Hi: QAM uses two carrier waves that are 90-degrees out of phases with each each and amplitude-modulates them. QAM only has two phases but can have more than two amplitude levels. Is there any modulation scheme that does the opposite -- i.e. the two carrier waves have only two amplitudes but with more than two phases? Thanks, Radium
Modulation scheme with multiple phases and a two amplitudes?
Started by ●May 16, 2008
Reply by ●May 16, 20082008-05-16
On Thu, 15 May 2008 21:56:05 -0700, "Green Xenon [Radium]" <glucegen1@excite.com> wrote:>Hi: > >QAM uses two carrier waves that are 90-degrees out of phases with each >each and amplitude-modulates them. QAM only has two phases but can have >more than two amplitude levels. Is there any modulation scheme that does >the opposite -- i.e. the two carrier waves have only two amplitudes but >with more than two phases? > > >Thanks, > >RadiumYou need to be a little more clear about what you mean. QAM constellations have way more than two phases in the possible symbols. QPSK has four. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by ●May 16, 20082008-05-16
On May 16, 12:56 pm, "Green Xenon [Radium]" <gluceg...@excite.com> wrote:> Hi: > > QAM uses two carrier waves that are 90-degrees out of phases with each > each and amplitude-modulates them. QAM only has two phases but can have > more than two amplitude levels. Is there any modulation scheme that does > the opposite -- i.e. the two carrier waves have only two amplitudes but > with more than two phases? > > Thanks, > > Radiumyea.. if you are talking abt channel coding methods for binary erasure channel such as Raptor code, you will encounter such kind of constellation diagram...
Reply by ●May 16, 20082008-05-16
Eric Jacobsen wrote:> On Thu, 15 May 2008 21:56:05 -0700, "Green Xenon [Radium]" > <glucegen1@excite.com> wrote: > >> Hi: >> >> QAM uses two carrier waves that are 90-degrees out of phases with each >> each and amplitude-modulates them. QAM only has two phases but can have >> more than two amplitude levels. Is there any modulation scheme that does >> the opposite -- i.e. the two carrier waves have only two amplitudes but >> with more than two phases? >> >> >> Thanks, >> >> Radium > > > You need to be a little more clear about what you mean. QAM > constellations have way more than two phases in the possible symbols. > QPSK has four.QPSK (or 8-PSK or more) has only one amplitude, unless you count "switched off" as a valid amplitude. He asked for something with 2 amplitudes. Steve
Reply by ●May 16, 20082008-05-16
On May 16, 12:56 am, "Green Xenon [Radium]" <gluceg...@excite.com> wrote:> Hi: > > QAM uses two carrier waves that are 90-degrees out of phases with each > each and amplitude-modulates them. QAM only has two phases but can have > more than two amplitude levels. Is there any modulation scheme that does > the opposite -- i.e. the two carrier waves have only two amplitudes but > with more than two phases? > > Thanks, > > Radium16-QAM. Jason
Reply by ●May 16, 20082008-05-16
On May 16, 12:34�am, Eric Jacobsen <eric.jacob...@ieee.org> wrote:> On Thu, 15 May 2008 21:56:05 -0700, "Green Xenon [Radium]" > > <gluceg...@excite.com> wrote: > >Hi: > > >QAM uses two carrier waves that are 90-degrees out of phases with each > >each and amplitude-modulates them. QAM only has two phases but can have > >more than two amplitude levels. Is there any modulation scheme that does > >the opposite -- i.e. the two carrier waves have only two amplitudes but > >with more than two phases? > > >Thanks, > > >Radium > > You need to be a little more clear about what you mean. � QAM > constellations have way more than two phases in the possible symbols. > QPSK has four. > > Eric Jacobsen > Minister of Algorithms > Abineau Communicationshttp://www.ericjacobsen.org > > Blog:http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.phpI think the OP used the worng term which led to a misunderstanding of the question. QAM uses two orthogonal bases with varying amplitudes to construct the constelation. What if three orthogonal bases are used? How about n bases? As an analogy, think of the i, j unit vectors defining a plane. You can make any combination of amplitude and angles on the defined plane, even though there only two bases. This is QAM. Now think of i, j, and k forming a 3-D hyperplane. Further, let the set of all vectors in this hyperplane be a combination of the three bases with amplitudes +1 and -1. Is there such an equivalent in data transmission? I believe this is the question being asked. Maurice Givens
Reply by ●May 16, 20082008-05-16
Let's do a bit of careful deconstruction on the OP:> QAM uses two carrier waves that are 90-degrees out of phases with each > each and amplitude-modulates them.I assume from this that you're referring to I/Q complex baseband modulation. In this you're correct - the phases are fixed at 90deg and by varying amplitudes we can create any 2-D vector. Different types/ orders of QAM will have different sets of discrete amplitudes.> QAM only has two phases but can have > more than two amplitude levels. Is there any modulation scheme that does > the opposite -- i.e. the two carrier waves have only two amplitudes but > with more than two phases?Interesting idea. It seems that mathematically there are an infinite number of ways to generate 2-D vectors with various combinations of amplitude & phase. The end results are all the same though, and using quadrature carriers (that are orthogonal and hence give maximum coverage of a space with minimum required amplitude variation of the I/ Q carriers) is simplest. I suppose if you were trying to avoid a patent that this might be one way to do it though. Eric
Reply by ●May 16, 20082008-05-16
On May 16, 12:56�am, "Green Xenon [Radium]" <gluceg...@excite.com> wrote:> Is there any modulation scheme that does > the opposite -- i.e. the two carrier waves have only two amplitudes but > with more than two phases?Star QAM. Darrell function y = starqam16(d, r, mode) % %STARQAM16 Quadrature Amplitude Modulation with 16 point star shaped % constellation as opposed to traditional square shaped. A % star shaped constellation is essentially a set of concentric % PSK rings. For a 16 symbol constellation, there are two % PSK rings with 8 symbols per ring. % % The primary benfit of a star constellation versus a square % constellation is that, with differential encoding, there is % no need for pilot assistance in a faded envrionment. The % least significant bit selects the outer (1) or inner ring (0), % and a gray coding scheme is used on each ring. The exact % mapping is given by: % % 000 - 0 degree phase shift % 100 - 45 degree phase shift % 101 - 90 degree phase shift % 111 - 135 degree phase shift % 110 - 180 degree phase shift % 010 - 225 degree phase shift % 011 - 270 degree phase shift % 001 - 315 degree phase shift % % y = starqam16(d, r, mode) % % r and mode are optional arguements. r specifies the % inner/outer ring ratio and defaults to 1.8. mode specifies % either 'modulation' or 'demodulation.' By default, the % function checks to see if the input matrix is real or % imaginary and chooses mode = 'modulate' or mode = % 'demodulate', respectively. % j = sqrt(-1); % Parse parameters. if (nargin < 1) error('\nNot enough input arguments!\n'); end if (nargin == 1) r = 1.8; if isreal(d) mode = 'modulate'; else mode = 'demodulate'; end end if (nargin == 2) if isreal(d) mode = 'modulate'; else mode = 'demodulate'; end end if (nargin > 3) error('\nToo many input arguments!\n'); end if (nargout > 1) error('\nToo many output arguments!\n'); end row(d); %%%%%%%%%%%%%% % Demodulate % %%%%%%%%%%%%%% if (strcmp(mode,'demodulate') == 1) % Calculate phase difference with hard decision slicing phi = angle(d) - cat(2, 0, angle(d(1:length(d)-1))); phi(find(phi<0)) = 2*pi + phi(find(phi<0)); sliced_phi = mod(quant(phi,pi/4), 2*pi); p = [ 0 % 000 - 0 degree phase shift 4 % 001 - 315 degree phase shift 5 % 010 - 225 degree phase shift 7 % 011 - 270 degree phase shift 6 % 100 - 45 degree phase shift 2 % 101 - 90 degree phase shift 3 % 110 - 180 degree phase shift 1 ]; % 111 - 135 degree phase shift y = 2*p((4/pi)*sliced_phi + 1); % Calculate magnitude difference with hard decision slicing A = abs(d) - cat(2, 1, abs(d(1:length(d)-1))); y(find(abs(A)>(r-1)/2)) = y(find(abs(A)>(r-1)/2)) + 1; %%%%%%%%%%%%%% % Modulate % %%%%%%%%%%%%%% elseif (strcmp(mode,'modulate') == 1) p = [ 0*pi/4 % 000 - 0 degree phase shift 7*pi/4 % 001 - 315 degree phase shift 5*pi/4 % 010 - 225 degree phase shift 6*pi/4 % 011 - 270 degree phase shift 1*pi/4 % 100 - 45 degree phase shift 2*pi/4 % 101 - 90 degree phase shift 4*pi/4 % 110 - 180 degree phase shift 3*pi/4 ]; % 111 - 135 degree phase shift input_bits = dec2bin(d, 4); radius = (r-1)*mod(cumsum(bin2dec(input_bits(:,4))),2) + 1; phase = mod(cumsum(p(1+bin2dec(input_bits(:,1:3)))),2*pi); y = radius .* exp(j*phase); else error(sprintf('\nUnsupported mode %s\n', mode)); end
Reply by ●May 16, 20082008-05-16
maury <maury001@core.com> writes:> On May 16, 12:34�am, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >> On Thu, 15 May 2008 21:56:05 -0700, "Green Xenon [Radium]" >> >> <gluceg...@excite.com> wrote: >> >Hi: >> >> >QAM uses two carrier waves that are 90-degrees out of phases with each >> >each and amplitude-modulates them. QAM only has two phases but can have >> >more than two amplitude levels. Is there any modulation scheme that does >> >the opposite -- i.e. the two carrier waves have only two amplitudes but >> >with more than two phases? >> >> >Thanks, >> >> >Radium >> >> You need to be a little more clear about what you mean. � QAM >> constellations have way more than two phases in the possible symbols. >> QPSK has four. >> >> Eric Jacobsen >> Minister of Algorithms >> Abineau Communicationshttp://www.ericjacobsen.org >> >> Blog:http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php > > I think the OP used the worng term which led to a misunderstanding of > the question. QAM uses two orthogonal bases with varying amplitudes > to construct the constelation. What if three orthogonal bases are > used? How about n bases? As an analogy, think of the i, j unit > vectors defining a plane. You can make any combination of amplitude > and angles on the defined plane, even though there only two bases. > This is QAM. Now think of i, j, and k forming a 3-D hyperplane. > Further, let the set of all vectors in this hyperplane be a > combination of the three bases with amplitudes +1 and -1. Is there > such an equivalent in data transmission? I believe this is the > question being asked.I think you're right, Maury. The answer is that, for simple amplitude modulation, the dimension of the vector space for this type of modulation is two - that is essentially what you've already stated. The reason that this is the case is that basis vectors in this space are sinusoids, and there can only be a maximum of two linearly independent vectors (at the same frequency) of this type. -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●May 16, 20082008-05-16
On Fri, 16 May 2008 07:42:41 -0700 (PDT), maury <maury001@core.com> wrote:>On May 16, 12:34�am, Eric Jacobsen <eric.jacob...@ieee.org> wrote: >> On Thu, 15 May 2008 21:56:05 -0700, "Green Xenon [Radium]" >> >> <gluceg...@excite.com> wrote: >> >Hi: >> >> >QAM uses two carrier waves that are 90-degrees out of phases with each >> >each and amplitude-modulates them. QAM only has two phases but can have >> >more than two amplitude levels. Is there any modulation scheme that does >> >the opposite -- i.e. the two carrier waves have only two amplitudes but >> >with more than two phases? >> >> >Thanks, >> >> >Radium >> >> You need to be a little more clear about what you mean. � QAM >> constellations have way more than two phases in the possible symbols. >> QPSK has four. >> >> Eric Jacobsen >> Minister of Algorithms >> Abineau Communicationshttp://www.ericjacobsen.org >> >> Blog:http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php > >I think the OP used the worng term which led to a misunderstanding of >the question. QAM uses two orthogonal bases with varying amplitudes >to construct the constelation. What if three orthogonal bases are >used? How about n bases? As an analogy, think of the i, j unit >vectors defining a plane. You can make any combination of amplitude >and angles on the defined plane, even though there only two bases. >This is QAM. Now think of i, j, and k forming a 3-D hyperplane. >Further, let the set of all vectors in this hyperplane be a >combination of the three bases with amplitudes +1 and -1. Is there >such an equivalent in data transmission? I believe this is the >question being asked. > >Maurice GivensHi, Maurice. Good to see you around again (or maybe I've just not been paying attention). I think you may be right, but I wasn't willing to assume. Rather than answer a question that wasn't asked, I was hoping to get the OP to clarify. FWIW, that wouldn't be a new idea. Somebody was trying to sell that around the comm circuit about twelve years ago, about the same time people were trying to sell the original variants of VPSK. I've since come to call these sorts of things "techno-scams", and it's always disappointing to me to see people pushing things like that, and even more disappointing to me to see other people give them money. The idea that was being sold at the time was to take a quadrature signal and use it as the input to each leg of the next quadrature signal, making a 4-D hyperplane, as you've described it. So, I1 + jQ1 makes up IT, and I2 + jQ2 makes up QT, so the transmitted signal is then IT + jQT. Conceptually you can go back and add as many dimensions as you want, since one can expand the 'tree' as far as you want. The selling point was that one could increase the modulation density, or the bps/Hz, as much as one wanted. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
