SNR penalty due to Linear Interpolation

Hi All

As we know that due to relative motion between TX and RX, the transmitted
signal undergoes expansion/compression. And due to this symbol and phase
synchronization is lost.

I have simulated this perticular thing, where I am using matlab's resample
function to introduce this expansion/compression. 

Now, at receiver I have used adaptive linear interpolation to correct this
expansion/compression. This technique works really nice up to 10 m/s of
velocity.

Now, the thing about synchronisation is that, if your receiver is not
synchronised then it is going to fail and if it is synchronised within
training period, then *ideally* you should get same BER performance.

But when I did simulation, i.e. BER vs SNR, I found that you have to pay
heavy penalty in terms of SNR, alomst 6 dB at BER of 10^-5.

Also, when I say there is no doppler, means no expansion/compression, I am
still getting the same BER.

One thing I am sure about is that I have tested this algorithm on recorded
signals and it works great. 

But my aim is to make it work at low SNR.

This expansion/compression is *Multirate Signal Processing* topic. 

Can anybody please suggest me good book or tutorial to start with. I have
seen book by Fred J harris, but that is not useful.

Also I was thinking, can I apply traditional timing recovery techniques on
this doppler corrupted signal?

Your opinion matters a lot.

Thanks

Chintan

On Mar 18, 2:25&#4294967295;pm, "cpshah99" <cpsha...@rediffmail.com> wrote:
> Hi All
>
> As we know that due to relative motion between TX and RX, the transmitted
> signal undergoes expansion/compression. And due to this symbol and phase
> synchronization is lost.
>
> I have simulated this perticular thing, where I am using matlab's resample
> function to introduce this expansion/compression.
>
> Now, at receiver I have used adaptive linear interpolation to correct this
> expansion/compression. This technique works really nice up to 10 m/s of
> velocity.
>
> Now, the thing about synchronisation is that, if your receiver is not
> synchronised then it is going to fail and if it is synchronised within
> training period, then *ideally* you should get same BER performance.
>
> But when I did simulation, i.e. BER vs SNR, I found that you have to pay
> heavy penalty in terms of SNR, alomst 6 dB at BER of 10^-5.
>
> Also, when I say there is no doppler, means no expansion/compression, I am
> still getting the same BER.

Yes, FIR-based (Farrow) interpolators are not perfect.  You can do a
test as follows:  for different values of fractional delay \tau, and
frequency
f, compute the MSE between:
* reference signal cos(2\pi f (t+\theta)) .
* output of the filter to approximate delay by \tau when the input is
cos(2\pi f t).
Don't forget to compensate for filter processing delay.

You'll see that the MSE depends on \tau and f, or more correctly on
the ratio
between f and your sampling rate fs.

>
> One thing I am sure about is that I have tested this algorithm on recorded
> signals and it works great.
>
> But my aim is to make it work at low SNR.
>
> This expansion/compression is *Multirate Signal Processing* topic.
>
> Can anybody please suggest me good book or tutorial to start with. I have
> seen book by Fred J harris, but that is not useful.

I think I learned most of this from Myer/Moeneclaey/Fechtel, and also
from
Gardner's original papers.

>
> Also I was thinking, can I apply traditional timing recovery techniques on
> this doppler corrupted signal?

To some extent, but if the Doppler is "large" then you will lost some
performance for sure.  How much you lose can be approximated
analytically or by simulation.

>
> Your opinion matters a lot.
>
> Thanks
>
> Chintan

Sorry, there are no easy answers in digital communication.  But it is
useful to learn how to either analytically derive or approximate, or
to
design a simulation to compute the "cost" of each imperfection.

Julius

Hi Julius

Thanks for replying.

This time I did what u had suggested before in some previous posts.

Initially I assumed that I know what is the doppler at RX, so just do the
resampling of the received signal, and I am getting exact BER plot what I
should get.

Now, for adaptive Interpolation (or adaptive doppler compensation),symbol
by symbol, I am getting this offset. I can see that my receiver faces
problem in converging the interpolation factor.

I have also seen the book that u suggested, by Meyrs et al. Horrible
book.

What is this wavelet transforms? I just know this *term*, as I have seen
some paper on it that address expansion/compression.

I know nothing is easy. I also know how it feels when u solve the
problem.

But it is just what i find is that this subject is not treated anywhere in
good manner.

Thanks a lot again.

Chintan

On Mar 18, 3:37&#4294967295;pm, "cpshah99" <cpsha...@rediffmail.com> wrote:
> Hi Julius
>
> Thanks for replying.
>
> This time I did what u had suggested before in some previous posts.
>
> Initially I assumed that I know what is the doppler at RX, so just do the
> resampling of the received signal, and I am getting exact BER plot what I
> should get.
>
> Now, for adaptive Interpolation (or adaptive doppler compensation),symbol
> by symbol, I am getting this offset. I can see that my receiver faces
> problem in converging the interpolation factor.

Then the problem must be in the tracking system.  A
common problem is figuring out the "gain" in the
feedback loop.

Just like any closed-loop control problem it is good to
construct a test case that is effectively a "step input".
For example, make a test signal that has delay
\tau_1 for a while, then abruptly change to \tau_2.
See if your synchronizer can "track" this.

>
> I have also seen the book that u suggested, by Meyrs et al. Horrible
> book.

I'm sure it's not everybody's favorite book but as far
as single-carrier communication is concerned, it's pretty
much the only book I use these days.  In fact, when I
see Moeneclaey in a few weeks I will beg him to teach
me about multi-carrier systems or share his notes.

>
> What is this wavelet transforms? I just know this *term*, as I have seen
> some paper on it that address expansion/compression.
>
> I know nothing is easy. I also know how it feels when u solve the
> problem.
>
> But it is just what i find is that this subject is not treated anywhere in
> good manner.

This means good job security for people who understand it :-).
But in seriousness, there are so many factors that it is difficult
to write a book about this.  The closest thing that I have found
is Myer/Moeneclaey/Fechtel.  For the sake of precision, they
wrote in a very terse, academic style.

Not to be apologetic for their writing style, but this is quite an
advanced topic, so it will be difficult for sure.  An alternative
approach to their writing style is to write a tutorial, which you
will find many, on one or two smaller topics.  I think people like
to cite the very basic tutorial by Luis Litwin (who I used to
know) on symbol synchronization.  But that document will not
tell you how well it works, or any detail on the performance
limits.  For that, you need something like
Myer/Moeneclaey/Fechtel.

In fact, if you look in Proakis' book, he has only a little treatise
on synchronization.  That's probably good enough for most
people, but I'm not one to judge.

I will even admit that I had bought a copy of that book in 1997,
but I didn't read it until I took Myer's "masters class" in 2000,
and still didn't fully appreciate the book until I've done work on
several modems now.

>
> Thanks a lot again.
>
> Chintan

Hi

I just forgot to mention this: in my simulation I update the Interpolation
factor I as below:

I=I+Kp*\theta; where I(0)=1, \theta=Im{conj{I}\hat{I}} where I is training
and \hat{I} is soft estimate of symbol. and Kp=constant.

Now, If I keep Kp=1e-5; this works fine up to doppler of 1 m/s. But the
doppler that I am dealing is 2 m/s (and some acceleration effect) and I
have to keep Kp=2e-5; This makes this thing worse.


Even I get the same motivation that *if I solve this*, I will be expert
*to some extent* and I will get job :)

I guess I will have to start reading this Myer book finally. It is just
that it is written in some different style. The proakis book is just
incomplete.

Well, I guess even u must have gone thru same troubles.

thanks a lot.

Chintan

cpshah99 wrote:
> Hi All
> 
> As we know that due to relative motion between TX and RX, the transmitted
> signal undergoes expansion/compression. And due to this symbol and phase
> synchronization is lost.
> 
> I have simulated this perticular thing, where I am using matlab's resample
> function to introduce this expansion/compression. 

Are you sure this is right? The expansion and dilation apply to the 
entire signal, carrier and modulation. Resampling alters that relationship.

   ...

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

>cpshah99 wrote:
>> Hi All
>> 
>> As we know that due to relative motion between TX and RX, the
transmitted
>> signal undergoes expansion/compression. And due to this symbol and
phase
>> synchronization is lost.
>> 
>> I have simulated this perticular thing, where I am using matlab's
resample
>> function to introduce this expansion/compression. 
>
>Are you sure this is right? The expansion and dilation apply to the 
>entire signal, carrier and modulation. Resampling alters that
relationship.

%%%%

Hi Jerry

I think what I have done is correct. I am resampling the carrier modulated
signal. So this carrier phase and timing impairements. 

And the good thing is that at RX, using adaptive linear iterpolator, it
locks to the value of velocity but at higher SNR.

I am thinking I need to do detail study of this topic.

Thanks

Chintan

On Mar 18, 5:19&#4294967295;pm, "cpshah99" <cpsha...@rediffmail.com> wrote:
>
> Hi Jerry
>
> I think what I have done is correct. I am resampling the carrier modulated
> signal. So this carrier phase and timing impairements.
>
> And the good thing is that at RX, using adaptive linear iterpolator, it
> locks to the value of velocity but at higher SNR.
>
> I am thinking I need to do detail study of this topic.
>
> Thanks
>
> Chintan

If you use a loop filter, the bandwidth of this filter has to be
sufficiently
high to handle the Doppler.  And that means that the filter admits
more
noise.  This is covered in Myer/Moeneclaey/Fechtel, page 97 ....

>If you use a loop filter, the bandwidth of this filter has to be
>sufficiently
>high to handle the Doppler.  And that means that the filter admits
>more
>noise.  This is covered in Myer/Moeneclaey/Fechtel, page 97 ....
>

Thanks again.

I will have a look at this.

>On Mar 18, 5:19=A0pm, "cpshah99" <cpsha...@rediffmail.com> wrote:
>>
>> Hi Jerry
>>
>> I think what I have done is correct. I am resampling the carrier
modulate=
>d
>> signal. So this carrier phase and timing impairements.
>>
>> And the good thing is that at RX, using adaptive linear iterpolator,
it
>> locks to the value of velocity but at higher SNR.
>>
>> I am thinking I need to do detail study of this topic.
>>
>> Thanks
>>
>> Chintan
>
>If you use a loop filter, the bandwidth of this filter has to be
>sufficiently
>high to handle the Doppler.  And that means that the filter admits
>more
>noise.  This is covered in Myer/Moeneclaey/Fechtel, page 97 ....

I've never tried this, but it should be possible to keep the bandwidth of
the loop filter narrow. Radar systems use Kalman and related techniques to
track the ebb and flow of target doppler, as the target manoeuvres. It
should be possible to use such an approach to make the loop adjust in a
focused manner, rather than just widening the loop, and letting it move
around in a rather unfocused manner. Of course, if your target tracking
algorithm gets fooled by tricky manoeuvres, you might regret trying this.
Watch out for targets doing inverted half loops, and reversing their
Doppler shift in a few seconds. :-\

Regards,
Steve