Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM), also sometimes called discrete multitone modulation (DMT), is a transmission technique based upon the idea of frequency-division multiplexing (FDM).

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.

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.

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.

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.

An extremely important benefit from using multiple sub-carriers is that because each carrier operates at a relatively low bitrate, the duration of each symbol is relatively long. If one sends, say, a million bits per second over a single baseband channel, then the duration of each bit must be under a microsecond. This imposes severe constraints on sychronization and removal of multipath interference. If the same million bits per second are spread among N subcarriers, the duration of each bit can be longer by a factor of N, and the constraints of timing and multipath sensitivity are greatly relaxed. For moving vehicles, the doppler effect on signal timing is another constraint that causes difficulties for some other modulation schemes.

OFDM modulation and demodulation are typically (as of 2001) implemented using digital filter banks generally using the Fast Fourier Transform (FFT).

Although highly complex, COFDM has high performance under even very challenging channel conditions.

By combining the OFDM technique with error-correcting codes, adaptive equalization and reconfigurable modulation, COFDM has the following properties:

resistance against link dispersion
resistance against slowly changing phase distortion and fading
resistance against multipath using guard interval and cyclic prefix
resistance against frequency response nulls and constant frequency interference
resistance against burst noise

COFDM also generally has a nearly 'white' spectrum, giving it benign electromagnetic interference properties with respect to other signals.

Some COFDM systems use some of the sub-carriers to carry pilot signals, which are used for frequency synchronization. (Loss of synchronization causes errors in the decoded data).

In wide area broadcasting, receivers can benefit from receiving signals from several spatially dispersed transmitters simultaneously, since transmitters will only destructively interfere with each other on a limited number of subcarriers, whereas in general they will actually reinforce coverage over a wide area. This is very beneficial in many countries, as it permits the operation of national single frequency networks, and avoids the replication of program content on different carrier frequencies which is necessary with FM or other forms of radio broadcasting. Also, because effectively the bit rate is slowed down on each sub-carrier, the effects of "ghosting" are much reduced. Such single frequency networks utilise the available spectrum more effectively than existing analogue radio networks.

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.

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

Usage

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

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.

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.

Wireless LAN

OFDM is also now being used in some wireless LAN applications, including WiMAX and IEEE 802.11a/g (and the defunct European alternative HIPERLAN/2). 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 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 ( $\mu s$ )
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

Digital radio and television

DVB-T's implementation of COFDM

COFDM is also now widely used in Europe and elsewhere where the Eureka 147 Digital Audio Broadcast (DAB) standard has been adopted for digital radio broadcasting, and also for terrestrial digital TV in 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.

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.

DRM and Eureka-147's (DAB) implementation of COFDM

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.

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.

Flash-OFDM

Flash-OFDM 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. In early 2004, prior to corporate merging settlements with Sprint PCS, Nextel Communications; A North American wireless provider known for its robust and industry-leading technologies, began a test-trial of Flarion and their state-of-the-art Flash-OFDM application in the Raleigh/Durham, North Carolina region. Dubbed Project Triangle, the trial was so successful, the engineering trial moved directly into a marketing trial, until Nextel was forced to scrap the project in June 2005, succumbing to then-merging Sprint PCS's plans to go with 1xEV-DO as their next generation network. Had the deal gone through, it would have been Flarion's largest application and investment in their technology.

In the summer of 2005, Flarion was acquired by QualComm Inc, to increase its market leadership in the 3G and the post 3G world.

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.

Ideal encoder

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

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 M_i; in general they can have different length. Then each sequence is represented by a complex number a_i according to any kind of modulation (QAM, PSK, etc.). The sequence of a_i 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.

Mathematical Description

The low-pass equivalent OFDM signal is expressed as

$\nu (t)=\sum _{k=0}^{N-1}I_{k}e^{i2\pi kt/T},\quad 0\leq t<T,$

where $\{I_{k}\}$ are the data symbols, $N$ is the number of subcarriers, and $T$ is the OFDM block time. The subcarriers spacing of $1/T$ Hz makes the subcarriers orthogonal; this property is expressed as

${\frac {1}{T}}\int _{0}^{T}\left(e^{i2\pi k_{1}t/T}\right)^{*}\left(e^{i2\pi k_{2}t/T}\right)dt={\frac {1}{T}}\int _{0}^{T}e^{i2\pi (k_{2}-k_{1})t/T}dt={\begin{cases}1,&k_{1}=k_{2},\\0,&k_{1}\neq k_{2},\end{cases}}$

where $(\cdot )^{*}$ denotes the complex conjugate operator.

To avoid intersymbol interference in multipath fading channels, a guard interval $-T_{\mathrm {g} }\leq t<0$ , where $T_{\mathrm {g} }$ 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 $T_{\mathrm {g} }$ of the OFDM block. The OFDM signal with cyclic prefix is thus:

$\nu (t)=\sum _{k=0}^{N-1}I_{k}e^{i2\pi kt/T},\quad -T_{\mathrm {g} }\leq t<T.$

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 $f_{c}$ . In general, the transmitted signal can be represented as

$s(t)=\Re \left\{\nu (t)e^{i2\pi f_{c}t}\right\}.$

For a wireless application:

$s(t)=\sum _{k=0}^{N-1}|I_{k}|\cos \left(2\pi [f_{c}+k/T]t+\arg[I_{k}]\right).$

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)

References

Chang, R. W. (1966). Synthesis of band-limited orthogonal signals for multi-channel data transmission, Bell System Technical Journal 46, 1775-1796.
Chang, R. W. & and Gibbey, R. A. (1968). A theoretical study of performance of an orthogonal multiplexing data transmission scheme, IEEE Transactions on Communications Technology 16 (4), 529-540.
Saltzberg, B. R. (1967). Performance of an efficient parallel data transmission system, IEEE Transactions on Communications Technology 15 (6), 805-811.
Bahai, A. R. S., Saltzberg, B. R., Ergen, M. (2004)., Multi Carrier Digital Communications: Theory and Applications of OFDM, Springer, 2004.
Brad Morris, "Optimization of a Broadband Modulation Scheme for the Indoor Radio Channel", M.Sc. Thesis, University of Calgary, September 1993. (150Mbit/s OFDM wilreless LAN - Prototype)
"Detailed OFDM Modeling in Network Simulation of Mobile Ad Hoc Networks," G. Yeung, M. Takai, R. Bagrodia, A. Mehrnia, B. Daneshrad. In Proceedings of the 18th Workshop on Parallel and Distributed Simulation (PADS 2004), May 16-19, 2004.
"The how and why of COFDM" Jonathan Stott. EBU: EBU Technical Review 278 (winter 1998).

External links

Stott, 1997 [2] Technical presentation by J H Stott of the BBC's R&D division, delivered at the 20 International Television Symposium in 1997; this URL accessed 24 Jan 2006.
Page on Orthogonal Frequency Division Multiplexing at http://www.iss.rwth-aachen.de/Projekte/Theo/OFDM/node6.html accessed on 13th Nov. 2002.
Siemens demos 360 Mbit/s wireless
US patent in 1994 for wireless data transmission, the patent "tree" rooted on this patent has upwards of 20000 nodes and leaves references.
Palowireless OFDM Resource Center Articles, news and resources