BPSK,QPSK,16-QAM constellation points
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From: tommala on 6 Dec 2009 09:07 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 for BPSK the points will have following coordinates(in the complex plane): (+-sqrt(Eb),0)
From: Vladimir Vassilevsky on 6 Dec 2009 10:29 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? For fair comparison of modulations, average transmit power should be the same. This should give you some food for thought. VLV
From: Eric Jacobsen on 6 Dec 2009 11:55 On 12/6/2009 8:29 AM, Vladimir Vassilevsky wrote: > > > 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? > > For fair comparison of modulations, average transmit power should be the > same. This should give you some food for thought. > > VLV Not only that, you must take into account the gain of any processing steps between the modulating constellation mapper and the receiver. This includes any filtering, mixing, rescaling, gain control, or whatever other steps may be included. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: Eric Jacobsen on 6 Dec 2009 12:09 On 12/6/2009 9:55 AM, Eric Jacobsen wrote: > On 12/6/2009 8:29 AM, Vladimir Vassilevsky wrote: >> >> >> 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? >> >> For fair comparison of modulations, average transmit power should be the >> same. This should give you some food for thought. >> >> VLV > > Not only that, you must take into account the gain of any processing > steps between the modulating constellation mapper and the receiver. This > includes any filtering, mixing, rescaling, gain control, or whatever > other steps may be included. > Which, duh, more or less boils down to what VV said. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: Vladimir Vassilevsky on 6 Dec 2009 12:13
Eric Jacobsen wrote: > On 12/6/2009 8:29 AM, Vladimir Vassilevsky wrote: > >> >> >> 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? >> >> >> For fair comparison of modulations, average transmit power should be the >> same. This should give you some food for thought. > Not only that, you must take into account the gain of any processing > steps between the modulating constellation mapper and the receiver. This > includes any filtering, mixing, rescaling, gain control, or whatever > other steps may be included. I guess it depends on what point one is trying to make by comparison. For example, Proakis uses bits per second per Hz of bandwidth vs Eb/No at a given error rate as "universal" figure of merit. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com |