Hi Tom,
why do/I/ have to advertise the PFB approach? Arguing against Mueller &
Müller feels strange. Anyway:
Mueller & Müller in the classical, real valued approach [1, eq (49), p.
524] in its core is
eqn. (49) page 524
with $z_k$ being the timing estimate ,$x_k$ being the input samples, and
$a_k$ the decisions (in our case, -1/+1 [2], so $E\{a_k^2\}\equiv 1$).
Assume timing is correct, ie. $z_{k-1} = 0$, but we have fading so that
$|x_k| = \epsilon |x_{k-1}|,\quad 0<\epsilon \ll 1$;
then regardless of $a_{k-1}$, the term $|x_k a_{k-1}| \ll|x_{k-1}a_k|$,
and hence
$z_k \approx -\frac12 {x_{k-1}a_k}$
Now, $a_k$ is exactly the decision we don't want to put much trust in,
because it's a symbol decision with especially bad $\frac{E_s}{N_0}$.
Effectively, you get the bit error probability increase as a factor to
your timing error probability density, as if things weren't bad enough!
PFB is cooler because
1. PFB!
2. the derivate is a linear operation, so amplitude changes in the
input signal at least have the same effect on the error correction
magnitude.
Cheers,
Marcus
[1] http://2n3904.net/library/MM_Clock_Recovery.pdf
[2]
https://github.com/gnuradio/gnuradio/blob/master/gr-digital/lib/clock_recovery_mm_ff_impl.cc#L83
On 31.07.2015 01:06, Tom Rondeau wrote:
> On Thu, Jul 30, 2015 at 3:03 PM, Iluta V <[email protected]
> <mailto:[email protected]>> wrote:
>
> Hi, Tom,
>
> Could you be more specific where exactly it is not "the right
> algorithm"? We'd appreciate that and would correct that in own
> work as well, if Security Research Assessment made a mistake here.
>
> I will be looking forward to your response,
>
> Iluta
>
>
>
> Iluta,
>
> I shouldn't be so hard on the M&M block. In most situations, it's
> tended to work fine, but it's suboptimal. It's based on hardware
> techniques of clock recovery that approximate a derivative. The PFB
> algorithm actually calculates the derivative to the numerical
> approximation required by setting the number of filterbank arms. So
> the results are much better. You also get to apply your own filter to
> this block so you don't have to apply a separate matched filter.
>
> Also, and I can't find any papers on this, but fred harris tells me
> that the M&M algorithm behaves particularly poorly in fading environments.
>
> Tom
>
>
>
>
> On Thu, Jul 30, 2015 at 9:55 PM, Tom Rondeau <[email protected]
> <mailto:[email protected]>> wrote:
>
> On Thu, Jul 30, 2015 at 2:38 PM, Iluta V <[email protected]
> <mailto:[email protected]>> wrote:
>
> Research paper CONVERTING RADIO SIGNALS TO DATA PACKETS
> (Examination of Using GNU Radio Companion for Security
> Research and Assessment) deals with Clock Recovery MM, I
> attached the paper, have a look at:
>
> 6.Section 6.Counting the Bits
> 7.Analyzing Demodulated Data
>
> Both deal with Clock Recovery MM usage and has flowgraphs.
>
> Best regards,
>
> Iluta
>
>
>
> That's great, and I'm glad they got it to work for their
> application. Looks like they provide a good explanation of its
> use, too. Still, it's not the right algorithm.
>
>
>
>
> Tom
>
>
>
>
> On Thu, Jul 30, 2015 at 9:23 PM, Tom Rondeau
> <[email protected] <mailto:[email protected]>> wrote:
>
> Another point to keep in mind is that the M&M block
> isn't great in fading environments. It's really
> suboptimal in general. Look at the pfb_clock_recovery
> block, instead.
>
> Tom
>
>
> On Thu, Jul 30, 2015 at 2:18 PM, Daniel Camara
> <[email protected]
> <mailto:[email protected]>> wrote:
>
> Hi Klauss,
>
> You could also take a look at
>
> https://www.tablix.org/~avian/blog/archives/2015/03/notes_on_m_m_clock_recovery/
>
> <https://www.tablix.org/%7Eavian/blog/archives/2015/03/notes_on_m_m_clock_recovery/>,
> it helped me quite a bit!
>
> Best regards...
>
> Daniel
>
> On Thu, Jul 30, 2015 at 7:17 PM, Martin Braun
> <[email protected]
> <mailto:[email protected]>> wrote:
>
> Klaus,
>
> the manual page for this block has a paper
> reference in it:
>
> http://gnuradio.org/doc/doxygen/classgr_1_1digital_1_1clock__recovery__mm__ff.html#details
>
> M
>
> On 30.07.2015 10:16, Klauss Wolfeinstein wrote:
> > Hello,
> >
> > I would like to find a proper documentation
> on MM algorithm block (paper
> > for example). Any ideas ?
> >
> > Thank you.
> >
> > Regards.
> >
>
>
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>
>
> --
> Best regards...
>
> Daniel
>
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