In GNURadio's PSK tutorial they place the costas loop after clock sync and linear equalizer. This seems odd to me.
I'm thinking that it's easier to lock onto a carrier frequency at the higher RF sample rate rather than on the clocked symbols. And similarly it seems to me that it should be easier to to clock recovery on the frequency-synced post-costas signal.
It will also presumably be easier to use a correlation estimator after the costas loop, too. And correlation estimator has to be done before clock sync, since it uses the clock sync information to sync.
Indeed, my experiments decoding data always seem to work better when I start with the costas loop.
But I claim no expertise, so I assume the GNU Radio tutorial is correct. But why is it correct?