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.