First, in the use of the QPSK, there is a problem, which called phase vague.

There are four stable states, ,

which may lead to the serious mistake in the decoding.

 

Furthermore, it is expensive to implement the coherent detector. If we use the method of differential coherent detector, it is not necessary to use the local oscillator.

So, we choose the differential encoding.

 

The mapping between bits and phase difference.