# Linear vs Nonlinear modulation as their carrier recovery algorithm?

Started by April 1, 2008
```Dear all,

Just found this great forum on DSP. This is my first post and hope someone
can help.

I am searching for the knowledge on GMSK demodulation and found that some
articles say that some carrier/timing recovery algorithms (like Gardner,
Early-Late etc) are only applicable to LINEAR modulation scheme.

my questions are:
1) what does linear and nonlinear modulation mean? what is the difference
between them?
2) what are the carrier phase and timing recovery algorithms that are
applicable to GMSK demodulation (BT=0.3 and h=0.5)?

Thank you.

Richard

```
```On Tue, 01 Apr 2008 05:22:08 -0500, richard_zhang wrote:

> Dear all,
>
> Just found this great forum on DSP. This is my first post and hope
> someone can help.
>
> I am searching for the knowledge on GMSK demodulation and found that
> some articles say that some carrier/timing recovery algorithms (like
> Gardner, Early-Late etc) are only applicable to LINEAR modulation
> scheme.
>
> my questions are:
> 1) what does linear and nonlinear modulation mean? what is the
> difference between them?
> 2) what are the carrier phase and timing recovery algorithms that are
> applicable to GMSK demodulation (BT=0.3 and h=0.5)?
>
A linear modulation scheme is one where the operation of going from the
information signal (call it si(t)) to the modulated signal (call it sm
(t)) is a linear one, i.e. it obeys superposition.  This definition is
almost always extended to mean a signal where si(t) is derived from a
binary stream.

So if you define si(t) to be +1 or -1, with changes occurring on the bit
times, and sm(t) = cos(w*t) * si(t), then you have PSK and the modulation
scheme is linear.

MSK (not GMSK) can be viewed as a linear modulation scheme (see http://
www.wescottdesign.com/articles/MSK/mskTop.html for details), so one can
use those methods to decode it.  GMSK, on the other hand, is _not_ a
linear modulation scheme -- phase modulation isn't linear, MSK is a
special case where you can express the modulation without using phase
modulation, and GMSK isn't.

But.  For GMSK that isn't too heavily filtered you can close your eyes to
the 'G' and demodulate it as MSK.  Your phase recovery won't be optimal,
but it may well be good enough.  Your recovered signal going into the bit
slicer will have a lot of ISI, but for a strong signal you can ignore it,
or for a weaker signal you can do some channel compensation.

I'm not a GMSK expert, so I've just exhausted my store of practical
knowledge.  I know the above works well for BT=0.3 and BT=0.5, because
I've done it.  Whether it's the best all-around compromise method for
demodulating GMSK -- I dunno.  One of these days I should get a book that
shows how to demodulate GMSK, because it sure doesn't seem to be out
there on the web.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
```
```
richard_zhang wrote:

> Dear all,
>
> Just found this great forum on DSP. This is my first post and hope someone
> can help.
>
> I am searching for the knowledge on GMSK demodulation and found that some
> articles say that some carrier/timing recovery algorithms (like Gardner,
> Early-Late etc) are only applicable to LINEAR modulation scheme.

This is not right. The approaches to the carrier/timing recovery are
always the same - maximum likelihood. There is a difference in the minor
technical details.

> my questions are:
> 1) what does linear and nonlinear modulation mean? what is the difference
> between them?

If the signal is a linear function of the modulation, then the
modulation is linear.

> 2) what are the carrier phase and timing recovery algorithms that are
> applicable to GMSK demodulation (BT=0.3 and h=0.5)?

There are many. It depends on how optimal do you want to be, how big is
the carrier offset compared to the bit rate, how much of the
processing you can afford and if it has to be done causally or you are
processing the recorded chunk of signal. In the simplest case, the
timing can be recovered from the incoherent demodulation; the carrier
can be recovered by decision directed PLL if required.