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What is OFDM (orthogonal frequency-division multiplexing)?

A scheme that splits data across many mutually orthogonal subcarriers, modulates each at a low symbol rate and sends them in parallel. Setting the subcarrier spacing to the reciprocal of the symbol length lets the subcarriers be separated without interfering even though their spectra overlap. It is robust against multipath and is used in wireless LANs, 4G LTE, 5G NR, digital terrestrial broadcasting and more.

Japanese name: OFDM(直交周波数分割多重)

OFDM (orthogonal frequency-division multiplexing) appears in 9 practice questions across 1 topic, including Wireless Communication Basics.

Field: Wireless Communication Basics

What orthogonal means

In OFDM the subcarrier spacing Δf is set to the reciprocal of the symbol length T (Δf = 1/T). Every subcarrier then oscillates exactly an integer number of times within one symbol, so multiplying two different subcarriers and summing over one symbol gives zero. This is what orthogonal means, and it lets the receiver extract each subcarrier's component even though the spectra of neighboring subcarriers overlap. Compared with conventional frequency-division multiplexing, which leaves gaps (guard bands) between carriers, the spectrum is used more efficiently.

Implementation with the FFT and the cyclic prefix

Instead of generating each subcarrier with its own oscillator, the transmitter modulates them all at once with an inverse fast Fourier transform (IFFT) and the receiver demodulates them with a fast Fourier transform (FFT). The ability to do this computation efficiently in digital circuits is one reason OFDM spread. In addition, a cyclic prefix (CP), made by copying the end of each symbol to its beginning, prevents intersymbol interference from waves that arrive late via multipath and preserves orthogonality.

Weaknesses and countermeasures

An OFDM signal is the sum of many subcarriers, so its peak-to-average power ratio (PAPR) is large; the power amplifier must be used in its linear region, which tends to lower efficiency. Frequency offsets (oscillator errors or Doppler shift) and phase noise also break the orthogonality between subcarriers and cause interference. For these reasons, mobile uplinks use DFT-spread OFDM with lower PAPR, and higher frequency bands use wider subcarrier spacing.

Try it: questions about OFDM (orthogonal frequency-division multiplexing)

Which describes OFDM (orthogonal frequency-division multiplexing)?

  1. AA scheme that splits data across many mutually orthogonal subcarriers sent in parallel; by setting the subcarrier spacing to the reciprocal of the symbol length, the subcarriers can be separated without interfering even though their spectra overlap
  2. BA scheme that modulates a single carrier at a high symbol rate, which is resistant to multipath delay because the symbols are short
  3. CA scheme in which each user's signal is multiplied by a different spreading code and sent at the same time on the same frequency
Show answer and explanation

Answer: A. A scheme that splits data across many mutually orthogonal subcarriers sent in parallel; by setting the subcarrier spacing to the reciprocal of the symbol length, the subcarriers can be separated without interfering even though their spectra overlap

OFDM splits the data across many subcarriers, modulates each at a low symbol rate and sends them in parallel. When the subcarrier spacing is the reciprocal of the symbol length, the subcarriers are mutually orthogonal even though their spectra overlap, so the receiver can separate them and the spectrum is used efficiently. Because each subcarrier's symbols are long, the scheme is resistant to multipath delay. Processing is done efficiently with an inverse fast Fourier transform (IFFT) at the transmitter and a fast Fourier transform (FFT) at the receiver, and OFDM is used in wireless LANs, 4G LTE, 5G NR, digital terrestrial broadcasting and more.

In OFDM, which is the main purpose of the cyclic prefix (CP), formed by copying part of the end of each symbol to its beginning?

  1. ATo lower the ratio of peak to average power (PAPR) of the transmitted signal and raise the efficiency of the power amplifier
  2. BTo repeat data at the start of the symbol so that errors can be detected instead of using error-correcting codes
  3. CTo absorb interference from the previous symbol caused by multipath waves that arrive late, and to preserve the orthogonality between subcarriers
Show answer and explanation

Answer: C. To absorb interference from the previous symbol caused by multipath waves that arrive late, and to preserve the orthogonality between subcarriers

Waves that arrive late via multipath overlap the end of the previous symbol onto the start of the next (intersymbol interference). If the CP is longer than the spread of delays (delay spread), this overlap stays within the CP, and the interference is removed when the receiver discards the CP before processing. In addition, because the CP is a copy of the end of the symbol, late-arriving waves also look periodic within the interval processed by the FFT, so orthogonality between subcarriers is preserved. In exchange, the CP adds time during which no data is sent, lowering transmission efficiency.

FAQ

How do OFDM and OFDMA differ?

OFDM is a modulation and multiplexing scheme that sends data on many subcarriers. OFDMA is a multiple-access scheme that assigns OFDM subcarriers, in units divided by time and frequency, to different users so that several users communicate at once. OFDMA is used in the 4G LTE downlink, in 5G NR and in wireless LANs from IEEE 802.11ax onward.

Why is it robust against multipath?

Because the data is split across many subcarriers, each subcarrier's symbols are long, so the delay of late-arriving waves is small compared with a symbol. The delay can also be absorbed within the cyclic prefix. Even with frequency-selective fading, in which received power drops at certain frequencies, only some subcarriers are affected, and error-correcting codes can make up for them.

OFDM (orthogonal frequency-division multiplexing) in the explanations

Questions that mention OFDM (orthogonal frequency-division multiplexing) (9)

  1. Which describes OFDM (orthogonal frequency-division multiplexing)?
  2. In OFDM, which is the main purpose of the cyclic prefix (CP), formed by copying part of the end of each symbol to its beginning?
  3. In OFDM, the symbol length excluding the CP is the reciprocal of the subcarrier spacing. When the subcarrier spacing is widened from 15 kHz to 60 kHz, which is closest to the symbol length excluding the CP?
  4. Which is the most appropriate main reason that the 4G LTE uplink (transmission from terminal to base station) adopted SC-FDMA (DFT-spread OFDM) rather than the OFDMA used in the downlink?
  5. In a transmitter sending OFDM or multilevel QAM signals, which is the main reason for operating the power amplifier (PA) at a point below where its output saturates (with back-off)?
  6. In radio communication, which is the phenomenon in which waves reflected by buildings and other objects arrive late because of differing path lengths, interfere with the directly arriving wave, and cause the received power to drop sharply at certain locations or frequencies?
  7. A terminal receiving a 2 GHz radio wave is approaching the base station at 30 m/s (108 km/h). Taking the speed of light as 3×10⁸ m/s, which is closest to the magnitude of the frequency shift (Doppler shift) of the wave received by the terminal?
  8. Which multiple-access scheme lets several users use the same frequency at the same time and distinguishes their signals by a different code for each user?
  9. Which describes OFDMA (orthogonal frequency-division multiple access)?

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Related terms

Fast Fourier transform (FFT) Discrete Fourier transform QAM (quadrature amplitude modulation) Fading Beamforming Bluetooth Low Energy (BLE) Direct-conversion receiver Free-space path loss (FSPL) Hidden node problem Link budget

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