OFDM belongs to the class of multicarrier modulation schemes. Because the operation can transmit multiple carriers simultaneously, noise does not influence OFDM to the same degree as single-carrier modulation.

OFDM operation divides a high-rate data stream into low-rate data substreams by decomposing the transmission frequency band into a number of contiguous individually modulated subcarriers. This set of parallel and orthogonal subcarriers carry the data stream occupying almost the same bandwidth as a wideband channel. By using narrow orthogonal subcarriers, the OFDM signal gains robustness over a frequency-selective fading channel and eliminates adjacent subcarrier interference. Intersymbol interference (ISI) is reduced because the lower data rate substreams have symbol durations larger than the channel delay spread.

This image shows a frequency domain representation of orthogonal subcarriers in an OFDM waveform.

The transmitter applies inverse fast Fourier transform (IFFT) to N symbols at a time. Typically, the output of the IFFT is the sum of the N orthogonal sinusoids:

x(t)=∑k=0N−1Xkej2πkΔft, 0≤t≤T,

where {Xk} are data symbols, and T is the OFDM symbol time. The data symbols Xk are typically complex and can be from any digital modulation alphabet (for example, QPSK, 16-QAM, 64-QAM, etc.).

Note

The MATLAB® implementation of the discrete Fourier transform normalizes the output of the IFFT by 1/N. For more information, see Discrete Fourier Transform of Vector on the ifft reference page.

The subcarrier spacing is Δf = 1/T, ensuring that the subcarriers are orthogonal over each symbol period:

1T∫0T(ej2πmΔft)*(ej2πnΔft) dt=1T∫0Tej2π(m−n)Δft dt=0 for m≠n.

An OFDM modulator consists of a serial-to-parallel conversion followed by a bank of N complex modulators, individually corresponding to each OFDM subcarrier.