The signal to noise ratio (S/N) of an FM link can be improved by increasing the modulation index (up to a certain point).
Mi = Fd / Fm
An approximate rule for the bandwidth (Bw) of a FM signal is given by:
Bw = 2(Fd + Fm) - (this is called Carson's rule).
As the modulation index grows (Fd » Fm) the bandwidth becomes proportional to the frequency deviation. So at large values of Mi doubling the deviation doubles the channel bandwidth.
Increasing the deviation increases the output voltage of the de-modulated signal at the receiver. Doubling the deviation doubles the output voltage and hence results in a 6db (power) improvement.
However doubling the channel Bandwidth also doubles the received noise power (i.e. 3db). Thus with an FM signal a 3db improvement in S/N can be achieved for each doubling of FM bandwidth. I.e. channel bandwidth can be traided for S/N.
This is called the FM improvement factor.
For this to work practically the carrier peaks must be more than the noise peaks - where the RMS power of the carrier (C) is greater than the channel noise (N) by 10dB (C/N).
This is called the FM improvement threshold.
Thus the improvement for a given transmit power only holds while the received channel noise for the widened channel is 10dB less than the carrier power.