Time varying channel

Hi All

I have been facing this problem for some long time and I have lost my
patience. and I am not able to solve it. I would be really thankful if you
can show me some way out.

Problem: to model time varying frequency selective multipath channel.

My simulation is at baseband, one sample per symbol and QPSK modulation.
And the delay are symbol spaced.

lets say there are three paths. If the channel is time invariant then I
can convolve my signal with channel and thats it. But how do I add
variations depending on the speed of vehicle?

What I have done so far:

generate first order auto-regressive process, using IIR filter, i.e.

h(k)=s*h(k-1)+v; where v is complex noise with some variance

so for the first path: g1=0.407+h;
second path: g2=0.815+h;
third path: g3=0.407+h;

the values that I have selected are: s=0.95 and variance for v=4e-4;
which gives rician fading channel.


But how can I take into account the velocity?

How can I model the same variation using FIR filter?

The carrier freq fc=12KHz, symbol rate=4KHz and velocity=5 m/s.

Or what is the best way to model time varying channel?

Your help will greatly appreciated.

Thanking you.

Chintan

On Thu, 20 Nov 2008 09:27:30 -0600, "cpshah99"
<cpshah99@rediffmail.com> wrote:

>Hi All
>
>I have been facing this problem for some long time and I have lost my
>patience. and I am not able to solve it. I would be really thankful if you
>can show me some way out.
>
>Problem: to model time varying frequency selective multipath channel.
>
>My simulation is at baseband, one sample per symbol and QPSK modulation.
>And the delay are symbol spaced.
>
>lets say there are three paths. If the channel is time invariant then I
>can convolve my signal with channel and thats it. But how do I add
>variations depending on the speed of vehicle?
>
>What I have done so far:
>
>generate first order auto-regressive process, using IIR filter, i.e.
>
>h(k)=s*h(k-1)+v; where v is complex noise with some variance
>
>so for the first path: g1=0.407+h;
>second path: g2=0.815+h;
>third path: g3=0.407+h;
>
>the values that I have selected are: s=0.95 and variance for v=4e-4;
>which gives rician fading channel.
>
>
>But how can I take into account the velocity?
>
>How can I model the same variation using FIR filter?
>
>The carrier freq fc=12KHz, symbol rate=4KHz and velocity=5 m/s.
>
>Or what is the best way to model time varying channel?
>
>Your help will greatly appreciated.
>
>Thanking you.
>
>Chintan

A few thoughts for you:

Is the signal continuous or bursty?   If it's bursty, how long are the
transmissions?

Many wireless systems are bursty and the coherence time of the channel
is longer than the longest burst that may be transmitted.    This
means that modelling is typically done by randomly selecting a channel
instance from a statistical model that remains static for each burst.
In other words, the channel is assumed to be static for each
transmission.

Is your carrier frequency really 12kHz?   Is the transmission medium
really frequency selective with only a 4kHz bandwidth?

Usually channel models are FIR models, and doppler is modelled by
statistical variation in the taps depending on the environment and
application.   Check Jakes wireless models or the ITU mobile wireless
models for examples.


Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

>A few thoughts for you:
>
>Is the signal continuous or bursty?   If it's bursty, how long are the
>transmissions?
>
>Many wireless systems are bursty and the coherence time of the channel
>is longer than the longest burst that may be transmitted.    This
>means that modelling is typically done by randomly selecting a channel
>instance from a statistical model that remains static for each burst.
>In other words, the channel is assumed to be static for each
>transmission.
>
>Is your carrier frequency really 12kHz?   Is the transmission medium
>really frequency selective with only a 4kHz bandwidth?
>
>Usually channel models are FIR models, and doppler is modelled by
>statistical variation in the taps depending on the environment and
>application.   Check Jakes wireless models or the ITU mobile wireless
>models for examples.
>

%%%

Hi Eric

Thanks a lot.

I actually forgot to mention that I am working on underwater comms.

So, yeah, the Fc=12 KHz and the BW B=4KHz and the packet size is 2511
symbols including 511 long training sequence. 

So lets say, there r just two paths. and the delay between them is 10e-3
sec. So the total number of interfering symbols are 40.

Now if the channel is time invariant, then the ISI signal can be given
as:

isi=0.8946*[x zeros(1,40)] + 0.4468*[zeros(1,40) x]; where x is the signal
to be transmitted. the values 0.8946 and 0.4468 are chosen randomly and
normalised.

But my problem is, how put variations on top of this values, taking into
account vehicle speed.

And I have not found any good treatment, from simulation point of view, in
any good book.

Thanks a lot again.

Chintan

On Nov 20, 10:27&#4294967295;am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> Hi All
>
> I have been facing this problem for some long time and I have lost my
> patience. and I am not able to solve it. I would be really thankful if you
> can show me some way out.
>
> Problem: to model time varying frequency selective multipath channel.
>
> My simulation is at baseband, one sample per symbol and QPSK modulation.
> And the delay are symbol spaced.
>
> lets say there are three paths. If the channel is time invariant then I
> can convolve my signal with channel and thats it. But how do I add
> variations depending on the speed of vehicle?
>

The best reference for time-varying, locally time-invariant channels
is
Kailath's classical treatment.  You have been asking this question as
if looking for a magical cure, but I'm not sure what ails you :-).

http://dspace.mit.edu/handle/1721.1/11319

Hi Julius

Thanks for the link. I will study this thesis for sure.

But the problem is if I use uncorrelated rayleigh fading on each path,
then the receiver fails because LMS algorithm is not good enough to track
the changes in channel (I guess).

The way I am generating uncorrelated rayleigh is 

ray=sqrt(0.5)*(randn(1,1000)+j*randn(1,1000));

So I thought to make it rician channel and I got one paper which models
rician channel using first order IIR filter. But it does nt take into
account the velocity.

Or may be I am confused to the core about this perticular topic.

I would really appreciate if somebody can explain me this perticular
thing. 

May be I am asking a lot but I dont need any code but a better
understanding of this topic.


Thanks  again.

Chintan

On Fri, 21 Nov 2008 03:48:14 -0600, "cpshah99"
<cpshah99@rediffmail.com> wrote:

>Hi Julius
>
>Thanks for the link. I will study this thesis for sure.
>
>But the problem is if I use uncorrelated rayleigh fading on each path,
>then the receiver fails because LMS algorithm is not good enough to track
>the changes in channel (I guess).
>
>The way I am generating uncorrelated rayleigh is 
>
>ray=sqrt(0.5)*(randn(1,1000)+j*randn(1,1000));
>
>So I thought to make it rician channel and I got one paper which models
>rician channel using first order IIR filter. But it does nt take into
>account the velocity.
>
>Or may be I am confused to the core about this perticular topic.
>
>I would really appreciate if somebody can explain me this perticular
>thing. 
>
>May be I am asking a lot but I dont need any code but a better
>understanding of this topic.
>
>
>Thanks  again.
>
>Chintan

I'm not sure you're going to get there easily with an IIR model.

Consider a FIR model where the taps are the channel impulse response.
At baseband the taps are complex valued and the phase of each will be
a result of the path length for that particular reflected path.   As
the terminal moves (or as the reflector moves), the length of that
path changes and therefore causes phase rotation at that filter tap.
Since the path length at each tap is different and the reflector path
geometries can be pretty different for each path, the amount and rate
of rotation at each ray can differ.

So you have an n-ray model where each ray contributes to a susbtantial
amount of energy at some particular tap(s) in the FIR model, and the
phase rotation of that particular tap will be affected by the motion
of the terminals and the reflector.    Each ray may result in a
different rate of rotation for it's corresponding tap.

How fast each tap rotates depends on the model, how differently they
rotate depends on the model as well.   The trick is matching the model
to accurately reflect the environment for your application.

The underwater stuff is a mystery to me other than I suspect it's
typically wetter than an rf wireless enviroment.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

Hi Eric

It is really wetter than RF and to be honest I am going mad.

Let me try something. Forget the medium. The discussion is at baseband,
one sample per symbol.

Let say the packet length is 2511 symbols (Training + Data). And limit the
multipath to just two. The data rate of the system is 4000. 

We know that time invariant case is very easy.

Now, let say the max doppler frequency fd=8 Hz.( f_c*v/c, where f_c=12KHz,
v=1 m/s and c=1500 m/s for underwater).

If I generate a complex gaussian noise and pass it thru a FIR filter with
the cut off freq= fd.

Then the o/p of filter can be used to multiply the signal.

noise=randn(1,2511)+j*randn(1,2511);
B=fir1(100,8/2000);
out=filter(B,1,noise);

Can I do this?


Regards,

Chintan

On Nov 21, 11:45&#4294967295;am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> Hi Eric
>
> It is really wetter than RF and to be honest I am going mad.
>
> Let me try something. Forget the medium. The discussion is at baseband,
> one sample per symbol.
>
> Let say the packet length is 2511 symbols (Training + Data). And limit the
> multipath to just two. The data rate of the system is 4000.
>
> We know that time invariant case is very easy.
>
> Now, let say the max doppler frequency fd=8 Hz.( f_c*v/c, where f_c=12KHz,
> v=1 m/s and c=1500 m/s for underwater).
>
> If I generate a complex gaussian noise and pass it thru a FIR filter with
> the cut off freq= fd.
>
> Then the o/p of filter can be used to multiply the signal.
>
> noise=randn(1,2511)+j*randn(1,2511);
> B=fir1(100,8/2000);
> out=filter(B,1,noise);
>
> Can I do this?
>
> Regards,
>
> Chintan

this may help you

look up info on Agilent 11757B

Mark

>this may help you
>
>look up info on Agilent 11757B
>
>Mark
>
>

%%%

Hi Mark

Thanks but this product is not available anymore and the AN is also not
tht gr8.

Thanks a anyways.

Chintan

On Nov 24, 5:34&#4294967295;am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> >this may help you
>
> >look up info on Agilent 11757B
>
> >Mark
>
> %%%
>
> Hi Mark
>
> Thanks but this product is not available anymore and the AN is also not
> tht gr8.
>
> Thanks a anyways.
>
> Chintan

the point is that it is implemented simply as a bunch of digital delay
lines...

it takes the original signal, delays it, attenuates it and adds it
back in...

with the correct choice of delay, that alone makes a frequency
selective channel..

if you also add a small frequency offset to the delayed path, that
makes it time varying...

it's actually very simple..
Mark