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# Discussion Groups | Comp.DSP | time varying noise

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# time varying noise - 2005-02-18 03:11:00

```Hi folks,

I am modelling OFDM over a time varying channel using MATLAB. I want to
examine system performance as a function of receiver SNR. What I want
to know is how to specify the receiver noise power, given that the
received signal power is non-stationary. I have a couple of ideas but
they could both be wrong...

1. Ensure that the time-varying channel h always satisfies sum(h_i^2) 1; That way the received
power is the same at all instants in time,
regardless of the channel. Thus it is easy to know what noise level to
add for a given SNR. I'm not sure this is realistic.

non-stationary noise at the correct (time-varying) level to maintain a

Any other ideas?

---------------------------
The Porter-Boy
"Lovely day for a Guinness"

```
______________________________

# Re: time varying noise - Rune Allnor - 2005-02-18 03:34:00

```porterbo...@yahoo.com wrote:
> Hi folks,
>
> I am modelling OFDM over a time varying channel using MATLAB. I want
to
> examine system performance as a function of receiver SNR.

OK... so by "time varying channel" you mean that given constant
emitted signal power from the transmitter, the recieved signal power
varies?

> What I want
> to know is how to specify the receiver noise power, given that the
> received signal power is non-stationary. I have a couple of ideas but
> they could both be wrong...
>
> 1. Ensure that the time-varying channel h always satisfies sum(h_i^2)
> 1; That way the received power is the same at all instants in time,
> regardless of the channel. Thus it is easy to know what noise level
to
> add for a given SNR. I'm not sure this is realistic.

It's probably not realistic. But if the signal power varies, this
would be the obvious place to start.

> non-stationary noise at the correct (time-varying) level to maintain
a

Hmmmm.... depends on the type of noise you want to include. In a
multi-path environment, one mighte expect this sort of behaviour
from reflected paths. This would be coherent noise.

> Any other ideas?

In a true, time-varying scenario, there would probably be a little
bit of each noise component. I'd start with idea 1, and go on from
there after I get a little experience with how the system works.

Rune

```
______________________________

# Re: time varying noise - 2005-02-18 11:13:00

```> OK... so by "time varying channel" you mean that given constant
> emitted signal power from the transmitter, the recieved signal power
> varies?

Yes, and also its spectrum.

> > non-stationary noise at the correct (time-varying) level to
maintain
> a
>
> Hmmmm.... depends on the type of noise you want to include. In a
> multi-path environment, one mighte expect this sort of behaviour
> from reflected paths. This would be coherent noise.

Well, I dont think this is realistic either, but it's the best idea I
have. By continuously monitoring the receive power (in simulation only)
I can inject noise at the exact level to give me the target receiver
SNR. Admittedly this never happens in real life, but otherwise, how do
people generate (from simulation) those nice BER v. SNR curves?

> In a true, time-varying scenario, there would probably be a little
> bit of each noise component. I'd start with idea 1, and go on from
> there after I get a little experience with how the system works.

Thanks Rune. In fact I think idea two is better. The problem with idea
1 is that I have an AGC in the simulation. If the receiver power never
changes (as in idea 1) then I dont get to test my nifty AGC design...
so I am going with idea 2 for the moment. I am wide open to any better
suggestions...

```
______________________________

# Re: time varying noise - Col Brown - 2005-02-18 12:09:00

```p...@yahoo.com wrote in message
> Hi folks,
>

ello

> I am modelling OFDM over a time varying channel using MATLAB. I want to
> examine system performance as a function of receiver SNR. What I want
> to know is how to specify the receiver noise power, given that the
> received signal power is non-stationary. I have a couple of ideas but
> they could both be wrong...
>
> 1. Ensure that the time-varying channel h always satisfies sum(h_i^2) > 1; That way the
received power is the same at all instants in time,
> regardless of the channel. Thus it is easy to know what noise level to
> add for a given SNR. I'm not sure this is realistic.
>

Okay, this is all about what it is you want to show.  First off let me
give you a quick run through what it is that 'people' generally do.
For a fading channel, the channel taps are usually specified such that
sum(|h_i|^2) = 1 (see the ETSI channels if you don't believe me).  So,
with zero Doppler, you encounter a channel that gives you the same
input and output power.  However, if we start to add fading, then the
channel taps will wander around their initial values, but in the end,
the long term mean of the fading = 1 and the long term average gain of
the channel = 1.  Clear so far?

Now, if all you want to do is measure the BER performance in the
presence of fading, then you want to see the performance when the
channel is good and also when the channel is bad (nulled); but, you
know that the long term gain of the channel h = 1, so therefore, the
SNR can be set in relation to the power of your transmitted modulation
scheme.  In other words, you don't have to measure the power at the
that approximated the power of your mod scheme, you just set the noise
power in relation to the power of the transmitted signal.  phew!  This
is the fixed SNR case that you mentioned.

I hope you're with me so far.  Now, when using the above method, you
need to ensure 2 things, so that people can't shoot your results down
in one fell swoop.  First, you have to run the sims long enough so
that you count enough bit errors for the error rate you want to show.
Second, you need to run the sims long enough to ensure that you've hit
'statistically' the correct number of peaks and troughs for the fading
channel.  Now, if you're still reading after all this and are now
thinking, "I'm not interested in the BER performance anyway!", then
i'll stop here.  If on the other hand, you are interested in BER, then
perhaps we can re-post and I'll explain how to ensure the 2nd criteria
is satisfied.

One last thing before we all fall asleep.  There are ocassions where
you do want to change the SNR such that you get a constant SNR over
the fading channel, but they are really only useful results for people
who are looking at higher layer stuff like scheduling and H-ARQ and
the like.  If you're interested in this, then i'll have to trawl my
memory and come up with a good example of when you *should* change the
SNR!

> "Lovely day for a Guinness"

Indeed it is, Friday.

col
```
______________________________

# Re: time varying noise - Mark - 2005-02-18 13:18:00

```p...@yahoo.com wrote:
> Hi folks,
>
> I am modelling OFDM over a time varying channel using MATLAB. I want
to
> examine system performance as a function of receiver SNR. What I want
> to know is how to specify the receiver noise power, given that the
> received signal power is non-stationary. I have a couple of ideas but
> they could both be wrong...
>
> 1. Ensure that the time-varying channel h always satisfies sum(h_i^2)
> 1; That way the received power is the same at all instants in time,
> regardless of the channel. Thus it is easy to know what noise level
to
> add for a given SNR. I'm not sure this is realistic.
>
> non-stationary noise at the correct (time-varying) level to maintain
a
>
> Any other ideas?
>
> ---------------------------
> The Porter-Boy
> "Lovely day for a Guinness"

Noise is measured as average power.

If the noise is changing then you need to decide how long to average
for.  Depends on how fast the noise is changing. Normally the noise is
changing very very slowly relative to the modulation symbol period.
For the measurment to have any meaning, the noise should be averaged
over a time where it is essentially constant and that should be at
least several (10 to 100 or more ) modulation symbol times.

Mark

Mark

```
______________________________

# Re: time varying noise - porterboy - 2005-02-22 10:20:00

```> Okay, this is all about what it is you want to show.  First off let me
> give you a quick run through what it is that 'people' generally do.
> For a fading channel, the channel taps are usually specified such that
> sum(|h_i|^2) = 1 (see the ETSI channels if you don't believe me).  So,
> with zero Doppler, you encounter a channel that gives you the same
> input and output power.  However, if we start to add fading, then the
> channel taps will wander around their initial values, but in the end,
> the long term mean of the fading = 1 and the long term average gain of
> the channel = 1.  Clear so far?

Crystal. Although I see my simulation time disappearing over the
horizon...

> Now, if all you want to do is measure the BER performance in the
> presence of fading, then you want to see the performance when the
> channel is good and also when the channel is bad (nulled); but, you
> know that the long term gain of the channel h = 1, so therefore, the
> SNR can be set in relation to the power of your transmitted modulation
> scheme.

If the rx power is constant in the mean, should I just turn off my
AGC? I guess I can keep it running right, since it's only a scaling
factor, which scales the noise and the signal equally, not affecting
my SNR and hence my BER (assuming unlimited dynamic range for the
moment).

> In other words, you don't have to measure the power at the
> that approximated the power of your mod scheme, you just set the noise
> power in relation to the power of the transmitted signal.  phew!  This
> is the fixed SNR case that you mentioned.
>
> I hope you're with me so far.

Very clear. Although as I said above, if the rx power has to be fixed
over the long run, I can see that much longer simulations will have to
be run than if the rx power is tracked, and appropriate time-varying

> Now, when using the above method, you
> need to ensure 2 things, so that people can't shoot your results down
> in one fell swoop.  First, you have to run the sims long enough so
> that you count enough bit errors for the error rate you want to show.
> Second, you need to run the sims long enough to ensure that you've hit
> 'statistically' the correct number of peaks and troughs for the fading
> channel.  Now, if you're still reading after all this and are now
> thinking, "I'm not interested in the BER performance anyway!", then
> i'll stop here.  If on the other hand, you are interested in BER, then
> perhaps we can re-post and I'll explain how to ensure the 2nd criteria
> is satisfied.

Yup, I'm after the BER. Sorry I should have said that when I said
"performance".

> One last thing before we all fall asleep.  There are ocassions where
> you do want to change the SNR such that you get a constant SNR over
> the fading channel, but they are really only useful results for people
> who are looking at higher layer stuff like scheduling and H-ARQ and
> the like.  If you're interested in this, then i'll have to trawl my
> memory and come up with a good example of when you *should* change the
> SNR!

No, this is beyond what I want... I'm only interested in Physical
layer stuff. Thanks for that Col, it gave me a much better

PB
```
______________________________

# Re: time varying noise - 2005-02-22 14:53:00

```porterboy wrote:
> > Okay, this is all about what it is you want to show.  First off let
me
> > give you a quick run through what it is that 'people' generally do.

> > For a fading channel, the channel taps are usually specified such
that
> > sum(|h_i|^2) = 1 (see the ETSI channels if you don't believe me).
So,
> > with zero Doppler, you encounter a channel that gives you the same
> > input and output power.  However, if we start to add fading, then
the
> > channel taps will wander around their initial values, but in the
end,
> > the long term mean of the fading = 1 and the long term average gain
of
> > the channel = 1.  Clear so far?
>
> Crystal. Although I see my simulation time disappearing over the
> horizon...
>

Yep, but that's what is required i'm afraid.

> > Now, if all you want to do is measure the BER performance in the
> > presence of fading, then you want to see the performance when the
> > channel is good and also when the channel is bad (nulled); but, you
> > know that the long term gain of the channel h = 1, so therefore,
the
> > SNR can be set in relation to the power of your transmitted
modulation
> > scheme.
>
> If the rx power is constant in the mean, should I just turn off my
> AGC? I guess I can keep it running right, since it's only a scaling
> factor, which scales the noise and the signal equally, not affecting
> my SNR and hence my BER (assuming unlimited dynamic range for the
> moment).
>

Yep, the AGC just levels out your signal so that you can get within
your dynamic range.  It'll scale both noise and signal equally.

> > In other words, you don't have to measure the power at the
something
> > that approximated the power of your mod scheme, you just set the
noise
> > power in relation to the power of the transmitted signal.  phew!
This
> > is the fixed SNR case that you mentioned.
> >
> > I hope you're with me so far.
>
> Very clear. Although as I said above, if the rx power has to be fixed
> over the long run, I can see that much longer simulations will have
to
> be run than if the rx power is tracked, and appropriate time-varying
>

Indeed, if you do it this way (track the noise), then you're really
cheating the results.  I guess it depends what you want to show?
There's another technique you can use and that is to generate the
results based on a static channel model.  You then have BER curves for
your different mod/coding schemes.  You can then sample this BER curve
depending on the SNR of your fading generator for a given Doppler
frequency Fd.  Oh, hang on, you have multipath right?...okay, it
doesn't quite work out like that then.  You have to account for the
destructive and constructive interference going on.  Forget what i said
here.

> > Now, when using the above method, you
> > need to ensure 2 things, so that people can't shoot your results
down
> > in one fell swoop.  First, you have to run the sims long enough so
> > that you count enough bit errors for the error rate you want to
show.
> > Second, you need to run the sims long enough to ensure that you've
hit
> > 'statistically' the correct number of peaks and troughs for the
> > channel.  Now, if you're still reading after all this and are now
> > thinking, "I'm not interested in the BER performance anyway!", then
> > i'll stop here.  If on the other hand, you are interested in BER,
then
> > perhaps we can re-post and I'll explain how to ensure the 2nd
criteria
> > is satisfied.
>
> Yup, I'm after the BER. Sorry I should have said that when I said
> "performance".
>

Well, it seems to me that you're gonna have to run sims for a long
time.  What Doppler freq (in relation to the bandwidth if you like) are
you running?  What I've done in the past is to say that i only want to
run the sims long enough such that the fading rate of the channel
matches the theoretical fading rate with nulls down to -20dB.  This may
shave off some simulation time for you.....just a suggestion.

> > One last thing before we all fall asleep.  There are ocassions
where
> > you do want to change the SNR such that you get a constant SNR over
> > the fading channel, but they are really only useful results for
people
> > who are looking at higher layer stuff like scheduling and H-ARQ and
> > the like.  If you're interested in this, then i'll have to trawl my
> > memory and come up with a good example of when you *should* change
the
> > SNR!
>
> No, this is beyond what I want... I'm only interested in Physical
> layer stuff. Thanks for that Col, it gave me a much better