Field Guide · algorithm

Also known as: OFDM, orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) splits a high-rate data stream across many closely spaced, mutually orthogonal subcarriers, each carrying a slow QAM symbol, and generates them all at once with an inverse FFT.1 By turning one fast, multipath- sensitive channel into hundreds of slow, nearly flat ones, OFDM makes high data rates robust to echoes and reduces equalization to a single complex multiply per subcarrier.

IFFT CP OFDM symbol FFT cyclic prefix absorbs multipath → one-tap equalizer per subcarrier
OFDM builds a symbol from many orthogonal subcarriers with an IFFT; a cyclic prefix guard makes each subcarrier a flat channel the receiver corrects with one tap.

How it works

The subcarriers are spaced exactly at the reciprocal of the symbol duration, Δf = 1/T. At that spacing each subcarrier’s spectral peak falls on the nulls of all the others, so they overlap heavily yet do not interfere — the meaning of orthogonal. Modulating and summing hundreds of sinusoids sounds expensive, but the sum is an inverse discrete Fourier transform of the subcarrier symbols, so a single IFFT produces the time-domain OFDM symbol and an FFT recovers the symbols at the receiver. This is what made OFDM practical.

The second key idea is the cyclic prefix (CP): a copy of the tail of each symbol is prepended as a guard interval. As long as the channel’s echo spread (delay spread) is shorter than the CP, multipath copies of the previous symbol decay within the guard and never bleed into the FFT window, eliminating inter-symbol interference. The CP also makes the channel appear cyclic, so each subcarrier experiences a single complex gain — the receiver corrects it with one-tap equalization (divide by the measured channel coefficient, from pilot subcarriers) instead of a long time-domain equalizer.

In practice

OFDM’s weaknesses are a high peak-to-average power ratio (PAPR), which stresses power amplifiers, and sensitivity to carrier frequency offset and phase noise, which erode subcarrier orthogonality. Real systems dedicate some subcarriers to pilots for channel and frequency tracking, null the edges as guard bands, and combine OFDM with strong forward error correction — “coded OFDM.”

Relevance to SDR

OFDM is everywhere in modern wideband RF: Wi-Fi (802.11a/g/n/ac/ax), LTE and 5G NR downlinks, DVB-T/T2 digital TV, DAB digital radio, and DOCSIS 3.1 cable. Its multiple-access sibling, OFDMA, assigns subcarrier groups to different users. GopherTrunk’s land-mobile trunking targets (P25, DMR, NXDN, TETRA) are single-carrier narrowband systems and do not use OFDM, so the scanner has no OFDM demodulator. It is documented here as the dominant wideband modulation of the broader RF world and the reason FFT hardware is central to modern radios.

Sources

  1. Orthogonal frequency-division multiplexing — Wikipedia, for subcarrier orthogonality, the IFFT/FFT implementation, and the cyclic prefix. ↩

See also