FPGA Central

Hello all,

Classic Gardner timing detector:

Gardner(x) = (x2 - x0)*x1

Where x0, x1, x2 are sampled in -1/2, 0, +1/2 of the symbol.
Essentially this detector finds the derivative of the energy after the
matched filter.

Let's take a different look at that. Consider the transition waveform
from one symbol to the next symbol. Take I and Q components of this
waveform:

I = x2 - x0
Q = -x0 + 2x1 - x2

Dual angle:

I*Q ~ = x0^2 + 2x1(x2-x0) - x2^2
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Proposed detector

Which equals to:

== 2*Gardner(x) + x0^2 - x2^2

Apparently (x0^2 - x2^2) averages out to zero assymptoticaly with the
infinite averaging, so, the whole thing eventually gets equvalent to the
Gardner detector. However, for the smaller averaging, the data related
noise of the proposed detector can be up to 2..3 times less then that of
Gardner. The AWGN behaviour is the similar for both detectors. So, it
turns out to be possible reducing the data noise without any additional
information.

What is the name of the wheel that I just reinvented?

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote:

>Hello all,
>
>Classic Gardner timing detector:
>
>Gardner(x) = (x2 - x0)*x1
>
>Where x0, x1, x2 are sampled in -1/2, 0, +1/2 of the symbol.
>Essentially this detector finds the derivative of the energy after the
>matched filter.
>
>Let's take a different look at that. Consider the transition waveform
>from one symbol to the next symbol. Take I and Q components of this
>waveform:
>
>I = x2 - x0
>Q = -x0 + 2x1 - x2
>
>Dual angle:
>
>I*Q ~ = x0^2 + 2x1(x2-x0) - x2^2
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>Proposed detector
>
>Which equals to:
>
>== 2*Gardner(x) + x0^2 - x2^2
>
>Apparently (x0^2 - x2^2) averages out to zero assymptoticaly with the
>infinite averaging, so, the whole thing eventually gets equvalent to the
>Gardner detector. However, for the smaller averaging, the data related
>noise of the proposed detector can be up to 2..3 times less then that of
>Gardner. The AWGN behaviour is the similar for both detectors. So, it
>turns out to be possible reducing the data noise without any additional
>information.
>
>What is the name of the wheel that I just reinvented?
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com

The following sounds suspiciously similar from the abstract.
I'll take a look at it next time I'm at the library.

http://ieeexplore.ieee.org/xpl/freea...isnumber=29703


Steve