Consider simple BPSK. Should the computation of Eb given the amplitude of an ideal bit include the effect of pulse-shaping? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Eb (energy per bit)
Started by ●August 5, 2013
Reply by ●August 5, 20132013-08-05
On Mon, 05 Aug 2013 14:39:44 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>Consider simple BPSK. Should the computation of Eb given the amplitude >of an ideal bit include the effect of pulse-shaping?It generally doesn't. Eb is just the total power divided by the bit rate. The pulse shape doesn't matter, since since things like Eb/No are power efficiency metrics. If you make a crappy Rx filter that causes a lot of ISI, you'll lose power efficiency.>-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.comEric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●August 5, 20132013-08-05
On 8/5/2013 1:39 PM, Randy Yates wrote:> Consider simple BPSK. Should the computation of Eb given the amplitude > of an ideal bit include the effect of pulse-shaping?Of course it should. Eb is average squared distance between "0" and "1". Vladimir Vassilevsky DSP and Mixed Signal Designs www.abvolt.com
Reply by ●August 5, 20132013-08-05
eric.jacobsen@ieee.org (Eric Jacobsen) writes:> On Mon, 05 Aug 2013 14:39:44 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > >>Consider simple BPSK. Should the computation of Eb given the amplitude >>of an ideal bit include the effect of pulse-shaping? > > It generally doesn't. Eb is just the total power divided by the bit > rate.Yeah, but "total power" (over a symbol period) depends on the pulse shape: Psym = (1 / Tsym) * \int_{0}^{Tsym} p^2(t) dt In fact, isn't Eb just Psym * Tsym (or Psym / R)? So Eb would be Eb = \int_{0}^{Tsym} p^2(t) dt ?> The pulse shape doesn't matter, since since things like Eb/No > are power efficiency metrics.I don't understand that statement.> If you make a crappy Rx filter that causes a lot of ISI, you'll lose > power efficiency.I could see that - such a filter would take energy from inside a symbol period and "smear" it outside the symbol period. (Although total energy should be conserved, not all would be used by the demodulator.) -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●August 5, 20132013-08-05
Randy Yates <yates@digitalsignallabs.com> writes:> eric.jacobsen@ieee.org (Eric Jacobsen) writes: > >> On Mon, 05 Aug 2013 14:39:44 -0400, Randy Yates >> <yates@digitalsignallabs.com> wrote: >> >>>Consider simple BPSK. Should the computation of Eb given the amplitude >>>of an ideal bit include the effect of pulse-shaping? >> >> It generally doesn't. Eb is just the total power divided by the bit >> rate. > > Yeah, but "total power" (over a symbol period) depends on the pulse shape: > > Psym = (1 / Tsym) * \int_{0}^{Tsym} p^2(t) dt > > In fact, isn't Eb just Psym * Tsym (or Psym / R)? So Eb would be > > Eb = \int_{0}^{Tsym} p^2(t) dt > > ?p(t) being the pulse shape. In the degenerate case (p(t) = 1), Eb = Tsym.>> The pulse shape doesn't matter, since since things like Eb/No >> are power efficiency metrics. > > I don't understand that statement. > >> If you make a crappy Rx filter that causes a lot of ISI, you'll lose >> power efficiency. > > I could see that - such a filter would take energy from inside a symbol > period and "smear" it outside the symbol period. (Although total energy > should be conserved, not all would be used by the demodulator.)-- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●August 5, 20132013-08-05
Vladimir Vassilevsky <nospam@nowhere.com> writes:> On 8/5/2013 1:39 PM, Randy Yates wrote: >> Consider simple BPSK. Should the computation of Eb given the amplitude >> of an ideal bit include the effect of pulse-shaping? > > Of course it should. Eb is average squared distance between "0" and > "1".Vlad: "Yes." Eric: "No." Randy: <head-spin> -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●August 5, 20132013-08-05
On Mon, 05 Aug 2013 17:01:14 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>eric.jacobsen@ieee.org (Eric Jacobsen) writes: > >> On Mon, 05 Aug 2013 14:39:44 -0400, Randy Yates >> <yates@digitalsignallabs.com> wrote: >> >>>Consider simple BPSK. Should the computation of Eb given the amplitude >>>of an ideal bit include the effect of pulse-shaping? >> >> It generally doesn't. Eb is just the total power divided by the bit >> rate. > >Yeah, but "total power" (over a symbol period) depends on the pulse shape: > > Psym = (1 / Tsym) * \int_{0}^{Tsym} p^2(t) dt > >In fact, isn't Eb just Psym * Tsym (or Psym / R)? So Eb would be > > Eb = \int_{0}^{Tsym} p^2(t) dt > >?The power one cares about managing is the transmit power, which is independent of pulse shape. That is the system resource that is being managed. This can be measured with a power meter in a real system or with the usual numerical methods if the signal is digitized. Separating individual symbol power levels isn't a typical thing to do and is not very straightforward. Measuring total power is pretty straightforward and normalizing to the bit rate is pretty easy, so that's typically what's done. The pulse shape doesn't need to ever enter into it. It is possible to do it the way you susggest but it's the much more difficult way to do it. It's also an unusual way to do it, so there's a risk of coming up with a result that doesn't match more common methods (due to subtle mistakes).>> The pulse shape doesn't matter, since since things like Eb/No >> are power efficiency metrics. > >I don't understand that statement.SNR, Es/No, Eb/No, etc., etc., are power efficiency metrics because the resource of interested being measured is the signal power. Improving performance on a BER curve, or a PER curve, is a demonstration of improving the use of the transmitted power. Getting more reliable bits per joule, so to speak. Another way to look at it is that if you're X dB from being where you need to be on an SNR or Eb/No, etc., performance curve, you can fix it by cranking up the Tx power X dB. That makes no statement about whatever the reason is for the X dB loss; it could be a channel impairment, it could be a mismatched filter pulse shape, it could be interference, whatever.>> If you make a crappy Rx filter that causes a lot of ISI, you'll lose >> power efficiency. > >I could see that - such a filter would take energy from inside a symbol >period and "smear" it outside the symbol period. (Although total energy >should be conserved, not all would be used by the demodulator.)The only point in the signal that matters for power efficiency is the sample that goes to the slicer for the decision. Everything in between that sample and the next decision sample is a "don't care", because they don't influence the decision. So the only sample at which ISI matters is that sample. In many eye diagrams the traces go all over the place except at the decision instant, and if the filter is well matched it'll converge there. It can "smear" anywhere it wants outside of that sample and still not have ISI that degrades performance, but if it disturbs the decision sample then performance will suffer. So any filter that provides matching at the symbol decision instant can provide performance at theoretical levels. There are an infinite number of such filter combinations at the Tx and Rx that can do this, so the only way performance is affected by the pulse filters is if they don't match. So, generally, the pulse shape doesn't matter when determining Eb, and doesn't matter even when determining performance for BER vs Eb/No, as long as the filters match. Usuallly FEC systems are evaluated assuming perfect matching (you don't even need to simulate a pulse filter, or even modulation), and often use Eb/No vs BER as a metric (or, depending on the system, PER vs SNR). So, no the pulse shape doesn't matter. If your system is losing performance it could be because the pulse filter is crappy, but it could be because of a lot of other things, too. A little more info in either one of the following links. The second one shows eye diagrams with matching filters. Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics: http://www.dsprelated.com/showarticle/168.php Pulse Shaping in Single-Carrier Communication Systems: http://www.dsprelated.com/showarticle/60.php ->Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.comEric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●August 5, 20132013-08-05
eric.jacobsen@ieee.org (Eric Jacobsen) writes:> On Mon, 05 Aug 2013 17:01:14 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > >>eric.jacobsen@ieee.org (Eric Jacobsen) writes: >> >>> On Mon, 05 Aug 2013 14:39:44 -0400, Randy Yates >>> <yates@digitalsignallabs.com> wrote: >>> >>>>Consider simple BPSK. Should the computation of Eb given the amplitude >>>>of an ideal bit include the effect of pulse-shaping? >>> >>> It generally doesn't. Eb is just the total power divided by the bit >>> rate. >> >>Yeah, but "total power" (over a symbol period) depends on the pulse shape: >> >> Psym = (1 / Tsym) * \int_{0}^{Tsym} p^2(t) dt >> >>In fact, isn't Eb just Psym * Tsym (or Psym / R)? So Eb would be >> >> Eb = \int_{0}^{Tsym} p^2(t) dt >> >>? > > The power one cares about managing is the transmit power, which is > independent of pulse shape.Well I'm having a problem with this statement right out of the gate, Eric. We are talking about *average* transmit power, right? Here's a (gross) counterexample: Let s1(t) = 1, 0 < t < 0.01, and s1(t) = s1(t+1) otherwise. Let s2(t) = 1. These two signals have different pulse shapes. Do they both have the same average power? Perhaps the underlying link here is that the total energy in a pulse is constant (say, normalized to 1), no matter how the pulse is spread out in time. Is that true? In that case the average power would be constant no matter what the shape is. (My example above violates this assumption, so that's why it doesn't work.) I'm snipping the rest since it's irrelevent if we can't get past this 1st principle. However, your articles do look tasty! :) -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●August 5, 20132013-08-05
On 8/5/2013 4:04 PM, Randy Yates wrote:> Vladimir Vassilevsky <nospam@nowhere.com> writes: > >> On 8/5/2013 1:39 PM, Randy Yates wrote: >>> Consider simple BPSK. Should the computation of Eb given the amplitude >>> of an ideal bit include the effect of pulse-shaping? >> >> Of course it should. Eb is average squared distance between "0" and >> "1". > > Vlad: "Yes." Eric: "No." Randy: <head-spin> >Jacobsen thinks if he adds unmodulated component to signal, it somehow changes Eb.
Reply by ●August 5, 20132013-08-05
Randy Yates <yates@digitalsignallabs.com> writes:> eric.jacobsen@ieee.org (Eric Jacobsen) writes: > >> On Mon, 05 Aug 2013 17:01:14 -0400, Randy Yates >> <yates@digitalsignallabs.com> wrote: >> >>>eric.jacobsen@ieee.org (Eric Jacobsen) writes: >>> >>>> On Mon, 05 Aug 2013 14:39:44 -0400, Randy Yates >>>> <yates@digitalsignallabs.com> wrote: >>>> >>>>>Consider simple BPSK. Should the computation of Eb given the amplitude >>>>>of an ideal bit include the effect of pulse-shaping? >>>> >>>> It generally doesn't. Eb is just the total power divided by the bit >>>> rate. >>> >>>Yeah, but "total power" (over a symbol period) depends on the pulse shape: >>> >>> Psym = (1 / Tsym) * \int_{0}^{Tsym} p^2(t) dt >>> >>>In fact, isn't Eb just Psym * Tsym (or Psym / R)? So Eb would be >>> >>> Eb = \int_{0}^{Tsym} p^2(t) dt >>> >>>? >> >> The power one cares about managing is the transmit power, which is >> independent of pulse shape. > > Well I'm having a problem with this statement right out of the gate, > Eric. We are talking about *average* transmit power, right?I see now we have failed to communicate. I think what you're trying to say is that, no matter what the pulse shape is, the transmitter gain will be bumped up so that maximum power is utilized. Correct? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
