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

 From: Avi Caciularu Subject: Re: [Discuss-gnuradio] expectation maximization for fir channel estimation Date: Wed, 21 Nov 2018 14:27:08 +0200

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 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?
> _______________________________________________