802.11 OFDM Data Rates – The Math Behind The Numbers

Introduction

As a WiFi admin, you are probably familiar with WiFi Data Rates and the concept of DRS (Dynamic Rate Switching/Shifting/Selection).
Numbers like 6Mbit/s, 54MBit/s, 144MBit/s, 300MBit/s and 400MBit/s all look pretty familiar – but what are they based on?
The numbers are not random at all – the data rates of OFDM PHYs (802.11a, 802.11g, 802.11n, 802.11ac) are all based on the same single formula, which consists of 5 variables:

Data Subcarriers (number of subcarriers that transmit modulated data)
Modulation (amount of bits each data subcarrier can represent; predefined mix and match possibilities with coding)
Coding (defines how much of the modulated data is useful data and how much of it is for error correction; predefined mix and match possibilities with modulation)
Spatial Streams (number of unique MIMO data streams that can be sent in parallel)
Symbol Interval Time (the sum of Data Interval Time + Guard Interval)

I’d like keep this blogpost short and sexy, and just show how you can calculate the different data rates based on these numbers.
In the following days and weeks, I’m going to publish additional blogposts, where I’ll explain the different variables thoroughly, and link them in this blogpost.

Formula

With the variables described above, the following formula is used to calculate OFDM data rates:

Data Subcarriers * Modulation * Coding * Spatial Streams / (Data Interval Time + Guard Interval) = Data Rate in Bits/Microsecond = Data Rate in Mbit/s

Possible Values Of Variables

802.11a

802.11g

802.11n

802.11ac

Data Subcarriers

108

234

468

Modulation & Coding

BPSK 1/2

BPSK 3/4

QPSK 1/2

QPSK 3/4

16QAM 1/2

16QAM 3/4

64QAM 2/3

64QAM 3/4

BPSK 1/2

BPSK 3/4

QPSK 1/2

QPSK 3/4

16QAM 1/2

16QAM 3/4

64QAM 2/3

64QAM 3/4

BPSK 1/2

QPSK 1/2

QPSK 3/4

16QAM 1/2

16QAM 3/4

64QAM 2/3

64QAM 3/4

64QAM 5/6

BPSK 1/2

QPSK 1/2

QPSK 3/4

16QAM 1/2

16QAM 3/4

64QAM 2/3

64QAM 3/4

64QAM 5/6

256QAM 3/4

256QAM 5/6

Spatial Streams

Symbol Interval Time

4us

3.6us

4us

3.6us

As you can see in the table above, Data Subcarriers, Symbol Interval Time and Spatial Streams are fixed values for 802.11a & 802.11g. Only Modulation and Coding are variable – therefore only a small number (8) of different data rates are possible for these PHYs.

In 802.11n & 802.11ac, all 5 numbers are variable and can be mixed almost randomly, leading to a massive amount of different possible data rates, making it impossible to keep all of them in mind:

http://mcsindex.com/

Examples

To wrap this blogpost up, here are the calculations of the 5 data rates I mentioned at the beginning of this blogpost:

Calculation	Data Rate	Description
*48 1 * 1/2 * 1 / (3.2u + 0.8u)**	6Mbit/s	Lowest possible Data Rate for 802.11a & 802.11g
*48 6 * 3/4 * 1 / (3.2u + 0.8u)**	54Mbit/s	Highest possible Data Rate for 802.11a & 802.11g
*52 6 * 5/6 * 2 / (3.2u + 0.4u)**	144.4Mbit/s	Highest possible Data Rate for 802.11n, where Channel Width = 20MHz, Spatial Streams = 2, Guard Interval = Short
*108 6 * 5/6 * 2 / (3.2u + 0.4u)**	300Mbit/s	Highest possible Data Rate for 802.11n, where Channel Width = 40MHz, Spatial Streams = 2, Guard Interval = Short
*108 8 * 5/6 * 2 / (3.2u + 0.4u)**	400Mbit/s	Highest possible Data Rate for 802.11ac, where Channel Width = 40MHz, Spatial Streams = 2, Guard Interval = Short