Orthogonal frequency division multiplexing

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OFDM ( Orthogonal Frequency Division Multiplexing , German Orthogonal Frequency Division Multiplexing ) is a special implementation of the multi-carrier modulation. A modulation method that uses several orthogonal carriers for digital data transmission. The method is thus a special form of FDM , in which the orthogonality of the carriers (i.e. the maximum of a carrier is on a zero crossing in its neighboring carriers ) reduces crosstalk between signals that are modulated onto neighboring carriers.

The useful information to be transmitted with a high data rate is first divided into several partial data streams with a low data rate. These partial data streams are each modulated individually with a conventional modulation method such as quadrature amplitude modulation with a narrow bandwidth and then the modulated RF signals are added. In order to be able to differentiate between the individual signals during demodulation in the receiver, it is necessary that the carriers in the function space are orthogonal to one another. This has the effect that the partial data streams influence each other as little as possible.

The advantage of OFDM is that it allows the data transmission to be easily adapted to the specifics of a transmission channel , such as a radio channel , through fine granulation. If there is a narrowband interference within the OFDM signal spectrum, carriers affected by the interference can be excluded from the data transmission. The overall data transfer rate is only reduced by a small fraction. In the case of broadband quadrature amplitude modulation with only one carrier, on the other hand, narrowband interference in the transmission channel can make complete data transmission impossible. Destructive interference from multipath reception also only affects individual carriers.

OFDM signal with four carriers in the frequency domain. The individual carriers are shown in different colors.

Modulation method

A symbol in OFDM with four carrier frequencies in the time domain

Each carrier is first modulated separately. Depending on which of the three free parameters frequency, amplitude and phase are used for this, it carries information of one or more bits per symbol step . With DAB 1 bit, with DVB-T 2, 4 or 6 bits and with DVB-T2 up to 8 bits are transmitted per symbol and carrier .

In OFDM, the signal profile of a symbol is made up of the sum of all modulated carriers. With OFDM, a very large number of bits are thus transmitted in parallel. If, for example, as in practical applications, around 7000 carriers are used and four bits are transmitted per carrier, a symbol has an information content of a maximum of 28,000 bits, which are transmitted in parallel in one symbol step. In practice, the number of bits is somewhat lower, as some carrier frequencies are used for synchronization, as a pilot tone and for operation. The channel coding for forward error correction also reduces the amount of user data.

In accordance with the small spectral distance between the carrier frequencies, modulation is carried out with only a small bandwidth . Therefore, the symbol duration with OFDM is much longer compared to single carrier methods. With a total bandwidth of 8 MHz and 7000 carrier frequencies, a symbol duration of 875 µs results as a rough guide, which corresponds to a symbol rate of 1143  baud . The maximum bit rate that can be achieved is around 32 Mbit / s. Various other parameters, such as the maximum delay spread for multi-path reception, must be taken into account for precise interpretation .

OFDM modulator

OFDM signals are generated with the complex computing inverse discrete Fourier transform ( IDFT ). The IDFT assumes that all subcarrier frequencies are orthogonal to one another. The block length of the IDFT corresponds to the number of subcarriers. IDFT can be implemented entirely in digital technology with digital signal processors , so that the high-frequency part of the circuit remains relatively simple.

Orthogonality exists if and only if:


OFDM demodulator

On the receiver side, the individual carriers must be separated from the composite signal. This could be done with individual filters, but if there are more than a handful of frequencies this becomes too expensive. Therefore, a fast Fourier transformation ( FFT ) is used in all OFDM decoders today, which reverses the IFFT at the transmitter. The input data of the FFT are the digitized values ​​of the signal from an analog-to-digital converter (ADC).

Synchronization to the received signal is problematic and time-consuming with an OFDM receiver, since the receiver does not have a direct supply of the transmission clock. Usually several synchronization levels run one after the other. First, the sample clock of the ADC and the frequency of the HF carrier must be adjusted so that all carriers fall exactly on the FFT frequencies (corresponds to a stretching / compression and shifting of the spectrum). Due to the presence of many echoes, there is a point in time when the impulse response has the greatest energy. From this point in time, conclusions can be drawn about the time span in which echoes are received and successive symbols are superimposed. It is found using certain reference symbols or pilot carriers with an auto-correlation. Finally, the phase reference required for quadrature amplitude modulation (QAM) must be extracted (so-called channel estimation ).

Depending on the OFDM method, various additional signals support this synchronization. With digital audio broadcasting (DAB), no energy at all is transmitted for one symbol (zero symbol) and then a so-called phase reference symbol for exact frequency and time synchronization. DVB-T uses a pattern of pilot tones that systematically migrates across the carriers . These pilot tones can be used to determine the phase change over frequency and time.


Coded Orthogonal Frequency-Division Multiplexing (COFDM) is a transmission method for digital information that supplements the OFDM modulation method with forward error correction within the symbol.

The strengths of COFDM lie in its resistance to general, disruptive multi-path reception and its echoes and the resulting possibility of being able to operate several spatially adjacent transmitters on the same transmission frequency as a so-called single frequency network . It is also suitable for mobile reception of signals transmitted with it.

COFDM as a transmission method is used in particular by Digital Audio Broadcasting (DAB), Digital Radio Mondiale (DRM) and the European digital television standard DVB-T .

By the simulcast or when multipath reception occurs to a symbol within the time constructive and destructive interference , resulting in the extinction or enhancement of individual carriers. However, since very many carrier frequencies are available in parallel within the channel and interferences are frequency-selective, only individual carriers are actually canceled or amplified at certain spatial reception points.

With OFDM there are basically the same physical problems as with single-carrier methods, but these disruptive influences of the interference can be greatly reduced by two methods, since the symbol duration with OFDM is much longer than single-carrier methods.

In addition to forward error correction through channel coding , the information to be transmitted is redundantly distributed over several carrier frequencies with COFDM. As a result, the COFDM receiver can reconstruct the correct user data information even if individual carrier frequencies are deleted by interference, and single-frequency transmitter operation with overlapping zones of the individual transmitters is possible.

A guard interval ensures that a "quiet time" is observed between two transmitted symbols so that consecutive symbols do not cross- talk . Typical protection times are between 1/32 symbol duration and 1/4 symbol duration. The length of the guard interval determines the possible intersymbol interference-free distance difference to the transmitters. With a rest time of 33 µs, distance differences of ten kilometers or more interfere, which allows transmitter distances of around 20 km, because extinction requires similar field strengths.


With Orthogonal Frequency Division Multiple Access (OFDMA), the OFDM subcarriers are distributed to more than one user channel. The prerequisite for the procedure is bidirectional radio communication, in which, in contrast to unidirectional communication, the channel can be measured. The transmitter is aware of the reception quality of the subcarriers for the individual users through continuous measurement. Based on this knowledge, he can optimize the use of the subcarriers and thus the spectral efficiency.

Application examples

The following table summarizes the typical key data of some OFDM or COFDM-based systems:

Transmission standard DAB , Eureka 147 DVB-T DVB-H T-DMB IEEE 802.11a LTE
Year of development 1995 1997 2004 2006 1999 2006
Frequency range
470 - 862
174 - 230
470-862 470-862 4915-5825 700, 800, 900, 1800, 2100, 2600 and much more
Bandwidth B
1.712 8, 7, 6 8, 7, 6 & 5 8th 20th 1.4, 3, 5, 10, 15, 20
Number of carriers N 192, 384, 768 or 1536 2K mode: 1705
8K mode: 6817
1705, 3409, 6817 1 (single beam)
3780 (multiple beam)
48 (+4 pilots) 72, 180, 300, 600, 900, 1200
Carrier modulation DQPSK QPSK (= 4-QAM), 16-QAM or 64-QAM QPSK, 16-QAM, or 64-QAM QPSK, 16-QAM, 32-QAM, or 64-QAM. BPSK, QPSK, 16-QAM or 64-QAM QPSK, 16-QAM, 64-QAM, or 256-QAM
Typical symbol length T S
2K mode: 224
8K mode: 896
224, 448, 896 500 (multiple carriers) 3.2 66.67
Guard interval T G
(part of T S )
1/4, 1/8, 1/16, 1/32 1/4, 1/8, 1/16, 1/32 1/4, 1/6, 1/9 1/4 1/14 (~ 4.76µs), 1/4 (16µs)
Carrier spacing
Δf = 1 / ( T S ) ≈ B / N
2K mode: 4464
8K mode: 1116
4464, 2232, 1116 8 M (single beam)
2000 (multiple beam)
312.5k 15000
User data rates R
( Mbit / s)
0.576-1.152 4.98 - 31.67
(typical 24)
3.7-23.8 4.81-32.49 6 - 54 3 - 300
Spectral efficiency R / B
(bit / s / Hz)
0.34-0.67 0.62-4.0 0.62-4.0 0.60-4.1 0.30-2.7
Inner FEC Convolutional code with code rates

1/4, 3/8 or 1/2

Convolutional code with code rates

1/2, 2/3, 3/4, 5/6 or 7/8

Convolutional code 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

Convolutional code with code rates

1/2, 2/3 or 3/4

External FEC None RS (204,188, t = 8) RS (204,188, t = 8) + MPE-FEC BCH code (762,752)
Maximum relative speeds
(km / h)
200-600 53 - 185 depending on
Interleaving depth
385 0.6-3.5 0.6-3.5 200-500


OFDM also stands for Optical Frequency Division Multiplexing , which is a synonymous term for wavelength division multiplexing . The term “Optical Frequency-Division Multiplexing” emphasizes, however, that this optical technology is a frequency multiplexing technology known from electrical communications engineering.


  • Khaled Fazel, Stefan Kaiser: Multi-Carrier and Spread Spectrum Systems. From OFDM and MC-CDMA to LTE and WiMAX. 2nd Edition. John Wiley & Sons, New York NY 2008, ISBN 978-0-470-99821-2 .
  • Ralph Spitschka: Synchronization Algorithms for OFDM Systems. Using the example of WLAN. VDM Verlag Dr. Müller, Saarbrücken 2008, ISBN 978-3-639-07596-0 .

Individual evidence

  1. ^ Long-Term Evolution (LTE): The vision beyond 3G , Nortel

Web links

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