A Question about Gardner TED

   Gardner TED for BPSk is e(r)=y(r-1/2)[y(r)-y(r-1)].that mean the
e(r) is related to y's amplitude and so related to
signal's power. But TED is attend to give a phasic error,which is
in[0,2*pi] and unrelated to signal's power. How
can I get the e(r) in zone [0,2*pi]? What's the normalization method?

On Jun 25, 9:17 am, peugeot888 <peugeot...@tom.com> wrote:
>    Gardner TED for BPSk is e(r)=y(r-1/2)[y(r)-y(r-1)].that mean the
> e(r) is related to y's amplitude and so related to
> signal's power. But TED is attend to give a phasic error,which is
> in[0,2*pi] and unrelated to signal's power. How
> can I get the e(r) in zone [0,2*pi]? What's the normalization method?

It's intended to give *delay* estimate, not phase estimate.

On Jun 25, 10:17 am, peugeot888 <peugeot...@tom.com> wrote:
>    Gardner TED for BPSk is e(r)=y(r-1/2)[y(r)-y(r-1)].that mean the
> e(r) is related to y's amplitude and so related to
> signal's power. But TED is attend to give a phasic error,which is
> in[0,2*pi] and unrelated to signal's power. How
> can I get the e(r) in zone [0,2*pi]? What's the normalization method?


Think of the TED

On Jun 25, 10:17 am, peugeot888 <peugeot...@tom.com> wrote:
>    Gardner TED for BPSk is e(r)=y(r-1/2)[y(r)-y(r-1)].that mean the
> e(r) is related to y's amplitude and so related to
> signal's power. But TED is attend to give a phasic error,which is
> in[0,2*pi] and unrelated to signal's power. How
> can I get the e(r) in zone [0,2*pi]? What's the normalization method?

Think of the TED as a "timing delay to number" converter, and the NCD
(numerically-controlled delay)  that follows the loop filter as a
"number to timing delay" converter ...

But what  is  unit for e(r)?  How can I express the delay?

"BERT" <callmevc@gmail.com> 
??????:1182783396.990637.224230@q75g2000hsh.googlegroups.com...
> On Jun 25, 10:17 am, peugeot888 <peugeot...@tom.com> wrote:
>>    Gardner TED for BPSk is e(r)=y(r-1/2)[y(r)-y(r-1)].that mean the
>> e(r) is related to y's amplitude and so related to
>> signal's power. But TED is attend to give a phasic error,which is
>> in[0,2*pi] and unrelated to signal's power. How
>> can I get the e(r) in zone [0,2*pi]? What's the normalization method?
>
> Think of the TED as a "timing delay to number" converter, and the NCD
> (numerically-controlled delay)  that follows the loop filter as a
> "number to timing delay" converter ...
> 

You need to do some homework and derive it, there's a
dependence on the pulse shape that you use in your
modulation.  It is commonly called the "gain" of the TED,
and it can be derived from the S-curve, which is the expected
output of the TED as a function of the true delay.

Do you have references on the terms I used above?


On Jun 26, 8:50 am, "peugeot888" <peugeot...@tom.com> wrote:
> But what  is  unit for e(r)?  How can I express the delay?
>
>

julius wrote:
> You need to do some homework and derive it, there's a
> dependence on the pulse shape that you use in your
> modulation.  It is commonly called the "gain" of the TED,
> and it can be derived from the S-curve, which is the expected
> output of the TED as a function of the true delay.
> 
> Do you have references on the terms I used above?

For pulse shape think excess bandwidth. Gardner works great with large 
excess bandwidth, and falls apart for very limited excess bandwidth.

In most practical cases, the result of the Gardner calculation should be 
thought of as little more than a "go left" or "go right" indication. 
Trying to use the actual magnitude of the result, rather than just its 
sign, works fine in a sterile noiseless model. In the real noisy world 
the impairments mean trying to scale the adjustment with the magnitude 
of the result can be less than spectacularly successful.

Steve

> In most practical cases, the result of the Gardner calculation should be
> thought of as little more than a "go left" or "go right" indication.
> Trying to use the actual magnitude of the result, rather than just its
> sign, works fine in a sterile noiseless model. In the real noisy world
> the impairments mean trying to scale the adjustment with the magnitude
> of the result can be less than spectacularly successful.
>

And, that is also why the Gardener TED works for a wide range of
modulation schemes including QAM. Anyways, you might want to consult
"Digital Communication Receivers" by H. Meyr et. al, for a more in-
depth treatment of this subject.

Vijay.

What references give the definition of  S-curve?I have look up
<Synchronization Techniques for Digital Receivers> . <Digital Communication 
Receivers Synchronization, Channel Estimation, and Signal Processing>
and <digital communications>.But I can't find the definition of  S-curve.
Could tell me the reference?thanks

"julius" <juliusk@gmail.com> 
??????:1182877605.962511.200660@q69g2000hsb.googlegroups.com...
> You need to do some homework and derive it, there's a
> dependence on the pulse shape that you use in your
> modulation.  It is commonly called the "gain" of the TED,
> and it can be derived from the S-curve, which is the expected
> output of the TED as a function of the true delay.
>
> Do you have references on the terms I used above?
>
>
> On Jun 26, 8:50 am, "peugeot888" <peugeot...@tom.com> wrote:
>> But what  is  unit for e(r)?  How can I express the delay?
>>
>>
>
> 

On Jun 27, 7:29 am, "peugeot888" <peugeot...@tom.com> wrote:
> What references give the definition of  S-curve?I have look up
> <Synchronization Techniques for Digital Receivers> . <Digital Communication
> Receivers Synchronization, Channel Estimation, and Signal Processing>
> and <digital communications>.But I can't find the definition of  S-curve.
> Could tell me the reference?thanks
>

Look again, it's definitely in d'Andrea and Mengali's "Synchronization
Techniques
for Digital Receivers."  You didn't give the authors names, but I
assume that
you were referring to the same book.

Julius