The History of Orthogonal Frequency-division Multiplexing

IEEE Communications Magazine • November 200926 0163-6804/09/$25.00 © 2009 IEEE

Orthogonal frequency-division multi-plexing (OFDM) is one of those ideasthat had been building for a very longtime, and became a practical realitywhen the appearance of mass marketapplications coincided with the avail-ability of efficient software and elec-tronic technologies. This articledescribes the background and some ofthe striking early development ofOFDM, with explanation of the motiva-tions for using it. I presume a broaddefinition of OFDM as frequency-divi-sion multiplexing (FDM) in which sub-channels overlap without interfering. Itdoes not not necessarily require the dis-crete Fourier transform (DFT) or itsfast Fourier transform (FFT) computa-tional method.

THE FDM BACKGROUNDThere is a long history behind FDM.Stimulated by telegraph companieshoping to multiply their profits,entrepreneurs and inventors of the1870s sought ways to multiply thecapacity of a telegraph transmission lineby carrying several noninterfering infor-mation channels. Time-division multi-

plexing (TDM) or more dynamic time-division multiple access (TDMA), withusers taking turns in using time slots,was invented by Baudot [1] and others,and was particularly useful when thetelegraph line was underutilized, withsignificant gaps between characters. Ofcourse, burst speed would be limited byintersymbol interference — the disper-sion of a pulse into its neighbors — forwhich there was not yet a good channelequalizer. There were many initiativeswith alternative multiplexing schemes.Edison’s “quadruplex” telegraphy sys-tem [edison.rutgers.edu/quad.htm], forexample, sent two messages simultane-ously (in each direction), one varyingamplitude and the other polarity.

Interest turned fairly early to fre-quency-division multiplexing. The evo-lution to the techniques known asmultitone or OFDM began in the inno-vations of the 1870s. Alexander Gra-ham Bell was initially funded by hisfuture father-in-law Gardiner Hubbardto work on “harmonic telegraphy,”which was FDM transmission of multi-ple telegraph channels [2], with theequipment shown in Fig. 1. His com-petitor Elisha Gray simultaneously

worked in this area and had an earlierpatent [3]. Thomas Edison was also inhot pursuit of the multitone telegraph[4]. The access facilities for these tech-niques might be considered early imple-mentations of digital subscriber line(DSL). However, Bell’s first love wastelephony, and he focused his energyon analog voice transmission ratherthan discrete-tone multiplexed telegra-phy.

FDM came into its largest generaluse in carrier systems for analog tele-phony. As described by Schwartz [5],FDM for analog voice signals may firsthave been demonstrated by GeorgeSquier, a major in the U.S. Army Sig-nal Corps, in 1910, in an apparatuswith one baseband and one passbandchannel. AT&T was skeptical, claimingtoo much dispersion and loss at thehigher frequencies it assumed wererequired. But AT&T deployed its ownfive-channel system in 1918 that usednot-so-high subcarrier frequencies andrepeaters. FDM became the main mul-tiplexing mechanism for telephone car-rier systems. Bandwidth and dispersionwere not serious problems with the rel-atively modest spacing of repeaters,

HISTORY OF COMMUNICATIONSEDITED BY MISCHA SCHWARTZ

OFDM, orthogonal frequency-division multiplexing, plays asignificant role in modern telecommunications, ranging from itsuse in DSL-modem technology to 802.11 Wi-Fi wireless systems.Work underway in next-generation mobile wireless systemsexploits the advantages of using OFDM techniques as well.OFDM combined with MIMO technology is expected to provideimmense improvements in wireless transmission capacity. We arepleased to have for this month’s History Column a succinct, yet

authoritative, history of this technology. Its author, Steve Wein-stein, a leader in the Communications Society and one of its pastPresidents, was one of the pioneers in the development of OFDMtechnology. He thus writes from personal experience in describingthe history of OFDM. We commend the article following to allreaders of IEEE Communications Magazine.

—Mischa Schwartz

INTRODUCTION TO “THE HISTORY OF OFDM”

THE HISTORY OF ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXINGSTEPHEN B. WEINSTEIN

Figure 1. Bell’s harmonic telegraph, using reeds responsive to different frequencies. Photos of replicas of theoriginal equipment used with permission of Telecommunications Museum, LaSalle, Quebec, Canada.

Transmitter Receiver

LYT-HISTORY-November 10/19/09 12:42 PM Page 26

Authorized licensed use limited to: Universitat Autonoma De Barcelona. Downloaded on November 27, 2009 at 19:48 from IEEE Xplore. Restrictions apply.

IEEE Communications Magazine • November 2009 27

and 8 kHz subchannel spacing was pro-vided for 4 kHz voice signals. The N2carrier system of the mid-1960s (Fig.2) used double sideband amplitudemodulation and transmitted up to 200miles [6].

With the introduction of digital tele-phony, FDM carrier systems with indi-vidual subchannels for voice signalsbegan, in the 1970s, to be replaced byTDM/FDM and pure TDM systems. Ofcourse, the higher the aggregate speedof a TDM transmission line, the widerthe bandwidth of this single channeland the greater the potential for inter-symbol interference. High-frequency(HF) radio systems had a particularlysevere transmission problem, with selec-tive fading (Fig. 3) across the transmis-sion bandwidth causing considerablepulse dispersion and intersymbol inter-ference.

The answer to this problem withserial data transmission in radio fre-quency (RF) channels (and later inDSL with severely distorted channels)was to go back to fine-grained FDM,concentrating data in the less fadedsubchannels. Each subchannel would beaffected by only a small part of thechannel characteristic (Fig. 4), whichcould be approximated by constantamplitude and phase. This narrow sub-channel could easily be equalized, in acomplex analytic model, by multiplica-tion by the inverse complex number.The hope that the saving in equaliza-tion effort would compensate for thegreater complexity of FDM became areality with OFDM.

DENSE SUBCHANNELSBut FDM, too, had drawbacks:• The waste of scarce wireless fre-

quency spectrum in guard spacesbetween the subchannels

• The large complexity of a multi-plicity of separate modulators forthe different subchannelsThe first problem was alleviated by

the concept of OFDM as an FDM sys-tem with subchannel signals havingoverlapping but non-interfering frequen-

cy spectra. Harmonic sinusoids were anobvious choice, since they are orthogo-nal on a period T of the fundamental(lowest) subcarrier signal. In an OFDMsystem sending complex data {an}, thesubchannel signals,

sn(t) = ang(t)exp(j2πfnt), fn = n/T, 0 ≤ n ≤ N–1, g(t) = 1 on the interval

0 < t < T and zero elsewhere, (1)

are mutually orthogonal despite over-lapping spectra. N, the number of sub-channels, is arbitrary and varies amongapplications. The rectangular pulseshape g(t) has a sin(f)/f spectrum mak-ing a subchannel spectrum heavily over-lap its neighbors, as shown in Fig. 5. AnOFDM signal block, on the interval T,can be defined as the sum of these sub-channel signals, and, ideally, one blockimmediately follows another. In theabsence of channel distortion, there isneither inter-subchannel nor intersym-bol interference.

It is easy to show [7] that an N-pointinverse DFT (IDFT) operating on the(possibly complex) data block {a0, a1,…, aN–1},

(2)

generates samples, at time intervalsT/N, of the OFDM signal that is thesum of the subchannel signals definedin Eq. 1. Operating on the received sig-nal with the DFT, like Eq. 2 but with anegative exponent, recovers the data.Figure 6 is a simplified illustration ofthe entire OFDM system, including thecyclic prefix operation described later.

With rectangular g(t) and a distortedchannel comes intersymbol interference,a problem addressed earlier, but there isthe advantage that the transmitter doesnot have to know the channel character-istic (although the receiver does, forequalization purposes). However, if thechannel characteristic is known at thetransmitter, many other pulse shapesare possible. Chang [8], in a fundamen-tal contribution to OFDM, developedgeneral conditions for the shapes ofpulses, defined as the combination oftransmitter filter and channel character-istic, with bandlimited but still overlap-ping spectra. Such pulses, including the

s a j nk Nk nn

N=

=

−∑ exp{ / },20

1π

HISTORY OF COMMUNICATIONS

Figure 2. N2 carrier system frequency spectrum for 12 telephone subchannels, derived from [6].

0 dB

168 –60 dB

176 264

kHz

Figure 3. Selective fading in an HF radio channel. Source: J. Stanley, "Observing Selec-tive Fading in Real Time with Dream Software," QEX, Jan-Feb 2007,www.arrl.org/qex/2007/01/stanley.pdf.

Carrier indexQX0701_Stan01

Channel transfer function/group delay

50

-80

Tran

sfer

fun

ctio

n (d

B)

Gro

up d

elay

(m

s)

-70

-60

-50

-40

-40

-20

0

20

40

0 100 150 200

Transfer functionGroup delay

LYT-HISTORY-November 10/19/09 12:49 PM 7


full cosine-rolloff pulse of Fig. 5, make aviable OFDM system “without inter-channel and intersymbol interferences.”

Figure 7 illustrates the Chang systemwith transmitting filters A1, …, Andepending on the magnitude of thechannel transfer function H(f). If thechannel characteristic is effectively flatacross a narrow subchannel, it may bepossible to effectively ignore the depen-dence on H(f). Chang assumed realdata for the amplitude modulation ineach subchannel.

Saltzberg [9] extended Chang’s workto complex data (e.g., quadrature ampli-tude modulation [QAM]). The systemhe described (Fig. 7) is now calledOFDM-OQAM (offset QAM). In orderto eliminate intersymbol and inter-sub-band interference (for a distortionlesstransmission channel), he showed thatthe timing of the in-phase and quadra-ture data streams should be staggeredby T/2 and adjacent subbands staggeredthe other way, as Fig. 8 indicates. Hedid not presume knowledge at the

transmitter of the channel; the transmitand receive filters, in tandem, have aNyquist characteristic. Saltzberg investi-gated the performance of Chang’smodel in a dispersive channel, assumingboth intersymbol and inter-subchannelinterference as well as phase offset, andtested alternative pulse characteristicsmeeting the Chang criteria. He generat-ed performance criteria in terms of theclassical eye opening derived fromsuperposed outputs with different datainput sequences. Chang and Gibby fol-lowed up with analysis of the perfor-mance of Salzberg’s system in thepresence of sampling time error, carrierphase offset, and phase distortions in itsfilters [10].

Hirosaki [11] contributed furtherenhancements to OFDM/OQAM, par-ticularly much faster processing throughreplacement of an N-point DFT with anN/2-point DFT, if the passband carrierfrequency is chosen such that the frac-tional part of f1/Δf is 0.5, where f1 is thelowest subcarrier and Δf is the subchan-nel spacing. For digital signal processor(DSP) implementation, he determinedthat his OFDM/OQAM design has a


28 IEEE Communications Magazine • November 2009

Figure 4. Approximation of a distorted channel, within a subband, by constant amplitudeand phase.

Channel spectrum

Amplitude

Phase

(f0)

A(f0)

Complex channel approximationwithin subband:H(f)≈A(f0)exp[j (f0)]

ff0

Figure 5. Rectangular and full-cosine-rolloff pulses and resulting OFDM spectra.

Rectangular pulse

t f f

Pulse spectrum OFDM spectrum Full cosine pulse spectrum

Full cosine OFDM spectrum

-T/2 T/2

Figure 6. OFDM system.

Data

Channel Simple equalization Cyclic extension

IDFT

aO,...,aN-1

sO,...,sN-1

DFT hO,...,hv

Figure 7. Chang system for OFDM with channel-dependent transmitter filters [8].

+

Noise

A1(f) exp{jα1(f)}a1(t)

First transmitting filter

Transmission medium

Nth transmitting filter

AN(f) exp{jαN(f)}aN(t)

A2(f) exp{jα2(f)}a2(t)

H(f) exp{j η (f)}h(t)

Data processing (receivers)




significant advantage over single-chan-nel data transmission.

Other researchers continued toimprove OFDM/OQAM. A particularinterest has been the design of pulsesthat are well localized (limited) in bothtime and frequency. The work ofBolcskei, Duhamel and Hleiss [12],yielding symmetric pulses that are welllocalized and realize performance closeto the optimum OFDM spectral effi-ciency, is a good example (Fig. 9).

SIGNAL GENERATION USINGTHE DFT AND ITS FFT

IMPLEMENTATION

The second problem of FDM, efficient-ly generating a multichannel, closelypacked (OFDM) data signal, was solvedby the FFT implementation of the DFT.Zimmerman and Kirsch published aremarkable paper on the design of anHF (high frequency) radio OFDMtransceiver (KATHRYN) in 1967 [13],following a 1965 article by Bello thatdescribed the system’s response to chan-nel impairments including use of a timeguard interval.

KATHRYN generated the orthogo-nal subchannel signals using the DFT inan analog hardware implementation.There were 34 subbchannels in a 3 KHzbandwidth, as shown in Fig. 10 togetherwith the equipment. The system appearsto have distributed power uniformlyover all subchannels, except for varyingthe transmission rate by using subchan-nels according to conditions. There wasbinary in-phase and quadrature modu-lation of each subcarrier, although

apparently not with the OFDM-OQAMinsights of later years, but there was theunderstanding that larger signal constel-lations could be used in the subchan-nels with better channel characteristics.

The transition to the FFT for gener-ating the DFT was soon to follow. PaulEbert, Jack Salz, and I were motivatedin the late 1960s to find a good applica-tion in data communication for therecently announced Cooley-Tukey fastFourier transform (FFT) algorithm[14], a reduced-complexity way to com-pute the discrete Fourier transformrequiring approximately NlogN opera-tions rather than N2. It was later discov-ered that the FFT may go back to thegreat mathematician Karl FriedrichGauss (around 1805) who used it tohelp calculate elements of a finiteFourier series for the computation of

asteroid orbits [15]. The FFT, exploit-ing the periodicity and symmetry prop-erties of exponentials, factors a lengthN DFT into a number of shorter-lengthDFTs with multiple re-use of the resultsof these shorter-length DFTs[cnx.org/content/m12026/latest/].

It became apparent to us that, sincethe DFT could generate a data signal inparallel subbands, greatly reducingequalization complexity at the cost ofthe complexity of generating the sub-band signals, the use of the FFT mightswing the advantage to OFDM over sin-gle-carrier systems. OFDM would also,as Zimmerman and Kirsch noted in1967, support flexible utilization of aspectrum that was subject to fading or(as in ADSL) frequency-selective inter-ference. We published our concept [7](Fig. 11) but there was little interest in


Figure 8. OFDM-OQAM implementation with staggered time-delayed subchannels(adapted from Saltzberg [9] and Hirosaki [11]). Only two transmitter subchannels areshown, with the pattern repeating for additional subchannel pairs and with a compara-ble structure in the receiver.

ChannelM

T/20 1

Ch Stream Delay cos2π(fc)t

sin2π(fc)t

G(f)

0 2 G(f)

1 1

cos2π(fc+1/T)t

sin2π(fc+1/T)tT/2

Data inputs withsymbol rate 1/T

G(f)

1 2 G(f)

Figure 9. OFDM/OQAM pulse shaping filter time and frequency characteristics, for a pulse well localized in both time and frequency[12].

20-0.2

0

0.2

0.4

0.6

0.8

1

40 60 0.10-80

-60

-40

-20

0

0.2 0.3 0.4

Mag

nitu

de (

dB)



this approach within our voiceband datacommunication division at Bell Labora-tories. It did not even seem worthwhileapplying for a patent. The big applica-tion areas of ADSL, wireless communi-cations, and digital audio and videobroadcasting (DAB-DVB) were yet tocome.

Using the FFT made OFDM viable,but the debate over the relative com-plexity of OFDM signal processing andsingle carrier wide-channel equalizationcontinues to this day. Sari [16] and oth-ers [17, 18] noted that generating anddetecting an OFDM signal is similar toequalizing a single carrier system in thefrequency domain. The flexibility ofOFDM appears to have made it thewinner in current practice.

ADSL: THE FIRST MAJOROFDM APPLICATION

Although, as exemplified by theKATHRYN system of the mid-1960s,wireless applications apparently preced-ed wired ones, the first major consumer-oriented application was in ADSL(asymmetric digital subscriber line).DSL had been investigated at Bell Labswhere Gitlin and others defined single-channel systems that could work atmegabit rate on subscriber lines as longas 18 kilofeet [19], and studies weremade in the late 1980s of alternativeimplementations using OFDM and CAP(carrierless amplitude-phase modula-tion, a variation on single-carrier QAM).Performance seemed comparable andBell Labs subsequently developed CAPmodems building on its long experience

with voiceband modems. ADSL, with amuch higher transmission rate towardthe subscriber, was defined by Lechlei-der and his colleagues at Bellcorearound the same time. Much subse-quent development of ADSL and higherspeed DSL systems was pursued at BellLabs by Lawrence and his colleagues[20]. It was left to Cioffi and his compa-ny, Amati, to develop discrete multitone(DMT, essentially OFDM) [21].

Amati’s prototype DMT ADSLmodem won a competition with CAP ina Bellcore-sponsored test in January,1993. There were a number of reasonsfor the success of multitone, but the mainone, as suggested to me by John Cioffi,may have been its capability to avoidexpending power in parts of the spec-trum characterized by very large noise ora deep channel null, a capability difficultto achieve for single-carrier systems. TheShannon capacity-achieving water-pour-ing analysis, illustrated in Fig. 13 wherepower (water) is poured onto the curverepresenting the ratio of noise power tochannel magnitude squared, can result inislands where no power at all should beplaced. The Amati group devised dynam-ic bit assignment strategies that assigneddata (and signal power) in accordancewith the fluctuating channel and noiseconditions typical of a twisted pair sub-scriber line. A second Bellcore-sponsoredcompetition for very high speed DSL(VDSL), held in 2003, also showed bet-ter performance for DMT.

The original and still prevalentADSL1 technology [22] uses a 256-pointDFT with subcarriers separated by4.3125 kHz and a (block) symbol rateof 4000/s. Including a guard period of

40 samples, the sampling rate of thetransmitted signal is 2.208 million/s.The data rate is any multiple of 32 kb/sup to approximately 8 Mb/s. Subbands0–32 (except for a few lowest subbandsconsumed by analog telephone serviceand a guard band) are used forupstream transmission and subbands33–255 for downstream. The total sub-scriber line bandwidth, upstream anddownstream, is about 1.1 MHz.

For the later ADSL2+ on shortersubscriber lines, 512 subbands are used,and the sampling rate is 4.416 million/s,realizing a maximum data rate of about24 Mb/s. The still newer VDSL, inhybrid systems with the shortest sub-scriber lines, can use the same subcarri-er spacing and symbol rate as doesADSL but up to 4096 subbands, con-suming about 17.6 MHz of bandwidth.Alternatively, VDSL can use an 8 kHzsymbol rate and 8.625 kHz subcarrierspacing, supporting up to 150 Mb/sdownstream data rate and 75 Mb/supstream. Upstream and downstreamgroups of subbands are distributed overthe total bandwidth.

Despite early development ofADSL1 in the United States, the firstDMT ADSL deployments, using Amatiequipment, were in other countries,beginning with British Telecom in late1993 and early 1994, offering 2.024Mb/s downstream. France Telecomdeployed an 8 Mb/s system (on relative-ly short subscriber lines) in 1994,Deutsche Telekom deployed 2 Mb/sand 8 Mb/s systems in 1994, TelecomItalia offered 4 Mb/s and 8 Mb/s ADSLin 1994/1995, and Telstra initiated a 6Mb/s system (including live video) in


30 IEEE Communications Magazine • November 2009

Figure 10. The 1967 KATHRYN high-frequency radio OFDM system [13].

13.3 ms

12

82 Hz subband spacing

3 KHz

0

3334

Time

Frequency(before translation to RF)





Australia in 1994/1995. Finally, in 1997,a group of Bell operating companies inthe United States decided to go withDMT ADSL. Texas Instruments pur-chased Amati in late 1997 for $450 mil-lion, the first big economic success foran OFDM equipment manufacturer.

MEETING OFDMCHALLENGES: THE CYCLICPREFIX AND OVERCOMINGHIGH PEAK TO AVERAGE

RATIO

Pulse localization such as that used inOFDM-OQAM can minimize intersym-bol interference, but for ordinaryOFDM with a rectangular pulse a dis-persive channel causes intersymbolinterference. It can be mitigated by atime-domain guard interval betweenOFDM symbols (blocks), or by a cyclicprefix to the OFDM block. The propor-tional overhead cost is minimized byuse of long OFDM symbols (large N).

A guard interval equal to the “mem-ory” (dispersion time) ν of the channel,during which no energy is transmitted,is the simplest solution. However, thechannel is used more efficiently if some-thing is transmitted during the guardspace that contributes to the signalenergy without introducing intersymbolinterference.1 This is the cyclic prefix,the repetition of the last part of thetransmitted signal during the prefixinterval, as suggested in Fig. 14. Assum-

ing the channel is known at the receiv-er, the OFDM data block may be verysimply detected as described below.

The cyclic prefix was, to the author’sknowledge, first proposed by Peled andRuiz [23] in 1980. The involvement of acirculant matrix has long been recog-nized, but Jack Salz2 recently developeda particularly elegant circulant matrixexplanation for why the input data-IDFT-cyclic prefix-channel-DFT seriesof operations decouples the subchan-nels and makes detection easy, withoutthe transmitter needing any knowledgeof the channel.

Assume transmitted signal samples(sN–ν, …, sN–1, s0, s1, ……, sN–1), wherethe first ν elements are the cyclic prefixrepeating the last ν samples of theOFDM signal samples generated by theIDFT operating on the input data (a0,…, aN–1). The samples of the channelimpulse response are (h0, …, hν). Con-volving the transmitted signal vectorwith the channel (Fig. 6) yields the sam-pled received signal (r–ν, …, r–1, r0, r1,…, rN–1, rN, …, rN+ν), of which only r0through rN–1 are applied to the DFTprocessor. If the channel has, for exam-

ple, memory ν = 2, a little mathematicsshows that these operations can beexpressed as

(3)

where the elements at the upper right ofthe equivalent channel matrix HC(between the DFT and the IDFT) repre-sent the effect of the cyclic prefix. Thismatrix is a circulant matrix in which eachrow is a cyclic shift of the row above it.(H0, …, H3) are frequency-domain sam-ples of the channel transfer function.

h0

H0

H1

H2

H3

0

h1 h0 0

h2 h1 h0

0 h2

h2 h1

h2

h1

0

0

0

h0

DFT

IDFT a = a

1 A null prefix can be used at the transmitter,with the cyclic prefix inserted in the receiver, atsome performance cost.

2 Unpublished, referenced here by permission ofJack Salz.

Figure 11. Original figures from 1971 Weinstein-Ebert paper [7]. Left: system including simple (one complex multiplication) equaliza-tion; Right: multiple subchannel tones.

05cos(1OTTt/T)T

+1

Sampleat intervals

kΔt/2

{rk}2N-1 {z1}2N-1

Channel H(f)

a1^

-b1^

Sourcedn=an+jbn,

n=0,1,...,N-1DFT

DFTEqualiz.transfor-mation

y(t)

y(t)

(Real partonly)

Low-passfilter 04cos(8TTt/T)

T-1

03cos(6TTt/T)T

+1

02cos(4TTt/T)T

+1

01cos(2TTt/T)T-1

00T

+1k=01=1

Figure 12. John Cioffi (center, dark suit) and his Amati colleagues reassem-bled in 2005 for this photograph with their experimental multitone modem of1993 (plastic box on top) and its early commercial successor. [Photo courtesyJohn Cioffi.]



IEEE Communications Magazine • November 200932

Equation 3 comes from the mathe-matics of singular value decomposition[24], which demonstrate that a matrix isdiagonalized if it is postmultiplied bythe matrix whose columns are its eigen-vectors, and premultiplied by the conju-gate transpose of that eigenvectormatrix. It is a remarkable fact that theeigenvector matrix for any circulantmatrix (which can be generated fromany channel characteristic) is always thesame and is simply the matrix whosecolumns are the powers of the Nth rootof one (i.e., the matrix that defines theDFT). If HC is our channel circulantmatrix, F1 is the IDFT matrix, and F2 isthe DFT matrix (the complex transposeof F1), then F2HCF1 is the diagonalmatrix Λ whose elements are the eigen-values of HC. These can be shown to bethe values of the channel transfer func-tion at the discrete subchannel frequen-cies. The data can be recovered fromthe output samples in Eq. 3 by simplydividing each element of the outputvector by the appropriate value of thechannel transfer function.

The high peak to average powerratio (PAPR) of OFDM was as seriousa problem as intersymbol interference.An intuitive example is when the samemodulation level is used for all the sub-carrier sinusoids; at t = 0 they will allhave the same polarity and add up to alarge value. High peak values occurinfrequently but can be very high. Forexample, for an unmodified 256-pointOFDM signal, Han and Lee computed

that the peak-to-average ratio exceeds11.3 dB for less than 0.1 percent of theOFDM data blocks [25]. They discuss anumber of approaches to limiting peak-to-average power including amplitudeclipping, coding, tone reservation orinjection, dynamic constellation exten-sion, and various signal formation tech-niques such as mapping andinterleaving, which will not be describedhere. Greenstein and Fitzgerald con-tributed early work on signal phasing tominimize high PAPR [26].

OTHER APPLICATIONSADSL was the first widely used applica-tion for FFT-based OFDM, but the pre-decessor of another application,OFDM-based frequency-hopping sys-tems, was a 1942 patent of Hedy KieslerMarkey, better known as the film starHedy Lamarr [27]. The objective, dur-ing World War II, was a jam-resistantcommunication channel for guiding tor-pedoes, and Lamarr’s solution was ran-dom movement among frequencychannels that would thwart the narrow-band jamming systems. Although thesystem of Fig. 15 used a tunable hard-ware oscillator rather than a DFT, itillustrated one more motivation forgenerating a signal utilizing many sub-channels rather than a single-carriersystem.

The concept of frequency hopping isnow a popular spread spectrum tech-nique for avoiding interference if not

outright jamming. It was notably imple-mented in the Bluetooth standard(IEEE 802.15.1). More recently, itappeared in the context of cellularmobile communications in the FlarionFlash OFDM system [28], now a prod-uct of Qualcomm, which uses fast hop-ping among the OFDM subbands toprovide flexibility to accommodate dif-ferent classes of IP (Internet Protocol)traffic, and to minimize interferencebetween mobile units on either side ofa cell boundary.

With resistance to fast selective fad-ing in mind, Cimini [29] explored appli-cation of OFDM to the difficultenvironment of cellular mobile systems.The KATHRYN and other early sys-tems presumed slow fading, unlike thatexperienced in a vehicle moving at 60mi/h. Coupling OFDM with correctionsusing pilot tones, he noted “largeimprovements in BER [bit error rate]performance in a flat Rayleigh fadingenvironment.” He commented that “theaveraging ability of the OFDM system,which makes the bursty Rayleigh chan-nel appear nearly Gaussian, providesthis large BER improvement.”

The other major two-way wirelessapplications of OFDM include WiFi(IEEE 802.11a, available from stan-dards.ieee.org/getieee802/802.11.html),in which a 64-point transform is stan-dard with only 48 of the subbands used,and in WiMAX (IEEE 802.16) wherethe DFT may have as many as 4096points, or as few as 128, to accommo-date channels ranging from the nominal20 MHz down the order of 1 MHz.Researchers have explored how OFDMcan be utilized in a multiple access sys-tem (OFDMA) (mentor.ieee.org/802.22/file/05/22-05-0005-01-0000-ofdma-tutorial-ieee802-22-jan-05.ppt)where corrections must be made for thedifferent downlink channels to differentusers [30], and for the differences indelay, amplitude, and phase among thespatially distributed contributions in theuplink channel. Cognitive radio systems


Figure 13. “Water pouring,” showing the optimum allocation of transmittedpower that realizes channel capacity. For simplicity, only the positive-frequen-cy spectrum is shown.

Channel

f (frequency)

N(f)/IH(f)I2

Figure 14. Transmission of OFDM pulses with guard interval and with a cyclic prefix.

1 2

1 2

Guard interval

T+V 2(T+V) Transmitted

Received

Time

1 2

Sample here only.

1 2

Cyclic prefix

T+V 2(T+V)

(Continued on page 34)



IEEE Communications Magazine • November 200934

are a significant application area [31].OFDM is associated with one of the

major newer application areas ofOFDM, audio and video broadcasting,as exemplified by Sari and Karam’sanalysis of the application to cable tele-vision systems [32] and the terrestrialbroadcast (DVB-T) work of Reimers[33]. The DVB-T broadcaster (Fig. 16)uses a 2048 (“2K”) or 8192 (“8K”) DFTand employs coded OFDM (COFDM)[34]. The serial baseband bitstream isdistributed over multiple subbands forrobustness against multipath channelsand against narrowband interferers. Alengthened guard interval, up to onefourth the OFDM symbol length, pro-vides added protection at the cost oflower spectral efficiency. Spectral effi-ciency ranges from 0.62 bits/sec/Hz to

3.27 bits/sec/Hz, in an 8 MHz channel,depending on the code rate (1/2 to 7/8)and the modulation (QPSK, 16-QAM,64-QAM). DVB has been extended to amore mobile-friendly version, DVB-H(handheld), that has been adopted as astandard of the European Union. Thestandard (“8K”) version of DVB-Hemploys an 8192-point DFT but onlyuses 6817 active subcarriers spaced by1.116KHz, of which 6048 carry userdata [www.dvb-h.org/PDF/DVB-H FactSheet.0808.pdf] [35]. A “4K” mode isalso available in DVB-H but not inDVB-T.

Within the past several years,OFDM has been applied to long-hauloptical communication networks, whereit can help reduce the degradations ofchromatic dispersion [36]. The newestapplication area in optical communica-tions is in local access, for example in

PONs (passive optical networks), wherethe fine granularity of the subbandsprovides many opportunities for config-uring a range of services and virtual pri-vate networks [37].

An additional new application areais in ultrawideband (UWB) personalarea networks using OFDM. In thisapplication (IEEE 802.15.3a), the spec-trum is segmented in 528 MHz chunks,each supporting 128 OFDM subchan-nels. A communication session canjump among chunks and subchannelsfrom one OFDM symbol to the next.

WHERE CAN IT GO NEXT?OFDM does not necessarily have to usesinusoidal carriers. There has beenexploratory work in the use of prolatespheroidal [38] and wavelet [39] trans-forms. We are likely to see it appear inmany forms to meet different needs. Itwill continue to have competition withalternatives [40]. OFDM is one of thosetechniques that had to wait quietly forgenerations until technology made itpractical. As computational technologycontinues to advance, and with lower-power “green radio” becoming animportant goal, we can expect evenmore innovative applications in thenear future.

REFERENCES[1] K. G. Beauchamp, History of Telegraphy, IEE,

2001, p. 394.[2] U.S. patent 174,465, “Improvement in Teleg-

raphy,” Alexander Graham Bell, Mar. 7,1876.

[3] U.S. Patent 166,095, “Electrical Telegraph forTransmitting Musical Tones,” Elisha Gray,July 27, 1875.

[4] U.S. Patent 182,996, “Acoustic Telegraph,”Thomas Edison, Oct. 10, 1876.

[5] M. Schwartz, “The Origins of Carrier Multi-plexing: Major George Owen Squier andAT&T,” IEEE Commun. Mag., May, 2008, pp.20–24. Original paper: G. Squier, “MultiplexTelephony and Telegraphy by Means of Elec-tric Waves Guided BY Wires,” Trans. AIEE,


Figure 16. The DVB-T system [34].

Symbolmapping

Innerinterleaver

Inner FECencoder

Puncturedconvolutional

code

Outerinterleaver

Data

Baseband inter-face and syncseparator

Sync inversion,energy dispersal

TransmitterAntenna

Clock

Outer FECencoder

Reed-SolomonRS (204,188)

D/A OFDMAdaptation oftransmissionframe

Guardinterval

Pilots andTPS data

Figure 15. Part of the figure from the frequency-hopping system [27] co-invented byHedy Lamarr (photo).

(Continued from page 32)




vol. 30 pt. 2, 1911, pp. 1675–80.[6] H. Boyd and F. Herr, “The N2 Carrier Termi-

nal — Objectives and Analysis,” and W.Lundry and L. Willey, “The N2 Carrier Termi-nal Circuit Design,” Bell Sys. Tech. J., vol. 44,no. 5, May–June 1965, pp. 731–85.

[7] S. B. Weinstein and P. M. Ebert, “Data Trans-mission for Frequency-Division MultiplexingUsing the Discrete Fourier Transform,” IEEETrans. Commun. Tech., vol. 19, no. 5, Oct.1971, pp. 628–34. An earlier publicationwas J. Salz and S. B. Weinstein, “FourierTransform Communication System,” Proc.ACM Conf. Comp.and Commun., Pine Moun-tain, GA, Oct. 1969.

[8] R. W. Chang, “High-Speed Multichannel DataTransmission with Bandlimited OrthogonalSignals,” Bell Sys. Tech. J., vol. 45, Dec.1966, pp. 1775–96; see also U.S. Patent3,488,445, Jan. 6, 1970.

[9] B. R. Saltzberg, “Performance of an EfficientParallel Data Transmission System,” IEEETrans. Commun. Tech., vol. 15, no. 6, Dec.1967, pp. 805–11.

[10] R. W. Chang and R. A. Gibby, “A Theoreti-cal Study of Performance of an OrthogonalMultiplexing Data Transmission Scheme,”IEEE Trans. Commun. Tech., vol. 16, no. 4,Aug. 1968, pp. 529–40.

[11] B. Hirosaki, “An Orthogonally MultiplexedQAM System Using the Discrete FourierTransform,” IEEE Trans. Commun., vol. COM-29, no. 7, July, 1981. See also “An Analysisof Automatic Equalizers for OrthogonallyMultiplexed QAM Systems,” IEEE Trans.Commun., vol. COM-28, no. 1, pp. 73–83.

[12] H. Bolcskei, P. Duhamel, and R. Hleiss,“Design of Pulse Shaping OFDM/OQAM Sys-tems for High Data-Rate Tranmission OverWireless Channels,” Proc. ICC 1999, pp.559–64.

[13] M. S. Zimmerman and A. L. Kirsch, “TheAN/GSC-10 (KATHRYN) Variable Rate DataModem for HF Radio,” IEEE Trans. Commun.Tech., vol. COM-15, no. 2, Apr. 1967; seealso Bellow’s earlier but less complete intro-duction to KATHRYN in vol. COM-13, no. 9,Sept. 1965.

[14] J. Cooley and J. Tukey, “An Algorithm forthe Machine Calculation of Complex FourierSeries,” Math. Comp., vol. 19, 1965, pp.297–301.

[15] M. Heideman, D. Johnson, and C. Burrus,“Gauss and the History of the Fast FourierTransform,” IEEE ASSP Mag., vol. 1, no. 4,1984, pp. 14–21.

[16] H. Sari, G. Karam, and I. Jeanclaude, “Trans-mission Techniques for Digital Terrestrial TVBroadcasting,” IEEE Commun. Mag., Feb.1995, pp. 100–09.

[17] A. Czylwik, “Comparison Between ActiveOFDM and Single Carrier Modulation withFrequency Domain Equalization,” Proc. 1997IEEE VTC, Phoenix, AZ, 1997.

[18] S.L. Ariyavisitakul et al., “Frequency DomainEqualization for Single-Carrier BroadbandWireless Systems,” IEEE Commun. Mag.,2002.

[19] U.S. Patent 4,924,492, May 8, 1990,“Method and Apparatus for WidebandTransmission of Digital Signals Between, forExample, a Telephone Central Office andCustomer Premises,” invented by R. D. Gitlin,S. K. Rao, J-J. Werner, and N. S. Zervos.

[20] S. Ahamed and V. Lawrence, IntelligentBroadband Multinmedia Networks, Springer,1997.

[21] J. Bingham, “Multicarrier Modulation forData Transmission: An Idea Whose Time HasCome,” IEEE Commun. Mag., vol. 2, no. 5,May, 1990, pp. 5–14.

[22] K. Sistanizadeh, P. Chow, and J. Cioffi,“Multi-Tone Transmission for AsymmetricDigital Subscriber Lines,” Proc. IEEE ICC,1993, vol. 2 pp. 756–60.

[23] R. Peled and A. Ruiz, “Frequency DomainData Transmission using Reduced Computa-tional Complexity Algorithms,” Proc. IEEEInt’l. Conf. Acoustics, Speech, and Sig. Proc.,1980, Denver, CO, pp. 964–67.

[24] V. Madisetti and D. Williams, Digital SignalProcessing Handbook, IEEE Press and CRCPress, 1998.

[25] S. Han and J. Lee, “An Overview of Peak-to-Average Power Ratio Reduction Techniquesfor Multicarrier Transmission,” IEEE WirelessCommun., vol. 12, no. 2, Apr. 2005, pp.56–65.

[26] L. Greenstein and P. Fitzgerald, “PhasingMultitone Signals to Minimize Peak Factors,”IEEE Trans. Commun., vol. 29, no. 7, 1981,pp. 1072–74.

[27] U.S. Patent 2,292,387, H. Kiesler Markey etal., “Secret Communication System,” Aug.11, 1942.

[28] M. Corson, “A New Paradigm for IP-BasedCellular Networks,” IEEE IT Professional, vol.3, no. 6, Nov.–Dec. 2001, pp. 20–29.

[29] L. Cimini, “Analysis and Simulation of aDigital Mobile Channel Using OrthogonalFrequency Division Mutiplexing,” IEEE Trans.Commun., vol. 33, no. 7, July, 1985, pp.665–75.

[30] D. Kivanc and H. Liu, “Subcarrier Allocationand Power Control for OFDMA,” Proc. 34thAsilomar Conf. Sig., Sys. and Computers,Oct. 2000, pp. 147–51.

[31] F-S. Chu and K.C. Chen, “Radio ResourceAllocation in OFDMA Cognitive Radio Sys-tems,” Proc. IEEE PIMRC ’07.

[32] H. Sari and G. Karam, “Orthogonal Fre-quency-Division Multiple Access and itsApplication to CATV, Networks,” Euro. Trans.Telecommun, vol. 9, no. 6, Nov.–Dec. 1998,pp. 507–16.

[33] U. Reimers, “Digital Video Broadcasting,”IEEE Commun. Mag., vol. 36, no. 10, June,1998, pp. 104–10.

[34] B. LeFloch, M. Alard, and C. Berrou “CodedOrthogonal Frequency Division Multiplex,”Proc. IEEE, vol. 83, June, 1995, pp. 982–96.

[35] ETSI EN 302 304: “DVB-H: Transmission Sys-tem for Handheld Terminals,” v1.1.1, Euro.Broadcasting Union, Nov. 2004; dvb-h.org/PDF/DVB-H percent20Specification per-cent20- percent20En302304.V1.1.1.pdf

[36] W. Shieh et al., “Coherent Optical OFDM:Has Its Time Come?,” J. Opt. Net., vol. 7 $3,2008, pp. 234–55.

[37] D. Qian et al., “10-Gb/s OFDMA-PON forDelivery of Heterogeneous Services,” Proc.OFC/NFOEC 2008.

[38] T. Marzetta and J. Salz, “Singular ValueDecomposition of a Matrix-Valued ImpulseResponse,” Proc. ICAASP ’05, pp.IV.913–IV.916.

[39] V. K. Jain and B. Myers, “OWSS: A New Sig-naling System for 100-150 Mb/s WLANs,”IEEE Wireless Commun., vol. 10, no. 4, Aug.2003, pp. 16–24.

[40] L. Hanzo et al., OFDM and MC-CDMA forBroadband Multi-User Communications,WLANs and Broadcasting, IEEE Press andWiley, 2003.




The History of Orthogonal Frequency-division Multiplexing

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