Peak to average power ratio

Hello,
Please help me to understand this term, Peak to average power ratio , with respect to a transmitter (power amplifier design) . In a system employing pi/4DQPSK modulation , 4 slot TDMA system at data rate of 36Kbps what would be the peak to average ratio.

To be specific it is required to know the peak to average ratio in a TETRA transmitter.

thank you

Well....certain types of modulation do not have "constant envelope", even some that you would initially think of as having it. Imagine a BPSK modulation, where you start at 0 degrees and then suddenly change to 180 degrees. If there are any energy storage components, like a bandpass filter, in the system, then the phase at the filter output does not instantaneously go from 0 to 180, even though the input to the filter pretty much does. The filter has energy bouncing around inside of it at "0" degrees, and now has new energy coming into it at "180" degrees. So the energy stored inside of the filter has to wink out and change phase states. At the filter output, that looks like the amplitude of the signal dropped half way inbetween the 0 and 180 states, ie not constant envelope modulation anymore!

Now if you pass this non-constant envelope modulation thru some mildly non-linear devices, like a transmit amplifier, when the amplitude momentarily winks out you end up with 1) a phase error due to am to pm conversion in the amplifier, and 2) unwanted emissions sidebands due to 3rd order and 5th order intermodulation products.

So the bigger the peak to average ratio is, the more linearly you hav to run your transmit amplifier. A common way to do this is to "back off" the power level coming out of your amplifier, such as running a 1 watt amplifier at only 1/4 watt output power. More complex ways to solve this problem are to use predistorters, feedforward amplifiers, or more interesting modulation schemes that do not have so big of an amplitude change component.