Where does the 54 Mbps figure come from anyway?
Have you ever wondered why both 802.11a and 802.11g have maximum speeds of 54 Mbps?
It is tempting to take a pen and a paper and do some calculations taking into account the bandwidth and the modulation scheme. But you soon realise that you get nowhere.
That is because you need a few more details than just the BW and modulation, making the calculations a bit more cumbersome. But just a bit – let me show you how:
It all boils down to the OFDM subcarriers. In 802.11a/g there are 64 subcarriers, each with a bandwidth of 312.5 KHz. The subcarriers’ bandwidth is a standarised number resulting from the 64-point FFT sampling:
20 MHz / 64 = 0.3125 MHz = 312.5 KHz
Not every subcarrier is used to transmit data though. For the 802.11a/g protocols, the breakdown is:
- 48 data subcarriers
- 4 pilot subcarriers
- 12 unused subcarriers
Each subcarrier can “carry” one QAM symbol per cycle. At 312.5 KHz, you can fit 312,500 symbols in one second, meaning that each symbol takes 3.2 μs:
1/312.5 KHz = 3.2 μs.
However, we cannot fill every second with actual symbols. A Guard Interval (GI) is required to avoid intersymbol interference (ISI) caused by propagation delays. In 802.11a/g, the GI is 0.8 μs. This brings the number of symbols per second down to 250,000 (on each subcarrier):
1/(3.2 μs+ 0.8 μs) = 250,000 symbols/subcarrier
Now on the modulation: the highest modulation level supported is QAM-64, meaning that each QAM symbol equals to 6 bits:
250,000 symbols = 1,500,000 bits = 1.5 Mbps
However, not every bit corresponds to actual data – some bits are introduced in the stream for error detection and correction. The “Coding Rate” for QAM-64 is 3/4, meaning that for every four bits, three are data and one is error check. Same as with the Guard Interval, this pulls the actual data rate further down – by 75%:
75% of 1.5 Mbps = 1.125 Mbps
Now we are at the end of our calculation: we just have to aggregate the data rate for each of the 48 subcarriers:
48 x 1.125 Mbps = 54 Mbps
These calculations are valid for any data rate on any OFDM-based signal, including 802.11n and 802.11ac (obviously changing the number of data subcarriers, spatial streams, GI and Coding Rates). Just follow the steps and you can’t go wrong!
What if…?
The 54 Mbps of 802.11a/g is the result of design trade-offs involving multiple factors, such as implementation complexity, resilience against interference, and available bandwidth.
But let’s assume ideal conditions, with no propagation delays, intersymbol interference, or error transmissions. What would the maximum data rate be?
If we can use all the available bandwidth, that means that all the 64 subcarriers are available for data. Also, every subcarrier can carry 312,500 symbols, as the GI is zero.
These 312,500 symbols equal to 1,875,000 bits in QAM-64. All of them carrying data, as there is no need to use bits for error check!
Now, let’s multiply these 1,875,000 bits (1.875 Mbps) by the number of data subcarriers (64):
64 x 1.875 Mbps = 120 Mbps !
In ideal, non-realistic conditions, the maximum data rate would be 66 Mbps faster than the actual data rates on 802.11a/g. This is more than double the actual maximum data rates! Sweet, but unachievable.