AM-AM and AM-PM plots
The AM-AM and AM-PM plots are based on a model that assumes the input to the power amplifier is a single unmodulated tone.  According to the model, the output of the power amplifier is a tone of the same frequency with a gain and phase shift that are functions of the input amplitude.  If the input is $A \exp{(j(\omega t+\theta))}$, the output is $g_A(|A|)A \exp{(j(\omega t+\theta+g_\theta(|A|)))}$.  Here $g_A()$ and $g_\theta()$ are functions that compute the gain and phase shift as a function of the input magnitude.

Therefore, in order to build an AM-AM and AM-PM model, you need to input a tone into the system and sweep its power over a wide range, measuring the gain and phase shift at each input power.  When the drive level is low enough that the amplifier operation is linear, you should find that the gain and phase shifts stop changing as the input power changes.  At higher drive levels, the gain and phase shifts will change substantially as a function of the input drive level.  You need to make measurements that span the drive levels at which you might operate the power amplifier, down to the level at which the amplifier becomes linear.

Although power amplifier AM-AM and AM-PM curves are typically measured using tones, you could use another waveform instead.  However, developing a model using a waveform with a time-varying envelope is a more open-ended problem, because the input amplitude varies both with time and with drive level.

Keep in mind that the AM-AM and AM-PM curves represent a simplified model.  That simplicity makes it easy to use, but also limits its accuracy.