Timing Error Detection using Gardner and other methods

Hi,
   I simulated a QPSK Symbol Rrror Recovery mechanism using interpolation
menthod. I used a gardner TED which works only for the case where there is
a symbol trensition. I would like to know of any algorithm which works for
the case even without trnsition. (I didnt find Muller-Muller method very
good). 

What if I want to simulate Symbol recovery using the same interpolation
method for 16-QAM. What algorithm would be suitable for TED of the QAM
system.

Thanks
Best Regards
Rajenish

On Wed, 07 Dec 2005 04:14:28 -0600, "Rajenish_jain"
<rajenish.jain@gmail.com> wrote:

>Hi,
>   I simulated a QPSK Symbol Rrror Recovery mechanism using interpolation
>menthod. I used a gardner TED which works only for the case where there is
>a symbol trensition. I would like to know of any algorithm which works for
>the case even without trnsition. (I didnt find Muller-Muller method very
>good). 
>
>What if I want to simulate Symbol recovery using the same interpolation
>method for 16-QAM. What algorithm would be suitable for TED of the QAM
>system.

If there's no transition then the signal is essentially DC and there's
no way to determine the symbol boundaries.   So no detector can
provide timing information when there's no transition, and this is one
reason it's important to have a scrambler in the system to keep the
entropy high enough that the detector always works.

Some of the "better" detectors know enough to generate exactly zero
when no transition is detected in order to minimize the noise input to
the timing loop.

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Hi,

Eric Jacobsen wrote:

>On Wed, 07 Dec 2005 04:14:28 -0600, "Rajenish_jain"
><rajenish.jain@gmail.com> wrote:
>
>  
>
>>Hi,
>>  I simulated a QPSK Symbol Rrror Recovery mechanism using interpolation
>>menthod. I used a gardner TED which works only for the case where there is
>>a symbol trensition. I would like to know of any algorithm which works for
>>the case even without trnsition. (I didnt find Muller-Muller method very
>>good). 
>>
>>What if I want to simulate Symbol recovery using the same interpolation
>>method for 16-QAM. What algorithm would be suitable for TED of the QAM
>>system.
>>    
>>
>
>If there's no transition then the signal is essentially DC and there's
>no way to determine the symbol boundaries.   So no detector can
>provide timing information when there's no transition, and this is one
>reason it's important to have a scrambler in the system to keep the
>entropy high enough that the detector always works.
>
>Some of the "better" detectors know enough to generate exactly zero
>when no transition is detected in order to minimize the noise input to
>the timing loop.
>  
>
That answers Rajenish's first paragraph well, but misses his second.

Gardner works OK for 16-QAM, or even much higher orders, with a couple 
of caveats - you need more damping, and training sequences may have issues.

Because a scrambler is always used for real world QAM, the transition 
density is kept high, and the transitions kept fairly random. A Gardner 
test on any individual transition produces a rather variable result. 
However, the average of a few results from a scrambled sequence forms a 
cost function which homes the timing correctly. You need to use more 
damping in the Gardner test, than you would with QPSK, to provide 
appropriate averaging. Other than that, the same test will track the 
symbols OK. The only thing to watch is that you don't make the damping 
so great that you cannot track the greatest transmitter to receiver 
symbol clock rate mismatch you might face.

Many QAM systems, such as telephone line modems, use an initial training 
phase where the transmitter alternates between two states. This is the 
section of the signal where you need to achieve your initial timing lock 
on the symbols. In many QAM training sequences, especially the more 
recent ones, the alternating symbols are of equal magnitude, and a 
Gardner TED works fine. However, in some specs the states are not of 
equal magnitude. The Gardner TED algorithm tends to lock to such a 
signal with a fixed phase shift. It may be OK to just ignore this, and 
let things settle down when the higher entropy sections of the signal 
start. That really depends on how far out the timing is for the 
particular training sequence. It might be possible to apply a fixed 
sized kick to the symbol timing as the end of the alternating signal is 
detected. It does, however, always need to be considered, to see the 
design is unconditionally stable.

Regards,
Steve