SNR relation with modulation index and noise power
If $x(t)$ is your message signal, then you can write the AM signal as

$$s(t)=A[1+mx(t)]\cos\omega_0 t$$

where $A&gt;0$ is a real-valued constant, $m$ is the modulation index, and $\omega_0$ is the carrier frequency (in radians). If you assume that the noise added by the channel is white with power spectral density $N_0$, then the SNR after demodulation is

$$SNR=\frac{A^2m^2\overline{x^2(t)}}{4N_0B_x}$$

where $B_x$ is the bandwidth of the message $x(t)$ and $\overline{x^2(t)}$ is its average power.