Orthogonal frequency-division multiplexing


In telecommunications, orthogonal frequency-division multiplexing is a type of digital transmission used in digital modulation for 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/5G mobile communications.
OFDM is a frequency-division multiplexing scheme that was introduced by Robert W. Chang of Bell Labs in 1966. 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. 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. Each subcarrier is modulated with a conventional modulation scheme at a low symbol rate. This maintains total data rates similar to conventional single-carrier modulation schemes in the same bandwidth.
The main advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions 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 and use echoes and time-spreading to achieve a diversity gain, i.e. a signal-to-noise ratio improvement. This mechanism also facilitates the design of single frequency networks 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.
In coded orthogonal frequency-division multiplexing, forward error correction 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 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.

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

The OFDM-based multiple access technology OFDMA is also used in several 4G and pre-4G cellular networks, mobile broadband standards, the next generation WLAN and the wired portion of Hybrid fiber-coaxial networks:
The advantages and disadvantages listed below are further discussed in the [|Characteristics and principles of operation] section below.

Summary of advantages

  • High spectral efficiency as compared to other double sideband modulation schemes, spread spectrum, etc.
  • Can easily adapt to severe channel conditions without complex time-domain equalization.
  • Robust against narrow-band co-channel interference
  • Robust against intersymbol interference and fading caused by multipath propagation
  • Efficient implementation using fast Fourier transform
  • Low sensitivity to time synchronization errors
  • Tuned sub-channel receiver filters are not required
  • Facilitates single frequency networks

    Summary of disadvantages

  • Sensitive to Doppler shift
  • Sensitive to frequency synchronization problems
  • High peak-to-average-power ratio, requiring linear transmitter circuitry, which suffers from poor power efficiency
  • Loss of efficiency caused by cyclic prefix/guard interval

    Characteristics and principles of operation

Orthogonality

In OFDM, the subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other, meaning that crosstalk 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, 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.
The orthogonality also allows high spectral efficiency, with a total symbol rate near the Nyquist rate for the equivalent baseband 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.
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 . 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, 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. For example, a low-complexity scheme referred to as WCP-OFDM 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. Other ICI suppression techniques usually drastically increase the receiver complexity.

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 has to take less than the time for each symbol, which for example for DVB-T means the computation has to be done in or less.
For an -point FFT this may be approximated to:
The computational demand approximately scales linearly with FFT size so a double size FFT needs double the amount of time and vice versa. As a comparison an Intel Pentium III CPU at 1.266 GHz is able to calculate a FFT in using FFTW. Intel Pentium M at 1.6 GHz does it in Intel Core Duo at 3.0 GHz does it in.

Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes 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.
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.