I'm using a sin wave $s_{sc}(t) = d(t)\cos(\omega_{sc}t + \varphi_{sc})$ to modulate a carrier using phase modulation. I'm working on Matlab so I use the pmmod function to do so. It is not too complicated to understand what this function is doing, probably computing something like $\cos(\omega_c t + h s_{sc}(t) + \varphi_{ini})$ (with h the modulation index).
In order to demodulate it, I'm using the pmdemod function of Matlab. But for this one, I have absolutely no idea of what is happening in background. I tried to analyze the results obtained after a pmmod-pmdemod sequence, and this is what I observed on Matlab:
Regarding the convergence time, it seems that Matlab use a PLL in background. but what kind of PLL is it ? I'm very interested about the digital methods used to demodulate PM modulation and more particularly the maths behind it. But I cannot find any article/document/book about it (Or I just don't know what to search on google, because when I type "phase modulation" I just find article about CPM modulation or digital PSK/FSK modulation methods...).
Any help would be helpful :)