OFDM: Why WiFi Splits Data Across Hundreds of Subcarriers

Splitting one fast stream into many slow ones

Sending data as one very fast serial stream over a radio channel runs into a hard physical problem: real-world radio paths reflect off buildings, walls and terrain, so a receiver sees several delayed copies of the same signal (multipath). If a symbol is shorter than the delay spread between the earliest and latest copy, one symbol's echo smears into the next — inter-symbol interference (ISI) — and the error rate climbs fast as data rate rises.

OFDM (Orthogonal Frequency-Division Multiplexing) sidesteps this by splitting one fast data stream across N much slower parallel streams, each modulated onto its own subcarrier. Splitting into N streams stretches each symbol's duration by roughly a factor of N, so the same multipath delay spread that was catastrophic for one fast stream becomes a small fraction of one OFDM symbol's much longer duration — the fix is entirely in the time-frequency trade, not in eliminating multipath.

Orthogonality: why the subcarriers don't interfere

The subcarriers are spaced at exactly Δf = 1/T, where T is the useful symbol duration, and packed as tightly as physically possible while still being separable — this spacing is what makes OFDM spectrally efficient compared with older frequency-division schemes that needed guard bands between channels. At that exact spacing, every subcarrier's frequency sits precisely on the zero crossing of every other subcarrier's sinc-shaped spectrum, so when the receiver samples at the correct instant, the interference from all the other subcarriers is exactly zero even though their spectra visibly overlap:

subcarrier k:  s_k(t) = exp( j·2π·k·Δf·t ),   Δf = 1/T
∫₀ᵀ s_k(t)·s_m*(t) dt = 0    for k ≠ m     — orthogonality integral

Generating and demodulating dozens or hundreds of these subcarriers one at a time would be expensive; instead OFDM assembles a whole symbol's worth of subcarrier data in the frequency domain and runs a single Inverse Fast Fourier Transform (IFFT) to produce the time-domain waveform to transmit, and the receiver runs an FFT to recover the per-subcarrier data — the FFT/IFFT pair is exactly the machinery that makes hundreds of parallel orthogonal carriers computationally cheap, and is the reason OFDM only became practical once digital signal processors got fast enough to run it in real time.

The cyclic prefix: trading a little bandwidth for total ISI immunity

Stretching the symbol helps, but any nonzero multipath delay still smears a little energy from one OFDM symbol into the next at the boundary. The fix is the cyclic prefix (CP): before transmitting, copy the last portion of the time-domain symbol and prepend it to the front. As long as the CP is longer than the channel's maximum delay spread, all multipath echoes of one symbol land entirely within either that symbol's own CP or its own body, never bleeding into the next symbol — and the receiver simply discards the CP before running the FFT.

The CP has a second, subtler purpose: because the copied prefix makes the transmitted waveform periodic over one symbol, a linear convolution with the channel's impulse response becomes mathematically equivalent to a circular convolution over that period. That is exactly the operation the FFT diagonalises, which is why a whole frequency-selective multipath channel collapses to a single complex multiplicative gain per subcarrier at the receiver, rather than a nasty per-sample convolution — one-tap equalisation, not a full deconvolution problem, is what makes OFDM receivers cheap.

Where it is used, and the price you pay

OFDM underlies WiFi (802.11a/g/n/ac/ax), 4G LTE, DVB-T digital television and ADSL/VDSL (as the closely related DMT). The CP is not free: in 802.11a/g it is 800 ns out of a 4 μs symbol, a 20% overhead in bandwidth and power purely to buy multipath immunity. OFDM's other well-known weakness is a high peak-to-average power ratio (PAPR) — summing many independently modulated subcarriers occasionally produces a large constructive spike, forcing power amplifiers to be run with extra headroom (back-off) and reducing efficiency, a major reason later standards like 5G's uplink favour PAPR-reduced variants such as SC-FDMA.

Frequently asked questions

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