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Tx and Rx filters gains and energies

Started by commsignal September 3, 2013
Hi All,
   Although it is a basic question but I couldn't find its answer in any
available reference. When we filter the signal at the Tx and Rx, how should
we adjust the filter gains or filter energies to keep the overall energy
figures correct *at every stage*. For example, should Tx filter gain be
necessarily set to the oversampling factor, or what should be the Rx filter
gain.
Thanks.	 

_____________________________		
Posted through www.DSPRelated.com
>Hi All, > Although it is a basic question but I couldn't find its answer in any >available reference. When we filter the signal at the Tx and Rx, how
should
>we adjust the filter gains or filter energies to keep the overall energy >figures correct *at every stage*. For example, should Tx filter gain be >necessarily set to the oversampling factor, or what should be the Rx
filter
>gain. >Thanks. > >_____________________________ >Posted through www.DSPRelated.com >
There are many side-questions which I'm not clear about regarding the above. 1. Does convolution with a unit energy filter conserve the energy of the input signal? 2. The universal definition of the energy itself is \sum |x(n)^2. Shouldn't it be \sum |x(n)^2 * (sampling time)? 3. Should the square-root raised cosine pulse be unit energy, or the overall Tx/Rx combination (raised cosine) be unit energy? Also, according to which definition of energy in question 2 above. 4. I get correct BER results for many different Tx and Rx filter scalings. What is the correct method? It is important because any blocks before it will affect the energy entering the system blocks at each stage. Thanks for any available feedback. _____________________________ Posted through www.DSPRelated.com
Hi,

thinking about samples, "power" is probably more appropriate. A sample
represents a certain power, valid over its duration. If you oversample (use
more samples), the duration of each sample scales down accordingly. The
energy per sample reduces, the sample value remains unchanged and so does
the overall power. 

There is no right or wrong. One way to look at it is to see samples
representing a continuous-time waveform. Regardless how many samples you
take, the level of the waveform (and thus, individual samples) remain
unchanged.

One thing that needs attention is adding noise, because a given power
spreads over the whole covered bandwidth. So when you inject AWGN at an
oversampled rate, the noise power needs to scale accordingly, as you want a
given power density now over a wider bandwidth.

Defining "the" gain of a filter is quite a topic in itself, conceptually
simple but messy in calculations. 
Often, 0 Hz is convenient (i.e. sum of taps in a FIR filter), but you'll
have to re-think the problem every time. 

Yes, a pulse shaping filter dissipates some power, but if the noise
bandwidth equals the cutoff frequency, the effective gain is often 1 (check
case-by-case).	 

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On Tue, 03 Sep 2013 18:13:49 -0500, commsignal wrote:

>>Hi All, >> Although it is a basic question but I couldn't find its answer in any >>available reference. When we filter the signal at the Tx and Rx, how > should >>we adjust the filter gains or filter energies to keep the overall energy >>figures correct *at every stage*. For example, should Tx filter gain be >>necessarily set to the oversampling factor, or what should be the Rx > filter >>gain. >>Thanks. >> >>_____________________________ >>Posted through www.DSPRelated.com >> >> > There are many side-questions which I'm not clear about regarding the > above. > 1. Does convolution with a unit energy filter conserve the energy of the > input signal? > 2. The universal definition of the energy itself is \sum |x(n)^2. > Shouldn't it be \sum |x(n)^2 * (sampling time)? > 3. Should the square-root raised cosine pulse be unit energy, or the > overall Tx/Rx combination (raised cosine) be unit energy? Also, > according to which definition of energy in question 2 above. > 4. I get correct BER results for many different Tx and Rx filter > scalings. What is the correct method? It is important because any blocks > before it will affect the energy entering the system blocks at each > stage.
First, I feel you need to be very careful about the use of the word "energy" in a signal-processing context. "Energy" means something quite concrete when you're talking about physical phenomenon (such as radio waves) which happen to be carrying signals. But even with analog electronics, once you get those signals into your signal processing hardware, the meaning of "energy" breaks down. (Note, too, that in practical implementations you'll find yourself caring more about power than energy -- yes, the energy of a specific bit is important, but when you're trying to design a radio receiver it's the power that impinges on the antenna, and the noise power of the electronics, that you deal with directly.) I think it is much more sensible once you're inside your signal processing environment (be it analog electronics, digital hardware, or hydro-pneumatic arrangements powered by slave girls on exercise bikes) that you think in terms of signal levels -- voltage, numbers, PSI, whatever. Your goal is to make sure that the signal is not corrupted on the small end by noise, distortion, or sweat dripping into the hydraulic fluid, and to make sure that the signal is not corrupted on the large end by saturating amplifiers, numeric overflow, or muscle cramps. To answer your individual questions: 1: No. Try it. But first do this thought experiment: Take a unit-energy filter and a unit-energy signal (by whatever definition of "unit energy" floats your boat). Take the filter to have a spectrum that is totally disjoint from the signal. Now run the signal through the filter -- what is the resulting energy? 2: It doesn't matter. You're just using "energy" as a metaphor for the real thing, here. 3: See my answer to (2) above, and guess at my opinion. 4: "The" correct method is to choose _a_ correct method out of the infinite number possible that works well for you. The real stumbling block -- that you have to deal with no matter what -- is that as soon as your signal is transmitted in the _real world_, then energy (or more properly, power) does matter. What really matters is that you get the signal to your detector as unmolested as possible, and that when it gets there you have a way to predict the Eb/No. You'll find that with real-world problems in radio communication, you often can't do any better than to come up with a very rough estimate of Eb/No, because both signal and noise are subject to multiple effects that you have little control over. At this point you will find that all of the science that you're learning is merely the pallet and paint that you use as tools to exercise the art of communications system design. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
"all of the science that you're learning is merely the pallet and paint
that you use as tools to exercise the art of communications system
design."

Never read such a good philosophical statement in a technical context.
Thanks.	 

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Posted through www.DSPRelated.com
This doesn't directly answer your question, but I always start from the analog part, and then work my way back to baseband, and then to symbols, when I think about power / gain / SNR scaling. 

In digital, when you ignore overflow and quantization, everything is almost always correct up to a scaling factor, so conversely scaling factor almost always doesn't really matter unless you are doing fixed-point. It's the analog that matters.