Why is channel estimation done after synchronization and why does it work?

I am interested in Software Defined Radio communications where almost all processing is pushed to the digital domain.

I'm wondering why is channel estimation done after frequency and phase synchronization?

Shouldn't channel estimation be done before to take into account multi-path and other effects? Why can't channel estimation and frequency/phase synchronization be done simultaneously?

I took a digital communications course but the book sort of skipped these areas which is a fatal flaw.

• I suppose it depends how you're estimating the channel. As an example of why you might do channel estimation after synchronization, consider the example of a coherent-receiver communication system that uses a training sequence for that purpose. In order to observe the training sequence as corrupted by the channel, you need to synchronize in timing and phase first. Aug 5, 2018 at 23:50
• I understand but what about the corruption to the carrier caused by the channel? Have any recommendations for literature in this area? Aug 5, 2018 at 23:57
• I guess the other issue is, how quickly does the center frequency offset rotate the constellation. If it is not much within channel coherence time I suppose you don't really need to do carrier tracking. Aug 6, 2018 at 0:09
• You're right, the channel response might degrade your ability to perform synchronization. But it's a bit of a chicken-and-egg problem: in order to estimate the channel, you need to do so based on criteria from the signal observed at the receiver. Much of the time, those criteria are dependent on the data encoded in the signal, so you need to synchronize first. If you had a channel estimation method that wasn't dependent on the data, then it's possible you could do it first. One example would be the constant modulus algorithm (CMA) equalizer, which can be used before carrier synchronization. Aug 6, 2018 at 0:33
• It depends on your definition of the channel. If your channel model includes the local oscillator of the receiver, then you could say that channel estimation would include phase synchronization. That’s not usually how it’s modeled in my experience. Aug 6, 2018 at 23:05