Continuous Phase Modulation The wikipedia article on continuous-phase modulation states the following:


  For instance, with QPSK the carrier instantaneously jumps from a sine to a cosine (i.e. a 90 degree phase shift) whenever one of the two message bits of the current symbol differs from the two message bits of the previous symbol. This discontinuity requires a relatively large percentage of the power to occur outside of the intended band (e.g., high fractional out-of-band power), leading to poor spectral efficiency. 


I want to know how this is true since in M-ary PSK the amplitude is constant so isn't the power constant too?
What is important is the envelope of the modulated signal. For M-PSK, due to the phase discontinuities, the envelope droops every time there is a phase transition. The envelope even goes to zero if there is a phase transition of $180$ degrees. So M-PSK does not have a constant envelope.

Changes in the envelope are largely reduced by using offset QPSK (OQPSK), and they are completely eliminated by using continuous-phase modulation schemes, such as minimum-shift keying (MSK), which is a special case of OQPSK.

Take a look at these related questions and its answers: Q1, Q2, Q3.