Re: FLL Band-Edge

[Marcus Müller]

Hard questions!

On 15.01.21 23:40, Kristoff wrote:
> Doesn't a PLL also track the frequency of the source (in addition to its
> phase)?

* PLL: Able to *correct* small frequency errors: yes, but a frequency
error in a first-order phase control loop will pose a constant offset
error, thus still leading to increased symbol error rates. That's
because a frequency is just a phase that increases linearly with time;
in other words, every symbol gets (frequency error)/(symbol rate) in
constant phase offset, PLUS the phase noise that the PLL is meant to
correct.
* PLL: Able to actually *track* a frequency error: yes, if it has a
control loop atop of the phase control loop that looks for the constant
phase offset above and corrects that prior to then tracking the
remaining phase error

> So what would be the reason to use a FLL and not a PLL?

There's certainly reasons I didn't think of yet, but:

* PLL needs knowledge of the constellation; FLL only knowledge of the
pulse shape (best case) or rough knowledge of the bandwidth of the
signal. You can often determine the bandwidth long before you can have a
reasonable guess at the constellation.
* A PLL can't ever solve frequency errors that are multiples of the
(symbol rate)/(number of symmetry angles)
* It's not either/or, often it's a combination of both systems, where
you start with a wide loop filter bandwidth for the FLL until you
"center in" your bandwidth well enough, then you reduce the FLL's loop
filter bandwidth, so that random signal fluctuations and noise don't
make your frequency "jump around". After the FLL, you can have a PLL
with a lower bandwidth than what you'd need if there was no prior
"rough" frequency correction.
* If it was actually done the full fred harris way (see the GRCon'17
video), then a phase estimate would also come out of the FLL – gotten
from the whole band, which is pretty robust, in basic theory at least.

Best regards,
Marcus