Passband modulation 

Analog modulation 
Digital modulation 
Hierarchical modulation 
Spread spectrum 
See also 
In telecommunications, orthogonal frequencydivision multiplexing (OFDM) is a type of digital transmission used in digital modulation for encoding digital (binary) data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G/5G mobile communications.^{[1]}
OFDM is a frequencydivision multiplexing (FDM) scheme that was introduced by Robert W. Chang of Bell Labs in 1966.^{[2]}^{[3]}^{[4]} In OFDM, the incoming bitstream representing the data to be sent is divided into multiple streams. Multiple closely spaced orthogonal subcarrier signals with overlapping spectra are transmitted, with each carrier modulated with bits from the incoming stream so multiple bits are being transmitted in parallel.^{[5]} 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.^{[6]} Each subcarrier (signal) is modulated with a conventional modulation scheme (such as quadrature amplitude modulation or phaseshift keying) at a low symbol rate. This maintains total data rates similar to conventional singlecarrier modulation schemes in the same bandwidth.^{[7]}
The main advantage of OFDM over singlecarrier schemes is its ability to cope with severe channel conditions (for example, attenuation of high frequencies in a long copper wire, narrowband interference and frequencyselective fading due to multipath) without the need for 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 eliminate intersymbol interference (ISI) and use echoes and timespreading (in analog television visible as ghosting and blurring, respectively) to achieve a diversity gain, i.e. a signaltonoise ratio improvement. This mechanism also facilitates the design of single frequency networks (SFNs) where several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be recombined constructively, sparing interference of a traditional singlecarrier system.
In coded orthogonal frequencydivision 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 effects. COFDM was introduced by Alard in 1986^{[8]}^{[9]}^{[10]} for Digital Audio Broadcasting for Eureka Project 147. In practice, OFDM has become used in combination with such coding and interleaving, so that the terms COFDM and OFDM coapply to common applications.^{[11]}^{[12]}
The following list is a summary of existing OFDMbased standards and products. For further details, see the Usage section at the end of the article.
The OFDMbased multiple access technology OFDMA is also used in several 4G and pre4G cellular networks, mobile broadband standards, the next generation WLAN and the wired portion of Hybrid fibercoaxial networks:^{[citation needed]}
The advantages and disadvantages listed below are further discussed in the Characteristics and principles of operation section below.
Conceptually, OFDM is a specialized frequencydivision multiplexing (FDM) method, with the additional constraint that all subcarrier signals within a communication channel are orthogonal to one another.
In OFDM, the subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other, meaning that crosstalk between the subchannels is eliminated and intercarrier guard bands are not required. This greatly simplifies the design of both the transmitter and the receiver; unlike conventional FDM, a separate filter for each subchannel is not required.
The orthogonality requires that the subcarrier spacing is Hertz, where T_{U} seconds is the useful symbol duration (the receiverside window size), and k is a positive integer, typically equal to 1. This stipulates that each carrier frequency undergoes k more complete cycles per symbol period than the previous carrier. Therefore, with N subcarriers, 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 for the equivalent baseband signal (i.e., near half the Nyquist rate for the doubleside band physical passband signal). Almost the whole available frequency band can be used. OFDM generally has a nearly 'white' spectrum, giving it benign electromagnetic interference properties with respect to other cochannel users.
OFDM requires very accurate frequency synchronization between the receiver and the transmitter; with frequency deviation the subcarriers will no longer be orthogonal, causing intercarrier interference (ICI) (i.e., crosstalk between the subcarriers). 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,^{[15]} and is an important factor limiting the use of OFDM in highspeed vehicles. In order to mitigate ICI in such scenarios, one can shape each subcarrier in order to minimize the interference resulting in a nonorthogonal subcarriers overlapping.^{[16]} For example, a lowcomplexity scheme referred to as WCPOFDM (Weighted Cyclic Prefix Orthogonal FrequencyDivision Multiplexing) consists of using short filters at the transmitter output in order to perform a potentially nonrectangular pulse shaping and a near perfect reconstruction using a singletap per subcarrier equalization.^{[17]} Other ICI suppression techniques usually drastically increase the receiver complexity.^{[18]}
The orthogonality allows for efficient modulator and demodulator implementation using the FFT algorithm on the receiver side, and inverse FFT on the sender side. Although the principles and some of the benefits have been known since the 1960s, OFDM is popular for wideband communications today by way of lowcost digital signal processing components that can efficiently calculate the FFT.
The time to compute the inverseFFT or FFT has to take less than the time for each symbol,^{[19]}^{: 84 } which for example for DVBT (FFT 8k) means the computation has to be done in 896 µs or less.
For an 8192point FFT this may be approximated to:^{[19]}^{[clarification needed]}
The computational demand approximately scales linearly with FFT size so a double size FFT needs double the amount of time and vice versa.^{[19]}^{: 83 } As a comparison an Intel Pentium III CPU at 1.266 GHz is able to calculate a 8192 point FFT in 576 µs using FFTW.^{[20]} Intel Pentium M at 1.6 GHz does it in 387 µs.^{[21]} Intel Core Duo at 3.0 GHz does it in 96.8 µs.^{[22]}
One key principle of OFDM is that since low symbol rate modulation schemes (i.e., where the symbols are relatively long compared to the channel time characteristics) suffer less from intersymbol interference caused by multipath propagation, it is advantageous to transmit a number of lowrate streams in parallel instead of a single highrate stream. Since the duration of each symbol is long, it is feasible to insert a guard interval between the OFDM symbols, thus eliminating the intersymbol interference.
The guard interval also eliminates the need for a pulseshaping filter, and it reduces the sensitivity to time synchronization problems.
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.
In some standards such as Ultrawideband, in the interest of transmitted power, cyclic prefix is skipped and nothing is sent during the guard interval. The receiver will then have to mimic the cyclic prefix functionality by copying the end part of the OFDM symbol and adding it to the beginning portion.
The effects of frequencyselective channel conditions, for example fading caused by multipath propagation, can be considered as constant (flat) over an OFDM subchannel if the subchannel is sufficiently narrowbanded (i.e., if the number of subchannels is sufficiently large). This makes frequency domain equalization possible at the receiver, which is far simpler than the timedomain equalization used in conventional singlecarrier modulation. In OFDM, the equalizer only has to multiply each detected subcarrier (each Fourier coefficient) in each OFDM symbol by a constant complex number, or a rarely changed value. On a fundamental level, simpler digital equalizers are better because they require fewer operations, which translates to fewer roundoff errors in the equalizer. Those roundoff errors can be viewed as numerical noise and are inevitable.
If differential modulation such as DPSK or DQPSK is applied to each subcarrier, equalization can be completely omitted, since these noncoherent schemes are insensitive to slowly changing amplitude and phase distortion.
In a sense, improvements in FIR equalization using FFTs or partial FFTs leads mathematically closer to OFDM,^{[citation needed]} but the OFDM technique is easier to understand and implement, and the subchannels can be independently adapted in other ways than varying equalization coefficients, such as switching between different QAM constellation patterns and errorcorrection schemes to match individual subchannel noise and interference characteristics.^{[clarification needed]}
Some of the subcarriers in some of the OFDM symbols may carry pilot signals for measurement of the channel conditions^{[23]}^{[24]} (i.e., the equalizer gain and phase shift for each subcarrier). Pilot signals and training symbols (preambles) may also be used for time synchronization (to avoid intersymbol interference, ISI) and frequency synchronization (to avoid intercarrier interference, ICI, caused by Doppler shift).
OFDM was initially used for wired and stationary wireless communications. However, with an increasing number of applications operating in highly mobile environments, the effect of dispersive fading caused by a combination of multipath propagation and doppler shift is more significant. Over the last decade, research has been done on how to equalize OFDM transmission over doubly selective channels.^{[25]}^{[26]}^{[27]}
OFDM is invariably used in conjunction with channel coding (forward error correction), and almost always uses frequency and/or time interleaving.
Frequency (subcarrier) interleaving increases resistance to frequencyselective channel conditions such as fading. For example, when a part of the channel bandwidth fades, 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 bitstream rather than being concentrated. Similarly, time interleaving ensures that bits that are originally close together in the bitstream 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 flatfading (where the whole channel bandwidth fades at the same time).
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bitstream 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 similar design of audio data encoding makes compact disc (CD) playback robust.
A classical type of error correction coding used with OFDMbased systems is convolutional coding, often concatenated with ReedSolomon coding. Usually, additional interleaving (on top of the time and frequency interleaving mentioned above) in between the two layers of coding is implemented. The choice for ReedSolomon coding as the outer error correction code is based on the observation that the Viterbi decoder used for inner convolutional decoding produces short error bursts when there is a high concentration of errors, and ReedSolomon codes are inherently well suited to correcting bursts of errors.
Newer systems, however, usually now adopt nearoptimal types of error correction codes 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, which perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel. Some systems that have implemented these codes have concatenated them with either ReedSolomon (for example on the MediaFLO system) or BCH codes (on the DVBS2 system) to improve upon an error floor inherent to these codes at high signaltonoise ratios.^{[28]}
The resilience to severe channel conditions can be further enhanced if information about the channel is sent over a returnchannel. Based on this feedback information, adaptive modulation, channel coding and power allocation may be applied across all subcarriers, or individually to each subcarrier. In the latter case, if a particular range of frequencies suffers from interference or attenuation, the carriers within that range can be disabled or made to run slower by applying more robust modulation or error coding to those subcarriers.
The term discrete multitone modulation (DMT) denotes OFDMbased communication systems that adapt the transmission to the channel conditions individually for each subcarrier, by means of socalled bitloading. Examples are ADSL and VDSL.
The upstream and downstream speeds can be varied by allocating either more or fewer carriers for each purpose. Some forms of rateadaptive DSL use this feature in real time, so that the bitrate is adapted to the cochannel interference and bandwidth is allocated to whichever subscriber needs it most.
OFDM in its primary form is considered as a digital modulation technique, and not a multiuser channel access method, since it is used for transferring one bit stream over one communication channel using one sequence of OFDM symbols. However, OFDM can be combined with multiple access using time, frequency or coding separation of the users.
In orthogonal frequencydivision multiple access (OFDMA), frequencydivision multiple access is achieved by assigning different OFDM subchannels to different users. OFDMA supports differentiated quality of service by assigning different number of subcarriers to different users in a similar fashion as in CDMA, and thus complex packet scheduling or medium access control schemes can be avoided. OFDMA is used in:
OFDMA is also a candidate access method for the IEEE 802.22 Wireless Regional Area Networks (WRAN). The project aims at designing the first cognitive radiobased standard operating in the VHFlow UHF spectrum (TV spectrum).
In multicarrier codedivision multiple access (MCCDMA), also known as OFDMCDMA, OFDM is combined with CDMA spread spectrum communication for coding separation of the users. Cochannel interference can be mitigated, meaning that manual fixed channel allocation (FCA) frequency planning is simplified, or complex dynamic channel allocation (DCA) schemes are avoided.
In OFDMbased widearea 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 singlefrequency networks (SFN), where many transmitters send the same signal simultaneously over the same channel frequency. SFNs use the available spectrum more effectively than conventional multifrequency broadcast networks (MFN), where program content is replicated on different carrier frequencies. SFNs also result in a diversity gain in receivers situated midway between the transmitters. The coverage area is increased and the outage probability decreased in comparison to an MFN, due to increased received signal strength averaged over all subcarriers.
Although the guard interval only contains redundant data, which means that it reduces the capacity, some OFDMbased 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 cellsizes. 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.
A single frequency network is a form of transmitter macrodiversity. The concept can be further used in dynamic singlefrequency networks (DSFN), where the SFN grouping is changed from timeslot to timeslot.
OFDM may be combined with other forms of space diversity, for example antenna arrays and MIMO channels. This is done in the IEEE 802.11 Wireless LAN standards.
An OFDM signal exhibits a high peaktoaverage power ratio (PAPR) because the independent phases of the subcarriers mean that they will often combine constructively. Handling this high PAPR requires:
Any nonlinearity 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 nonlinear 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 outofband 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.
The crest factor CF (in dB) for an OFDM system with n uncorrelated subcarriers is^{[29]}
where CF_{c} is the crest factor (in dB) for each subcarrier. (CF_{c} is 3.01 dB for the sine waves used for BPSK and QPSK modulation).
For example, the DVBT signal in 2K mode is composed of 1705 subcarriers that are each QPSKmodulated, giving a crest factor of 35.32 dB.^{[29]}
Many PAPR (or crest factor) reduction techniques have been developed, for instance, based on iterative clipping.^{[30]} Over the years, numerous modeldriven approaches have been proposed to reduce the PAPR in communication systems. In recent years, there has been a growing interest in exploring datadriven models for PAPR reduction as part of ongoing research in endtoend communication networks. These datadriven models offer innovative solutions and new avenues of exploration to address the challenges posed by high PAPR effectively. By leveraging datadriven techniques, researchers aim to enhance the performance and efficiency of communication networks by optimizing power utilization. ^{[31]}
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB.^{[32]} As a comparison, each extra bit per sample increases the dynamic range by 6 dB.
The performance of any communication system can be measured in terms of its power efficiency and bandwidth efficiency. The power efficiency describes the ability of communication system to preserve bit error rate (BER) of the transmitted signal at low power levels. Bandwidth efficiency reflects how efficiently the allocated bandwidth is used and is defined as the throughput data rate per hertz in a given bandwidth. If the large number of subcarriers are used, the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel is defined as^{[33]}
where is the symbol rate in gigasymbols per second (Gsps), is the bandwidth of OFDM signal, and the factor of 2 is due to the two polarization states in the fiber.
There is saving of bandwidth by using multicarrier modulation with orthogonal frequencydivision multiplexing. So the bandwidth for multicarrier system is less in comparison with single carrier system and hence bandwidth efficiency of multicarrier system is larger than single carrier system.
S. no.  Transmission type  M in MQAM  No. of subcarriers  Bit rate  Fiber length  Received power, at BER of 10^{−9}  Bandwidth efficiency 

1  Single carrier  64  1  10 Gbit/s  20 km  −37.3 dBm  6.0000 
2  Multicarrier  64  128  10 Gbit/s  20 km  −36.3 dBm  10.6022 
There is only 1 dB increase in receiver power, but we get 76.7% improvement in bandwidth efficiency with using multicarrier transmission technique.
This section describes a simple idealized OFDM system model suitable for a timeinvariant AWGN channel.
An OFDM carrier signal is the sum of a number of orthogonal subcarriers, with baseband data on each subcarrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phaseshift keying (PSK). This composite baseband signal is typically used to modulate a main RF carrier.
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 bitrate than others.
An inverse FFT is computed on each set of symbols, giving a set of complex timedomain samples. These samples are then quadraturemixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using digitaltoanalogue 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 quadraturemixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on , so lowpass filters are used to reject these. The baseband signals are then sampled and digitised using analogtodigital 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 recombined into a serial stream, , which is an estimate of the original binary stream at the transmitter.
If subcarriers are used, and each subcarrier is modulated using alternative symbols, the OFDM symbol alphabet consists of combined symbols.
The lowpass equivalent OFDM filter is expressed as:
where are the data symbols, is the number of subcarriers, and is the OFDM symbol time. The subcarrier spacing of makes them orthogonal over each symbol period; this property is expressed as:
where denotes the complex conjugate operator and is the Kronecker delta.
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 . The OFDM signal with cyclic prefix is thus:
The lowpass signal filter above can be either real or complexvalued. Realvalued lowpass equivalent signals are typically transmitted at baseband—wireline applications such as DSL use this approach. For wireless applications, the lowpass signal is typically complexvalued; in which case, the transmitted signal is upconverted to a carrier frequency . In general, the transmitted signal can be represented as:
OFDM is used in:
Key features of some common OFDMbased systems are presented in the following table.
Standard name  DAB Eureka 147  DVBT  DVBH  DTMB  DVBT2  IEEE 802.11a 

Year ratified  1995  1997  2004  2006  2007  1999 
Frequency range of today's equipment (MHz) 
174–240, 1,452–1,492  470–862, 174–230  470–862  48–870  4,915–6,100  
Channel spacing, B (MHz) 
1.712  6, 7, 8  5, 6, 7, 8  6, 7, 8  1.7, 5, 6, 7, 8, 10  20 
FFT size, k = 1,024  Mode I: 2k Mode II: 512 Mode III: 256 Mode IV: 1k 
2k, 8k  2k, 4k, 8k  1 (singlecarrier) 4k (multicarrier) 
1k, 2k, 4k, 8k, 16k, 32k  64 
Number of nonsilent subcarriers, N  Mode I: 1,536 Mode II: 384 Mode III: 192 Mode IV: 768 
2K mode: 1,705 8K mode: 6,817 
1,705, 3,409, 6,817  1 (singlecarrier) 3,780 (multicarrier) 
853–27,841 (1K normal to 32K extended carrier mode)  52 
Subcarrier modulation scheme  π⁄4DQPSK  QPSK,^{[35]} 16QAM, 64QAM  QPSK,^{[35]} 16QAM, 64QAM  4QAM,^{[35]} 4QAMNR,^{[36]} 16QAM, 32QAM, 64QAM  QPSK, 16QAM, 64QAM, 256QAM  BPSK, QPSK,^{[35]} 16QAM, 64QAM 
Useful symbol length, T_{U} (μs) 
Mode I: 1,000 Mode II: 250 Mode III: 125 Mode IV: 500 
2K mode: 224 8K mode: 896 
224, 448, 896  500 (multicarrier)  112–3,584 (1K to 32K mode on 8 MHz channel)  3.2 
Additional guard interval, T_{G}/T_{U} 
24.6% (all modes)  1⁄4, 1⁄8, 1⁄16, 1⁄32  1⁄4, 1⁄8, 1⁄16, 1⁄32  1⁄4, 1⁄6, 1⁄9  1/128, 1/32, 1/16, 19/256, 1/8, 19/128, 1/4 (for 32k mode maximum 1/8) 
1⁄4 
Subcarrier spacing, (Hz) 
Mode I: 1,000 Mode II: 4,000 Mode III: 8,000 Mode IV: 2,000 
2K mode: 4,464 8K mode: 1,116 
4,464, 2,232, 1,116  8 M (singlecarrier) 2,000 (multicarrier) 
279–8,929 (32K down to 1K mode)  312.5 K 
Net bit rate, R (Mbit/s) 
0.576–1.152  4.98–31.67 (typ. 24.13) 
3.7–23.8  4.81–32.49  Typically 35.4  6–54 
Link spectral efficiency, R/B (bit/s·Hz) 
0.34–0.67  0.62–4.0 (typ. 3.0)  0.62–4.0  0.60–4.1  0.87–6.65  0.30–2.7 
Inner FEC  Conv. coding with equal error protection code rates: 1⁄4, 3⁄8, 4⁄9, 1⁄2, 4⁄7, 2⁄3, 3⁄4, 4⁄5 Unequal error protection with avg. code rates of: 
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 
LDPC: 1⁄2, 3⁄5, 2⁄3, 3⁄4, 4⁄5, 5⁄6  Conv. coding with code rates: 1⁄2, 2⁄3, or 3⁄4 
Outer FEC  Optional RS (120, 110, t = 5)  RS (204, 188, t = 8)  RS (204, 188, t = 8) + MPEFEC  BCH code (762, 752)  BCH code  None 
Maximum travelling speed (km/h) 
200–600  53–185, varies with transmission frequency  
Time interleaving depth (ms) 
384  0.6–3.5  0.6–3.5  200–500  Up to 250 (500 with extension frame)  
Adaptive transmission  None  None  None  None  
Multiple access method  None  None  None  None  
Typical source coding  192 kbit/s MPEG2 Audio layer 2  2–18 Mbit/s Standard – HDTV H.264 or MPEG2  H.264  Not defined (video: MPEG2, H.264, H.265 and/or AVS+; audio: MP2 or DRA or AC3)  H.264 or MPEG2 (audio: AAC HE, Dolby Digital AC3 (A52), MPEG2 AL 2) 
OFDM is used in ADSL connections that follow the ANSI T1.413 and G.dmt (ITU G.992.1) standards, where it is called discrete multitone modulation (DMT).^{[37]} DSL achieves highspeed data connections on existing copper wires. OFDM is also used in the successor standards ADSL2, ADSL2+, VDSL, VDSL2, and G.fast. ADSL2 uses variable subcarrier modulation, ranging from BPSK to 32768QAM (in ADSL terminology this is referred to as bitloading, or bit per tone, 1 to 15 bits per subcarrier).
Long copper wires suffer from attenuation at high frequencies. The fact that OFDM can cope with this frequency selective attenuation and with narrowband interference are the main reasons it is frequently used in applications such as ADSL modems.
OFDM is used by many powerline devices to extend digital connections through power wiring. Adaptive modulation is particularly important with such a noisy channel as electrical wiring. Some medium speed smart metering modems, "Prime" and "G3" use OFDM at modest frequencies (30–100 kHz) with modest numbers of channels (several hundred) in order to overcome the intersymbol interference in the power line environment.^{[38]} The IEEE 1901 standards include two incompatible physical layers that both use OFDM.^{[39]} The ITUT G.hn standard, which provides highspeed local area networking over existing home wiring (power lines, phone lines and coaxial cables) is based on a PHY layer that specifies OFDM with adaptive modulation and a LowDensity ParityCheck (LDPC) FEC code.^{[34]}
OFDM is extensively used in wireless LAN and MAN applications, including IEEE 802.11a/g/n and WiMAX.
IEEE 802.11a/g/n, operating in the 2.4 and 5 GHz bands, specifies perstream airside data rates ranging from 6 to 54 Mbit/s. If both devices can use "HT mode" (added with 802.11n), the top 20 MHz perstream rate is increased to 72.2 Mbit/s, with the option of data rates between 13.5 and 150 Mbit/s using a 40 MHz channel. Four different modulation schemes are used: BPSK, QPSK, 16QAM, and 64QAM, along with a set of error correcting rates (1/2–5/6). The multitude of choices allows the system to adapt the optimum data rate for the current signal conditions.
OFDM is also now being used in the WiMedia/Ecma368 standard for highspeed wireless personal area networks in the 3.1–10.6 GHz ultrawideband spectrum (see MultiBandOFDM).
Much of Europe and Asia has adopted OFDM for terrestrial broadcasting of digital television (DVBT, DVBH and TDMB) and radio (EUREKA 147 DAB, Digital Radio Mondiale, HD Radio and TDMB).
By Directive of the European Commission, all television services transmitted to viewers in the European Community must use a transmission system that has been standardized by a recognized European standardization body,^{[40]} and such a standard has been developed and codified by the DVB Project, Digital Video Broadcasting (DVB); Framing structure, channel coding and modulation for digital terrestrial television.^{[41]} Customarily referred to as DVBT, the standard calls for the exclusive use of COFDM for modulation. DVBT is now widely used in Europe and elsewhere for terrestrial digital TV.
The ground segments of the Digital Audio Radio Service (SDARS) systems used by XM Satellite Radio and Sirius Satellite Radio are transmitted using Coded OFDM (COFDM).^{[42]} The word "coded" comes from the use of forward error correction (FEC).^{[5]}
The question of the relative technical merits of COFDM versus 8VSB for terrestrial digital television has been a subject of some controversy, especially between European and North American technologists and regulators. The United States has rejected several proposals to adopt the COFDMbased DVBT system for its digital television services, and for many years has opted to use 8VSB (vestigial sideband modulation) exclusively for terrestrial digital television.^{[43]} However, in November 2017, the FCC approved a voluntary transition to ATSC 3.0, a new broadcast standard which is based on COFDM. Unlike the first digital television transition in America, TV stations will not be assigned separate frequencies to transmit ATSC 3.0 and are not required to switch to ATSC 3.0 by any deadline. Televisions sold in the U.S. are also not required to include ATSC 3.0 tuning capabilities. Fullpowered television stations are permitted to make the switch to ATSC 3.0, as long as they continue to make their main channel available through a simulcast agreement with another inmarket station (with a similar coverage area) through at least November 2022.^{[44]}
One of the major benefits provided by COFDM is in rendering radio broadcasts relatively immune to multipath distortion and signal fading due to atmospheric conditions or passing aircraft. Proponents of COFDM argue it resists multipath far better than 8VSB. Early 8VSB DTV (digital television) receivers often had difficulty receiving a signal. Also, COFDM allows singlefrequency networks, which is not possible with 8VSB.
However, newer 8VSB receivers are far better at dealing with multipath, hence the difference in performance may diminish with advances in equalizer design.^{[45]}
COFDM is also used for other radio standards, for Digital Audio Broadcasting (DAB), the standard for digital audio broadcasting at VHF frequencies, for Digital Radio Mondiale (DRM), the standard for digital broadcasting at shortwave and medium wave frequencies (below 30 MHz) and for DRM+ a more recently introduced standard for digital audio broadcasting at VHF frequencies. (30 to 174 MHz)
The United States 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.
Both Digital Radio Mondiale and HD Radio are classified as inband onchannel systems, unlike Eureka 147 (DAB: Digital Audio Broadcasting) which uses separate VHF or UHF frequency bands instead.
The bandsegmented transmission orthogonal frequencydivision multiplexing (BSTOFDM) system proposed for Japan (in the ISDBT, ISDBTSB, and ISDBC broadcasting systems) improves upon COFDM by exploiting the fact that some OFDM carriers may be modulated differently from others within the same multiplex. Some forms of COFDM already offer this kind of hierarchical modulation, though BSTOFDM is intended to make it more flexible. 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 composed 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 highmultipath environment.
Ultrawideband (UWB) wireless personal area network technology may also use OFDM, such as in Multiband OFDM (MBOFDM). 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.
Fast lowlatency access with seamless handoff orthogonal frequencydivision multiplexing (FlashOFDM), also referred to as FOFDM, was based on OFDM and also specified higher protocol layers. It was developed by Flarion, and purchased by Qualcomm in January 2006.^{[46]}^{[47]} FlashOFDM was marketed as a packetswitched cellular bearer, to compete with GSM and 3G networks. As an example, 450 MHz frequency bands previously used by NMT450 and CNet C450 (both 1G analogue networks, now mostly decommissioned) in Europe are being licensed to FlashOFDM operators.^{[citation needed]}
In Finland, the license holder Digita began deployment of a nationwide "@450" wireless network in parts of the country since April 2007. It was purchased by Datame in 2011.^{[48]} In February 2012 Datame announced they would upgrade the 450 MHz network to competing CDMA2000 technology.^{[49]}
Slovak Telekom in Slovakia offers FlashOFDM connections^{[50]} with a maximum downstream speed of 5.3 Mbit/s, and a maximum upstream speed of 1.8 Mbit/s, with a coverage of over 70 percent of Slovak population.^{[citation needed]} The FlashOFDM network was switched off in the majority of Slovakia on 30 September 2015.^{[51]}
TMobile Germany used FlashOFDM to backhaul WiFi HotSpots on the Deutsche Bahn's ICE high speed trains between 2005 and 2015, until switching over to UMTS and LTE.^{[52]}
American wireless carrier Nextel Communications field tested wireless broadband network technologies including FlashOFDM in 2005.^{[53]} Sprint purchased the carrier in 2006 and decided to deploy the mobile version of WiMAX, which is based on Scalable Orthogonal FrequencyDivision Multiple Access (SOFDMA) technology.^{[54]}
Citizens Telephone Cooperative launched a mobile broadband service based on FlashOFDM technology to subscribers in parts of Virginia in March 2006. The maximum speed available was 1.5 Mbit/s.^{[55]} The service was discontinued on April 30, 2009.^{[56]}
VOFDM was proposed by XiangGen Xia in 2000 (Proceedings of ICC 2000, New Orleans, and IEEE Trans. on Communications, Aug. 2001) for single transmit antenna systems. VOFDM replaces each scalar value in the conventional OFDM by a vector value and is a bridge between OFDM and the single carrier frequency domain equalizer (SCFDE). When the vector size is , it is OFDM and when the vector size is at least the channel length and the FFT size is , it is SCFDE.
In VOFDM, assume is the vector size, and each scalarvalued signal in OFDM is replaced by a vectorvalued signal of vector size , . One takes the point IFFT of , componentwisely and gets another vector sequence of the same vector size , . Then, one adds a vector CP of length to this vector sequence as
This vector sequence is converted to a scalar sequence by sequentializing all the vectors of size , which is transmitted at a transmit antenna sequentially.
At the receiver, the received scalar sequence is first converted to the vector sequence of vector size . When the CP length satisfies , then, after the vector CP is removed from the vector sequence and the point FFT is implemented componentwisely to the vector sequence of length , one obtains
where are additive white noise and and is the following polyphase matrix of the ISI channel :
where is the th polyphase component of the channel . From (1), one can see that the original ISI channel is converted to many vector subchannels of vector size . There is no ISI across these vector subchannels but there is ISI inside each vector subchannel. In each vector subchannel, at most many symbols are interfered each other. Clearly, when the vector size , the above VOFDM returns to OFDM and when and , it becomes the SCFDE. The vector size is a parameter that one can choose freely and properly in practice and controls the ISI level. There may be a tradeoff between vector size , demodulation complexity at the receiver, and FFT size, for a given channel bandwidth.
Note that the length of the CP part in the sequential form does not have to be an integer multiple of the vector size, . One can truncate the above vectorized CP to a sequential CP of length not less than the ISI channel length, which will not affect the above demodulation.
Also note that there exist many other different generalizations/forms of OFDM, to see their essential differences, it is critical to see their corresponding received signal equations to demodulate. The above VOFDM is the earliest and the only one that achieves the received signal equation (1) and/or its equivalent form, although it may have different implementations at transmitter vs. different IFFT algorithms.
It has been shown (Yabo Li et al., IEEE Trans. on Signal Processing, Oct. 2012) that applying the MMSE linear receiver to each vector subchannel (1), it achieves multipath diversity and/or signal space diversity. This is because the vectorized channel matrices in (1) are pseudocirculant and can be diagonalized by the point DFT/IDFT matrix with some diagonal phase shift matrices. Then, the right hand side DFT/IDFT matrix and the th diagonal phase shift matrix in the diagonalization can be thought of the precoding to the input information symbol vector in the th sub vector channel, and all the vectorized subchannels become diagonal channels of discrete frequency components from the point DFT of the original ISI channel. It may collect the multipath diversity and/or signal space diversity similar to the precoding to collect the signal space diversity for single antenna systems to combat wireless fading or the diagonal spacetime block coding to collect the spatial diversity for multiple antenna systems. The details are referred to the IEEE TCOM and IEEE TSP papers mentioned above.
OFDM has become an interesting technique for power line communications (PLC). In this area of research, a wavelet transform is introduced to replace the DFT as the method of creating orthogonal frequencies. This is due to the advantages wavelets offer, which are particularly useful on noisy power lines.^{[57]}
Instead of using an IDFT to create the sender signal, the wavelet OFDM uses a synthesis bank consisting of a band transmultiplexer followed by the transform function
On the receiver side, an analysis bank is used to demodulate the signal again. This bank contains an inverse transform
followed by another band transmultiplexer. The relationship between both transform functions is
An example of WOFDM uses the Perfect Reconstruction Cosine Modulated Filter Bank (PRCMFB)^{[58]} and Extended Lapped Transform (ELT)^{[59]}^{[60]} is used for the wavelet TF. Thus, and are given as
These two functions are their respective inverses, and can be used to modulate and demodulate a given input sequence. Just as in the case of DFT, the wavelet transform creates orthogonal waves with , , ..., . The orthogonality ensures that they do not interfere with each other and can be sent simultaneously. At the receiver, , , ..., are used to reconstruct the data sequence once more.
WOFDM is an evolution of the standard OFDM, with certain advantages.
Mainly, the sidelobe levels of WOFDM are lower. This results in less ICI, as well as greater robustness to narrowband interference. These two properties are especially useful in PLC, where most of the lines aren't shielded against EMnoise, which creates noisy channels and noise spikes.
A comparison between the two modulation techniques also reveals that the complexity of both algorithms remains approximately the same.^{[57]}
The vast majority of implementations of OFDM use the fast Fourier transform (FFT). However, there exist other orthogonal transforms that can be used. For example, OFDM systems based on the discrete Hartley transform (DHT) ^{[61]} and the wavelet transform have been investigated.
((cite book))
: CS1 maint: location (link)
Terrestrial 
 

Satellite 
 
Codecs  
Subcarrier signals  
