Can the intelligence message of an FM signal be cross-modulated to another center frequency due to non-linearities? Can the intelligence message of an FM signal be cross-modulated to a  a different frequency by non-linearities, but with the FM modulating message remaining (relatively) intact on the new frequency?
This isn't really trying to solve a particular problem, but I'm trying to understand if this is possible, and if the math checks out.  In FM two-way radio, sometimes users experience &quot;bleed over&quot; from another channel.  I've heard intermodulation or cross-modulation being cited as the cause.  Reading the literature however I can't find this phenomenon discussed.  I'm Using Leon Couch, Digital and Analog Communications Systems by the way.
Studying non-linearities; intermodulation and cross modulation, I see that the 3rd order output is:
$$V_{out} = K_{0} + K_{1}V_{in} + K_{2}V_{in}^2 + K_{3}V_{in}^3$$
If you put signals into the system where
$$V_{in} = A_{1}\sin(\omega_1t) + A_{2}\sin(\omega_2t)$$
Then part of the third order outputs are:
\begin{align}3K_{3}A_{1}^2A_{2}\sin(\omega_1t)^2\sin(\omega_2t)  =   \frac{3}{2}&amp;K_{3}A_{1}^2A_{2}\{[\sin(\omega_2t) \\&amp;- \frac{1}{2}\big[\sin(2\omega_1 + \omega_2)t + \sin(2\omega_1 - \omega_2)t\big]\}\end{align}
and another
Generally it's explained that term $\sin(2\omega_1 - \omega_2)t$ accounts for intermodulation distortion that is difficult to filter because it is close to the desired signal.  Also they show that if there is any amplitude variation on signal 1, that it can amplitude modulate signal 2, because
$$\frac{3}{2}K_{3}A_{1}^2A_{2}\sin(\omega_2t)$$
But I never see a discussion of an FM signal being cross-modulated onto another FM signal.  It seems to me that if signal 2 is an FM signal as:   $\sin\big((\omega_2 \pm \Delta\omega) t\big) $. then the cross modulating term:
\begin{align}
\sin(2 \omega_1t - \omega_2t)  &amp;=  \sin\big(2\omega_1t - (\omega_2 \pm \Delta\omega)t\big)\\   
&amp;= \sin\bigg(\big(2\omega_1 - (\omega_2 \pm \Delta \omega)\big)t\bigg)\\
&amp; = \sin\bigg(\big(2\omega_1 - \omega_2 \mp \Delta \omega\big)t\bigg)\\
&amp; = \sin\big((2\omega_1 - \omega_2)t \mp \Delta \omega t\big)
\end{align}
Which looks to me like the modulating signal would be impressed on the intermodulation product $\sin((2\omega_1 - \omega_2)t$
It seems to me about the same as super-heterodyning the message signal, which would be the $ \Delta\omega t$
Of course my reasoning might be totally incorrect.
Like I said, I've never been able to find a mathematical or physics treatment of the phenomenon, but I've heard people argue that it happens, and others argue that in the FM domain cross modulation will only cause noise, not the imparting of an intelligent signal on another signal like in AM.
Yes and no,   it can't be intermodded onto another SIGNAL, but it can be intermodded onto another CHANNEL.  For example, if you are monitoring 144 MHz, an FM signal on 145 MHz and on 146 MHz CAN, due to non-linearity, end up being heard on 144 MHz.  But it can't be modulated onto an existing signal on 144 MHz.
Mark