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I have an IQ data of QPSK signal , when I apply a PLL loop I obtain constellation in figure below. What is this phenomenon, and how can I obtain the good constellation??

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The second figure is about variation angles, is there any idea about the red countoured effect?

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after adding symbol syncronisation , i obtain constellation below , but there is also sommes error that causes incorrect demapping ;; is there any suggestion ????

enter image description here

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I suspect you're not doing symbol synchronization. You need to synchronize and then sample the output of your receiver filter at the correct times. Only then will you see the tradiational constellation diagram. Look for "Gardner algorithm" on this website; another well-known algorithm is Mueller and Muller.

One thing you can do to get confidence that your signal is correct is to plot its eye diagram. If the eye is open, then all you need to do is synchronize and sample. If it's closed, you have a different problem.

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The phenomenon is called InterSymbol Interference, ISI: https://en.wikipedia.org/wiki/Intersymbol_interference, and it is a measurement of the quality of the received signal, as you already noticed. As mentioned in the first answer, find a way for a good synchronous decoder. See How to soft decode DQPSK? for more on soft decoding. It is possible that you may have a need for the adaptive equalizer, and you can use the symbol error as the adaptation criterion. That should widen the eye. Also, it would be good if you can apply certain synchronization sequence at the beginning, the one that will help to do the proper synchronization. In this cases, typically, the decoder works in two modes: coarse and fine. in the coarse mode, the receiving side has different parameters (PLL for example), that have a goal to coarsely synchronize the symbols. In the fine mode, PLL (or other decoder parameters) are changed, so the error is reduced. At this point, symbol errors should be smaller. At this point, the equalizer could be turned on, so the ISI error is further reduced. That I how some or most of the modems are working.

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