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Interpolation and the additive white gaussian noise

Started by Prasanna July 19, 2006
Prasanna wrote:

> ... All the channel sees is the output of the RRC filter, > and the channel adds white gaussian noise to each of those samples. No?
No. The noise isn't white after it passes through the filter. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
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> The noise is added after the signal is RRC filtered. The noise is added > at the output of the RRC transmit filter. > > >
But is is BEFORE the RRC filter in the receiver. The SNR is measured (calculated) after the RRC filter in the RECEIVER. Otherwise you would have to include all the noise in the entire universe from DC to daylight in the SNR calculation and that is obvioulsy not correct. Mark
Prasanna wrote:
> Jerry Avins wrote: >> Prasanna wrote: >> >>> ... All the channel sees is the output of the RRC filter, >>> and the channel adds white gaussian noise to each of those samples. No? >> No. The noise isn't white after it passes through the filter. > > The noise is added after the signal is RRC filtered. The noise is added > at the output of the RRC transmit filter.
RRC filtering is used so that the effect of identical cascaded filters (see "matched filters") will be a raised cosine, which theoretically eliminated ISI. The noise is filtered by the receiver before it is demodulated. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Prasanna wrote:
> Jerry Avins wrote: >> Prasanna wrote: >>> Dear all, >>> >>> The following problem recently came up in one of my simulations. I have >>> a PSK modulated RRC filtered signal that I have to transmit over the >>> AWGN channel. Before RRC filtering, I interpolate the IQ signal to >>> twice the Nyquist rate. >> Do you mean that there are components of the signal up to and including >> half the sample rate? that can't work. > > It will. Because it is four times over sampling already.
What does "... two setups: The first one transmits the RRC filtered signal at twice the Nyquist rate ..." mean? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Jerry Avins wrote:

> Prasanna wrote: > > Jerry Avins wrote: > >> Prasanna wrote: > >>> Dear all, > >>> > >>> The following problem recently came up in one of my simulations. I ha=
ve
> >>> a PSK modulated RRC filtered signal that I have to transmit over the > >>> AWGN channel. Before RRC filtering, I interpolate the IQ signal to > >>> twice the Nyquist rate. > >> Do you mean that there are components of the signal up to and including > >> half the sample rate? that can't work. > > > > It will. Because it is four times over sampling already. > > What does "... two setups: The first one transmits the RRC filtered > signal at twice the Nyquist rate ..." mean?
What is Nyquist rate? Supposing the signal spectrum extends from -B/2 to +B/2, the Nyquist sampling rate would be B. And twice the Nyquist rate would mean 2B.
> > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF
Jerry Avins wrote:

> Prasanna wrote: > > Jerry Avins wrote: > >> Prasanna wrote: > >> > >>> ... All the channel sees is the output of the RRC filter, > >>> and the channel adds white gaussian noise to each of those samples. N=
o?
> >> No. The noise isn't white after it passes through the filter. > > > > The noise is added after the signal is RRC filtered. The noise is added > > at the output of the RRC transmit filter. > > RRC filtering is used so that the effect of identical cascaded filters > (see "matched filters") will be a raised cosine, which theoretically > eliminated ISI. The noise is filtered by the receiver before it is > demodulated.
That is all well and good. But I just still dont understand how I should add noise to an oversampled signal at the output of the transmitter.
> > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF
Mark wrote:

> > The noise is added after the signal is RRC filtered. The noise is added > > at the output of the RRC transmit filter. > > > > > > But is is BEFORE the RRC filter in the receiver. The SNR is measured > (calculated) after the RRC filter in the RECEIVER. > > Otherwise you would have to include all the noise in the entire > universe from DC to daylight in the SNR calculation and that is > obvioulsy not correct.
Okay. So if the signal is spread between -B/2 and +B/2, the noise should also be white between -B/2 and +B/2 with a power spectrum of height N0. And what prevents me from having a white noise over -Inf to +Inf with a power spectrum of height N0? Which is what I get when I add white noise to an oversampled signal, right?
> > Mark
Prasanna wrote:
> Mark wrote: > >>> The noise is added after the signal is RRC filtered. The noise is added >>> at the output of the RRC transmit filter. >>> >> But is is BEFORE the RRC filter in the receiver. The SNR is measured >> (calculated) after the RRC filter in the RECEIVER. >> >> Otherwise you would have to include all the noise in the entire >> universe from DC to daylight in the SNR calculation and that is >> obvioulsy not correct. > > Okay. So if the signal is spread between -B/2 and +B/2, the noise > should also be white between -B/2 and +B/2 with a power spectrum of > height N0. And what prevents me from having a white noise over -Inf to > +Inf with a power spectrum of height N0? Which is what I get when I add > white noise to an oversampled signal, right?
The receiver's filter takes it out. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Prasanna wrote:
> Jerry Avins wrote: > >> Prasanna wrote: >>> Jerry Avins wrote: >>>> Prasanna wrote: >>>> >>>>> ... All the channel sees is the output of the RRC filter, >>>>> and the channel adds white gaussian noise to each of those samples. No? >>>> No. The noise isn't white after it passes through the filter. >>> The noise is added after the signal is RRC filtered. The noise is added >>> at the output of the RRC transmit filter. >> RRC filtering is used so that the effect of identical cascaded filters >> (see "matched filters") will be a raised cosine, which theoretically >> eliminated ISI. The noise is filtered by the receiver before it is >> demodulated. > > That is all well and good. But I just still dont understand how I > should add noise to an oversampled signal at the output of the > transmitter.
It's not what comes out of the transmitter that affects the error rate, but what gets into the detector. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������