# difference between linear modulation and non-linear modulation scheme?

As shown in title: what's the difference between linear modulation and non-linear modulation scheme?

I can not find the formal definition of this. And there is a different determination for the FSK modulation (linear and non-linear).

FSK is non-linear

FSK is linear and can be classified using likely-hood ratio function

While the GMSK is non-linear according to the searched results, however I don't know why.

Thanks for any help.

According to this source:

Digital modulation techniques are classified as linear if:

• The amplitude of the transmitted signal varies linearly with the modulating digital signal, $m(t)$.
• They usually do not have a constant envelope
• They are more spectral efficient.
• Poor power efficiency

The only other "linearity"-reference I could find was in the same course slides:

For Frequency Modulation, the relationship between received power and quality is non-linear (Rapid increase in quality for an increase in received power).

For Amplitude Modulation there is a linear relationship between the received signal quality and received signal power.

But I am not totally convinced that this is at the basis of the definition (I'm also not totally unconvinced).

IMHO, I think they started out calling the AM scheme linear, as $AM(a\cdot V_{in}) = a\cdot AM(V_{in})$, and then they started playing with the phase ((Q)PSK) and just labeled it as linear as well, while it isn't strictly true.

[EDIT] I also found this which seems to support my last remark.