Orthogonal frequency division multiplexing
OFDM ( Orthogonal Frequency Division Multiplexing , German Orthogonal Frequency Division Multiplexing ) is a special implementation of the multicarrier 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.
Modulation method
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 DVBT 2, 4 or 6 bits and with DVBT2 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 multipath reception, must be taken into account for precise interpretation .
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 highfrequency part of the circuit remains relatively simple.
Orthogonality exists if and only if:
reception
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 analogtodigital converter (ADC).
Synchronization to the received signal is problematic and timeconsuming 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 autocorrelation. Finally, the phase reference required for quadrature amplitude modulation (QAM) must be extracted (socalled 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 socalled phase reference symbol for exact frequency and time synchronization. DVBT 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.
COFDM
Coded Orthogonal FrequencyDivision 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 multipath reception and its echoes and the resulting possibility of being able to operate several spatially adjacent transmitters on the same transmission frequency as a socalled 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 DVBT .
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 frequencyselective, only individual carriers are actually canceled or amplified at certain spatial reception points.
With OFDM there are basically the same physical problems as with singlecarrier 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 singlecarrier 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 singlefrequency 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 interferencefree 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.
OFDMA
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
 Digital Audio Broadcasting (DAB) with 192 to 1536 carriers (on approx. 1.5 MHz bandwidth)
 Digital Radio Mondiale (DRM) with 88 to 460 carriers (on approx. 4 to 20 kHz bandwidth)
 DVBC with DOCSIS 3.1
 DVBT with 2048, 4096, or 8192 carriers  depending on the mode 2k, 4k (only with DVBH) or 8k (on approx. 6.5 to 7.5 MHz bandwidth)
 WLAN according to IEEE 802.11a , IEEE 802.11g and IEEE 802.11n
 ADSL (Asymmetric Digital Subscriber Line) with 32 carriers for the upstream and 190 for the downstream (each 4.3125 kHz over approx. 1 MHz bandwidth; see also DMT )
 VDSL
 Powerline z. B. Homeplug AV
 G.fast
 LTE (Long Term Evolution)
 WiMAX according to IEEE 802.16.22004 for NLOS connections with 256 carriers (recommended by the WiMAX forum) or 2048 carriers
 C WUSB , Bluetooth 3.0 and WiNet , all of which are based on the ECMA368 standard
The following table summarizes the typical key data of some OFDM or COFDMbased systems:
Transmission standard  DAB , Eureka 147  DVBT  DVBH  TDMB  IEEE 802.11a  LTE 

Year of development  1995  1997  2004  2006  1999  2006 
Frequency range (MHz) 
174240 14521492 
470  862 174  230 
470862  470862  49155825  700, 800, 900, 1800, 2100, 2600 and much more 
Bandwidth B (MHz) 
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 (= 4QAM), 16QAM or 64QAM  QPSK, 16QAM, or 64QAM  QPSK, 16QAM, 32QAM, or 64QAM.  BPSK, QPSK, 16QAM or 64QAM  QPSK, 16QAM, 64QAM, or 256QAM 
Typical symbol length T _{S} (μs) 
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 (Hz) 
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) 
0.5761.152  4.98  31.67 (typical 24) 
3.723.8  4.8132.49  6  54  3  300 
Spectral efficiency R / B (bit / s / Hz) 
0.340.67  0.624.0  0.624.0  0.604.1  0.302.7  
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) + MPEFEC  BCH code (762,752)  
Maximum relative speeds (km / h) 
200600  53  185 depending on frequency 
350  
Interleaving depth (ms) 
385  0.63.5  0.63.5  200500 
Others
OFDM also stands for Optical Frequency Division Multiplexing , which is a synonymous term for wavelength division multiplexing . The term “Optical FrequencyDivision Multiplexing” emphasizes, however, that this optical technology is a frequency multiplexing technology known from electrical communications engineering.
literature
 Khaled Fazel, Stefan Kaiser: MultiCarrier and Spread Spectrum Systems. From OFDM and MCCDMA to LTE and WiMAX. 2nd Edition. John Wiley & Sons, New York NY 2008, ISBN 9780470998212 .
 Ralph Spitschka: Synchronization Algorithms for OFDM Systems. Using the example of WLAN. VDM Verlag Dr. Müller, Saarbrücken 2008, ISBN 9783639075960 .