Editing Orthogonal frequency-division multiplexing (section)

{{Short description|Method of encoding digital data on multiple carrier frequencies}}
{{Modulation techniques}}
In [[telecommunications]], '''orthogonal frequency-division multiplexing''' ('''OFDM''') is a type of [[digital transmission]] used in digital [[modulation]] for encoding digital (binary) data on multiple [[Carrier wave|carrier]] frequencies. OFDM has developed into a popular scheme for [[wideband]] [[digital communication]], used in applications such as digital television and audio broadcasting, [[Digital subscriber line|DSL]] [[internet access]], [[wireless network]]s, [[Power-line communication|power line networks]], and [[4G]]/[[5G]] mobile communications.<ref name="ergen">{{cite book |title= Mobile Broadband: including WiMAX and LTE |publisher= Springer Science+Business Media |year= 2009 |author= [[Mustafa Ergen]] |isbn= 978-0-387-68189-4 |doi= 10.1007/978-0-387-68192-4 }}</ref>

OFDM is a [[frequency-division multiplexing]] (FDM) scheme that was introduced by Robert W. Chang of [[Bell Labs]] in 1966.<ref>{{cite journal |title= The history of orthogonal frequency-division multiplexing|journal=IEEE Communications Magazine|volume=47|issue=11|pages=26–35|publisher=IEEE Communications Magazine ( Volume: 47, Issue: 11, November 2009 )|doi=10.1109/MCOM.2009.5307460|date=November 2009|last1=Weinstein|first1=S. B.|s2cid=29001312}}</ref><ref name=chang/><ref name=patent/> In OFDM, the incoming [[bitstream]] representing the data to be sent is divided into multiple streams. Multiple closely spaced [[orthogonal functions|orthogonal]] subcarrier signals with overlapping spectra are transmitted, with each carrier [[modulation|modulated]] with [[binary digit|bits]] from the incoming stream so multiple bits are being transmitted in parallel.<ref name=cobas>[https://web.archive.org/web/20140202131631/http://www.webe.org/papers05/rohde-cofdm.pdf webe.org - 2&nbsp;GHz BAS Relocation Tech-Fair, COFDM Technology Basics]. 2007-03-02</ref><!--page8--> Demodulation is based on [[fast Fourier transform]] algorithms. OFDM was improved by Weinstein and Ebert in 1971 with the introduction of a [[guard interval]], providing better orthogonality in transmission channels affected by multipath propagation.<ref name=weinstein/> Each subcarrier (signal) is modulated with a conventional modulation scheme (such as [[quadrature amplitude modulation]] or [[phase-shift keying]]) at a low [[symbol rate]]. This maintains total data rates similar to conventional single-carrier modulation schemes in the same bandwidth.<ref>Ahmad R. S. Bahai, Burton R. Saltzberg, Mustafa Ergen, Multi-carrier digital communications - Theory and applications of OFDM. Springer (November 2004 )</ref>

[[File:Raised-cosine-ISI.svg|thumb|right|Consecutive raised-cosine impulses, demonstrating zero-[[Intersymbol Interference|ISI property]]; these closely resemble OFDM power spectrum (frequency domain).]]

The main advantage of OFDM over single-carrier schemes is its ability to cope with severe [[Communication channel|channel]] conditions (for example, [[attenuation distortion|attenuation]] of high frequencies in a long copper wire, narrowband [[Interference (communication)|interference]] and frequency-selective [[fading]] due to [[Multipath propagation|multipath]]) without the need for complex equalization filters. Channel [[Equalization (communications)|equalization]] is simplified because OFDM may be viewed as using many slowly modulated [[narrowband]] signals rather than one rapidly modulated [[wideband]] signal. The low symbol rate makes the use of a guard interval between symbols affordable, making it possible to eliminate [[intersymbol interference]] (ISI) and use echoes and time-spreading (in [[analog television]] visible as [[Ghosting (television)|ghosting]] and blurring, respectively) to achieve a [[diversity gain]], i.e. a [[signal-to-noise ratio]] improvement. This mechanism also facilitates the design of [[single frequency network]]s (SFNs) where several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be re-combined constructively, sparing interference of a traditional single-carrier system.

In '''coded orthogonal frequency-division multiplexing''' ('''COFDM'''), [[forward error correction]] (convolutional coding) and time/frequency interleaving are applied to the signal being transmitted. This is done to overcome errors in mobile communication channels affected by multipath propagation and [[Doppler effect]]s. COFDM was introduced by Alard in 1986<ref name=brevet>{{Cite patent|country=WO|number=8800417|title=Method and installation for digital communication, particularly between and toward moving vehicle|pubdate=1988-01-14|assign1=[[Centre national d'études des télécommunications]]|assign2=[[TDF Group|Telediffusion de France]]
|inventor1-last=Pommier |inventor1-first=Daniel|inventor2-last=Alard |inventor2-first=Michel}}</ref><ref name=EBU>{{cite web |publisher= EBU Technical Review n°224, p.187|date= August 1987  |title= Principles of modulation and channel coding for digital broadcasting for mobile receivers| url=https://tech.ebu.ch/docs/techreview/trev_224-alard.pdf}}</ref><ref>{{cite journal|doi=10.1109/5.387096|title=Coded orthogonal frequency division multiplex &#91;TV broadcasting&#93;|journal=Proceedings of the IEEE|volume=83|issue=6|pages=982–996|year=1995|last1=Le Floch|first1=B.|last2=Alard|first2=M.|last3=Berrou|first3=C.|url=http://www.kn-s.dlr.de/People/Kaiser/Papers/VTC99_Robertson_Kaiser.ps|archive-url=https://web.archive.org/web/20140703191957/http://www.kn-s.dlr.de/People/Kaiser/Papers/VTC99_Robertson_Kaiser.ps|archive-date=2014-07-03|url-access=subscription}}</ref> for [[Digital Audio Broadcasting]] for [[Eureka (organisation)|Eureka]] Project 147. In practice, OFDM has become used in combination with such coding and interleaving, so that the terms COFDM and OFDM co-apply to common applications.<ref>{{cite journal |title=Orthogonal transmultiplexers in communication: a review |journal=IEEE Transactions on Signal Processing |volume=46 |issue=4 |pages=979–995 |first=Ali |display-authors=etal |last=Akansu |publisher=IEEE Trans. On Signal Processing, Vol. 46, No. 4, April 1998 |doi=10.1109/78.668551 |year=1998 |bibcode=1998ITSP...46..979D |url=http://www.lss.supelec.fr/files/UGllcnJlIERVSEFNRUw=_00668551(TSP1998).pdf |citeseerx=10.1.1.46.3342 |access-date=2019-09-24 |archive-date=2022-04-01 |archive-url=https://web.archive.org/web/20220401013025/http://www.lss.supelec.fr/files/UGllcnJlIERVSEFNRUw=_00668551(TSP1998).pdf |url-status=dead }}</ref><ref>{{cite web|url=http://sna.csie.ndhu.edu.tw/~cnyang/MCCDMA/tsld004.htm|last=Yang|first=James Ching-Nung|date=October 10, 2001|publisher=Department of Computer Science and Information Engineering National Dong Hwa University|location=Shoufeng, Hualien, Taiwan|title=What is OFDM and COFDM?|access-date=2017-04-16}}</ref>