Orthogonal frequency-division multiplexing

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In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital 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 mobile communications.

Carrier wave waveform (usually sinusoidal) that is modulated (modified) with an input signal for the purpose of conveying information

In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform that is modulated (modified) with an input signal for the purpose of conveying information. This carrier wave usually has a much higher frequency than the input signal does. The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave, or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing. The term originated in radio communication, where the carrier wave is the radio wave which carries the information (modulation) through the air from the transmitter to the receiver. The term is also used for an unmodulated emission in the absence of any modulating signal.

In communications, a system is wideband when the message bandwidth significantly exceeds the coherence bandwidth of the channel. Some communication links have such a high data rate that they are forced to use a wide bandwidth; other links may have relatively low data rates, but deliberately use a wider bandwidth than "necessary" for that data rate in order to gain other advantages; see spread spectrum.

Digital subscriber line is a family of technologies that are used to transmit digital data over telephone lines. In telecommunications marketing, the term DSL is widely understood to mean asymmetric digital subscriber line (ADSL), the most commonly installed DSL technology, for Internet access.


In coded orthogonal frequency-division multiplexing (COFDM), forward error correction (convolutional coding) and time/frequency interleaving are applied to the signal being transmitted. This is done to overcome errors in mobile communication channels affected by multipath propagation and Doppler effects. COFDM was introduced by Alard in 1986 [1] [2] [3] 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 co-apply to common applications. [4] [5]

In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is the sender encodes the message in a redundant way, most often by using an error-correcting code (ECC).

In wireless telecommunications, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings.

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.

OFDM is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier modulation method. OFDM was introduced by Chang of Bell Labs in 1966. [6] [7] [8] Numerous closely spaced orthogonal subcarrier signals with overlapping spectra are emitted to carry data. [9] 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. [10] Each subcarrier (signal) is modulated with a conventional modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low symbol rate. This maintains total data rates similar to conventional single-carrier modulation schemes in the same bandwidth.

Frequency-division multiplexing multiplexing dividing a comm medium into non-overlapping frequency bands, each carrying a separate signal

In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency bands, each of which is used to carry a separate signal. This allows a single transmission medium such as a cable or optical fiber to be shared by multiple independent signals. Another use is to carry separate serial bits or segments of a higher rate signal in parallel.

Bell Labs Research and scientific development company

Nokia Bell Labs is an industrial research and scientific development company owned by Finnish company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world. Bell Labs has its origins in the complex past of the Bell System.

Data facts represented for handling

Data is a set of values of subjects with respect to qualitative or quantitative variables.

The main 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 eliminate intersymbol interference (ISI) and use echoes and time-spreading (in analog television visible as ghosting and blurring, respectively) to achieve a diversity gain, i.e. a signal-to-noise ratio improvement. This mechanism also facilitates the design of single frequency networks (SFNs) where several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be re-combined constructively, sparing interference of a traditional single-carrier system.

Communication channel a fysical or logical connection used for transmission of information

A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used to convey an information signal, for example a digital bit stream, from one or several senders to one or several receivers. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second.

Attenuation distortion is the distortion of an analog signal that occurs during transmission when the transmission medium does not have a flat frequency response across the bandwidth of the medium or the frequency spectrum of the signal.

In electronic communications, especially in telecommunications, an interference is that which modifies a signal in a disruptive manner, as it travels along a channel between its source and receiver. The term is often used to refer to the addition of unwanted signals to a useful signal. Common examples are:

Example of applications

The following list is a summary of existing OFDM-based standards and products. For further details, see the Usage section at the end of the article.

Wired version mostly known as Discrete Multi-tone Transmission (DMT)

Very high speed digital subscriber line (VDSL) and very high speed digital subscriber line 2 (VDSL2) are digital subscriber line (DSL) technologies providing data transmission faster than asymmetric digital subscriber line (ADSL).

Plain old telephone service (POTS), or plain ordinary telephone service, is a retronym for voice-grade telephone service employing analog signal transmission over copper loops. POTS was the standard service offering from telephone companies from 1876 until 1988 in the United States when the Integrated Services Digital Network (ISDN) Basic Rate Interface (BRI) was introduced, followed by cellular telephone systems, and voice over IP (VoIP). POTS remains the basic form of residential and small business service connection to the telephone network in many parts of the world. The term reflects the technology that has been available since the introduction of the public telephone system in the late 19th century, in a form mostly unchanged despite the introduction of Touch-Tone dialing, electronic telephone exchanges and fiber-optic communication into the public switched telephone network (PSTN).

Copper Chemical element with atomic number 29

Copper is a chemical element with the symbol Cu and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkish-orange color. Copper is used as a conductor of heat and electricity, as a building material, and as a constituent of various metal alloys, such as sterling silver used in jewelry, cupronickel used to make marine hardware and coins, and constantan used in strain gauges and thermocouples for temperature measurement.


The OFDM-based multiple access technology OFDMA is also used in several 4G and pre-4G cellular networks, mobile broadband standards and the next generation WLAN:

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and principles of operation section below.

Summary of advantages

Summary of disadvantages

Characteristics and principles of operation


Conceptually, OFDM is a specialized frequency-division 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 cross-talk between the sub-channels is eliminated and inter-carrier 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 sub-channel is not required.

The orthogonality requires that the subcarrier spacing is Hertz, where TU seconds is the useful symbol duration (the receiver-side 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 BN·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 double-side 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 co-channel users.

A simple example: A useful symbol duration TU = 1 ms would require a subcarrier spacing of (or an integer multiple of that) for orthogonality. N = 1,000 subcarriers would result in a total passband bandwidth of NΔf = 1 MHz. For this symbol time, the required bandwidth in theory according to Nyquist is (half of the achieved bandwidth required by our scheme), where R is the bit rate and where N = 1,000 samples per symbol by FFT. If a guard interval is applied (see below), Nyquist bandwidth requirement would be even lower. The FFT would result in N = 1,000 samples per symbol. If no guard interval was applied, this would result in a base band complex valued signal with a sample rate of 1 MHz, which would require a baseband bandwidth of 0.5 MHz according to Nyquist. However, the passband RF signal is produced by multiplying the baseband signal with a carrier waveform (i.e., double-sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz. A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve almost half that bandwidth for the same symbol rate (i.e., twice as high spectral efficiency for the same symbol alphabet length). It is however more sensitive to multipath interference.

OFDM requires very accurate frequency synchronization between the receiver and the transmitter; with frequency deviation the subcarriers will no longer be orthogonal, causing inter-carrier interference (ICI) (i.e., cross-talk 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, [12] and is an important factor limiting the use of OFDM in high-speed vehicles. In order to mitigate ICI in such scenarios, one can shape each subcarrier in order to minimize the interference resulting in a non-orthogonal subcarriers overlapping. [13] For example, a low-complexity scheme referred to as WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists of using short filters at the transmitter output in order to perform a potentially non-rectangular pulse shaping and a near perfect reconstruction using a single-tap per subcarrier equalization. [14] Other ICI suppression techniques usually increase drastically the receiver complexity. [15]

Implementation using the FFT algorithm

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 low-cost digital signal processing components that can efficiently calculate the FFT.

The time to compute the inverse-FFT or FFT transform has to take less than the time for each symbol, [16] :84 which for example for DVB-T (FFT 8k) means the computation has to be done in 896 µs or less.

For an 8192-point FFT this may be approximated to: [16] [ 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. [16] :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. [17] Intel Pentium M at 1.6 GHz does it in 387 µs. [18] Intel Core Duo at 3.0 GHz does it in 96.8 µs. [19]

Guard interval for elimination of intersymbol interference

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 low-rate streams in parallel instead of a single high-rate 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 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 a 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.


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.

Simplified equalization

The effects of frequency-selective channel conditions, for example fading caused by multipath propagation, can be considered as constant (flat) over an OFDM sub-channel if the sub-channel is sufficiently narrow-banded (i.e., if the number of sub-channels is sufficiently large). This makes frequency domain equalization possible at the receiver, which is far simpler than the time-domain equalization used in conventional single-carrier 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 round-off errors in the equalizer. Those round-off errors can be viewed as numerical noise and are inevitable.

Our example: The OFDM equalization in the above numerical example would require one complex valued multiplication per subcarrier and symbol (i.e., complex multiplications per OFDM symbol; i.e., one million multiplications per second, at the receiver). The FFT algorithm requires [this is imprecise: over half of these complex multiplications are trivial, i.e. = to 1 and are not implemented in software or HW]. 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, in a naive implementation, 125 multiplications per symbol (i.e., 125 million multiplications per second). FFT techniques can be used to reduce the number of multiplications for an FIR filter-based time-domain equalizer to a number comparable with OFDM, at the cost of delay between reception and decoding which also becomes comparable with OFDM.

If differential modulation such as DPSK or DQPSK is applied to each subcarrier, equalization can be completely omitted, since these non-coherent 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 sub-channels can be independently adapted in other ways than varying equalization coefficients, such as switching between different QAM constellation patterns and error-correction schemes to match individual sub-channel 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 [20] [21] (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 inter-carrier 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 multi-path 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. [22] [23] [24]

Channel coding and interleaving

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 frequency-selective 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 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 fades 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 similar design of audio data encoding makes compact disc (CD) playback robust.

A classical type of error correction coding used with OFDM-based systems is convolutional coding, often concatenated with Reed-Solomon 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 Reed-Solomon 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 Reed-Solomon codes are inherently well suited to correcting bursts of errors.

Newer systems, however, usually now adopt near-optimal 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 Reed-Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to improve upon an error floor inherent to these codes at high signal-to-noise ratios. [25]

Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the channel is sent over a return-channel. 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 OFDM-based communication systems that adapt the transmission to the channel conditions individually for each subcarrier, by means of so-called bit-loading. 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 rate-adaptive DSL use this feature in real time, so that the bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever subscriber needs it most.

OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique, and not a multi-user 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 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 subcarriers 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:

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 radio-based standard operating in the VHF-low UHF spectrum (TV spectrum).

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, meaning that manual fixed channel allocation (FCA) frequency planning is simplified, or complex dynamic channel allocation (DCA) schemes are avoided.

Space diversity

In OFDM-based 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 (SFN), where many transmitters send the same signal simultaneously over the same channel frequency. SFNs use the available spectrum more effectively than conventional multi-frequency 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 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.

A single frequency network is a form of transmitter macrodiversity. The concept can be further used in dynamic single-frequency 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.

Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent phases of the subcarriers mean that they will often combine constructively. Handling this high PAPR requires:

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 trade-off 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.

The crest factor CF (in dB) for an OFDM system with n uncorrelated subcarriers is [26]

where CFc is the crest factor (in dB) for each subcarrier. (CFc is 3.01 dB for the sine waves used for BPSK and QPSK modulation).

For example, the DVB-T signal in 2K mode is composed of 1705 subcarriers that are each QPSK-modulated, giving a crest factor of 35.32 dB. [26]

Many crest factor reduction techniques have been developed.

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB. [27] As a comparison, each extra bit per sample increases the dynamic range with 6 dB.

Efficiency comparison between single carrier and multicarrier

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 [28]

where is the symbol rate in giga-symbols 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 frequency division 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 typeM in M-QAMNo. of subcarriersBit rateFiber lengthPower at the receiver (at BER of 10−9)Bandwidth efficiency
1.Single carrier64110 Gbit/s20 km−37.3 dBm 6.0000
2.Multicarrier6412810 Gbit/s20 km−36.3dBm10.6022

There is only 1dBm increase in receiver power, but we get 76.7% improvement in bandwidth efficiency with using multicarrier transmission technique.

Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant AWGN channel.


OFDM transmitter ideal.png

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 phase-shift 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 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, .


OFDM receiver ideal.png

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 analog-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.

Mathematical description

Subcarriers system of OFDM signals after FFT N-OFDM.jpg
Subcarriers system of OFDM signals after FFT

If subcarriers are used, and each subcarrier is modulated using alternative symbols, the OFDM symbol alphabet consists of combined symbols.

The low-pass equivalent OFDM signal 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 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 . In general, the transmitted signal can be represented as:


OFDM is used in:

OFDM system comparison table

Key features of some common OFDM-based systems are presented in the following table.

Standard name DAB Eureka 147 DVB-T DVB-H DMB-T/H DVB-T2 IEEE 802.11a
Ratified year199519972004200620071999
Frequency range of
today's equipment
174–240 MHz1.452–1.492 GHz470–862 MHz174–230 MHz470–862 MHz470–862 MHz4,915–6,100 MHz
Channel spacing, B
1.7126, 7, 85, 6, 7, 881.7, 5, 6, 7, 8, 1020
FFT size, k = 1,024Mode I: 2k
Mode II: 512
Mode III: 256
Mode IV: 1k
2k, 8k2k, 4k, 8k1 (single-carrier)
4k (multi-carrier)
1k, 2k, 4k, 8k, 16k, 32k64
Number of non-silent subcarriers, NMode I: 1,536
Mode II: 384
Mode III: 192
Mode IV: 768
2K mode: 1,705
8K mode: 6,817
1,705, 3,409, 6,8171 (single-carrier)
3,780 (multi-carrier)
853–27,841 (1K normal to 32K extended carrier mode)52
Subcarrier modulation schemeπ4-DQPSKQPSK, [30] 16QAM or 64QAMQPSK, [30] 16QAM or 64QAM4QAM, [30] 4QAM-NR, [31] 16QAM, 32QAM and 64QAM.QPSK, 16QAM, 64QAM, 256QAMBPSK, QPSK, [30] 16QAM or 64QAM
Useful symbol length, TU
Mode I: 1,000
Mode II: 250
Mode III: 125
Mode IV: 500
2K mode: 224
8K mode: 896
224, 448, 896500 (multi-carrier)112–3,584 (1K to 32K mode on 8 MHz channel)3.2
Additional guard interval, TG
(fraction of TU)
24.6% (all modes)14, 18, 116, 13214, 18, 116, 13214, 16, 191/128, 1/32, 1/16, 19/256, 1/8, 19/128, 1/4.
(For 32k mode maximum 1/8)
Subcarrier spacing

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, 1,1168 M (single-carrier)
2,000 (multi-carrier)
279–8,929 (32K down to 1K mode)312.5 K
Net bit rate, R
(typically 24.13)
3.7–23.84.81–32.49Typically 35.46–54
Link spectral efficiency R/B
0.34–0.670.62–4.0 (typ. 3.0)0.62–4.00.60–4.10.87–6.650.30–2.7
Inner FEC Conv. coding with equal error protection code rates:

14, 38, 49, 12, 47, 23, 34, 45

Unequal error protection with av. code rates of:
~0.34, 0.41, 0.50, 0.60, and 0.75

Conv. coding with code rates:

12, 23, 34, 56, or 78

Conv. coding with code rates:

12, 23, 34, 56, or 78

LDPC with code rates:

0.4, 0.6, or 0.8

LDPC: 12, 35, 23, 34, 45, 56 Conv. coding with code rates:

12, 23, or 34

Outer FEC (if any)Optional RS (120, 110, t = 5) RS (204, 188, t = 8) RS (204, 188, t = 8) + MPE-FEC BCH code (762, 752) BCH code
Maximum travelling speed
depending upon transmission frequency
Time interleaving depth
3840.6–3.50.6–3.5200–500Up to 250 (500 with extension frame)
Adaptive transmission,
if any
Multiple access method
(if any)
Typical source coding 192  kbit/s
MPEG2 Audio
layer 2
2–18 Mbit/s
Standard - HDTV
H.264 or MPEG2
H.264Not defined
(Video: MPEG-2, H.264 and/or AVS
Audio: MP2 or AC-3)
H.264 or MPEG2
(Audio: AAC HE, Dolby Digital AC-3 (A52), MPEG-2 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). [32] DSL achieves high-speed 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 bit-loading, 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 narrow-band interference are the main reasons it is frequently used in applications such as ADSL modems.

Powerline Technology

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. [33] The IEEE 1901 standards include two incompatible physical layers that both use OFDM. [34] The ITU-T G.hn standard, which provides high-speed 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 Low-Density Parity-Check (LDPC) FEC code. [29]

Wireless local area networks (LAN) and metropolitan area networks (MAN)

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 per-stream 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 per-stream 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, 16-QAM, and 64-QAM, 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.

Wireless personal area networks (PAN)

OFDM is also now being used in the WiMedia/Ecma-368 standard for high-speed wireless personal area networks in the 3.1–10.6 GHz ultrawideband spectrum (see MultiBand-OFDM).

Terrestrial digital radio and television broadcasting

Much of Europe and Asia has adopted OFDM for terrestrial broadcasting of digital television (DVB-T, DVB-H and T-DMB) and radio (EUREKA 147 DAB, Digital Radio Mondiale, HD Radio and T-DMB).


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, [35] 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. [36] Customarily referred to as DVB-T, the standard calls for the exclusive use of COFDM for modulation. DVB-T 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). [37] The word "coded" comes from the use of forward error correction (FEC). [9]


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 COFDM-based DVB-T system for its digital television services, and has instead opted for 8VSB (vestigial sideband modulation) operation.

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 single-frequency 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.[ citation needed ]

Digital radio

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 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.

Both Digital Radio Mondiale and HD Radio are classified as in-band on-channel systems, unlike Eureka 147 (DAB: Digital Audio Broadcasting) which uses separate VHF or UHF frequency bands instead.


The band-segmented transmission orthogonal frequency division multiplexing (BST-OFDM) system proposed for Japan (in the ISDB-T, ISDB-TSB, and ISDB-C 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 BST-OFDM 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 high-multipath environment.


Ultra-wideband (UWB) wireless personal area network technology may also use 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.


Fast low-latency access with seamless handoff orthogonal frequency division multiplexing (Flash-OFDM), also referred to as F-OFDM, was based on OFDM and also specified higher protocol layers. It was developed by Flarion, and purchased by Qualcomm in January 2006. [38] [39] Flash-OFDM was marketed as a packet-switched cellular bearer, to compete with GSM and 3G networks. As an example, 450 MHz frequency bands previously used by NMT-450 and C-Net C450 (both 1G analogue networks, now mostly decommissioned) in Europe are being licensed to Flash-OFDM 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. [40] In February 2012 Datame announced they would upgrade the 450 MHz network to competing CDMA2000 technology. [41]

Slovak Telekom in Slovakia offers Flash-OFDM connections [42] 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 Flash-OFDM network was switched off in the majority of Slovakia on 30 September 2015. [43]

T-Mobile Germany used Flash-OFDM to backhaul Wi-Fi HotSpots on the Deutsche Bahn's ICE high speed trains between 2005 and 2015, until switching over to UMTS and LTE. [44]

American wireless carrier Nextel Communications field tested wireless broadband network technologies including Flash-OFDM in 2005. [45] Sprint purchased the carrier in 2006 and decided to deploy the mobile version of WiMAX, which is based on Scalable Orthogonal Frequency Division Multiple Access (SOFDMA) technology. [46]

Citizens Telephone Cooperative launched a mobile broadband service based on Flash-OFDM technology to subscribers in parts of Virginia in March 2006. The maximum speed available was 1.5 Mbit/s. [47] The service was discontinued on April 30, 2009. [48]


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. [49]

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 W-OFDM uses the Perfect Reconstruction Cosine Modulated Filter Bank (PR-CMFB) and Extended Lapped Transform (ELT) 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.

Advantages over standard OFDM

W-OFDM is an evolution of the standard OFDM, with certain advantages.

Mainly, the sidelobe levels of W-OFDM 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 EM-noise, 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. [49]


See also

Related Research Articles

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. Most radio systems in the 20th century used frequency modulation (FM) or amplitude modulation (AM) for radio broadcast.

Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal. The modulation is accomplished by varying the sine and cosine inputs at a precise time. It is widely used for wireless LANs, RFID and Bluetooth communication.


In wireless communications, fading is variation of the attenuation of a signal with various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A fading channel is a communication channel that experiences fading. In wireless systems, fading may either be due to multipath propagation, referred to as multipath-induced fading, weather, or shadowing from obstacles affecting the wave propagation, sometimes referred to as shadow fading.

8VSB is the modulation method used for broadcast in the ATSC digital television standard. ATSC and 8VSB modulation is used primarily in North America; in contrast, the DVB-T standard uses COFDM.

Ultra-wideband is a radio technology that can use a very low energy level for short-range, high-bandwidth communications over a large portion of the radio spectrum. UWB has traditional applications in non-cooperative radar imaging. Most recent applications target sensor data collection, precision locating and tracking applications.

DVB-T is an abbreviation for "Digital Video Broadcasting — Terrestrial"; it is the DVB European-based consortium standard for the broadcast transmission of digital terrestrial television that was first published in 1997 and first broadcast in the UK in 1998. This system transmits compressed digital audio, digital video and other data in an MPEG transport stream, using coded orthogonal frequency-division multiplexing modulation. It is also the format widely used worldwide for Electronic News Gathering for transmission of video and audio from a mobile newsgathering vehicle to a central receive point.

A subcarrier is a sideband of a radio frequency carrier wave, which is modulated to send additional information. Examples include the provision of colour in a black and white television system or the provision of stereo in a monophonic radio broadcast. There is no physical difference between a carrier and a subcarrier; the "sub" implies that it has been derived from a carrier, which has been amplitude modulated by a steady signal and has a constant frequency relation to it.

Single-frequency network

A single-frequency network or SFN is a broadcast network where several transmitters simultaneously send the same signal over the same frequency channel.

Orthogonal frequency-division multiple access multi-user version of OFDM digital modulation

Orthogonal frequency-division multiple access (OFDMA) is a multi-user version of the popular orthogonal frequency-division multiplexing (OFDM) digital modulation scheme. Multiple access is achieved in OFDMA by assigning subsets of subcarriers to individual users. This allows simultaneous low-data-rate transmission from several users.

Multi-carrier code-division multiple access (MC-CDMA) is a multiple access scheme used in OFDM-based telecommunication systems, allowing the system to support multiple users at the same time over same frequency band.

In telecommunications, the term cyclic prefix refers to the prefixing of a symbol, with a repetition of the end. The receiver is typically configured to discard the cyclic prefix samples, but the cyclic prefix serves two purposes:

Single-carrier FDMA (SC-FDMA) is a frequency-division multiple access scheme. It is also called linearly precoded OFDMA (LP-OFDMA). Like other multiple access schemes, it deals with the assignment of multiple users to a shared communication resource. SC-FDMA can be interpreted as a linearly precoded OFDMA scheme, in the sense that it has an additional DFT processing step preceding the conventional OFDMA processing.

Carrier interferometry

Carrier Interferometry(CI) is a spread spectrum scheme designed to be used in an Orthogonal Frequency-Division Multiplexing (OFDM) communication system for multiplexing and multiple access, enabling the system to support multiple users at the same time over the same frequency band.

IEEE 802.11a-1999 or 802.11a was an amendment to the IEEE 802.11 wireless local network specifications that defined requirements for an orthogonal frequency division multiplexing (OFDM) communication system. It was originally designed to support wireless communication in the unlicensed national information infrastructure (U-NII) bands as regulated in the United States by the Code of Federal Regulations, Title 47, Section 15.407.

IEEE 802.11g-2003 or 802.11g is an amendment to the IEEE 802.11 specification that extended throughput to up to 54 Mbit/s using the same 2.4 GHz band as 802.11b. This specification under the marketing name of Wi-Fi has been implemented all over the world. The 802.11g protocol is now Clause 19 of the published IEEE 802.11-2007 standard, and Clause 19 of the published IEEE 802.11-2012 standard.

Underwater acoustic communication

Underwater acoustic communication is a technique of sending and receiving messages below water. There are several ways of employing such communication but the most common is by using hydrophones. Underwater communication is difficult due to factors such as multi-path propagation, time variations of the channel, small available bandwidth and strong signal attenuation, especially over long ranges. Compared to terrestrial communication, underwater communication has low data rates because it uses acoustic waves instead of electromagnetic waves.

Multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) is the dominant air interface for 4G and 5G broadband wireless communications. It combines multiple-input, multiple-output (MIMO) technology, which multiplies capacity by transmitting different signals over multiple antennas, and orthogonal frequency-division multiplexing (OFDM), which divides a radio channel into a large number of closely spaced subchannels to provide more reliable communications at high speeds. Research conducted during the mid-1990s showed that while MIMO can be used with other popular air interfaces such as time-division multiple access (TDMA) and code-division multiple access (CDMA), the combination of MIMO and OFDM is most practical at higher data rates.

Carrier frequency offset (CFO) is one of many non-ideal conditions that may affect in baseband receiver design. In designing a baseband receiver, we should notice not only the degradation invoked by non-ideal channel and noise, we should also regard RF and analog parts as the main consideration. Those non-idealities include sampling clock offset, IQ imbalance, power amplifier, phase noise and carrier frequency offset nonlinearity.

Non-orthogonal frequency-division multiplexing Method of encoding digital data on multiple carrier frequencies

Non-orthogonal frequency-division multiplexing (N-OFDM) is a method of encoding digital data on multiple carrier frequencies with non-orthogonal intervals between frequency of sub-carriers.


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Further reading