[email protected] (rider) wrote in message news:<[email protected] com>...
> Kevin!
>
> Thanks for the reply again. For sometimes i have been confused by the
> term Interpolator itself. Interpolator (opposite of decimator) is
> normally used to mention an upsampling of the signal sample rate (zero
> insertion and then an anti-imaging filter). But here in case of timing
> recovery, they sometimes mention that Ti > Ts (means fi<fs , with
> reference to fig above), so it means the "interpolator" is actually
> decimating? So we may ask:
>
> 1) Is Ti always > Ts?
>
> 2) Whatever filter structure we may employ for interpolator (like
> farrow) , wouldn't it be running at a fix clock (like in hardware, the
> clock signal driving the output register of interpolator would be
> fix?) . So how does it adjust the phase, if it is outputting samples
> after a fixed time?
>
> Regards
> Rider

If the term interpolator is confusing you, try saying phase shifter.
That is what the filter is doing here. For example. Lets say you want
a root raised cosine filter at you receiver. I think your incoming
samples are at 8kHz, and your symbol rate is 1kHz. A +-4 symbol RRC
filter would be 65 samples long (since you usually add one and make it
odd). So, we could apply this 65 sample FIR every 4 incoming samples,
and feed the results into the equalizer at 2k/s, and let the Gardner
TED work out how well those samples are placed. However we have no way
to apply a fine timing correction when the TED says we need one.
Correcting by shifting in 8kHz samples is very coarse, and leads to
problems.

Now consider what happens if you ask the RRC filter designer to treat
the input sample rate as 16*8kHz, and the filter length as 16*65
samples. Now, if you have a very long set of coefficients. If you use
every 16th coeff. from this filter in the original RRC calculation,
you will end up with much the same result as before. However, if you
step along 1 coefficient, and take every 16th coeff. the RRC output
will be phase shifted by 1/16th of an 8kHz sample. Why? because those
coeffs were designed to be multiplied by samples 1/16th of an 8kHz
sample away from the samples you are actually using. You have 16 of
these phase shifting RRC filter coefficient sets spanning 0/16th of a
sample to 15/16th of a sample of phase shift.

Now, you have something fine enough to work with the TED. As the TED
keeps telling you to nudge the timing in a particular direction, you
step along the coefficient sets until you reach the end. Then you jump
back to the other end, and hop one whole 8kHz sample. Voila, smooth
TED operation.

For very higher order QAM 16 is probably not high enough. For simple
16 state QAM is may be overkill. You need to tune that figure to the
needs of your system, to stabilise the equalizer adaption and the
constellation sufficiently for you actual system.

Regards,
Steve