FPGA Central

Hi,

I have a question about the detection of ASK constellation. If I use M
detection, it seems that adding LFP will not affect the detectio
performance, and the BER is Q(sqrt(SNR/2))=Q(sqrt(E/sigma^2/2)), where
is the average signal energy and sigma^2 is the noise variance. However
if the LPF performs such that it does not affect the signal, whil
decreases the noise variance to sigma^2*C and C<1, now, if I still use th
detection formula, what I get is a better performance, i.e
Q(sqrt(E/(C*sigma^2)/2))<Q(sqrt(E/sigma^2/2)). Obviously, there i
something wrong here, but I can not figure out. Could anyone help me
thank you very much.

On Tue, 16 Oct 2007 07:15:13 -0500, Rona wrote:

> Hi,
>
> I have a question about the detection of ASK constellation. If I use ML
>
> detection, it seems that adding LFP will not affect the detection
>
> performance, and the BER is Q(sqrt(SNR/2))=Q(sqrt(E/sigma^2/2)), where E
>
> is the average signal energy and sigma^2 is the noise variance. However,
>
> if the LPF performs such that it does not affect the signal, while
>
> decreases the noise variance to sigma^2*C and C<1, now, if I still use the
>
> detection formula, what I get is a better performance, i.e.
>
> Q(sqrt(E/(C*sigma^2)/2))<Q(sqrt(E/sigma^2/2)). Obviously, there is
>
> something wrong here, but I can not figure out. Could anyone help me,
>
> thank you very much.

Maximum likelihood filtering uses a matched filter. If you use a low-pass
filter (that is your "LPF", right?) that doesn't intrude on the signal
bandwidth then it will neither affect the signal nor the noise within the
signal bandwidth -- so after filtering and before detection the signal and
noise levels will both be the same.

What _will_ be different is the level of noise _outside_ of the signal
bandwidth -- this will, indeed, be down.

What a pre-filter to the detection process _can_ do for you is reduce the
chances that noise will cause nonlinear effects that may corrupt your
signal. By definition if you've implemented your digital processing
correctly it's more likely that this would happen in your analog
electronics, but making such a filter part of a 'proper' digital
implementation may not be out of line.

--
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

>On Tue, 16 Oct 2007 07:15:13 -0500, Rona wrote:
>
>> Hi,
>>
>> I have a question about the detection of ASK constellation. If I us
ML
>>
>> detection, it seems that adding LFP will not affect the detection
>>
>> performance, and the BER is Q(sqrt(SNR/2))=Q(sqrt(E/sigma^2/2)), wher
E
>>
>> is the average signal energy and sigma^2 is the noise variance
However,
>>
>> if the LPF performs such that it does not affect the signal, while
>>
>> decreases the noise variance to sigma^2*C and C<1, now, if I still us
the
>>
>> detection formula, what I get is a better performance, i.e.
>>
>> Q(sqrt(E/(C*sigma^2)/2))<Q(sqrt(E/sigma^2/2)). Obviously, there is
>>
>> something wrong here, but I can not figure out. Could anyone help me,
>>
>> thank you very much.
>
>Maximum likelihood filtering uses a matched filter. If you use
low-pass
>filter (that is your "LPF", right?) that doesn't intrude on the signal
>bandwidth then it will neither affect the signal nor the noise withi
the
>signal bandwidth -- so after filtering and before detection the signa
and
>noise levels will both be the same.
>
>What _will_ be different is the level of noise _outside_ of the signal
>bandwidth -- this will, indeed, be down.
>
>What a pre-filter to the detection process _can_ do for you is reduc
the
>chances that noise will cause nonlinear effects that may corrupt your
>signal. By definition if you've implemented your digital processing
>correctly it's more likely that this would happen in your analog
>electronics, but making such a filter part of a 'proper' digital
>implementation may not be out of line.
>
>--
>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
>



Hi Tim,

Thanks a lot for your help.

As only the noise inside the signal bandwidth affects the detectio
performance, for a fixed power spectral density(PSD) of the noise and fo
two signal waveforms with same energy while different bandwidth, is th
system with the signal having smaller bandwidth gives better detectio
performance, as there are less noise (noise power=PSD*bandwidth) insid
the signal bandwidth?

Thanks again.

Rona

On Oct 18, 12:24 pm, "Rona" <ronaya...@yahoo.com> wrote:
> >On Tue, 16 Oct 2007 07:15:13 -0500, Rona wrote:
>
> >> Hi,
>
> >> I have a question about the detection of ASK constellation. If I use
> ML
>
> >> detection, it seems that adding LFP will not affect the detection
>
> >> performance, and the BER is Q(sqrt(SNR/2))=Q(sqrt(E/sigma^2/2)), where
> E
>
> >> is the average signal energy and sigma^2 is the noise variance.
> However,
>
> >> if the LPF performs such that it does not affect the signal, while
>
> >> decreases the noise variance to sigma^2*C and C<1, now, if I still use
> the
>
> >> detection formula, what I get is a better performance, i.e.
>
> >> Q(sqrt(E/(C*sigma^2)/2))<Q(sqrt(E/sigma^2/2)). Obviously, there is
>
> >> something wrong here, but I can not figure out. Could anyone help me,
>
> >> thank you very much.
>
> >Maximum likelihood filtering uses a matched filter. If you use a
> low-pass
> >filter (that is your "LPF", right?) that doesn't intrude on the signal
> >bandwidth then it will neither affect the signal nor the noise within
> the
> >signal bandwidth -- so after filtering and before detection the signal
> and
> >noise levels will both be the same.
>
> >What _will_ be different is the level of noise _outside_ of the signal
> >bandwidth -- this will, indeed, be down.
>
> >What a pre-filter to the detection process _can_ do for you is reduce
> the
> >chances that noise will cause nonlinear effects that may corrupt your
> >signal. By definition if you've implemented your digital processing
> >correctly it's more likely that this would happen in your analog
> >electronics, but making such a filter part of a 'proper' digital
> >implementation may not be out of line.
>
> >--
> >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
>
> Hi Tim,
>
> Thanks a lot for your help.
>
> As only the noise inside the signal bandwidth affects the detection
> performance, for a fixed power spectral density(PSD) of the noise and for
> two signal waveforms with same energy while different bandwidth, is the
> system with the signal having smaller bandwidth gives better detection
> performance, as there are less noise (noise power=PSD*bandwidth) inside
> the signal bandwidth?
>
> Thanks again.
>
> Rona

Yes, this can be true, if as you said the signal power remains
constant. The result is that you have the same signal power occupying
a bandwidth that contains less noise power than the wider-band case,
so your SNR increases, and your detection performance will improve.
This is one reason why lowering the bitrate of your system can improve
your BER.

Jason

On Oct 18, 6:15 pm, cincy...@gmail.com wrote:
> On Oct 18, 12:24 pm, "Rona" <ronaya...@yahoo.com> wrote:
>
>
>
> > >On Tue, 16 Oct 2007 07:15:13 -0500, Rona wrote:
>
> > >> Hi,
>
> > >> I have a question about the detection of ASK constellation. If I use
> > ML
>
> > >> detection, it seems that adding LFP will not affect the detection
>
> > >> performance, and the BER is Q(sqrt(SNR/2))=Q(sqrt(E/sigma^2/2)), where
> > E
>
> > >> is the average signal energy and sigma^2 is the noise variance.
> > However,
>
> > >> if the LPF performs such that it does not affect the signal, while
>
> > >> decreases the noise variance to sigma^2*C and C<1, now, if I still use
> > the
>
> > >> detection formula, what I get is a better performance, i.e.
>
> > >> Q(sqrt(E/(C*sigma^2)/2))<Q(sqrt(E/sigma^2/2)). Obviously, there is
>
> > >> something wrong here, but I can not figure out. Could anyone help me,
>
> > >> thank you very much.
>
> > >Maximum likelihood filtering uses a matched filter. If you use a
> > low-pass
> > >filter (that is your "LPF", right?) that doesn't intrude on the signal
> > >bandwidth then it will neither affect the signal nor the noise within
> > the
> > >signal bandwidth -- so after filtering and before detection the signal
> > and
> > >noise levels will both be the same.
>
> > >What _will_ be different is the level of noise _outside_ of the signal
> > >bandwidth -- this will, indeed, be down.
>
> > >What a pre-filter to the detection process _can_ do for you is reduce
> > the
> > >chances that noise will cause nonlinear effects that may corrupt your
> > >signal. By definition if you've implemented your digital processing
> > >correctly it's more likely that this would happen in your analog
> > >electronics, but making such a filter part of a 'proper' digital
> > >implementation may not be out of line.
>
> > >--
> > >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
>
> > Hi Tim,
>
> > Thanks a lot for your help.
>
> > As only the noise inside the signal bandwidth affects the detection
> > performance, for a fixed power spectral density(PSD) of the noise and for
> > two signal waveforms with same energy while different bandwidth, is the
> > system with the signal having smaller bandwidth gives better detection
> > performance, as there are less noise (noise power=PSD*bandwidth) inside
> > the signal bandwidth?
>
> > Thanks again.
>
> Yes, this can be true, if as you said the signal power remains
> constant. The result is that you have the same signal power occupying
> a bandwidth that contains less noise power than the wider-band case,
> so your SNR increases, and your detection performance will improve.
> This is one reason why lowering the bitrate of your system can improve
> your BER.

However, if the symbol energy remains constant, then Eb/No will be the
same in both cases, so the performance will be identical.

--
Oli