Inside Wi-Fi and 5G: OFDM and the Modern Wireless Link

The enemy: echoes that smear your symbols

Stand in a tiled bathroom and clap once: you hear not a single crack but a brief smear of echoes. Radio does exactly the same thing. The signal from a Wi-Fi router reaches your laptop directly, but copies also bounce off walls, the fridge, and the person walking past, each arriving a few nanoseconds later. Engineers call this multipath, and at high data rates it is lethal. If you transmit one symbol every 50 nanoseconds and a reflected copy lands 200 nanoseconds late, four old symbols are still arriving while the new one starts. They overlap and blur into mush — inter-symbol interference (ISI).

Earlier rungs in this track taught you to pack more bits per symbol using QAM, and to chase the Shannon limit with clever modulation. But there is a cruel tradeoff: the faster you send symbols, the shorter each one is, and the more devastating a fixed-length echo becomes. A single-carrier radio fights ISI with a heavy equalizer — a filter that tries to undo the channel's smearing. At Wi-Fi speeds that equalizer would need dozens of taps and brutal compute. There has to be a better way.

OFDM: a choir of orthogonal subcarriers

Orthogonal frequency-division multiplexing (OFDM) takes that high-rate bitstream and sprays it across hundreds of closely spaced subcarriers, each a narrow tone carrying its own slow QAM symbol. A 20 MHz Wi-Fi channel, for example, is sliced into 64 subcarriers spaced 312.5 kHz apart; 5G can stack thousands. Because each subcarrier is narrow, its symbols are long — microseconds rather than nanoseconds — so multipath echoes become a tiny nuisance instead of a catastrophe.

The magic word is orthogonal. The subcarriers are packed so tightly that each one's peak sits exactly on the zero-crossings of all its neighbors. They overlap in frequency yet never interfere — like singers whose voices blend in the air but can still be told apart. This is a refined kind of frequency-division multiplexing, but with zero guard bands wasted between channels, which is why OFDM is so spectrally efficient.

The last trick that makes OFDM bulletproof against echoes is the cyclic prefix (CP). Before transmitting each symbol, you copy a chunk from its tail and paste it onto the front as a guard interval. As long as every echo arrives within that guard window, the overlap falls harmlessly into the cyclic prefix and is simply discarded at the receiver. Even better, the copied prefix makes the channel look like a *circular* convolution, which turns equalization into something almost trivially cheap — one complex multiply per subcarrier, as we will see.

Time:  ...|  CP  |======= OFDM symbol N =======|  CP  |==== symbol N+1 ====|...
            ^copy of tail

Frequency (one 20 MHz Wi-Fi symbol, 64 subcarriers):

  |  |  |  |  |  |  |  |  |  |  |  |   <- each tone carries one QAM point
  +--+--+--+--+--+--+--+--+--+--+--+
  ^peak of one tone = zero of every other tone  (orthogonality)

  312.5 kHz spacing x 64 = 20 MHz channel

A full transceiver, block by block

Now let us assemble the whole machine — the modem (modulator/demodulator) at the heart of every Wi-Fi chip and phone. Follow one packet of your data from app to antenna and back. Each block is a topic from earlier rungs, finally snapping into place.

1. Source coding strips redundancy from your data (the video is already H.265-compressed) so the radio only sends information that matters.
2. Channel coding adds redundancy back, but the *smart* kind: an error-correcting code (FEC) like an LDPC code lets the receiver fix bit errors with no retransmission.
3. QAM mapping groups bits into constellation points — 4 bits per symbol for 16-QAM, 8 bits for 256-QAM — turning a bitstream into complex I/Q numbers.
4. OFDM (IFFT + cyclic prefix) loads those I/Q points onto subcarriers and synthesizes the time-domain waveform with one inverse FFT, then prepends the CP.
5. Upconversion mixes the baseband waveform up to the carrier (2.4/5/6 GHz for Wi-Fi, 3.5 GHz or 28 GHz for 5G); a power amplifier drives the antenna.
6. On the far side: downconversion, then a matched filter maximizes SNR per sample, FFT recovers each subcarrier, a one-tap equalizer corrects the channel, QAM demapping and FEC decoding rebuild your bits.

TRANSMITTER                                         RECEIVER

 bits                                                bits
  |  source coding                         FEC decode  ^
  v  (compress)                          (fix errors)  |
  +--> channel coding (FEC) --+        +-- QAM demap ---+
                              |        |
  +--> QAM map (I/Q) ---------+        +-- 1-tap equalize
                              |        |   (per subcarrier)
  +--> IFFT + cyclic prefix --+        +-- FFT ---------+
                              |        |
  +--> upconvert + PA --------+        +-- matched filter
                              |        |  + downconvert
                            ((( ~ ))) -------> ((( ~ )))
                            antenna   CHANNEL  antenna
                                  (multipath, noise, fading)

Pushing toward Shannon: MIMO and adaptive modulation

A basic OFDM link is good, but the Shannon limit says a channel with 30 dB of signal-to-noise can carry roughly 10 bits per second per hertz. Real radios reach for that ceiling with two more tricks. First, adaptive modulation and coding (AMC): the radio constantly measures channel quality and picks the densest scheme it can sustain — 256-QAM with light FEC when you sit beside the router, dropping to rugged QPSK with heavy FEC when you wander to the garden. Wi-Fi and 5G re-choose this hundreds of times a second.

Second, and even bigger: MIMO (multiple-input multiple-output). Put several antennas at each end, and the rich multipath that once was your enemy becomes your friend. Because each antenna pair sees a slightly different blend of echoes, the radio can solve a small linear system and send *several independent data streams in the same channel at the same time* — spatial multiplexing. Two antennas can roughly double capacity; the massive MIMO base stations in 5G run 64 or more, steering tight beams of energy straight at each phone.

Shannon:  C = B * log2(1 + SNR)

  B = 80 MHz Wi-Fi channel,  SNR = 1000 (30 dB)
  C = 80e6 * log2(1001) = 80e6 * 9.97 ~ 800 Mbit/s   (single stream)

  With 4x4 MIMO (4 spatial streams):  ~ 3.2 Gbit/s
  Add 256-QAM + LDPC near the Shannon edge -> Wi-Fi 6 multi-gigabit

Where the link is headed: from 5G to 6G

The same OFDM-plus-MIMO skeleton scales astonishingly far. DSL squeezes OFDM (there called DMT) down your copper phone line; LTE and 5G use it on licensed spectrum; Wi-Fi 6 and 7 push it to 320 MHz channels and 4096-QAM. The differences are mostly knobs: subcarrier spacing, frame timing, how aggressively you schedule users. 5G added OFDMA, where one OFDM symbol is split among many users at once — time-and-frequency multiplexing at fine grain — so a base station can serve a stadium of phones efficiently.

So where next? 6G research (targeting roughly 2030) reaches into the sub-terahertz bands above 100 GHz, where there is oceans of bandwidth but signals barely travel and are blocked by a raised hand. Taming that needs ultra-massive MIMO with hundreds of elements, and possibly reconfigurable intelligent surfaces — walls papered with tiny controllable reflectors that bend a beam around an obstacle. Expect AI-native air interfaces that learn the channel instead of assuming a textbook model, and integrated sensing and communication, where the same waveform that carries your data also images the room like radar.