Hi everyone,
I have a question regarding the pi/4-shifted QPSK modulation.
I have been reading a lot of websites, including this forum, but I still
cannot get the answer.
Regarding pi/4 shifted QPSK, which is the correct one?
(1)
Phase is shifted pi/4 after every symbol. This means that even if the same
word is transmitted, the point on the constellation will shift by pi/4
everytime..
Q Q Q
| 00 |
01 | 00 | 00 | 11
| | |
-------------- I =======> 01----------11 I ======> --------------
I
| next | next |
10 | 11 symbol | symbol 01 | 10
| 10 |
and so on...
(2)
Phase is picked alternately from one of the constellations below. For
example, if the same word is transmitted continuously, the point on the
constellation would go back and forth between 2 constellation points..
Q Q
| 00
01 | 00 |
| |
-------------- I 01----------11 I
| |
10 | 11 |
| 10
And is this the same for pi/4-shifted DQPSK (except that the symbols
represent phase jumps instead of phase position)?
Thanks for your help!
Hiroki
pi/4-shifted QPSK
Started by ●November 18, 2010
Reply by ●November 18, 20102010-11-18
On Nov 18, 6:54=A0am, "hiroki" <azrilel@n_o_s_p_a_m.gmail.com> wrote:> Hi everyone, > > I have a question regarding the pi/4-shifted QPSK modulation. > I have been reading a lot of websites, including this forum, but I still > cannot get the answer. > > Regarding pi/4 shifted QPSK, which is the correct one? > > (1) > Phase is shifted pi/4 after every symbol. This means that even if the sam=e> word is transmitted, the point on the constellation will shift by pi/4 > everytime.. > > =A0 =A0 =A0Q =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 ==A0Q =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Q> =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=00 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 |> =A0 01 =A0| =A000 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 | ==A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 00 =A0 | =A0 11> =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=| =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0|> -------------- I =A0 =A0=3D=3D=3D=3D=3D=3D=3D> =A0 =A001----------11 I ==A0=3D=3D=3D=3D=3D=3D> =A0--------------> I > =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 next =A0 =A0 =A0 =A0 =A0 =A0| ==A0 =A0 =A0 =A0 =A0 =A0 next =A0 =A0 =A0 =A0 |> =A0 10 =A0| =A011 =A0 =A0 =A0 =A0 =A0symbol =A0 =A0 =A0 =A0 =A0 | =A0 =A0==A0 =A0 =A0 =A0symbol =A0 01 =A0 | =A0 10> =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=10 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 |> > and so on... > > (2) > Phase is picked alternately from one of the constellations below. For > example, if the same word is transmitted continuously, the point on the > constellation would go back and forth between 2 constellation points.. > > =A0 =A0 =A0Q =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 ==A0Q =A0 =A0 =A0 =A0> =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=00 =A0 =A0 =A0 =A0 =A0> =A0 01 =A0| =A000 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 | ==A0 =A0 =A0 =A0 =A0 =A0> =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=| =A0 =A0 =A0 =A0 =A0> -------------- I =A0 =A0 =A0 =A0 =A0 =A0 =A0 01----------11 I > =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=|> =A0 10 =A0| =A011 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 | > =A0 =A0 =A0 | =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=10> > And is this the same for pi/4-shifted DQPSK (except that the symbols > represent phase jumps instead of phase position)? > > Thanks for your help! > > HirokiDefine "correct"? There is no one size fits all in communications, it all depends on cost/application, etc. For example, some modern garage door openers still use regenerative receiver circuits simply because they're cheap and easy to build. If I understand your two situations (which I'm not completely sure I do given the constellations didn't translate well to text), (1) would simply be differential phase shift keying. Look this up and investigate the pertinent trade-offs. (2) I think would be better implemented using minimum shift keying. Again, research this and compare with (1) to see which better suits your current needs.
Reply by ●November 18, 20102010-11-18
"hiroki" <azrilel@n_o_s_p_a_m.gmail.com> writes:> Hi everyone, > > I have a question regarding the pi/4-shifted QPSK modulation. > I have been reading a lot of websites, including this forum, but I still > cannot get the answer. > > Regarding pi/4 shifted QPSK, which is the correct one? > > (1) > Phase is shifted pi/4 after every symbol. This means that even if the same > word is transmitted, the point on the constellation will shift by pi/4 > everytime.. > > Q Q Q > | 00 | > 01 | 00 | 00 | 11 > | | | > -------------- I =======> 01----------11 I ======> -------------- > I > | next | next | > 10 | 11 symbol | symbol 01 | 10 > | 10 | > > and so on... > > > > (2) > Phase is picked alternately from one of the constellations below. For > example, if the same word is transmitted continuously, the point on the > constellation would go back and forth between 2 constellation points.. > > Q Q > | 00 > 01 | 00 | > | | > -------------- I 01----------11 I > | | > 10 | 11 | > | 10 > > > And is this the same for pi/4-shifted DQPSK (except that the symbols > represent phase jumps instead of phase position)? > > > Thanks for your help! > > > HirokiHi Hiroki, I believe the "correct" one is (2). It is essentially f[n] = Re{e^{i * 2 * pi * ( (I[n] / 4) + ((n mod 2) / 8) ) }, where I[n] is information symbol n, I[n] \in {0, 1, 2, 3}. -- Randy Yates % "The dreamer, the unwoken fool - Digital Signal Labs % in dreams, no pain will kiss the brow..." mailto://yates@ieee.org % http://www.digitalsignallabs.com % 'Eldorado Overture', *Eldorado*, ELO
Reply by ●November 18, 20102010-11-18
Randy Yates <yates@ieee.org> writes:> [...] > f[n] = Re{e^{i * 2 * pi * ( (I[n] / 4) + ((n mod 2) / 8) ) },Er, take out the Re{} function - this is complex baseband: f[n] = e^{i * 2 * pi * ( (I[n] / 4) + ((n mod 2) / 8) ) -- Randy Yates % "Rollin' and riding and slippin' and Digital Signal Labs % sliding, it's magic." mailto://yates@ieee.org % http://www.digitalsignallabs.com % 'Living' Thing', *A New World Record*, ELO
Reply by ●November 18, 20102010-11-18
>Hi everyone, > >I have a question regarding the pi/4-shifted QPSK modulation. >I have been reading a lot of websites, including this forum, but I still >cannot get the answer. > >Regarding pi/4 shifted QPSK, which is the correct one? > >(1) >Phase is shifted pi/4 after every symbol. This means that even if thesame>word is transmitted, the point on the constellation will shift by pi/4 >everytime.. > > Q Q Q > | 00 | > 01 | 00 | 00 | 11 > | | | >-------------- I =======> 01----------11 I ======> -------------- >I > | next | next | > 10 | 11 symbol | symbol 01 | 10 > | 10 | > >and so on... > > > >(2) >Phase is picked alternately from one of the constellations below. For >example, if the same word is transmitted continuously, the point on the >constellation would go back and forth between 2 constellation points.. > > Q Q > | 00 > 01 | 00 | > | | >-------------- I 01----------11 I > | | > 10 | 11 | > | 10 > > >And is this the same for pi/4-shifted DQPSK (except that the symbols >represent phase jumps instead of phase position)? > > >Thanks for your help! > > >Hiroki > > >%%% Not sure what your question is but I am assuming that you want to know what is QPSK and what is pi/4-QPSK. Since there are two bits per symbol in QPSK, you need to group consecutive bits to form a symbol. Lets say your information bits are 00011011. So after grouping, you will get 00, 01, 10 and 11. Now in QPSK modulation, you can map 00 to either +1, +j, -1 or -j. And the same for other groups (01,10,11). One possible mapping is: 00 -> +1 01 -> +j 10 -> -1 11 -> -j However, if you decide to go for pi/4-QPSK, then your mapping can be 00 -> (+1+j)/sqrt(2) 01 -> (-1+j)/sqrt(2) 10 -> (-1-j)/sqrt(2) 11 -> (+1-j)/sqrt(2) These mappings are for non-Gray labels. If you decide to go for Gray mapping, then you will have to make minor change. I leave that to you. IHTH Chintan
Reply by ●November 18, 20102010-11-18
hiroki wrote:> Hi everyone, > > I have a question regarding the pi/4-shifted QPSK modulation. > I have been reading a lot of websites, including this forum, but I still > cannot get the answer. > > Regarding pi/4 shifted QPSK, which is the correct one? > > (1) > Phase is shifted pi/4 after every symbol.> (2) > Phase is picked alternately from one of the constellations below. For > example, if the same word is transmitted continuously, the point on the > constellation would go back and forth between 2 constellation points.> And is this the same for pi/4-shifted DQPSK (except that the symbols > represent phase jumps instead of phase position)?First variant is preferred. In the second variant, the receiver has to be synchronized to the toggle of the phase. This buys nothing but creates an additional complexity. If you meant the Pi/4-DQPSK modulation used in TETRA or IS-54, it is the first variant. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
