Noise variance

Hi 

In soft demapper, we need either value of SNR or noise variance sigma. Now
in real time we do not know both of these. 

And lets say that we know variance of white noise but as the signal passes
through equaliser, we get filtered noise with different variance. So how to
find variance of filtered noise.

Help in this respect will be greatly appreciated.

Thanks
Chintan 

cpshah99 wrote:

> Hi 
> 
> In soft demapper, we need either value of SNR or noise variance sigma.

It depends.

> Now
> in real time we do not know both of these. 

In real time we can now both of these althoigh we generally don't need it.

> And lets say that we know variance of white noise but as the signal passes
> through equaliser, we get filtered noise with different variance. So how to
> find variance of filtered noise.

Just like any other noise.

> 
> Help in this respect will be greatly appreciated.

How much is the great appreciation?


VLV

Hi VLV

Thank you for replying. But how to find noise variance of the equalised
signal?

And why it depends for Soft Demapper?

Your help is really appreciated. :)

Thanks again.
Chintan
>
>
>cpshah99 wrote:
>
>> Hi 
>> 
>> In soft demapper, we need either value of SNR or noise variance sigma.
>
>It depends.
>
>> Now
>> in real time we do not know both of these. 
>
>In real time we can now both of these althoigh we generally don't need
it.
>
>> And lets say that we know variance of white noise but as the signal
passes
>> through equaliser, we get filtered noise with different variance. So
how to
>> find variance of filtered noise.
>
>Just like any other noise.
>
>> 
>> Help in this respect will be greatly appreciated.
>
>How much is the great appreciation?
>
>
>VLV
>
>

Hi Chintan,
I think you are asking how a known frequency response affects the variance
of white noise passing through it. 

Imagine that the white noise is broken into its component sinusoids. 
Since its random noise, each of these sinusoids is uncorrelated with the
other sinusoids.  So, to find the variance of the total signal, take the
amplitude of each sinusoid, square it, and sum.  

The known frequency response changes the amplitude of each sinusoid. So to
find the total change in the variance, square each point in the frequency
response and sum.

Hope this helps.  If it doesn't, you probably need to rephrase your
question.
Regards,
Steve    

On Feb 18, 4:54 am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> Hi VLV
>
> Thank you for replying. But how to find noise variance of the equalised
> signal?
>
> And why it depends for Soft Demapper?
>
> Your help is really appreciated. :)
>
> Thanks again.
> Chintan
>
>
>
> >cpshah99 wrote:
>
> >> Hi
>
> >> In soft demapper, we need either value of SNR or noise variance sigma.
>
> >It depends.
>
> >> Now
> >> in real time we do not know both of these.
>
> >In real time we can now both of these althoigh we generally don't need
> it.
>
> >> And lets say that we know variance of white noise but as the signal
> passes
> >> through equaliser, we get filtered noise with different variance. So
> how to
> >> find variance of filtered noise.
>
> >Just like any other noise.
>
> >> Help in this respect will be greatly appreciated.
>
> >How much is the great appreciation?
>
> >VLV

I'm assuming you're trying to design a soft-in, soft-out demapper that
operates in the presence of AWGN. If you can make the assumption that
your input bits are equally likely to be ones and zeros (i.e. you have
a perfect source encoder), then you don't necessarily need to know the
noise variance. If you're working in the metric domain, for example,
your input metrics are going to nominally be something like:

|z - x_i|^2/No + k

where z is your channel observation, x_i is the i-th noise-free symbol
location (i.e. one of the positions in your signal constellation), No
is twice the noise variance, and k is an additive constant common to
all of the terms (it comes from the constant term in front of the AWGN
pdf; since the transformation to the metric domain uses a logarithm,
it becomes additive).

Here's where your goal is important: if you're trying to minimize
sequence error, then you would do min-sum processing on these metrics;
i.e. for each allowable configuration of the demapper, you'll sum up
all of the input metrics corresponding to the inputs for each
configuration, then find the minimum total metric that you then use to
derive your output metrics. Since a multiplicative constant (like No)
commutes with the min operator, it doesn't matter whether you have it
in there or not. Only the relative ordering of the metric values is
important; their values are not. Therefore, you can leave the No value
out and you will still get correct demapping. The same argument allows
you to neglect the additive constant k.

However, if you're aiming to minimize bit error, you would use min*-
sum processing, where min*(x,y) = -ln(1 + exp(-x) + exp(-y)).
Multiplicative constants do not commute with the min* operator, so in
most cases, you do need to know the SNR, or have a good estimate of it
in order to get acceptable performance. Therefore, in a practical
system where it might be difficult to know Eb/No, using MAP sequence
detection with min-sum processing is more reasonable.

Jason

>On Feb 18, 4:54 am, "cpshah99" <cpsha...@rediffmail.com> wrote:
>> Hi VLV
>>
>> Thank you for replying. But how to find noise variance of the
equalised
>> signal?
>>
>> And why it depends for Soft Demapper?
>>
>> Your help is really appreciated. :)
>>
>> Thanks again.
>> Chintan
>>
>>
>>
>> >cpshah99 wrote:
>>
>> >> Hi
>>
>> >> In soft demapper, we need either value of SNR or noise variance
sigma.
>>
>> >It depends.
>>
>> >> Now
>> >> in real time we do not know both of these.
>>
>> >In real time we can now both of these althoigh we generally don't
need
>> it.
>>
>> >> And lets say that we know variance of white noise but as the signal
>> passes
>> >> through equaliser, we get filtered noise with different variance.
So
>> how to
>> >> find variance of filtered noise.
>>
>> >Just like any other noise.
>>
>> >> Help in this respect will be greatly appreciated.
>>
>> >How much is the great appreciation?
>>
>> >VLV
>
>I'm assuming you're trying to design a soft-in, soft-out demapper that
>operates in the presence of AWGN. If you can make the assumption that
>your input bits are equally likely to be ones and zeros (i.e. you have
>a perfect source encoder), then you don't necessarily need to know the
>noise variance. If you're working in the metric domain, for example,
>your input metrics are going to nominally be something like:
>
>|z - x_i|^2/No + k
>
>where z is your channel observation, x_i is the i-th noise-free symbol
>location (i.e. one of the positions in your signal constellation), No
>is twice the noise variance, and k is an additive constant common to
>all of the terms (it comes from the constant term in front of the AWGN
>pdf; since the transformation to the metric domain uses a logarithm,
>it becomes additive).
>
>Here's where your goal is important: if you're trying to minimize
>sequence error, then you would do min-sum processing on these metrics;
>i.e. for each allowable configuration of the demapper, you'll sum up
>all of the input metrics corresponding to the inputs for each
>configuration, then find the minimum total metric that you then use to
>derive your output metrics. Since a multiplicative constant (like No)
>commutes with the min operator, it doesn't matter whether you have it
>in there or not. Only the relative ordering of the metric values is
>important; their values are not. Therefore, you can leave the No value
>out and you will still get correct demapping. The same argument allows
>you to neglect the additive constant k.
>
>However, if you're aiming to minimize bit error, you would use min*-
>sum processing, where min*(x,y) = -ln(1 + exp(-x) + exp(-y)).
>Multiplicative constants do not commute with the min* operator, so in
>most cases, you do need to know the SNR, or have a good estimate of it
>in order to get acceptable performance. Therefore, in a practical
>system where it might be difficult to know Eb/No, using MAP sequence
>detection with min-sum processing is more reasonable.
>
>Jason
>
HI Jason

Thank you very much. You have understood my question. What I have is
recorded signals from real time experiment where the channels is time and
freq varying. Now I have downconverted this received signal to baseband.
And I have passed this baseband signal thru DFE. Now the output of DFE is
soft QPSK symbol.

My aim is to design soft in soft out demapper. I had designed Soft
demmaper from Bauch's paper. But in that i had used noise variance.

Please explain me once again if you can.

Thanking you

Chintan