THE 6ITERBI ALGORITHM 6!.
• IS USED FOR DECODING 4HIS ALGORITHM IS CAPABLE OF USING THE CHANNEL STATE INFORMATION OBTAINED FROM A PILOT SEQUENCE SEE 3ECTION 4HE DECODING IS PERFORMED BY MINIMIZING THE METRIC ) 8 M nnnBG M nnn JX M ` W M J.

FREQUENCY BAND AFTER 3

• GNO NUMBER OF SUBCARRIERS AND /&$- SYMBOLS THE PARAMETERS !.
• AND 3GNO ARE CHOSEN TO MAXIMIZE THE DIVERSITY OF THE SYSTEM !.
• STATIONARY CHANNEL MAKES IT POSSIBLE TO MEASURE THE 3.2 ON EACH SUBCHANNEL AND ASSIGN INDIVIDUAL NUMBERS OF TRANSMITTED BITS !.
• SUBOPTIMAL WAY OF PERFORMING BIT LOADING TO ACHIEVE A HIGH DATA RATE WHILE MAINTAINING A CONSTANT SYMBOL ERROR PROBABILITY ACROSS ALL SUBCHANNELS IS PRESENTED BY 4U ; = )N HIS ALGORITHM THE BIT LOADING FACTORS ARE CALCULATED ACCORDING TO A J KNF t $ J F J o C *} J u ` KNF ".

OF BITS CARRIED BY SUBCHANNEL J

• GREAT DEAL OF EdORT IS THEREFORE SPENT ON DESIGNING ACCURATE FREQUENCY SYNCHRONIZERS FOR /&$- !S IN ANY DIGITAL COMMUNICATION SYSTEM THERE ARE TWO ALTERNATIVES FOR MODULATION CO HERENT OR DIdERENTIAL 4HE %UROPEAN $!".
• SYSTEM USES DIdERENTIAL 103+ WHILE THE PROPOSED SCHEME FOR $6" IS COHERENT 1!- $IdERENTIAL 03+ IS SUITABLE FOR LOW DATA RATES AND GIVES SIMPLE AND INEXPENSIVE RECEIVERS WHICH IS IMPORTANT FOR PORTABLE CONSUMER PRODUCTS LIKE $!".
• RECEIVERS (OWEVER IN $6" THE DATA RATE IS MUCH HIGHER AND LOW BIT ERROR RATES ARE DIbCULT TO OBTAIN WITH DIdERENTIAL 03+ !.
• 4HE AUTHORS WOULD LIKE TO EXTEND THEIR GRATITUDE TO THE STAd AT 4ELIA 2ESEARCH !" ,ULE¥ AND THE COLLEAGUES AT THE $IVISION OF 3IGNAL 0ROCESSING ,ULE¥ 5NIVERSITY OF 4ECHNOLOGY FOR PROVIDING VALUABLE COMMENTS AND CORRECTIONS !PPENDIX !.
• The authors.

WHICH CAN BE VIEWED AS A CROSSCORRELATION FUNCTION IN THE TIME FREQUENCY PLANE 4HE BI ORTHOGONALITY OF

• .OTE THAT THE SYSTEM IS INSENSITIVE TO A &IGURE !.
• MBIGUITY FUNCTION FOR A RECTANGULAR PULSE AND CYCLIC PREçX WITH LENGTHS ~ AND 3 BO RESPECTIVELY.

TIME DELAY LESS THAN 3

• #HINI -ULTICARRIER MODULATION IN FREQUENCY SELECTIVE FADING CHANNELS 0H$ THESIS #ARLETON 5NIVERSITY /TTAWA #ANADA ; = !.
• #HINI - 3 %L 4ANANY AND 3 ! -AHMOUD 4RANSMISSION OF HIGH RATE !4- PACKETS OVER INDOOR RADIO CHANNELS )%%% * 3ELECT !REAS #OMMUN Ô !PR ; = 0 3 #HOW "ANDWIDTH OPTIMIZED DIGITAL TRANSMISSION TECHNIQUES FOR SPECTRALLY SHAPED CHANNELS WITH IMPULSE NOISE 0H$ THESIS 3TANFORD 5NIVERSITY #!.
• OdSET %LECTRON ,ETT Ô $EC ; = 4 +ELLER ET AL 2EPORT ON DIGITAL AUDIO RADIO LABORATORY TESTS 4ECHNICAL REPORT %LECTRONIC )NDUSTRIES !SSOCIATION MODULATION AND CODING STRATEGY FOR 2ICIAN FADING CHANNELS )%%% * 3ELECT !REAS #OMMUN Ô $EC ; = 0 -OOSE ! TECHNIQUE FOR ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING FREQUENCY OdSET CORRECTION )%%% 4RANS #OMMUN Ô /CT ; = !.
• /PPENHEIM AND 2 3CHAFER $ISCRETE TIME SIGNAL PROCESSING 0RENTICE (ALL ; = !.
• FOR BROADBAND MOBILE COMMUNICATION )N 0ROC 2!#% -OBILE #OMMUN 3UMMIT PAGES Ô #ASCAIS .OV ; = ( 2OHLING AND 2 'R¼NHEID -ULTICARRIER TRANSMISSION.

CYCLIC CONVOLUTION CYCLIC EXTENSION

• CYCLIC PREçX Ô $!" SEE DIGITAL AUDIO BROADCASTING $!03+ SEE DIdERENTIAL AMPLITUDE AND PHASE SHIFT KEYING DECISION DIRECTION DECODING DEMODULATION.
• $&4 SEE DISCRETE &OURIER TRANSFORM DIdERENTIAL AMPLITUDE AND PHASE SHIFT KEYING $!03+ DIGITAL AUDIO BROADCASTING $!".
• STAN DARDS INSTITUTE %UCLIDEAN INNER PRODUCT %UROPEAN TELECOMMUNICATIONS.

FADING

• SEE MULTIPLE ACCESS &%84 SEE CROSSTALK çLTER BANK çNITE IMPULSE RESPONSE &)2 SEPARABLE 7IENER &)2 SEE çLTER &ISCHER &- SEE MODULATION GUARD SPACE (¶HER (ARTOG ($3, SEE DIGITAL SUBSCRIBER LINES (UGHES )#) SEE INTERCHANNEL INTERFERENCE.
• )$&4 SEE DISCRETE &OURIER TRANSFORM INTERCHANNEL INTERFERENCE )#).

INTERLEAVING

• )3) )3) SEE INTERSYMBOL INTERFERENCE *AKES LATTICE ,EUNG LOCALIZATION ,ORENTZIAN POWER DENSITY SPECTRUM LOW RANK APPROXIMATION METRIC -, SEE ESTIMATOR --3% SEE ESTIMATOR MOBILE TERMINAL MODEL CONTINUOUS TIME MODEL DIGITAL IMPLEMENTATION DISCRETE TIME MODEL MODULATION CARRIERLESS AMPLITUDE PHASE #!0 COHERENT DIdERENTIAL FREQUENCY &- PULSE AMPLITUDE 0!- QUADRATURE AMPLITUDE.
• 1!- TRELLIS CODED 4#- MULTIPATH PROPAGATION MULTIPLE ACCESS CODE DIVISION #$-!.
• MULTIRESOLUTION .%84 SEE CROSSTALK NOISE ADDITIVE WHITE 'AUSSIAN !7'.

RANK REDUCTION 2EED 2UIZ

• 3ALTZBERG SAMPLING NON SYNCHRONIZED SYNCHRONIZED SAMPLING THEOREM SCATTERING SIGNAL TO INTERFERENCE RATIO 3)2 SINGLE FREQUENCY NETWORKS SINGLE CARRIER SYSTEM 3)2 SEE SIGNAL TO INTERFERENCE RATIO 3OLOMON SUBCARRIER SUBCHANNEL SYNCHRONIZATION.
• CARRIER FREQUENCY COARSE çNE SAMPLING FREQUENCY SYMBOL SYSTEM MARGIN 4#- SEE MODULATION 4$-! SEE MULTIPLE ACCESS TELEPHONE ACCESS NETWORK TRACKING 4U 46 UPLINK UPSTREAM 6$3, SEE DIGITAL SUBSCRIBER LINES 6ITERBI ALGORITHM SOFT OUTPUT 7ARNER 7EINSTEIN 7ERNER 7IENER PROCESS.

Full text

LUND UNIVERSITY
PO Box 117
221 00 Lund
+46 46-222 00 00
An introduction to orthogonal frequency-division multiplexing
Edfors, Ove; Sandell, Magnus; van de Beek, Jan-Jaap; Landström, Daniel; Sjöberg, Frank
1996
Link to publication
Citation for published version (APA):
Edfors, O., Sandell, M., van de Beek, J-J., Landström, D., & Sjöberg, F. (1996).
An introduction to orthogonal
frequency-division multiplexing
. (Div. of Signal Processing, Research Report; Vol. TULEA 1996:16). Luleå
University of Technology.
Total number of authors:
5
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!N INTRODUCTION TO ORTHOGONAL FREQUENCYDIVISION
MU LT IP LEX ING
/V E %DFORS -A GNUS 3ANDELL *AN*AA P VAN DE "EEK
$ANIEL ,ANDSTR¶M &RANK 3J¶BERG
3EPTEM BER 

!BSTRACT
4H IS REPORT IS AN INTRODUCTIO N TO ORTHOGONAL FR EQUENCYDIVISION MULTIPLEXING /&$- 4HE FOCUS
IS ON SIGNAL PROCESSING AREAS PURSUED BY OUR RESEARC H GROUP AT ,ULE¥ 5NIV ERSITY OF 4EC HNOLOGY
7E PRESENT AN HISTORICAL BACKGROUND AND SOME FREQUEN TLY USED SYSTEM MODELS 4YPICAL AREAS OF
AP PLIC A TIO NS AR E ALSO DESCRIBED BOTH WIR E LES S AND WIRED )N ADDITION TO THE GENER A L OVER VIEW
THE ADDRESSED AREAS INCLUDE SYNCHRONIZATION CHANNEL ESTIMATION AND C HANNEL CODING "OTH
TIME AND FREQUENCY SYNC HRONIZATION ARE DESCRIBED AND THE EdECTS OF SYNC HRONIZATION ERRORS
ARE PRESEN TED $IdERENT TYPES OF C HANNEL ESTIMATORS ARE DESCRIBED WHERE THE FOCUS IS ON LOW
COMPLEXITY ALGORITHMS AND IN THIS CON TEXT ADVAN TAGES AND DISADVAN TAGES OF COHERENT AND
DIdERENTIAL MODULATION ARE ALSO DISCUSSED #HANNEL CODING IS DESCRIBED BOTH FOR WIRELESS AND
WIRED SYSTEMS AND POIN TERS ARE INCLUDED TO EV ALUATION TOOLS AND BITLOADING ALGORITHMS !N
EXTENSIV E BIBLIOGRAPH Y IS ALSO INCLUDED

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "4his report is an introduction to orthogonal frequency division multiplexing /&$- 4he focus is on signal processing areas pursued by our research group at ,ule¥ 5niversity of 4echnology 7e present an historical background and some frequently used system models 4ypical areas of applications are also described both wireless and wired )n addition to the general overview the addressed areas include synchronization channel estimation and channel coding "OTH TIME AND FREQUENCY SYNCHRONIZATION ARE DESCRIBED AND THE EdECTS OF SYNCHRONIZATION ERRORS ARE PRESENTED $IdERENT TYPES OF CHANNEL ESTIMATORS ARE DESCRIBED WHERE THE FOCUS IS ON LOW COMPLEXITY ALGORITHMS AND IN THIS CONTEXT ADVANTAGES AND DISADVANTAGES OF COHERENT AND DIdERENTIAL MODULATION ARE ALSO DISCUSSED #HANNEL CODING IS DESCRIBED BOTH FOR WIRELESS AND WIRED SYSTEMS AND POINTERS ARE INCLUDED TO EVALUATION TOOLS AND BITLOADING ALGORITHMS !N EXTENSIVE BIBLIOGRAPHY IS ALSO INCLUDED" ?

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