"Kevin Neilson" <[email protected]> wrote in message news:<8oOac.52137$K91.127528@attbi_s02>...
> "rider" <[email protected]> wrote in message
> news:[email protected] om...
> > Hi!
> >
> > I have a query regarding the computation of Gardner Timing Error
> > detector (TED). Dr. Gardner on his article "A BPSK/QPSK Timing Error
> > Detector for Sampled Receivers" states that Timing Error (for BPSK)
> > can be computed as:
> >
> > U(r) = x(r-1/2)[x(r)-x(r-1)]
> >
> > He calls the samples x(r) as "STROBE" values and those like x(r-1/2)
> > as "MIDWAY"
> > between strobes [like x(r-1/2) is midway between x(r) and x(r-1)].
> >
> > Its also mentioned that this algorithm uses only 2 samples/symbol to
> > compute the error. I need to ask that:
> >
> > 1)What he means by these STROBE and MIDWAY values ,x(r) and x(r-1/2) ,
> > and how to compute them from the available 2 samples/symbol?
> >
> > 2) For the complete timing recovery loop, there is also an
> > interpolator. If the interpolator is fed with 2 samples/symbol, then
> > what is it computing? is it computing the midway value x(r-1/2) or
> > what?
> >
> > Regards
> > Rider
>
> You are sampling two samples per symbol, so if the loop is locked and you
> are sampling at the symbol instants and midway between the samples, then
> x(r-1), x(r-1/2), and x(r) will be three successive samples. These three
> would comprise two strobes and one midway or one strobe and two midway
> samples.
>
> The TED can be used to adjust a PLL that controls the sample clock. Then no
> interpolation is required; the sample clock is just adjusted so that the ADC
> samples at the correct points. That's mostly an older method. The other
> type of loop uses an ADC that samples at a constant rate, and then a
> resampling filter controlled by the loop interpolates the value at the
> sampling instant, which will be between the ADC samples. Before the loop is
> locked, the interpolator will not be sampling at the symbol instants, but
> the error value will be large and will push the loop until the interpolated
> values occur at the symbol instants and the midway points.
> -Kevin


Thanks Kevin!

Yes i m trying to follow the new method in which the sampling clock of
the receiver is fixed at Fs and an all-digital interpolation/TED loop
is use to recover timing. Like in the fig below:


(~) Fixed Clk --/--Fs= Nfb (fb=symbol clock , Fs=sampling clock)

Fs=1/Ts|-------------| Fi=1/Ti |---|
x(mTs)----|Interpolator |--------->|TED|
----^-------- ---
| |
|-------| |---------|
|Control|<-------------|Loop Fil |
--------- -----------


However, i still cant understand a point . When the Gardner algorithm
says it uses 2 samples/symbol, then does it mean that Fs in the above
figure SHOULD exactly be 2fb? In my work, i have chosen fb=1khz and
Fs=8khz. Do i have to decimate this 8khz signal to 2 Khz before
applying it to the interpolator or i can feed this 8Khz signal
directly?

Thanks