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From: Steve Pope on 7 Jul 2010 10:19
dvsarwate <dvsarwate(a)gmail.com> wrote:

>The noise power (and hence the equivalent
>noise bandwidth) is proportional to the area
>under the *square* of the transfer function.
>In this instance, the square of the RRC curve
>is the RC curve which has the same area for
>all choices of alpha in the range from 0 to 1.
>Yes, the noise passes only through the RRC
>filter in the receiver, but the noise power and
>equivalent noise bandwidth are determined
>by area under the square of the transfer function,
>RC, not the transfer function RRC. This fact
>was also pointed out succinctly by Vladimir
>Vassilevsky earlier in this thread.

I think of the "equivalent noise bandwidth" as
the bandwidth of a brick-wall filter that would result
in the same noise power at the receiver's demodulator.
Given a typical link model where wideband noise is added at the
receiver's input, this means that filtering within the
transmitter does not affect the equivalent noise bandwidth.

Is this not the correct way to look at it?

Steve
From: dvsarwate on 7 Jul 2010 10:59
On Jul 7, 9:19 am, spop...(a)speedymail.org (Steve Pope) wrote:
> dvsarwate  <dvsarw...(a)gmail.com> wrote:
> >The noise power (and hence the equivalent
> >noise bandwidth) is proportional to the area
> >under the *square* of the transfer function.
> >In this instance, the square of the RRC curve
> >is the RC curve which has the same area for
> >all choices of alpha in the range from 0 to 1.
> >Yes, the noise passes only through the RRC
> >filter in the receiver, but the noise power and
> >equivalent noise bandwidth are determined
> >by area under the square of the transfer function,
> >RC, not the transfer function RRC.  This fact
> >was also pointed out succinctly by Vladimir
> >Vassilevsky earlier in this thread.
>
> I think of the "equivalent noise bandwidth" as
> the bandwidth of a brick-wall filter that would result
> in the same noise power at the receiver's demodulator.
> Given a typical link model where wideband noise is added at the
> receiver's input, this means that filtering within the
> transmitter does not affect the equivalent noise bandwidth.
>
> Is this not the correct way to look at it?
>
> Steve

Yes, that is indeed the correct way to look at it. But
the issue is that with matched filtering, the SNR depends
on the *received* signal energy, not the energy of the
signal that appears at the output of the matched filter.
The signal at the matched filter output has an RC
spectrum and the ratio of the "signal bandwidth"
(however that is defined, -3 dB or rms or whatever)
to the equivalent noise bandwidth doesn't seem to
have much to do with SNR. "cl7teckie" (Paul) and
"Mark" obviously believe that this ratio (signal BW
to noise BW) is important, and perhaps it is important
in ways that I am unaware of. Maybe they can be
persuaded to give more details of the reasons for
their beliefs.

--Dilip Sarwate
From: cl7teckie on 7 Jul 2010 12:37
Hi Steve,

Well, per my point, I totally agree that the the equivalent noise bandwidth
does not change with different alpha. And this bandwidth definitely is not
affected by the transmitter.

However, I am asking over the SNR after the matched filtering.

Paul

>
>I think of the "equivalent noise bandwidth" as
>the bandwidth of a brick-wall filter that would result
>in the same noise power at the receiver's demodulator.
>Given a typical link model where wideband noise is added at the
>receiver's input, this means that filtering within the
>transmitter does not affect the equivalent noise bandwidth.
>
>Is this not the correct way to look at it?
>
>Steve
>
From: cl7teckie on 7 Jul 2010 12:49
Yes, let me clarify.

The question/doubt that I have is over measured SNR after matched
filtering, comparing with the CNR to the receiver. Is there a difference?
Some in the industry believed that is no difference, irregardless of Alpha
setting, while some believe there is indeed a minor difference. My simple
analysis seems to indicate that the signal power with RRC at the
transmitter may make the SNR after matched filter different from that of
the noise due to 'slightly different equivalent noise bandwidth. The doubt
that I have, is exactly where you pointed. But I still cannot figure out if
the RRC filter at the Tx affects the 'perceived' SNR after matched
filtering.

In the nutshell, I am wondering if the CNR at the receiver input any
difference from the measured SNR after matched filtering. Assuming pure
Gaussian and ideal conditions/filter.

Paul

>Yes, that is indeed the correct way to look at it. But
>the issue is that with matched filtering, the SNR depends
>on the *received* signal energy, not the energy of the
>signal that appears at the output of the matched filter.
>The signal at the matched filter output has an RC
>spectrum and the ratio of the "signal bandwidth"
>(however that is defined, -3 dB or rms or whatever)
>to the equivalent noise bandwidth doesn't seem to
>have much to do with SNR. "cl7teckie" (Paul) and
>"Mark" obviously believe that this ratio (signal BW
>to noise BW) is important, and perhaps it is important
>in ways that I am unaware of. Maybe they can be
>persuaded to give more details of the reasons for
>their beliefs.
>
>--Dilip Sarwate
>
From: Steve Pope on 7 Jul 2010 16:22
cl7teckie <paul(a)n_o_s_p_a_m.pixelmetrix.com> wrote:

>Well, per my point, I totally agree that the the equivalent noise bandwidth
>does not change with different alpha.

Under certain assumptions, such as there is no other filtering
in the receiver other than a RRC filter, there are no images,
aliases etc. this is true.

I'm not sure it's that significant a fact.

>However, I am asking over the SNR after the matched filtering.

I think this falls into the category of "what you see is what you get".

If you're trying to use measurements at RF as a proxy for
SNR at the demodulator, then you're on the hook for keeping
track of any and all system aspects that might affect your
understanding of the relationship between the two. But in
forming this understanding, you're unlikely to create any
widely applicable general rules about such measurements, since
all systems, and measurement scenarios, are subtly (at minimum)
different from each other.

In a previous life (at T.I.) I recall endless discussions
about how to relate "SNR in the receiver" with "SNR at the
input of the Viterbi decoder" in an OFDM system. It seemed
to me as soon as someone thought they knew "the rule" about
relating these two, some other impairment would get folded
in and that "rule" would break down.

So I would say the only real rule is: it is what it is.

Steve
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