Re: [Discuss-gnuradio] expectation maximization for fir channel estimation

[CEL]

Hi Avi,

nope, that's pretty specific, and I think the chances of someone else
randomly having implemented exactly these methods are rather slim; I
don't know of any implementation. However, BCJR is basically the basis
of turbo decoding, and there's turbo decoders built-in to GNU Radio. 

Best regards,
Marcus

On Wed, 2018-11-21 at 14:27 +0200, Avi Caciularu wrote:
> Thanks for your reply.
> What I actually meant is some kind of python implementation for one of the 
> following papers, for BPSK modulation:
> https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4303066
> https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=297849
> 
> for linear ISI fir channel model.
> 
> Thanks. 
> 
> On Wed, Nov 21, 2018 at 2:19 PM Müller, Marcus (CEL) <address@hidden> wrote:
> > Hi Avi,
> > 
> > I'm not quite sure what *exactly* you're looking for, i.e. if you're
> > really after the EM algorithm to find a MAP / ML estimate of the
> > channel coefficients, or whether you just want that channel estimate.
> > 
> > I really like the gr-adapt [1] module of channel estimators, especially
> > for its good documentation and examples, including recursive least
> > square estimation. My estimation theory is a bit weak on that front,
> > and I can't really tell you from the top of my head how EM compares to
> > RLS etc. What I do know is that such algorithms typically make no
> > guarantees on convergence rate¹; generally, Eigenvalue-based methods²
> > behave more gracefully, and if I'm not completely mistaken, Karel's RLS
> > belongs in that category.
> > 
> > What's the reason you're asking for this? I'm not aware of EM being a
> > common method for channel estimation, and from scrambling together my
> > bits of random measurement theory/estimation theory knowledge and
> > assembling the courage to say something about a field that I don't
> > remotely feel confident talking about: you'd need to come up with a
> > "coefficient likelihood function", something that takes in a very high-
> > dimensional vector as argument, and which you iteratively improve with
> > incoming data; that's basically a maximum likelihood parameter
> > estimator in every iteration step? Feels like if you put knowledge into
> > that ML step, you end up with a different form of parametric
> > estimators. Cool stuff! But, and that's a honest question: why?
> > 
> > Best regards,
> > Marcus
> > 
> > [1]https://github.com/karel/gr-adapt
> > 
> > ¹ in fact, I'd expect that thing to only guarantee converging on a
> > *local* minimum of error, not to the *global* one
> > ² so-called spectral estimators, with "spectrum" as in "set of 
> > Eigenvalues", not so much as in "frequency domain".
> > 
> > On Wed, 2018-11-21 at 10:50 +0200, Avi Caciularu wrote:
> > > Does anyone know where I can find implementation of that?
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