The difference between two constellations

Hi everybody!
Can somebody help me in understanding some things?
The two constellations are given: square constellation 4x4 (M=16) and circular (5,11) constellation, as shown at the figure below:


The question: Why might the square constellation be more practical?
The answer: The square constellation requires only two amplitudes and two orthogonal phases, whereas the circular constellation requires either two amplitudes and 15 or 16 phases, or numerous amplitudes with two orthogonal phases.

Can somebody explain me the answer? I see three amplitudes for square constellation. And what do they mean under "two orthogonal phases"?

lomaxe said:

Hi everybody!
Can somebody help me in understanding some things?
The two constellations are given: square constellation 4x4 (M=16) and circular (5,11) constellation, as shown at the figure below:

The question: Why might the square constellation be more practical?
The answer: The square constellation requires only two amplitudes and two orthogonal phases, whereas the circular constellation requires either two amplitudes and 15 or 16 phases, or numerous amplitudes with two orthogonal phases.

Can somebody explain me the answer? I see three amplitudes for square constellation. And what do they mean under "two orthogonal phases"?

Click to expand...

I see the square constellation as a combination of Amplitude-Phase shift keying i-e 4PSK(inner ring),8PSK(middle ring),4PSK(outer ring)......I think this is why you say that you see three amplitudes.
now coming back to the constellation......why do we use it because we want to see the decision boundaries clearly........in the square constellation the decision boundaries for the 2 4PSK (inner and outer ring) are common.......so if a phase of the complex envelop falls in these regions then the only thing left to decide is the amplitude....more over these points on the constellation fall on the decision boundaries for the 8PSK case and vice versa........

but we do not get this in the circular constellation.......

this might be an argument but i m not really sure......i just used my intuition ......

Hi,

Your comparison is between i) 16-QAM ii) 16-APSK.

Firstly do pay heed the answer is only correct for linear channel models.

The explanation for the answer

circular constellation requires either two amplitudes and 15 or 16 phases

Click to expand...

, the problem with having 16 phases is maximizing SNR performance and doing a ML detection based on (typically euclidean distance) is far more complex. If the phase is orthogonal the euclidean distance is maximized by virtue of the mapping in terms of I and Q components. The second option

numerous amplitudes with two orthogonal phases

Click to expand...

consists of too many amplitudes, which makes the system impractical to engineer besides the issue of maximizing the SNR performance given a maximum size of constellation once again is difficult.

That having said, there are plenty of non-linear channel (e.g. TWT's) performance for which the 2nd APSK model works better than QAM.

Hope this helps.

Thanks for the answers!
But I still do not understand why the author of the answer see two amplitudes (instead of three, as wee see) and what does he mean under 2 orthogonal phases....
May be the problem is that I don't understand the term "two orthogonal phases". Can somebody mark them at the figure by different colors?
For example I know the term "orthogonal signals".
cos and sin are orthogonal and we use them for building QPSK constellation. But what they mean under the term "orthogonal phases"?