In a BPSK simulation in which the data is sampled at one sample per symbol, the signal is already "filtered" to Fs / 2, and so noise is limited. However, if we are simulating at multiple samples per symbol, perhaps even hundreds, and we generate the required noise to get a specific Eb/No, then there is a LOT more noise "at the receiver" than in the one sample per symbol case. It is clear that in order for such a simulation to approach the theoretical BER vs Eb/No, there must be filtering done somewhere/somehow. How is it done? Is it through the pulse shaping filter? Or is it simply not done this way, i.e., if one wants theoretical performance one samples at one sample per symbol? Or is there some other approach? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Simulation Bandwidth Question
Started by ●August 22, 2013
Reply by ●August 22, 20132013-08-22
On Thu, 22 Aug 2013 06:41:53 -0400, Randy Yates wrote:> In a BPSK simulation in which the data is sampled at one sample per > symbol, the signal is already "filtered" to Fs / 2, and so noise is > limited. > > However, if we are simulating at multiple samples per symbol, perhaps > even hundreds, and we generate the required noise to get a specific > Eb/No, then there is a LOT more noise "at the receiver" than in the one > sample per symbol case. > > It is clear that in order for such a simulation to approach the > theoretical BER vs Eb/No, there must be filtering done > somewhere/somehow. How is it done? Is it through the pulse shaping > filter? Or is it simply not done this way, i.e., if one wants > theoretical performance one samples at one sample per symbol? Or is > there some other approach?The filtering is done in the matched filter. In a channel with known timing and phase, no distortion, and additive white Gaussian noise, the optimal filter for the pulse is a matched filter -- I think this is your "pulse shaping filter". -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 22, 20132013-08-22
On Thu, 22 Aug 2013 11:36:39 -0500, Tim Wescott <tim@seemywebsite.really> wrote:>On Thu, 22 Aug 2013 06:41:53 -0400, Randy Yates wrote: > >> In a BPSK simulation in which the data is sampled at one sample per >> symbol, the signal is already "filtered" to Fs / 2, and so noise is >> limited. >> >> However, if we are simulating at multiple samples per symbol, perhaps >> even hundreds, and we generate the required noise to get a specific >> Eb/No, then there is a LOT more noise "at the receiver" than in the one >> sample per symbol case. >> >> It is clear that in order for such a simulation to approach the >> theoretical BER vs Eb/No, there must be filtering done >> somewhere/somehow. How is it done? Is it through the pulse shaping >> filter? Or is it simply not done this way, i.e., if one wants >> theoretical performance one samples at one sample per symbol? Or is >> there some other approach? > >The filtering is done in the matched filter. In a channel with known >timing and phase, no distortion, and additive white Gaussian noise, the >optimal filter for the pulse is a matched filter -- I think this is your >"pulse shaping filter".Another way to look at this is that the decision slicer operates on one sample/symbol, so that has to have protection from aliasing. This is done, at a minimum, by the receiver matched filter (aka, pulse filter). For systems that need adjacent channel rejection, selectivity, etc., etc., additional filtering prior to the pulse filter is often needed.>-- > >Tim Wescott >Wescott Design Services >http://www.wescottdesign.com >Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●August 22, 20132013-08-22
eric.jacobsen@ieee.org (Eric Jacobsen) writes:> On Thu, 22 Aug 2013 11:36:39 -0500, Tim Wescott > <tim@seemywebsite.really> wrote: > >>On Thu, 22 Aug 2013 06:41:53 -0400, Randy Yates wrote: >> >>> In a BPSK simulation in which the data is sampled at one sample per >>> symbol, the signal is already "filtered" to Fs / 2, and so noise is >>> limited. >>> >>> However, if we are simulating at multiple samples per symbol, perhaps >>> even hundreds, and we generate the required noise to get a specific >>> Eb/No, then there is a LOT more noise "at the receiver" than in the one >>> sample per symbol case. >>> >>> It is clear that in order for such a simulation to approach the >>> theoretical BER vs Eb/No, there must be filtering done >>> somewhere/somehow. How is it done? Is it through the pulse shaping >>> filter? Or is it simply not done this way, i.e., if one wants >>> theoretical performance one samples at one sample per symbol? Or is >>> there some other approach? >> >>The filtering is done in the matched filter. In a channel with known >>timing and phase, no distortion, and additive white Gaussian noise, the >>optimal filter for the pulse is a matched filter -- I think this is your >>"pulse shaping filter". > > Another way to look at this is that the decision slicer operates on > one sample/symbol, so that has to have protection from aliasing. > This is done, at a minimum, by the receiver matched filter (aka, pulse > filter). > > For systems that need adjacent channel rejection, selectivity, etc., > etc., additional filtering prior to the pulse filter is often needed.OK, thanks Eric/Tim. Now how about same question with FSK instead of BPSK? ... :) As you know, the pulse shaping is done in the phase domain, not the signal domain. So how does one "optimally" filter THAT?!? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●August 22, 20132013-08-22
On Thu, 22 Aug 2013 17:29:20 -0400, Randy Yates wrote:> eric.jacobsen@ieee.org (Eric Jacobsen) writes: > >> On Thu, 22 Aug 2013 11:36:39 -0500, Tim Wescott >> <tim@seemywebsite.really> wrote: >> >>>On Thu, 22 Aug 2013 06:41:53 -0400, Randy Yates wrote: >>> >>>> In a BPSK simulation in which the data is sampled at one sample per >>>> symbol, the signal is already "filtered" to Fs / 2, and so noise is >>>> limited. >>>> >>>> However, if we are simulating at multiple samples per symbol, perhaps >>>> even hundreds, and we generate the required noise to get a specific >>>> Eb/No, then there is a LOT more noise "at the receiver" than in the >>>> one sample per symbol case. >>>> >>>> It is clear that in order for such a simulation to approach the >>>> theoretical BER vs Eb/No, there must be filtering done >>>> somewhere/somehow. How is it done? Is it through the pulse shaping >>>> filter? Or is it simply not done this way, i.e., if one wants >>>> theoretical performance one samples at one sample per symbol? Or is >>>> there some other approach? >>> >>>The filtering is done in the matched filter. In a channel with known >>>timing and phase, no distortion, and additive white Gaussian noise, the >>>optimal filter for the pulse is a matched filter -- I think this is >>>your "pulse shaping filter". >> >> Another way to look at this is that the decision slicer operates on one >> sample/symbol, so that has to have protection from aliasing. >> This is done, at a minimum, by the receiver matched filter (aka, pulse >> filter). >> >> For systems that need adjacent channel rejection, selectivity, etc., >> etc., additional filtering prior to the pulse filter is often needed.I suppose the egg-head answer to that is that the additional filtering makes the noise at the pulse-shaping filter look "white", or "white enough", or something.> OK, thanks Eric/Tim. Now how about same question with FSK instead of > BPSK? ... :) As you know, the pulse shaping is done in the phase domain, > not the signal domain. So how does one "optimally" filter THAT?!?Same sort of deal, except that it's not at all easy to come up with a definitive "optimal" filter. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 22, 20132013-08-22
>In a BPSK simulation in which the data is sampled at one sample per >symbol, the signal is already "filtered" to Fs / 2, and so noise is >limited. > >However, if we are simulating at multiple samples per symbol, perhaps >even hundreds, and we generate the required noise to get a specific >Eb/No, then there is a LOT more noise "at the receiver" than in the one >sample per symbol case. > >It is clear that in order for such a simulation to approach the >theoretical BER vs Eb/No, there must be filtering done >somewhere/somehow. How is it done? Is it through the pulse shaping >filter? Or is it simply not done this way, i.e., if one wants >theoretical performance one samples at one sample per symbol? Or is >there some other approach? >-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.com >I think that your question has another dimension. In addition to matched filtering at the receiver, for the simulation purpose, one must also take into account the no. of samples per symbol at the Tx while calculating the noise power. This approach along with matched filtering will make your simulation system independent of no. of samples per symbol. Check the exact relation on page 25 of the (original) document: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.46.2884&rep=rep1&type=pdf _____________________________ Posted through www.DSPRelated.com
Reply by ●August 23, 20132013-08-23
On Thursday, August 22, 2013 5:41:53 AM UTC-5, Randy Yates wrote:> In a BPSK simulation in which the data is sampled at one sample per > > symbol, the signal is already "filtered" to Fs / 2, and so noise is > > limited. > > > > However, if we are simulating at multiple samples per symbol, perhaps > > even hundreds, and we generate the required noise to get a specific > > Eb/No, then there is a LOT more noise "at the receiver" than in the one > > sample per symbol case. > > > > It is clear that in order for such a simulation to approach the > > theoretical BER vs Eb/No, there must be filtering done > > somewhere/somehow. How is it done? Is it through the pulse shaping > > filter? Or is it simply not done this way, i.e., if one wants > > theoretical performance one samples at one sample per symbol? Or is > > there some other approach? > > -- > > Randy Yates > > Digital Signal Labs > > http://www.digitalsignallabs.comRandy: I am not sure exactly how you want your simulation to work and what it is intended to do, but if it involves multiple samples per data bit, perhaps even multiple samples per period of the carrier, and the signal that you are looking at has already been processed through some filter (a RF filter intended to remove adjacent channel interference, out-of-band noise, etc) then the "AWGN" that you should be adding to each sample _might not_ really be AWGN in the usual sense of independent zero-mean Gaussian random variables. Rather, there can be correlation between the noise in adjacent samples, where the details depend on what assumptions you are making about said RF filtering. Dilip Sarwate
Reply by ●August 23, 20132013-08-23
>OK, thanks Eric/Tim. Now how about same question with FSK instead of >BPSK? ... :) As you know, the pulse shaping is done in the phase domain, >not the signal domain. So how does one "optimally" filter THAT?!? >--In theory you can "linearize" the signal, however, this may result in an infininte number of matched filters. For certain modulation indexes, this simplifies. For example consider continuous phase FSK with modulation index 1/2 (MSK). This requires only a half-cosine matched filter. Other modulation indexes that are the ratio of integers similarly reduce to a reasonable level. -Doug _____________________________ Posted through www.DSPRelated.com
Reply by ●August 25, 20132013-08-25
On Thursday, August 22, 2013 10:41:53 PM UTC+12, Randy Yates wrote:> In a BPSK simulation in which the data is sampled at one sample per > > symbol, the signal is already "filtered" to Fs / 2, and so noise is > > limited. > > > > However, if we are simulating at multiple samples per symbol, perhaps > > even hundreds, and we generate the required noise to get a specific > > Eb/No, then there is a LOT more noise "at the receiver" than in the one > > sample per symbol case. > > > > It is clear that in order for such a simulation to approach the > > theoretical BER vs Eb/No, there must be filtering done > > somewhere/somehow. How is it done? Is it through the pulse shaping > > filter? Or is it simply not done this way, i.e., if one wants > > theoretical performance one samples at one sample per symbol? Or is > > there some other approach? > > -- > > Randy Yates > > Digital Signal Labs > > http://www.digitalsignallabs.comDid I hear Simulating? Better not let our resident Vampyre hear you say that or you will qualify as a matlab stupindo.
Reply by ●August 26, 20132013-08-26
"DougB" <60916@dsprelated> writes:>>OK, thanks Eric/Tim. Now how about same question with FSK instead of >>BPSK? ... :) As you know, the pulse shaping is done in the phase domain, >>not the signal domain. So how does one "optimally" filter THAT?!? >>-- > > In theory you can "linearize" the signal, however, this may result in an > infininte number of matched filters. For certain modulation indexes, this > simplifies. For example consider continuous phase FSK with modulation > index 1/2 (MSK). This requires only a half-cosine matched filter. Other > modulation indexes that are the ratio of integers similarly reduce to a > reasonable level.Thanks Doug. I think I get you. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
