Orthogonal Frequency-Division Multiplexing (OFDM)

OFDM and frequency-selective channels

In single-carrier transmission, a wideband signal can be affected by frequency-selective fading. Multipath propagation can attenuate some frequency components more than others, which distorts the received waveform and can affect the whole signal band.

OFDM divides the band into many narrower, mutually orthogonal subcarriers. Each subcarrier carries a portion of the data, so the receiver can estimate and equalize their channel responses separately. Coding and interleaving can limit the effect of subcarriers that experience deep attenuation, which makes the waveform useful in multipath channels.

Orthogonality and spectral efficiency

Traditional multi-channel systems, such as FDM or WDM, can separate adjacent channels with unused spectral gaps called guard bands. The gaps reduce interference caused by filter roll-off and frequency or wavelength errors, but they also reduce spectral efficiency.

OFDM achieves high spectral efficiency by allowing the spectra of its subcarriers to overlap. The key to separating them is orthogonality.

Each rectangularly windowed subcarrier has a spectrum shaped like a $sinc(x)$ function. With spacing $\Delta f = 1/T_u$, the peak of one subcarrier coincides with nulls of the others at the ideal demodulation frequencies. The receiver can therefore recover one subcarrier while the overlapping spectra contribute zero correlation over the useful interval. This arrangement enables denser packing and higher spectral efficiency.

OFDM signal in frequency and time

Creating and interpreting an OFDM signal involves two related domains:

• In the frequency domain: An OFDM signal is defined by placing modulation symbols on individual subcarriers. Each subcarrier can use a digital scheme such as QPSK or 16-QAM; the selected symbol determines its amplitude and phase.
• In the time domain: The transmitted signal is the sum of the individually modulated subcarriers, represented by complex baseband samples or by their sine and cosine components after upconversion. The result can have a noise-like envelope. The relationship between the domains is implemented with the inverse FFT at the transmitter and the FFT at the receiver, using the Fast Fourier Transform (FFT).

A cyclic prefix (CP) copies the end of the useful time-domain symbol to its beginning. If its duration $T_{CP}$ covers the relevant maximum excess delay of the channel, the receiver can discard the CP and apply the FFT over the useful interval $T_u$. The total symbol interval is $T_s = T_u + T_{CP}$, so the CP adds overhead and does not remove the need for synchronization. For an evenly spaced $N$-point grid sampled at $F_s$ samples per second, $\Delta f = F_s/N = 1/T_u$; thus $F_s$ is expressed in samples per second, $T_u$ in seconds, and $\Delta f$ in hertz.

Modulation order, rate, and reach

Different modulation formats can be applied to OFDM subcarriers. A higher modulation order increases the number of bits per symbol but requires a higher SNR for a given target error rate and coding scheme. This can reduce reach under the same transmit power and channel conditions, but it does not produce a fixed reduction factor.

Actual reach also depends on symbol rate, occupied bandwidth, power, channel properties, FEC, target error rate, and DSP algorithms. Bits per symbol alone are therefore insufficient to determine a maximum link length.

OFDM applications

OFDM and related waveforms are used in communication systems that benefit from narrow subcarriers and frequency-domain equalization:

• Wireline access: ADSL and VDSL use Discrete Multitone (DMT), an OFDM-based multicarrier scheme; Power-Line Communication (PLC) systems also use OFDM variants.
• Wireless LAN: Wi-Fi standards including 802.11a, g, n, ac, and ax (Wi-Fi 6) include OFDM-based physical layers.
• Cellular networks: LTE uses OFDMA in the downlink and the OFDM-derived SC-FDMA waveform in the uplink. 5G NR specifies CP-OFDM and also supports DFT-s-OFDM for selected uplink transmissions.
• Digital broadcasting: Terrestrial digital television systems such as DVB-T/T2 and ATSC 3.0, as well as digital radio such as DAB, use OFDM-based waveforms.
• Elastic optical networks (EON): OFDM-based superchannels can allocate a selected number of subcarriers and vary their occupied bandwidth with the requested data rate. The resulting allocation can improve utilization of the optical-fiber spectrum, subject to implementation limits.