OFDM(A) Transmission in 3D

Wi-Fi doesn't send one fast signal: it splits the channel into hundreds of narrow subcarriers and sends them all at once, one OFDM symbol after another. See how channel width, guard interval and modulation shape the transmission.

Standard
Channel width
Guard interval
Modulation

The transmission: time, frequency and amplitude

Time runs to the right and frequency into the page. Each rounded lobe is one subcarrier during one OFDM symbol, drawn with the shape of its spectrum: its height is the amplitude and its colour the phase it carries. Neighbouring lobes overlap, each peaking where the others fall to zero. The flat orange strips are the guard intervals between symbols. Drag to turn the view; drag with the middle mouse button to move it.

View
Data subcarriers, coloured by phase Pilots Guard interval Transmitting now Echo inside the guard interval (harmless) Echo spilling into the next symbol (ISI)

To zoom the picture, click the view and scroll (or pinch, or Ctrl + scroll). Drag with the middle mouse button to move it; in top view a normal drag moves it too.

Echoes and intersymbol interference

Indoors and out, a reflection arrives a little after the direct signal: an echo. If the echo of one symbol is over before the guard interval ends, the receiver never hears it, because it only starts listening after the guard interval. If the echo lasts longer, the end of one symbol spills into the next. That's intersymbol interference (ISI).

Echo delay
Echo strength

What the receiver decodes from the last four symbols (dots), against the ideal points (rings), after it has corrected each subcarrier for the echo.

One symbol in time

What the antenna actually sends during the current symbol: all the subcarriers added together. A few individual subcarriers are drawn faintly; each fits a whole number of cycles into the symbol.

Sum of all subcarriers (I) A few subcarriers Guard interval, a copy of the symbol's end

Subcarriers in frequency

Zoomed in on 13 subcarriers of the current symbol. Their spectra overlap, but each one peaks exactly where all the others are zero, so they don't interfere. That's what "orthogonal" means in OFDM.

Zoom to

The calculation, step by step

Notes

Why split the channel into subcarriers

One wide signal would need very short symbols, and indoor reflections arriving a fraction of a microsecond late would smear each symbol into the next. Hundreds of narrow subcarriers can each use a long symbol (3.2 µs, or 12.8 µs in Wi-Fi 6), so the same reflections are only a small fraction of it. See the Multipath Simulator.

The guard interval

Each symbol starts with a short copy of its own end, the cyclic prefix. Late reflections of the previous symbol land in this guard time and are thrown away, and because the prefix is a copy, every subcarrier still fits a whole number of cycles in what the receiver keeps. A longer guard interval copes with longer delays (large rooms, outdoors) but spends more time not carrying new data.

Channel width

Doubling the width a little more than doubles the data subcarriers (52 → 108 in Wi-Fi 4/5, 234 → 468 in Wi-Fi 6), because proportionally fewer are needed as unused guard subcarriers at the edges. The symbol time stays the same, so the data rate slightly more than doubles.

Pilots, DC and guard subcarriers

Pilots carry known values so the receiver can track small frequency and phase drift. The DC subcarriers in the middle are left empty because radios have trouble there. The guard subcarriers at each edge are empty so the signal doesn't spill into the neighbouring channel.

Wi-Fi 6 symbols

Wi-Fi 6 packs subcarriers four times closer (78.125 kHz instead of 312.5 kHz), so each symbol is four times longer: 12.8 µs. The guard intervals are longer too (0.8, 1.6 or 3.2 µs), but take a smaller share of each symbol. Wi-Fi 7 uses the same symbols.

About this view

In the 3D view the guard interval is drawn flat, as a pause between symbols. In reality it carries a copy of the end of the symbol, as the "One symbol in time" chart shows. Subcarriers are shown at baseband (centred on 0) and the data values are random. The animation runs about a million times slower than a real transmission. Data rates are for one spatial stream at the fastest coding rate for each modulation.