Orthogonal Frequency Division Multiplexing

Orthogonal Frequency Division Multiplexing (OFDM) is special form of multi-carrier modulation, patented in 1970. It is particularly suited for transmission over a dispersive channel. (See further discussion of MCM over wireless channel.)

In a multipath channel, most conventional modulation techniques are sensitive to intersymbol interference unless the channel symbol rate is small compared to the delay spread of the channel. OFDM is significantly less sensitive to intersymbol interference, because a special set of signals is used to build the composite transmitted signal. The basic idea is that each bit occupies a frequency-time window which ensures little or no distortion of the waveform. In practice, it means that bits are transmitted in parallel over a number of frequency-nonselective channels. Applications of OFDM are found in

Digital Audio Broadcasting (DAB) and
Digital Video Broadcasting over the terrestrial network: Digital Terrestrial Television Broadcasting (DTTB). In the DTTB OFDM transmission standard, about 2,000 to 8,000 subcarriers are used.
UMTS. The UMTS Forum is selecting an appropriate radio solution for the third generation mobile standard, as a successor to GSM. OFDM is one of the five competing proposals.
Wireless LANs. OFDM is used in HIPERLAN Phase II, which supports 20 Mbit/s in propagation environments with delay spreads up to 1 msecond.

Figure: Signal spectrum of an OFDM signal, which consists of the spectra of many bits, in parallel. Rectangular pulses in time domain produce sinc-functions in frequency domain.

Above: signal spectrum as transmitted.
Below: as received in over a dispersive, time-invariant channel.

The effect of multipath scattering on OFDM differs from what happens to other forms of modulation. A qualitative description and mathematical description of OFDM is presented by Dusan Matic. Jean-Paul Linnartz reviews the effects of a Doppler spread and the associated rapid channel variations. Dusan Matic also studied the system design aspects of OFDM at mm-wavelengths.

Exercise

Consider two subcarrier signals, modulated with rectangular pulse shape of duration T. For which frequency offsets are the signals orthogonal? What is the effect of a mild channel dispersion on the orthogonality of the signals? Are the signals still orthogonal if the channel is changing rapidly?

Coded OFDM

Multi-Carrier Modulation on its own is not the solution to the problems of communication over unreliable multipath channels. The channel time dispersion will excessively attenuate some subcarriers such that the throughput on these sub-channels would be unacceptable small. Only if the joint signal of many subcarriers is processed appropriately, the diversity advantages of MCM can be exploited. The need for coding across subcarriers was addressed by Sari et al. warning against overly enthusiastic pursuit of MCM. The advantages of frequency-domain implementations of equalizers (using an FFT) should not be mistaken for an "inherent" diversity gain of OFDM, which may not exist.

Coding for wireless
Turbo coding for OFDM
Frequency Diversity

In an OFDM transmitter, blocks of k incoming bits are encoded into n channel bits. Before transmission, an n-point Inverse-FFT operation is performed. When the signals at the I-FFT output are transmitted sequentially, each of the n channel bits appears at a different (subcarrier) frequency. Such coding across subcarriers is necessary. If one subcarrier experiences deep fading, this leads to erasure of the bit on this subcarrier.

But of course coding across subcarriers is not the only mechanism that can be invoked to combat dispersion or to exploit diversity. Other possibilities are

Interleaving in frequency or time domain with coding in the other domain,
The use of different signal constellations at different frequencies, i.e., adapting the subcarrier bit rate to the channel state,
Signal spreading over various subcarriers, e.g., according to a linear matrix operation, as is proposed in Orthogonal Multi-Carrier Code Division Multiplexing.

If in a point-to-point MCM link, the receiver and the transmitter can cooperate by adaptively distributing of their power budget over the individual subcarriers. For instance, the signal-to-noise ratios selected according to Gallager's water-pouring theorem can (under certain conditions) be proved to be optimum. Efficient loading of the various subcarriers can for instance significantly enhance the performance of MCM over twisted pair telephone subscriber loops with crosstalk from other nearby copper pairs.

Implementational Aspects

Figure: OFDM transmitter using an (inverse) Fast Fourier Transform (FFT).

OFDM is not a constant-envelope modulation method. Therefore transmit power amplifiers must be highly linear.
OFDM receiver performance is very sensitive to phase noise.
Synchronization to an OFDM signal also requires frame synchronization, to support an FFT operation at the receiver.

Figure: Experimental OFDM transceiver at IMEC, Leuven.

Slides from IMEC tutorials: intro, turbo coding, turbo for OFDM

Single Frequency Networks

OFDM allows very efficient frequency reuse. Transmitters broadcasting the same program can use the same frequency in a Single Frequency Network.

Code Division Multiple Access

OFDM can be combined with CDMA transmission, e.g. in Multi-Carrier CDMA.

Channel Modeling

Many channel simulation models follow the narrowband model. Wideband channels are often simulated by extending the model assuming multiple time-delayed resolvable paths. This allows the simulation of the channel impulse response, including its stochastic behavior. To determine the performance of an multicarrier, OFDM or MC-CDMA system, another approach can be to model a set of fading subchannels. Considering a single subcarrier, the channel may be modelled as a narrowband fading channel, for instance with Rician or Rayleigh amplitude distributions. The collection of multiple subcarriers can be modelled as a set of mutually dependent fading channels. In such model, it is important to address correlation of the fading of various subchannels using the models of delay spread and coherence bandwidth. See a discussion of such model. Also: read about the discrete-frequency model for OFDM with Delay spread and Doppler.

Listen to an MP3 audio program about on OFDM, featuring Jeff Anderson (SONY), Geert Awater (Lucent), Helmut Boelsckei (Stanford U.) and Jean-Paul Linnartz (Philips).

SMIL
Synchronous
Multimedia

Animated audio tutorial on OFDM and MC-CDMA

JPL's Wireless Communication Reference Website

Chapter: Analog and Digital Transmission Section: Multi-Carrier Modulation