Demodulation in Rayleigh Flat Fading Channels A core part of demodulation in Flat-Fading channels is (assuming) the channel as a(random) constant complex number multiplied with your signal. This is done in order to de-rotate the symbol for decision making at the sampling time.

I'm wondering how you go about estimating what the complex number is? How do you estimate the phase change induced by the channel?
The short answer is: pilot symbols. 

The long(er) answer is: The sender periodically transmits known data symbols; this sequence is known to the recipient ahead of time.