"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