Orthogonal frequency-division multiplexing (OFDM) — essentially identical to Coded OFDM (COFDM) and Discrete multi-tone modulation (DMT) — is a frequency-division multiplexing (FDM) scheme utilized as a digital multi-carrier modulation method. A large number of closely-spaced orthogonal sub-carriers are used to carry data. The data are divided into several parallel data streams or channels, one for each sub-carrier. Each sub-carrier is modulated with a conventional modulation scheme (such as quadrature amplitude modulation or phase shift keying) at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in the same bandwidth.
OFDM has developed into a popular scheme for wideband digital communication, whether wireless or over copper wires, used in applications such as digital television and audio broadcasting, wireless networking and broadband internet access.
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions — for example, attenuation of high frequencies in a long copper wire, narrowband interference and frequency-selective fading due to multipath — without complex equalization filters. Channel 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 handle time-spreading and eliminate intersymbol interference (ISI). This mechanism also facilitates the design of single-frequency networks, where several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be combined constructively, rather than interfering as would typically occur in a traditional single-carrier system.
The orthogonality requires that the sub-carrier spacing is Δf = k/(TU) Hertz, where TU seconds is the useful symbol duration (the receiver side window size), and k is a positive integer, typically equal to 1. Therefore, with N sub-carriers, the total passband bandwidth will be B ≈ N·Δf (Hz).
The orthogonality also allows high spectral efficiency, with a total symbol rate near the Nyquist rate. Almost the whole available frequency band can be utilized. OFDM generally has a nearly 'white' spectrum, giving it benign electromagnetic interference properties with respect to other co-channel users.
OFDM requires very accurate frequency synchronization between the receiver and the transmitter; with frequency deviation the sub-carriers will no longer be orthogonal, causing inter-carrier interference (ICI), i.e. cross-talk between the sub-carriers. Frequency offsets are typically caused by mismatched transmitter and receiver oscillators, or by Doppler shift due to movement. While Doppler shift alone may be compensated for by the receiver, the situation is worsened when combined with multipath, as reflections will appear at various frequency offsets, which is much harder to correct. This effect typically worsens as speed increases, and is an important factor limiting the use of OFDM in high-speed vehicles. Several techniques for ICI suppression are suggested, but they may increase the receiver complexity.
The guard interval also eliminates the need for a pulse-shaping filter, and it reduces the sensitivity to time synchronization problems.
A simple example: If one sends a million symbols per second using conventional single-carrier modulation over a wireless channel, then the duration of each symbol would be one microsecond or less. This imposes severe constraints on synchronization and necessitates the removal of multipath interference. If the same million symbols per second are spread among one thousand sub-channels, the duration of each symbol can be longer by a factor of thousand, i.e. one millisecond, for orthogonality with approximately the same bandwidth. Assume that a guard interval of 1/8 of the symbol length is inserted between each symbol. Intersymbol interference can be avoided if the multipath time-spreading (the time between the reception of the first and the last echo) is shorter than the guard interval, i.e. 125 microseconds. This corresponds to a maximum difference of 37.5 kilometers between the lengths of the paths.
The cyclic prefix, which is transmitted during the guard interval, consists of the end of the OFDM symbol copied into the guard interval, and the guard interval is transmitted followed by the OFDM symbol. The reason that the guard interval consists of a copy of the end of the OFDM symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of the multipaths when it performs OFDM demodulation with the FFT.
Our example: The OFDM equalization in the above numerical example would require complex multiplications per OFDM symbol, i.e. one million multiplications per second, at the receiver. The FFT algorithm requires complex-valued multiplications per OFDM symbol, i.e. 10 million multiplications per second, at both the receiver and transmitter side. This should be compared with the corresponding one million symbols/second single-carrier modulation case mentioned in the example, where the equalization of 125 microseconds time-spreading using a FIR filter would require 125 multiplications per symbol, i.e. 125 million multiplications per second.
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement of the channel conditions, i.e. the equalizer gain and phase shift for each sub-carrier. Pilot signals and training symbols may also be used for time synchronization (to avoid inter-symbol interference, ISI) and frequency synchronization (to avoid inter-carrier interference, ICI, caused by Doppler shift).
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier, equalization can be completely omitted, since these non-coherent schemes are insensitive to slowly changing amplitude and phase distortion.
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel conditions such as fading. For example, when a part of the channel bandwidth is faded, frequency interleaving ensures that the bit errors that would result from those subcarriers in the faded part of the bandwidth are spread out in the bit-stream rather than being concentrated. Similarly, time interleaving ensures that bits that are originally close together in the bit-stream are transmitted far apart in time, thus mitigating against severe fading as would happen when travelling at high speed.
However, time interleaving is of little benefit in slowly fading channels, such as for stationary reception, and frequency interleaving offers little to no benefit for narrowband channels that suffer from flat-fading (where the whole channel bandwidth is faded at the same time).
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-stream that is presented to the error correction decoder, because when such decoders are presented with a high concentration of errors the decoder is unable to correct all the bit errors, and a burst of uncorrected errors occurs.
A common type of error correction coding used with OFDM-based systems is convolutional coding, which is often concatenated with Reed-Solomon coding. Convolutional coding is used as the inner code and Reed-Solomon coding is used for the outer code — usually with additional interleaving (on top of the time and frequency interleaving mentioned above) in between the two layers of coding. The reason why this combination of error correction coding is used is that the Viterbi decoder used for convolutional decoding produces short errors bursts when there is a high concentration of errors, and Reed-Solomon codes are inherently well-suited to correcting bursts of errors.
Newer systems, however, usually now adopt the near-optimal types of error correction coding that use the turbo decoding principle, where the decoder iterates towards the desired solution. Examples of such error correction coding types include turbo codes and LDPC codes. These codes only perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel, however, and some systems that have adopted these codes have concatenated them with either Reed-Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to improve performance further over the wireless channel.
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 the bitrate is adopted to the co-channel interference and bandwidth is allocated to whichever subscriber that needs it most.
In Orthogonal Frequency Division Multiple Access (OFDMA), frequency-division multiple access is achieved by assigning different OFDM sub-channels to different users. OFDMA supports differentiated quality-of-service by assigning different number of sub-carriers to different users in a similar fashion as in CDMA, and thus complex packet scheduling or media access control schemes can be avoided. OFDMA is used in the IEEE 802.16 Wireless MAN standard, commonly referred to as WiMAX.
In Multi-carrier code division multiple access (MC-CDMA), also known as OFDM-CDMA, OFDM is combined with CDMA spread spectrum communication for coding separation of the users. Co-channel interference can be mitigated against, meaning that manual fixed channel allocation (FCA) frequency planning is simplified, or complex dynamic channel allocation (DCA) schemes are avoided.
Although the guard interval only contains redundant data, which means that it reduces the capacity, some OFDM-based systems, such as some of the broadcasting systems, deliberately use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN, and longer guard intervals allow larger SFN cell-sizes. A rule of thumb for the maximum distance between transmitters in an SFN is equal to the distance a signal travels during the guard interval — for instance, a guard interval of 200 microseconds would allow transmitters to be spaced 60 km apart.
Single-frequency networks is a form of transmitter macrodiversity. The concept can be further utilized in Dynamic single-frequency networks (DSFN), where the SFN grouping is changed from timeslot to timeslot.
Any non-linearity in the signal chain will cause intermodulation distortion that
The linearity requirement is demanding, especially for transmitter RF output circuitry where amplifiers are often designed to be non-linear in order to minimise power consumption. In practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a judicious tradeoff against the above consequences. However, the transmitter output filter which is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that were clipped, so clipping is not an effective way to reduce PAPR.
Although the spectral efficiency of OFDM is attractive for both terrestrial and space communications, the high PAPR requirements have so far limited OFDM applications to terrestrial systems.
is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed into parallel streams, and each one mapped to a (possibly complex) symbol stream using some modulation constellation (QAM, PSK, etc.). Note that the constellations may be different, so some streams may carry a higher bit-rate than others.
An inverse FFT is computed on each set of symbols, giving a set of complex time-domain samples. These samples are then quadrature-mixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using digital-to-analogue converters (DACs); the analogue signals are then used to modulate cosine and sine waves at the carrier frequency, , respectively. These signals are then summed to give the transmission signal, .
The receiver picks up the signal , which is then quadrature-mixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on , so low-pass filters are used to reject these. The baseband signals are then sampled and digitised using analogue-to-digital converters (ADCs), and a forward FFT is used to convert back to the frequency domain.
This returns parallel streams, each of which is converted to a binary stream using an appropriate symbol detector. These streams are then re-combined into a serial stream, , which is an estimate of the original binary stream at the transmitter.
The low-pass equivalent OFDM signal is expressed as:
To avoid intersymbol interference in multipath fading channels, a guard interval of length is inserted prior to the OFDM block. During this interval, a cyclic prefix is transmitted such that the signal in the interval equals the signal in the interval
|Standard name||DAB Eureka 147||DVB-T||DVB-H||DMB-T/H||IEEE 802.11a|
| Frequency range of|
| 174 - 240|
1452 - 1492
| 470 - 862|
174 - 230
|470 - 862||470 – 862||4915 - 5825|
| Channel spacing B|
|1.712||8, 7, 6,||8, 7, 6 & 5||8||20|
|Number of subcarriers N||192, 384, 768 or 1536|| 2K mode: 1705|
8K mode: 6817
|1705, 3409, 6817|| 1 (single-carrier)|
|Subcarrier modulation scheme||DQPSK||QPSK, 16QAM or 64QAM||QPSK, 16QAM or 64QAM|| 4QAM, 4QAM-NR, |
16QAM, 32QAM and 64QAM.
|BPSK, QPSK, 16QAM or 64QAM|
| Useful symbol length TU|
|2K mode: 224|
8K mode: 896
|224, 448, 896||500 (multi-carrier)||3.2|
| Additional guard interval TG|
(Fraction of TU)
|1/4, 1/8, 1/16, 1/32||1/4, 1/8, 1/16, 1/32||1/4, 1/6, 1/9||1/4|
| Subcarrier spacing|
Δf = 1/(TU) ≈ B/N
|2K mode: 4464|
8K mode: 1116
|4464, 2232, 1116|| 8 M (single-carrier)|
| Net bit rate R|
|0.576 - 1.152|| 4.98 - 31.67|
|3.7 - 23.8||4.81 - 32.49||6 - 54|
| Link spectral efficiency R/B|
|0.34 - 0.67||0.62 - 4.0||0.62 - 4.0||0.60 - 4.1||0.30 - 2.7|
|Inner FEC||Conv coding with code rates 1/4, 3/8 or 1/2||Conv coding with code rates 1/2, 2/3, 3/4, 5/6 or 7/8||Conv coding with code rates 1/2, 2/3, 3/4, 5/6 or 7/8||LDPC with code rates 0.4, 0.6 or 0.8||Conv coding with code rates 1/2, 2/3 or 3/4|
|Outer FEC (if any)||None||RS(204,188,t=8)||RS(204,188,t=8) + MPE-FEC||BCH code (762,752)|
| Maximum travelling speed|
|200 - 600|| 53 - 185|
depends on transmission frequency
| Time interleaving depth|
|385||0.6 - 3.5||0.6 - 3.5||200 - 500|
| Adaptive transmission|
| Multiple access method|
|Typical source coding|| 192 kbit/s|
| 2 - 18 Mbit/s|
Standard - HDTV
H.264 or MPEG2
| Not defined|
(MPEG-2 or H.264 w/MP2)
Long copper wires suffer from attenuation at high frequencies. The fact that OFDM can cope with this frequency selective attenuation and with narrow-band interference are the main reasons it is frequently used in applications such as ADSL modems. 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.
For experimental amateur radio applications, 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. Four different modulation schemes are used: BPSK, QPSK, 16-QAM, and 64-QAM, along with a number of convolutional encoding schemes. This allows the system to adapt to the optimum data rate vs. error rate for the current conditions.
Clearwire, a wireless Internet Service Provider who provides access to metropolitan areas across the United States, utilizes OFDM in both their current 2.5 GHz network and the planned expansion of their WiMax network.
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. 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, hence the difference in performance may diminish with advances in demodulator design. Moreover, 8VSB modulation requires less power to transmit a signal the same distance, i.e., the received carrier-to-noise threshold is lower for the same bit error rate. In less-populated areas, 8VSB may have an advantage because of this. In urban areas, however, COFDM is believed to offer better reception than 8VSB.
In practice, it may be impossible to settle this debate without empirical history. One difficulty in fully assessing the two systems' relative performance in multipath environments is that the spatial distribution of multipath cannot be modeled well. Due to the chaotic nature of multipath, the process is non-stationary, both temporally and spatially, in the stochastic sense. Thus, the probability distribution of impaired receiving locations is not tractable.
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 (medium wave) and FM broadcasts.
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.
In Finland the license holder Digita has begun deployment of a nationwide " @450" wireless network, operational in parts of the country since April 2007 and planned coverage of all of Finland in 2009.
T-Mobile Germany uses Flash-OFDM to backhaul Wi-Fi HotSpots on the Deutsche Bahn's ICE high speed trains.
American wireless carrier Sprint Nextel had stated plans for field testing wireless broadband network technologies including Flash-OFDM for their 4G offering, for deployment using their nationwide 2.5GHz licences. Sprint subsequently decided to deploy the mobile version of WiMAX, which is based on SOFDMA, scalable orthogonal frequency division multiple access technology.
Citizens Telephone Cooperative launched a Flash-OFDM service to subscribers in parts of Virginia in March, 2006. The maximum speed available is 1.5 Mbit/s.
Digiweb Ltd. launched a mobile broadband network using FLASH-OFDM technology at 872 MHz in July 2007 in Ireland and also will be launching in Norway. Voice handsets are not yet available as of November 2007. The deployment is live in a small area north of Dublin only.
Butler Networks is currently trialing FLASH-OFDM technology in Denmark at 872 MHz.
In The Netherlands, KPN-telecom will start a pilot around July 2007.