Wifi Bandwidth - what am I missing?

[paulca]

So a normal Wifi channel is 20Mhz wide.  A higher rate channel is 40Mhz wide.

However the data rates supported on those channels (on 2.4Ghz) are 54Mbps and 108Mbps.

I missing something, but if memory serves me right, "bandwidth" is originally, literally that, the width of the band.  Now if I have a 20Mhz bandwidth, then surely my maximum data rate is 20Mhz/2 = 10Mbps.

What am I missing?

[IanB]

1 MHz ≠ 1 Mbps

[Paul Rose]

Nyquist formula in a noise free channel:

Rate = 2 * Bandwidth * log2( Number of Signal Levels )

There are lots of resources out there.  Here is one at random:

https://witestlab.poly.edu/blog/nyquist-formula-relating-data-rate-and-bandwidth/

[TK]

It is the modulation scheme (64 QAM for 802.11g) what gives you 54Mbps with WiFi.  802.11n / 802.11ac can do 256QAM modulation.  Cable Modem uses similar modulation schemes to achieve 1Gbps. 

[IDEngineer]

It is the modulation scheme (64 QAM for 802.11g) what gives you 54Mbps with WiFi.  802.11n / 802.11ac can do 256QAM modulation.  Cable Modem uses similar modulation schemes to achieve 1Gbps.

Exactly this. Modulation decouples you from a strict "bandwidth to bitrate" relationship. Spend a little time Googling modulation schemes - then think about how you'd craft a receiver to decode some of the dense constellation ones in real time. 

[radioactive]

For the 802.11g 54Mbps example,  you can imagine the 20 MHz being split up into 64 bins via the FFT algorithm.  This gives 64 channels (sub carriers) of 312.5 kHz wide.  Some of those carriers are nulled out for suppressing the band edges and also the DC null.   A few carriers (pilot carriers) do not contain modulation, but aid in detection, sync / phase reference, and amplitude equalization throughout the entire 20 MHz channel.  The remaining data carriers in the 54 Mbps case utilize 64 QAM for the modulation yielding 6 bits per symbol.  The 48 "data sub-carriers" end up providing 288 bits per OFDM symbol.  Some of those bits are used for forward error correction.  There is also a feature called cyclic prefix where some data from the previous OFDM symbol is appended to create a "guard" interval.  This helps prevent inter-symbol interference.   Pretty cool stuff to think about.  FFT is used on the receiver side and inverse FFT is used on the transmit side. 

If you are interested in reading about one of the first times someone really started thinking about how to do this before hardware could support it, refer to

Synthesis of Band‐Limited Orthogonal Signals for Multichannel Data Transmission
Robert W. Chang
https://archive.org/download/bstj45-10-1775/bstj45-10-1775.pdf

[Benta]

It's true that the channels are 20 MHz wide, but a contemporary WLAN connection spreads over several channels. The available channels are 1...13, but the connection allocations only works like like this:
802.11b: only use channels 1, 6, 11
802.11g/n: only use channels 1, 5, 9, 13

This also explains the congestion you often experience.

[macboy]

It's true that the channels are 20 MHz wide, but a contemporary WLAN connection spreads over several channels. The available channels are 1...13, but the connection allocations only works like like this:
802.11b: only use channels 1, 6, 11
802.11g/n: only use channels 1, 5, 9, 13

This also explains the congestion you often experience.

The 2.4 GHz WiFi "channels" are in fact only 5 MHz apart for some absurd reason. That is why it is necessary to use only 1,6,11 to avoid interference. If you use channel 1 and the neighbor uses channel 2, then 80% of your channel bandwidth overlaps, but the two networks can't see each other (different channel) and therefore do not perform time sharing of the channel. This means that the signal to noise ratio of both networks will be horrible and data rate suffers a lot. Following the 1,6,11 rule means no overlap so that all networks on each channel share nicely while also avoiding "noise" from the other networks on other channels. It takes only one @#$% neighbor to set up on one of the "free" adjacent channels ruin the airspace for everyone.
If you use 300 Mbps 802.11N then you likely use a double width 40 MHz wide channel, potentially causing even more grief for everyone.

Back to bandwidth vs. data rate, others have accurately noted that this is all due to QAM. I'll add that back in the days of dial-up, we had modems up to 56 kbps on a <4 kHz phone line.  These 56k modems didn't use QAM, but 33.6k ones did, and got well over 8 bits per symbol.  DSL is surprisingly similar to these old analog modems, using many, many separate 4 kHz wide channels to achieve high speed data over a few km of basic low bandwidth copper twisted pair (nothing like CAT-5/6).