Hi,
All Experts, Thanks for answering my question in last post
(especially Eric Jacobsen Sir), I have few questions on constellation
diagram. Please let know the the article/paper to understand below
points
if you know the answer,please help me out
1. How is the shape of constellation diagram decided? What are its
implications?
2, Why not 0 - phases in a 4-point QAM? Why ?
Thanks
aizza ahmed
questions on constellation diagram
Started by ●January 9, 2012
Reply by ●January 9, 20122012-01-09
On Mon, 9 Jan 2012 10:10:35 -0800 (PST), aizza ahmed <aizzaahmed@gmail.com> wrote:>Hi, > All Experts, Thanks for answering my question in last post >(especially Eric Jacobsen Sir), I have few questions on constellation >diagram. Please let know the the article/paper to understand below >points > >if you know the answer,please help me out > >1. How is the shape of constellation diagram decided? What are its >implications? >2, Why not 0 - phases in a 4-point QAM? Why ? > >Thanks >aizza ahmedAssuming I understand your question correctly: BPSK is often done with 0 and pi phases, and QPSK can be, too, it just doesn't make optimum use of the digital dynamic range. pi/4-QPSK alternates between QPSK constellations rotated by pi/4 and unrotated, so in the rotated case all four points fall on the axes. Eric Jacobsen Anchor Hill Communications www.anchorhill.com
Reply by ●January 9, 20122012-01-09
On Jan 9, 4:17�pm, eric.jacob...@ieee.org (Eric Jacobsen) wrote:> > BPSK is often done with 0 and pi phases, and QPSK can be, too, it just > doesn't make optimum use of the digital dynamic range. � pi/4-QPSK > alternates between QPSK constellations rotated by pi/4 and unrotated, > so in the rotated case all four points fall on the axes.Very nicely put! Additional points that could be noted are that QPSK with phases 0, pi/2, pi, 3pi/2 requires more digital dynamic range in both the I and Q branches, but in each (dibit) symbol interval, one of the branches has no signal. The transmitted power is the same, subject again to dynamic range constraints and peak power limitations if there are separate modulators (and possibly PAs) in each branch. For "conventional" QPSK with phases +/- pi/4 and +/- 3pi/4, signals are present in both I and Q branches at all times. With pi/4 QPSK, these two cases alternate, and so more dynamic range is needed in both the I and Q branches to accommodate the larger amplitude signals when the signal constellation is 0, pi/2, pi, 3pi/2. Dilip Sarwate
Reply by ●January 9, 20122012-01-09
On 9 Jan, 22:17, eric.jacob...@ieee.org (Eric Jacobsen) wrote:> On Mon, 9 Jan 2012 10:10:35 -0800 (PST), aizza ahmed > > <aizzaah...@gmail.com> wrote: > >Hi, > > � �All Experts, Thanks for answering my question in last post > >(especially Eric Jacobsen Sir), I have few questions on constellation > >diagram. Please let know the the article/paper to understand below > >points > > >if you know the answer,please help me out > > >1. How is the shape of constellation diagram decided? What are its > >implications? > >2, �Why not 0 - phases in a 4-point QAM? Why ? > > >Thanks > >aizza ahmed > > Assuming I understand your question correctly: > > BPSK ...Ouch! It seems i did not understand that question at all; I read 'constellation' as in astronomy... Rune
Reply by ●January 9, 20122012-01-09
On 1/9/12 6:13 PM, Rune Allnor wrote:> On 9 Jan, 22:17, eric.jacob...@ieee.org (Eric Jacobsen) wrote: >> >> BPSK ... > > Ouch! It seems i did not understand that question > at all; I read 'constellation' as in astronomy... >i remember when i first learned that "constellation" didn't mean "constellation". it was in an EE colloquium about some keying or coding about 3 decades ago. since then i have heard some other uses in the social and political realm. i'm no expert, but to answer the OP a little, i think that one of the issues in designing a constellation is to have a maximum distance metric between the points in the constellation so that when noise is added, it minimizes the probability of selecting the wrong symbol. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●January 9, 20122012-01-09
>On Mon, 9 Jan 2012 10:10:35 -0800 (PST), aizza ahmed ><aizzaahmed@gmail.com> wrote: > >>Hi, >> All Experts, Thanks for answering my question in last post >>(especially Eric Jacobsen Sir), I have few questions on constellation >>diagram. Please let know the the article/paper to understand below >>points >> >>if you know the answer,please help me out >> >>1. How is the shape of constellation diagram decided? What are its >>implications? >>2, Why not 0 - phases in a 4-point QAM? Why ? >> >>Thanks >>aizza ahmed > >Assuming I understand your question correctly: > >BPSK is often done with 0 and pi phases, and QPSK can be, too, it just >doesn't make optimum use of the digital dynamic range. pi/4-QPSK >alternates between QPSK constellations rotated by pi/4 and unrotated, >so in the rotated case all four points fall on the axes.Considering the original poster's first question I think its worth emphasising that this is not a constellation choice. It is merely an issue of interpretation at the receiver. If you interpret the QPSK points as being on axis the maths can be a pain. If you interpret them as being on the diagonals the maths is just easier. Dynamic range isn't usually much of an issue in the processing of something like QPSK. You need enough dynamic range to avoid clipping on the axes, in the initial stages of signal acquisition, when the constellation is still spinning. However, dynamic range is a big part of the answer to the original poster's first question, about reasons for the choice of constellation shape, especially for more complex constellations. It is highly desirable to limit the dynamic range of most transmitters, whether they are wireless or wireline ones. It may even be essential, such as to comply with regulations, or to live within the clipping range of PSTN signal. Many transmitters aren't that linear, which can be another reason to moderate the dynamic range. Clearly the constellation needs to keep the points as far apart as is practical. Older and simpler constellations were generally square, with perhaps the extreme peaks of the corners clipped. Modern constellations are often much more rounded. In some cases, like the V.34 and V.90 wireline modems, this was a make or break issue, and a lot of the development effort went into development of the constellation pattern. The issue is a bit more complex than just the constellation shape, as its usually the absolute peak of the transmitter's output which you want to constrain, and filtering may push that beyond the extremes of the constellation itself. Look up crest factor reduction, which is the term usually associated with this topic. Steve
Reply by ●January 9, 20122012-01-09
robert bristow-johnson <rbj@audioimagination.com> wrote: (snip)> i remember when i first learned that "constellation" didn't mean > "constellation". it was in an EE colloquium about some keying or coding > about 3 decades ago. since then i have heard some other uses in the > social and political realm.> i'm no expert, but to answer the OP a little, i think that one of the > issues in designing a constellation is to have a maximum distance metric > between the points in the constellation so that when noise is added, it > minimizes the probability of selecting the wrong symbol.I believe so. Maybe it is at least a little bit obvious, or maybe not, that the noise in amplitude/phase space (I-Q in rectangular coordinates) works out such that noise has circular symmetry. That is, such that the optimal patterns have equal distance between points on a 2D graph. -- glen
Reply by ●January 9, 20122012-01-09
On Jan 9, 9:00�pm, robert bristow-johnson <r...@audioimagination.com> wrote:> i think that one of the > issues in designing a constellation is to have a maximum distance metric > between the points in the constellation so that when noise is added, it > minimizes the probability of selecting the wrong symbol.Well, you need to be a bit careful how you express the matter. To a first order, you want to make the *minimum* distance between points as large as possible, that is, make nearest neighbors as far apart as possible in order to minimize the probability of selecting the wrong symbol. To a first order, it is the probability of selecting the neighbor (or coveting his wife :-) ) that is the problem. The chance of demodulating into a nearest other signal point dominates the error probability expression; the points far away matter far less.
Reply by ●January 10, 20122012-01-10
On 1/9/12 9:40 PM, glen herrmannsfeldt wrote:> robert bristow-johnson<rbj@audioimagination.com> wrote: > > (snip) >> i remember when i first learned that "constellation" didn't mean >> "constellation". it was in an EE colloquium about some keying or coding >> about 3 decades ago. since then i have heard some other uses in the >> social and political realm. > >> i'm no expert, but to answer the OP a little, i think that one of the >> issues in designing a constellation is to have a maximum distance metric >> between the points in the constellation so that when noise is added, it >> minimizes the probability of selecting the wrong symbol. > > I believe so. Maybe it is at least a little bit obvious, or maybe not, > that the noise in amplitude/phase space (I-Q in rectangular coordinates) > works out such that noise has circular symmetry.so a Euclidian distance metric is the appropriate metric.> That is, such that the > optimal patterns have equal distance between points on a 2D graph.i would think then that the constellation points should be arranged in a hexagonal honeycomb fashion, where, if you imagine the points to be in equally-spaced rows, that every alternate row should have their points horizontally offset by 1/2 the horizontal spacing. like this: * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ I | Q --> then the vertical spacing of the rows can be packed a little tighter (0.866 of the horizontal spacing between points) and you can pack in more symbols for the same maximum signal power (or, for a given number of symbols and a given maximum signal power, you can increase the spacing the to the most and get a lower error rate). -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●January 10, 20122012-01-10
On 1/9/12 9:54 PM, dvsarwate wrote:> On Jan 9, 9:00 pm, robert bristow-johnson<r...@audioimagination.com> > wrote: > >> i think that one of the >> issues in designing a constellation is to have a maximum distance metric >> between the points in the constellation so that when noise is added, it >> minimizes the probability of selecting the wrong symbol. > > > Well, you need to be a bit careful how you express the > matter. To a first order, you want to make the *minimum* > distance between points as large as possible, that is, > make nearest neighbors as far apart as possible in order to > minimize the probability of selecting the wrong symbol.i think i understand that. see my response to glen. i suggested a good constellation might be one in a hexagonal honeycomb pattern. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
