Replace one fast carrier by many slow ones. OFDM is how 802.11g, 802.11n, and every Wi-Fi generation since carry their data, and it is the key to surviving echoes.
1. DefinitionWhat is OFDM?
Orthogonal frequency-division multiplexing splits a channel into many narrow subcarriers. Each carries a few bits at a low symbol rate. “Orthogonal” means the subcarriers are spaced so that, at the centre of each one, every other subcarrier is exactly zero: they can overlap in frequency without interfering. A transmitter creates the whole signal with an inverse FFT, and a receiver separates it again with an FFT.
OFDM is a waveform, not a modulation. Each subcarrier still uses a modulation such as BPSK, QPSK or QAM. OFDM is the way the subcarriers are arranged and combined.
2. PurposeThe problem it solves
Inside a building a signal arrives by many paths, so echoes arrive a fraction of a microsecond late. On a single fast carrier the echoes smear into the next symbol. OFDM sends symbols that are long (3.2 microseconds) and adds a short copy at the front, the guard interval. An echo that arrives within it does no harm.
3. MechanismThe whole chain, with real numbers
Choose a data rate and follow the bits: the pipeline shows how many bits go in and out of every step for that rate, then the subcarriers, the bit-to-point mapping, the time signal and what an echo does.
5. MathematicsThe numbers behind it
- Subcarrier spacing = channel width / FFT size = 20 MHz / 64 = 312.5 kHz.
- Useful symbol time = 1 / spacing = 3.2 microseconds; guard interval 0.8 microseconds (a quarter of it); symbol interval 4 microseconds.
- Occupied bandwidth = 52 subcarriers x 312.5 kHz = 16.25 MHz inside the 20 MHz channel.
- Data rate = (data subcarriers x bits per subcarrier x coding rate) / symbol time. At 54 Mbit/s: 48 x 6 x 3/4 / 4 microseconds = 54 Mbit/s. At 6 Mbit/s: 48 x 1 x 1/2 / 4 microseconds = 6 Mbit/s.
- In 802.11n and 802.11ac the data subcarriers grow with channel width: 52 (20 MHz), 108 (40 MHz), 234 (80 MHz) and 468 (160 MHz). In 802.11ax and 802.11be symbols are four times longer (12.8 microseconds, 78.125 kHz spacing, a 256-point FFT in 20 MHz).
6. Real-world behaviourWhat OFDM means in practice
- Echo tolerance. A room whose echoes are longer than the guard interval causes inter-symbol interference, which is one reason very large open spaces can behave badly.
- Subcarriers fade separately. A reflection can cancel one part of the channel while leaving the rest fine, so a link can lose a few subcarriers and still work: this is why coding and interleaving matter.
- Sensitive to frequency errors. Orthogonality depends on both ends agreeing on frequency very precisely, which is one reason OFDM radios need good oscillators.
Practical validationProve it
- A spectrum analyser shows an OFDM 20 MHz signal as a flat-topped block about 16.25 MHz wide with sharp edges.
- In a capture, check the PHY type and data rate of frames (
wlan_radio.phy,wlan_radio.data_rate): OFDM frames use the 6 to 54 Mbit/s rates. - Question to answer: how would a longer guard interval change the rate, and when would it help?
Check your understandingQuick quiz
ReferencesSources and further reading
- IEEE Std 802.11-2020 (IEEE Xplore)
- IEEE 802.11 Working Group: standards timelines (approval and publication dates)
- IEEE 802.11 Working Group
Facts checked against IEEE Std 802.11-2020: clause 17 (Tables 17-4 and 17-5 for the data rates and timing, 17.3.5.9 for the pilots, Tables 17-11 to 17-15 for the constellation mappings), clause 18 (ERP-OFDM), and the HT and VHT subcarrier counts in Tables 19-6 and 21-5. The 802.11ax and 802.11be numbers follow from the same relationships (20 MHz / 256 = 78.125 kHz); they are not covered by the 2020 edition.