acquisition system with importance sampling

Hi
                In the acquisition of direct sequence spread spectrum
signals with low signal-to-noise ratio and wide dynamic range.the
system use all-digital quadrature demodulation of DS/SS signals.Long
pseudo-noise spread spectrum codes with carrier doppler are detected by
a method in which the signal is successively IF integrated,differential
detected and video integrated.
	After correlating the incoming signal for T seconds the prompt
in-phase and quadrature coherent correlator outputs can be expressed as
in:
	I(m)=SI(m)+nI(m);
	Q(m)=SQ(m)+nQ(m);
	where m is the index of the successive inputs of the non-coherent
correlation,I(m) and Q(m) are correspondingly the in-phase and
quadrature values resulting from the coherent integration.SI(m) and
SQ(m) are signal,nI(m) and nQ(m) are assumed to be zero mean Gaussian
distribution random variables.For analytical simulations,the hypothesis
is :
	-Hypothesis H0 corresponds to the case that only themal noise is
present.
	-Hypothesis H1 describes the case the desired signal is present.
	The differential acquisition can be mathematically expressed as :
	Y=Sum[XI(m)XI(m-1)+XQ(m)XQ(m-1),{m,1,N}];
	The signal detection analysis is done on hypothesis H0 and H1.With a
given probability of false alarm,the threshold value is computed of
false alarm,the threshold value is computed with hypothesis H0.The
probability of detection is computed with the computed threshold value
in hypothesis H1.but the pdf of H0 and H1 can't expressed with a
mathematics formula.So I want to simulation this performance.Because
the false alarm probability is 1e-5 or 1e-6.Importance sampling can
reducing run time in this simulation.I think that it can use g-method
importance sampling to simulation this system,but how to choose the
weight funciton ,that is alter the statistical properties of the noise
disturbution?Or still have other methods?

Thanks

tatsec wrote:
> Hi
>                 In the acquisition of direct sequence spread spectrum
> signals with low signal-to-noise ratio and wide dynamic range.the
> system use all-digital quadrature demodulation of DS/SS signals.Long
> pseudo-noise spread spectrum codes with carrier doppler are detected by
> a method in which the signal is successively IF integrated,differential
> detected and video integrated.
> 	After correlating the incoming signal for T seconds the prompt
> in-phase and quadrature coherent correlator outputs can be expressed as
> in:
> 	I(m)=SI(m)+nI(m);
> 	Q(m)=SQ(m)+nQ(m);
> 	where m is the index of the successive inputs of the non-coherent
> correlation,I(m) and Q(m) are correspondingly the in-phase and
> quadrature values resulting from the coherent integration.SI(m) and
> SQ(m) are signal,nI(m) and nQ(m) are assumed to be zero mean Gaussian
> distribution random variables.For analytical simulations,the hypothesis
> is :
> 	-Hypothesis H0 corresponds to the case that only themal noise is
> present.
> 	-Hypothesis H1 describes the case the desired signal is present.
> 	The differential acquisition can be mathematically expressed as :
> 	Y=Sum[XI(m)XI(m-1)+XQ(m)XQ(m-1),{m,1,N}];
> 	The signal detection analysis is done on hypothesis H0 and H1.With a
> given probability of false alarm,the threshold value is computed of
> false alarm,the threshold value is computed with hypothesis H0.The
> probability of detection is computed with the computed threshold value
> in hypothesis H1.but the pdf of H0 and H1 can't expressed with a
> mathematics formula.So I want to simulation this performance.Because
> the false alarm probability is 1e-5 or 1e-6.Importance sampling can
> reducing run time in this simulation.I think that it can use g-method
> importance sampling to simulation this system,but how to choose the
> weight funciton ,that is alter the statistical properties of the noise
> disturbution?Or still have other methods?

This sounds like a composite of a spec and a homework problem. What is 
"importance sampling"?

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

Also called biased sampling , this is one of the variance-reducing
techniques in Monte Carlo methods.
you can see this
website:http://rkb.home.cern.ch/rkb/AN16pp/node132.html
"Jerry Avins =D0=B4=B5=C0=A3=BA
"
> tatsec wrote:
> > Hi
> >                 In the acquisition of direct sequence spread spectrum
> > signals with low signal-to-noise ratio and wide dynamic range.the
> > system use all-digital quadrature demodulation of DS/SS signals.Long
> > pseudo-noise spread spectrum codes with carrier doppler are detected by
> > a method in which the signal is successively IF integrated,differential
> > detected and video integrated.
> > 	After correlating the incoming signal for T seconds the prompt
> > in-phase and quadrature coherent correlator outputs can be expressed as
> > in:
> > 	I(m)=3DSI(m)+nI(m);
> > 	Q(m)=3DSQ(m)+nQ(m);
> > 	where m is the index of the successive inputs of the non-coherent
> > correlation,I(m) and Q(m) are correspondingly the in-phase and
> > quadrature values resulting from the coherent integration.SI(m) and
> > SQ(m) are signal,nI(m) and nQ(m) are assumed to be zero mean Gaussian
> > distribution random variables.For analytical simulations,the hypothesis
> > is :
> > 	-Hypothesis H0 corresponds to the case that only themal noise is
> > present.
> > 	-Hypothesis H1 describes the case the desired signal is present.
> > 	The differential acquisition can be mathematically expressed as :
> > 	Y=3DSum[XI(m)XI(m-1)+XQ(m)XQ(m-1),{m,1,N}];
> > 	The signal detection analysis is done on hypothesis H0 and H1.With a
> > given probability of false alarm,the threshold value is computed of
> > false alarm,the threshold value is computed with hypothesis H0.The
> > probability of detection is computed with the computed threshold value
> > in hypothesis H1.but the pdf of H0 and H1 can't expressed with a
> > mathematics formula.So I want to simulation this performance.Because
> > the false alarm probability is 1e-5 or 1e-6.Importance sampling can
> > reducing run time in this simulation.I think that it can use g-method
> > importance sampling to simulation this system,but how to choose the
> > weight funciton ,that is alter the statistical properties of the noise
> > disturbution?Or still have other methods?
>
> This sounds like a composite of a spec and a homework problem. What is
> "importance sampling"?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=
=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=
=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=
=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=
=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=
=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5=A1=A5

On Wed, 20 Dec 2006 10:59:09 -0500, Jerry Avins <jya@ieee.org> wrote:

>tatsec wrote:
>> Hi
>>                 In the acquisition of direct sequence spread spectrum
>> signals with low signal-to-noise ratio and wide dynamic range.the
>> system use all-digital quadrature demodulation of DS/SS signals.Long
>> pseudo-noise spread spectrum codes with carrier doppler are detected by
>> a method in which the signal is successively IF integrated,differential
>> detected and video integrated.
>> 	After correlating the incoming signal for T seconds the prompt
>> in-phase and quadrature coherent correlator outputs can be expressed as
>> in:
>> 	I(m)=SI(m)+nI(m);
>> 	Q(m)=SQ(m)+nQ(m);
>> 	where m is the index of the successive inputs of the non-coherent
>> correlation,I(m) and Q(m) are correspondingly the in-phase and

  (snipped)
>
>This sounds like a composite of a spec and a homework problem. What is 
>"importance sampling"?
>
>Jerry

Jerry,
   would please stop clowning around and get down 
to the business of solving this problem for tatsec 
so that he doesn't have to?
:-)  :-)

See Ya',
[-Rick-]