Forum: GNU Radio Re: CPM timing recovery

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Achilleas A. (Guest)
on 2007-06-06 18:18
(Received via mailing list)
Bob,

this is not correct.

The CPM signal is by definition constant envelope.
It is defined as
s(t)=exp(j phi(t))
where
phi(t)= 2 pi int_0^t f(t') dt'
where
f(t)= h sum_k a_k p(t-kT).
Selecting the approprate pulse shape p(t) shapes the spectrum of CPM,
but regardless of the selection it has continuous phase
(not abrupt transitions) as the name suggests ;-) and constant envelope.
Thus the method you suggested (looking at the envelope variations)
will not work.

Achilleas


======================
Since the signal will not really have infinite bandwidth (instantaneous
transitions from one state to the next),  the envelope will not be of
constant modulus.  The signal will be amplitude modulated with a
component due to the data transitions.  Looking at the modulus or
modulus squared will reveal a line in the fft due to this amplitude
modulation.

Bob
Dan H. (Guest)
on 2007-06-06 21:00
(Received via mailing list)
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Nothing that modulates data has constant envelope. Plot the amplitude of
a BPSK or GMSK signal (after transmission, not simulation) sometime.

- -Dan

Achilleas A. wrote:
> f(t)= h sum_k a_k p(t-kT).
> Since the signal will not really have infinite bandwidth (instantaneous
> Discuss-gnuradio mailing list
> removed_email_address@domain.invalid
> http://lists.gnu.org/mailman/listinfo/discuss-gnuradio

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Tim M. (Guest)
on 2007-06-07 03:45
(Received via mailing list)
The point where theory meets practice is what makes engineering fun.

If when you say "Nothing that modulates data has constant envelope"

you mean it in the same sense that passbands are never truly flat and
bit
error rates are never 0, then I agree with you.   But I claim that a
received CPM signal has constant envelope to within some small
tollerence,
and I would argue 1% type numbers for magnitude variation are not out of
the
question.

Tim
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