OQPSK vs QPSK envelope query
Note that a QPSK signal using a band-limited pulse has an envelope that passes through zero every time there is a phase transition of $\pi$. So its envelope is not constant if all symbol transitions are allowed.

Offset QPSK (OQPSK) doesn't have phase transitions of $\pi$. By staggering the $I$ and $Q$ signals by half a symbol interval, the maximum phase transition is $\pi/2$, leading to an approximately constant envelope. Slight droops in the envelope (occurring at phase transitions of $\pi/2$) can be eliminated by hard-limiting.

Note that with an appropriate choice of the transmit pulse, phase transitions in OQPSK can be completely avoided. This results in a modulation scheme with an exactly constant envelope. One example of such a continuous-phase modulation is minimum-shift keying (MSK).

For more information on OQPSK take a look at this question and its answers. Also browse this site for other questions on OQPSK.