Orthogonal frequency-division multiplexing

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Orthogonal frequency-division multiplexing (OFDM), also sometimes called discrete multitone modulation (DMT), is a complex modulation technique for transmission based upon the idea of frequency-division multiplexing (FDM) where each frequency channel is modulated with a simpler modulation. In OFDM the frequencies and modulation of FDM are arranged to be orthogonal witheach other which almost eliminates the interference between channels. Although the principles and some of the benefits have been known for 40 years, it is made popular today by the lower cost and availability of digital signal processing components.

A number of extra useful benefits, particularly multipath resistance, arise when the data is coded with some Forward Error Correction (FEC) scheme prior to modulation called channel coding. This is called Coded OFDM abbreviated to COFDM.

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Comparison to FDM

In FDM, multiple signals are sent out at the same time, but on different frequencies. Most people are familiar with FDM from radio and television: normally, each station broadcasts on a particular frequency band (range of frequencies) or channel.

  • OFDM takes this concept further: In OFDM, a single transmitter transmits on many (typically dozens to thousands) different orthogonal frequencies (i.e. frequencies that are independent with respect to the relative phase relationship between the frequencies). Also, because the frequencies are so closely spaced, each one only has room for a Narrowband signal.
  • This modulation technique coupled with the use of advanced modulation techniques on each component, results in a signal with high resistance to interference.
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Coupling with "Channel Coding"

OFDM is almost always used in conjunction with channel coding—an error correction technique—to create coded orthogonal FDM or COFDM. It is a complex technology to implement, but it is now widely used in digital telecommunications systems to make it easier to encode and decode such signals. The system has been used in broadcasting as well as certain types of computer networking technology. This is particularly due to the fact that such signals show good resistance to multipath fading, best known as the source of "ghosting" on analog television broadcasts.

According to Stott, 1997 [1], "The 'COFDM magic' is achieved by the use of channel-state information (CSI). In the presence of CW interferers and/or a selective channel, some OFDM carriers will be worse affected than others." The channel coding thus allows the receiver to integrate information about the physical S/N ratios of the subchannels into the error correction of its Viterbi decoder, yielding significantly better performance than uncoded OFDM can attain with similar channel characteristics.

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Characteristics

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers, with baseband data on each sub-carrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phase-shift keying (PSK). This composite baseband signal is typically used to modulate a main RF carrier.

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Benefits

The benefits of using OFDM are many, including high spectrum efficiency, resistance against multipath interference (particularly in wireless communications), and ease of filtering out noise (if a particular range of frequencies suffers from interference, the carriers within that range can be disabled or made to run slower). Also, the upstream and downstream speeds can be varied by allocating either more or fewer carriers for each purpose. Some forms of Rate-adaptive DSL use this feature in real time, so that bandwidth is allocated to whichever stream needs it most.

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Disadvantages of OFDM

However, OFDM suffers from time-variations in the channel, or presence of a carrier frequency offset. This is due to the fact that the OFDM subcarriers are spaced closely in frequency. Imperfect frequency synchronization causes a loss in subcarrier orthogonality which severely degrades performance.

Because the signal is the sum of a large number of subcarriers, it tends to have a high peak-to-average power ratio (PAPR). Also, it is necessary to minimise intermodulation between the subcarriers, which would effectively raise the noise floor both in-channel and out of channel. For this reason circuitry must be very linear. This is demanding, especially in relation to high power RF circuitry, which also needs to be efficient in order to minimise power consumption.

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OFDM feature abstract

  • No intercarrier guard bands
  • Maximum spectral efficiency (Nyquist rate)
  • Easy implementation by FFTs
  • Controlled overlapping of bands
  • Very sensitive time-freq. synchronization
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Usage

OFDM is used in many communications systems such as: ADSL, Wireless LAN, Digital audio broadcasting, DVB, UWB and PLC.

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ADSL

OFDM is used in ADSL connections that follow the G.DMT (ITU G.992.1) standard. (Annex A refers to ADSL-over-POTS).

The fact that COFDM does not interfere easily with other signals is the main reason it is frequently used in applications such as ADSL modems in which existing copper wires are used to achieve high-speed data connections. The lack of interference means no wires need to be replaced (otherwise it would be cheaper to replace them with fiber). However, DSL cannot be used on every copper pair, interference may become significant if more than 25% of phone lines coming into a Central Office are used for DSL.

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HomePlug powerline alliance

OFDM is used by HomePlug devices to extend Ethernet connections to other rooms in a home through its power wiring. Adaptive modulation is particularly important with such a noisy channel as electrical wiring.

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Wireless Local Area Networks (LAN) and Metropolitan Area Networks (MAN)

OFDM is also now being used in some wireless LAN and MAN applications, including IEEE 802.11a/g (and the defunct European alternative HIPERLAN/2) and WiMAX. For amateur radio applications, experimental users have even hooked up commercial off-the-shelf ADSL equipment to radio transceivers which simply shift the bands used to the radio frequencies the user has licensed.

IEEE 802.11a, operating in the 5 GHz band, specifies airside data rates ranging from 6 to 54 Mbit/s. Below contains a listing of the eight specified PHY data rates. Four different modulation schemes are used: BPSK, 4-QAM, 16-QAM, and 64-QAM. Each higher performing modulation scheme requires better channel condition for accurate transmission. These modulation schemes are coupled with the various forward error correction convolutional encoding schemes to give a multitude of Number of data bits per symbol (Ndbps) performance.

Data Rate (Mbit/s) Modulation Coding Rate Ndbps 1472 byte Transfer Duration (<math>\mu s</math>)
6 BPSK 1/2 23 2012
9 BPSK 3/4 36 1344
12 4-QAM 1/2 48 1008
18 4-QAM 3/4 72 672
24 16-QAM 1/2 96 504
36 16-QAM 3/4 144 336
48 64-QAM 2/3 192 252
54 64-QAM 3/4 216 224
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Terrestrial digital radio and television broadcasting

Much of Europe and Asia has adopted COFDM for terrestrial broadcasting of television and radio. The television standard is called DVB-T and the radio standard is called DAB.

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DVB-T's implementation of COFDM for Digital Television

COFDM is also now widely used in Europe and elsewhere for terrestrial digital TV using the DVB-T standard. One of the major benefits provided by COFDM is that it renders radio broadcasts relatively immune to multipath distortion, and signal fading due to atmospheric conditions, or passing aircraft. The United States has rejected several proposals to adopt COFDM for its digital television services, and has instead opted for 8VSB (vestigial sideband modulation) operation. The question of the relative technical merits of COFDM versus 8VSB has been a subject of some controversy between Europe and USA.

The debate over 8VSB vs COFDM modulation is still ongoing. Proponents of COFDM argue that it resists multipath far better than 8VSB. Early 8VSB DTV (digital television) receivers often had difficulty receiving a signal in urban environments. However, newer 8VSB receivers are far better at dealing with multipath. Moreover, 8VSB modulation requires less power to transmit a signal the same distance. In less-populated areas, 8VSB often pulls ahead of COFDM because of this. In urban areas, however, COFDM still offers better reception than 8VSB.

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DRM and Eureka-147's (DAB) implementation of COFDM for Digital Audio Broadcasting

COFDM is also used for other radio standards, for Digital audio broadcasting (DAB), the standard for digital audio broadcasting at VHF frequencies and also for Digital Radio Mondiale (DRM), the standard for digital broadcasting at shortwave and mediumwave frequencies (below 30 MHz).

  • The USA again uses an alternate standard, a proprietary system developed by iBiquity dubbed "HD Radio" However, it uses COFDM as the underlying broadcast technology to add digital audio to AM (mediumwave) and FM broadcasts.
  • Both Digital Radio Mondiale and HD Radio are classified as in-band on-channel systems, unlike Eureka 147 (DAB: Digital audio broadcasting) which uses VHF or UHF broadcasts instead.
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Ultra wideband

UWB (ultra wideband) wireless personal area network technology may also utilise OFDM, such as in Multiband OFDM (MB-OFDM). This UWB specification is advocated by the WiMedia Alliance (formerly by both the Multiband OFDM Alliance {MBOA} and the WiMedia Alliance, but the two have now merged), and is one of the competing UWB radio interfaces.

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Flash-OFDM

Flash-OFDM (Fast Low-latency Access with Seamless Handoff Orthogonal Frequency Division Multiplexing) is a system that is based on OFDM and specifies also higher protocol layers. It has been developed and is marketed by Flarion. Flash-OFDM has generated interest as a packet-switched cellular bearer, on which area it would compete with GSM and 3G networks. As an example, old 450 MHz frequency bands that were used by NMT (an 1G analog network, now decommissioned) in Europe are being considered to be licenced to Flash-OFDM operators.

American wireless carrier Sprint Nextel has stated plans for using Flash-OFDM (along with other wireless broadband network technologies) for their 4G offering, which will be deployed using the licences they own nationwide in the 2.5GHz frequency range.

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BST-OFDM

The BST-OFDM (Band Segmented Transmission - Orthogonal Frequency Division Multiplexing) system proposed for Japan improves upon COFDM by exploiting the fact that some OFDM carriers may be modulated differently from others within the same multiplex. The 6 MHz television channel may therefore be "segmented", with different segments being modulated differently and used for different services.

It is possible, for example, to send an audio service on a segment that includes a segment comprised of a number of carriers, a data service on another segment and a television service on yet another segment - all within the same 6 MHz television channel. Furthermore, these may be modulated with different parameters so that, for example, the audio and data services could be optimized for mobile reception, while the television service is optimized for stationary reception in a high-multipath environment.

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Ideal encoder

The following picture shows the possible ideal structure of a OFDM encoder:

Image:Ofdm modulating diagram.png

The source S generates a flow of binary symbols. They are split up into several channels, thus creating short sequence of binary symbols. In the picture they are indicated with the name Mi; in general they can have different length. Then each sequence is represented by a complex number ai according to any kind of modulation (QAM, PSK, etc.). The sequence of ai to be transmitted is interpreted as the spectrum of the signal to be sent: so all the complex values are sent to a block that calculates the inverse Fourier transform using the FFT algorithm. Some zeros can be added at the beginning and at the end of the sequence. Then a header H is appended to the code at the output of the FFT. The obtained sequence will be, in general, complex-valued. The real and imaginary part are sent separately through the channel by QAM modulation. Before modulation, they are alternatively multiplied by (-1) in order to have a null mean value.

In general there can be a different modulating technique on each virtual channel. Since different symbols are sent on different samples of the spectrum of the signal to be sent, if the channel has a linear behavior, there can not be any interference between the different frequency, so any possibility of intersymbol interference is removed.

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Mathematical Description

The low-pass equivalent OFDM signal is expressed as

<math> \nu(t)=\sum_{k=0}^{N-1}I_ke^{i2\pi kt/T}, \quad 0\le t<T, </math> <p> where <math>\{I_k\}</math> are the data symbols, <math>N</math> is the number of subcarriers, and <math>T</math> is the OFDM block time. The subcarriers spacing of <math>1/T</math> Hz makes the subcarriers orthogonal; this property is expressed as <p align="center"> <math> \frac{1}{T}\int_0^{T}\left(e^{i2\pi k_1t/T}\right)^* \left(e^{i2\pi k_2t/T}\right)dt=\frac{1}{T}\int_0^{T}e^{i2\pi (k_2-k_1)t/T}dt = \begin{cases} 1, & k_1=k_2,\\ 0, & k_1\ne k_2, \end{cases} </math> <p>where <math>(\cdot)^*</math> denotes the complex conjugate operator. <p> To avoid intersymbol interference in multipath fading channels, a guard interval <math>-T_\mathrm{g}\le t < 0</math>, where <math>T_\mathrm{g}</math> is the guard period, is inserted prior to the OFDM block. During this interval, a cyclic prefix is transmitted. The cyclic prefix is equal to the last <math>T_\mathrm{g}</math> of the OFDM block. The OFDM signal with cyclic prefix is thus: <p align="center"> <math> \nu(t)=\sum_{k=0}^{N-1}I_ke^{i2\pi kt/T}, \quad -T_\mathrm{g}\le t<T. </math> <p> The low-pass signal above can be either real or complex-valued. Real-valued low-pass equivalent signals are typically transmitted at baseband—wireline applications such as DSL use this approach. For wireless applications, the low-pass signal is typically complex-valued; in which case, the transmitted signal is up-converted to a carrier frequency <math>f_c</math>. In general, the transmitted signal can be represented as <p align="center"> <math> s(t) = \Re\left\{\nu(t) e^{i2\pi f_c t}\right\}. </math> <p>For a wireless application: <p align="center"> <math> s(t) = \sum_{k=0}^{N-1}|I_k|\cos\left(2\pi [f_c + k/T]t + \arg[I_k]\right). </math>

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OFDM history

  • 1957: Kineplex, multi-carrier HF modem
  • 1966: Chang, Bell Labs: OFDM paper + patent
  • 1971: Weinstein & Ebert proposed use of FFT and guard interval
  • 1985: Cimini described use of OFDM for mobile communications
  • 1987: Alard & Lasalle: OFDM for digital broadcasting
  • 1993: Morris: Experimental 150Mbit/s OFDM wireless LAN
  • 1994: US Patent 5,282,222, Method and apparatus for multiple access between transceivers in wireless communications using OFDM spread spectrum
  • 1995: ETSI DAB standard: first OFDM based standard
  • 1997: ETSI DVB-T standard
  • 1998: Magic WAND project demonstrates OFDM modems for wireless LAN
  • 1999: IEEE 802.11a wireless LAN standard (Wi-Fi)
  • 2000: proprietary fixed wireless access (V-OFDM, Flash-OFDM, etc.)
  • 2002: IEEE 802.11g standard for wireless LAN
  • 2004: IEEE 802.16-2004 standard for wireless MAN (WiMAX)
  • 2004: ETSI DVB-H standard
  • 2004: Candidate for IEEE 802.15.3a standard for wireless PAN (MB-OFDM)
  • 2004: Candidate for IEEE 802.11n standard for next generation wireless LAN
  • 2005: Candidate for 3.75G mobile cellular standards (3GPP & 3GPP2)
  • 2005: Candidate for 4G standards (CJK)
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See also

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References

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External links

de:OFDM es:Modulación por división ortogonal de frecuencia fi:OFDM fr:Orthogonal Frequency Division Multiplexing he:DMT nb:OFDM nl:Orthogonal frequency division modulation pt:OFDM

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