OFDM coarse freq estimation I am trying to read OFDM synchronization paper by Schmidl and Cox. The math is slightly overwhelming. 

What is the formula that they use in implementation that distinguishes between coarse estimation and fine estimation? 

Secondly once fine frequency offset is done, how do you determine that you need to do coarse frequency synchronization or not?  What is it that you will check to determine it? If anybody could explain with a set of equations that would  be very helpful.
The key part of the paper seems to be section IV.  There, they estimate the frequency offset by:



where $P(d)$ is given by:



And then $\widehat{\Delta f}$ is given by



if $|\hat{\phi}| &lt; \pi$, or a correction is added:



otherwise.