BPSK,QPSK,16-QAM constellation points
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From: tommala on 6 Dec 2009 15:10 >On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote: > >> Hi everyone, >> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM >> modulator(using only constellation points coordinates). I figured out >> from wikipedia.org and "Digital Modulation Technique" that constellation >> points will have following coordinates(in the complex plane): >> 1) (+-sqrt(Eb),0) for BPSK >> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3) >> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for >> 16-QAM >> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK >> and QPSK. >> I think there is a mistake in constellation points representation above. >> Do You have any ideas? >> Thank You in advance for any remarks. > >BPSK : . . > > . . >QPSK : > . . > > > . . . . > > . . . . >16-QAM: > . . . . > > . . . . > > > > > > > > >-- >www.wescottdesign.com > I know how constellations look but don't know how connect its points coordinates with Eb. Dilip Warrier can You write sth more about r.How it is related to Eb? Maybe where can I find mathematical considerations of constellation points if such exist.
From: Tim Wescott on 6 Dec 2009 15:57 On Sun, 06 Dec 2009 14:10:17 -0600, tommala wrote: >>On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote: >> >>> Hi everyone, >>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM >>> modulator(using only constellation points coordinates). I figured out >>> from wikipedia.org and "Digital Modulation Technique" that > constellation >>> points will have following coordinates(in the complex plane): >>> 1) (+-sqrt(Eb),0) for BPSK >>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3) >>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for >>> 16-QAM >>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK >>> and QPSK. >>> I think there is a mistake in constellation points representation > above. >>> Do You have any ideas? >>> Thank You in advance for any remarks. >> >>BPSK : . . >> >> . . >>QPSK : >> . . >> >> >> . . . . >> >> . . . . >>16-QAM: >> . . . . >> >> . . . . >> >> >> >> >> >> >> >> >>-- >>www.wescottdesign.com >> > I know how constellations look but don't know how connect its points > coordinates with Eb. > > Dilip Warrier can You write sth more about r.How it is related to Eb? > Maybe where can I find mathematical considerations of constellation > points if such exist. Then you need to understand the connection between Eb and the position of the point on the constellation. Once you do, you will both understand exactly how to connect a constellation's point to the Eb for that case, and you will understand why folks start using the word "average" when they talk about the Eb of a 16-QAM signal. So -- I assume you're transmitting these constellations on some sort of a sinusoidal carrier, with the real axis mapped to the in-phase portion of the signal, and the imaginary axis mapped to the quadrature portion of the signal. If that is, indeed, what you're doing, and if you know where a symbol lies on the complex plane, what is the energy of that symbol? Until you can answer that question, you're not ready for any answers you get from us. Once you _do_ answer that question, you may not need to look to us for answers. -- www.wescottdesign.com
From: Eric Jacobsen on 6 Dec 2009 16:15 On 12/6/2009 1:10 PM, tommala wrote: >> On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote: >> >>> Hi everyone, >>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM >>> modulator(using only constellation points coordinates). I figured out >>> from wikipedia.org and "Digital Modulation Technique" that > constellation >>> points will have following coordinates(in the complex plane): >>> 1) (+-sqrt(Eb),0) for BPSK >>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3) >>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for >>> 16-QAM >>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK >>> and QPSK. >>> I think there is a mistake in constellation points representation > above. >>> Do You have any ideas? >>> Thank You in advance for any remarks. >> BPSK : . . >> >> . . >> QPSK : >> . . >> >> >> . . . . >> >> . . . . >> 16-QAM: >> . . . . >> >> . . . . >> >> >> >> >> >> >> >> >> -- >> www.wescottdesign.com >> > I know how constellations look but don't know how connect its points > coordinates with Eb. > > Dilip Warrier can You write sth more about r.How it is related to Eb? > Maybe where can I find mathematical considerations of constellation points > if such exist. Can you compute the SNR? Carrier to Noise ratio (C/N)? If so, it's a pretty straightforward transformation from S/N or C/N to Eb/No. The nature of the transformation is described in many textbooks. Here are some hints: Eb is a bit energy measurement. What's the relationship between the total signal power and the amount of energy proportional to a single bit? No is the noise power per unit Hz bandwidth. If you know the noise power computed from the symbol constellation, that can be converted to No pretty easily. So, to compute SNR, you need to know the signal power and the noise power. Eb and No can be computed from each of those, respectively. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: tommala on 6 Dec 2009 17:13 >On 12/6/2009 1:10 PM, tommala wrote: >>> On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote: >>> >>>> Hi everyone, >>>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM >>>> modulator(using only constellation points coordinates). I figured out >>>> from wikipedia.org and "Digital Modulation Technique" that >> constellation >>>> points will have following coordinates(in the complex plane): >>>> 1) (+-sqrt(Eb),0) for BPSK >>>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3) >>>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) for >>>> 16-QAM >>>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for BPSK >>>> and QPSK. >>>> I think there is a mistake in constellation points representation >> above. >>>> Do You have any ideas? >>>> Thank You in advance for any remarks. >>> BPSK : . . >>> >>> . . >>> QPSK : >>> . . >>> >>> >>> . . . . >>> >>> . . . . >>> 16-QAM: >>> . . . . >>> >>> . . . . >>> >>> >>> >>> >>> >>> >>> >>> >>> -- >>> www.wescottdesign.com >>> >> I know how constellations look but don't know how connect its points >> coordinates with Eb. >> >> Dilip Warrier can You write sth more about r.How it is related to Eb? >> Maybe where can I find mathematical considerations of constellation points >> if such exist. > >Can you compute the SNR? Carrier to Noise ratio (C/N)? > >If so, it's a pretty straightforward transformation from S/N or C/N to >Eb/No. The nature of the transformation is described in many textbooks. > >Here are some hints: > >Eb is a bit energy measurement. What's the relationship between the >total signal power and the amount of energy proportional to a single bit? > >No is the noise power per unit Hz bandwidth. If you know the noise >power computed from the symbol constellation, that can be converted to >No pretty easily. > >So, to compute SNR, you need to know the signal power and the noise >power. Eb and No can be computed from each of those, respectively. > >-- >Eric Jacobsen >Minister of Algorithms >Abineau Communications >http://www.abineau.com > I can't compute SNR nor C/N. Even I don't have to. The simulation has GUI in which user can choose (Eb/No)min; (Eb/No)max and (Eb/No)step (Eb/No in [dB]). The program compute in the loop for every i=Eb/No from (Eb/No)min to (Eb/No)max BER as ratio=number of wrong received bits/number of total transmitted bits. In the loop I calculate Eb as Eb=No*pow(10,i/10)where No is constant number e.g. 1 [W/Hz]. I assume Eb constant for every modulation. And my problem is to correct connect Eb with point coordinates. P.S. signal power=Eb*bit rate noise power=No*bandwidth
From: Tim Wescott on 6 Dec 2009 17:21
On Sun, 06 Dec 2009 16:13:15 -0600, tommala wrote: >>On 12/6/2009 1:10 PM, tommala wrote: >>>> On Sun, 06 Dec 2009 08:18:32 -0600, tommala wrote: >>>> >>>>> Hi everyone, >>>>> I am trying to write a base band simulation of BPSK,QPSK and 16-QAM >>>>> modulator(using only constellation points coordinates). I figured > out >>>>> from wikipedia.org and "Digital Modulation Technique" that >>> constellation >>>>> points will have following coordinates(in the complex plane): >>>>> 1) (+-sqrt(Eb),0) for BPSK >>>>> 2) (+-sqrt(2Eb/2),+-sqrt(2Eb/2)) for QPSK 3) >>>>> (+-sqrt(4Eb/2);+-sqrt(4Eb/2)) and (+-3sqrt(4Eb/2);+-3sqrt(4Eb/2)) > for >>>>> 16-QAM >>>>> But after simulation I get BER=f(Eb/No) for 16-QAM lower than for > BPSK >>>>> and QPSK. >>>>> I think there is a mistake in constellation points representation >>> above. >>>>> Do You have any ideas? >>>>> Thank You in advance for any remarks. >>>> BPSK : . . >>>> >>>> . . >>>> QPSK : >>>> . . >>>> >>>> >>>> . . . . >>>> >>>> . . . . >>>> 16-QAM: >>>> . . . . >>>> >>>> . . . . >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> -- >>>> www.wescottdesign.com >>>> >>> I know how constellations look but don't know how connect its points >>> coordinates with Eb. >>> >>> Dilip Warrier can You write sth more about r.How it is related to Eb? >>> Maybe where can I find mathematical considerations of constellation > points >>> if such exist. >> >>Can you compute the SNR? Carrier to Noise ratio (C/N)? >> >>If so, it's a pretty straightforward transformation from S/N or C/N to >>Eb/No. The nature of the transformation is described in many textbooks. >> >>Here are some hints: >> >>Eb is a bit energy measurement. What's the relationship between the >>total signal power and the amount of energy proportional to a single > bit? >> >>No is the noise power per unit Hz bandwidth. If you know the noise >>power computed from the symbol constellation, that can be converted to >>No pretty easily. >> >>So, to compute SNR, you need to know the signal power and the noise >>power. Eb and No can be computed from each of those, respectively. >> >>-- >>Eric Jacobsen >>Minister of Algorithms >>Abineau Communications >>http://www.abineau.com >> >> > I can't compute SNR nor C/N. Translation "I'm not qualified to do what I'm trying" > Even I don't have to. Translation "and I don't care" > The simulation has GUI in which user can choose (Eb/No)min; > (Eb/No)max and (Eb/No)step (Eb/No in [dB]). > The program compute in the loop for every i=Eb/No from (Eb/No)min to > (Eb/No)max BER as ratio=number of wrong received bits/number of total > transmitted bits. > In the loop I calculate Eb as Eb=No*pow(10,i/10)where No is constant > number e.g. 1 [W/Hz]. > I assume Eb constant for every modulation. Translation "I expect to conduct my entire professional career dependent on software that someone else writes, and I don't see a problem with that. > And my problem is to correct > connect Eb with point coordinates. > I think your problem is bigger than that. -- www.wescottdesign.com |