The use of frequency modulation provides in general a useful improvement in signal to noise under certain conditions.  The most important condition is that the input signal to noise ratio exceeds a threshold value.  Below this threshold, the signal to noise output deteriorates rapidly, and for low inputs the signal to noise is worse than SSB.

In amateur use, narrow band FM (NBFM) is used.  Commonly this uses a standard 5kHz deviation at a channel spacing of 25kHz.   When the channel spacing is reduced to 12.5kHz, the maximum deviation must be reduced to 2.5kHz.  The theoretical analysis of FM systems below threshold is difficult, and so the best approach is to measure it.  [A description of the method used to measure it is given below].  Here is a graph of the measured performance of NBFM (with 2.4kHz deviation) compared with SSB.


The graph shows the output signal to noise ratio measured at audio as a function of signal level from a signal generator (into an OZ2M 4m transverter driving the K3 transceiver, but this is unimportant). 
You will see that there is an improvement when using NBFM at high signal levels of about 5.2dB. 
But note that there is a threshold value of signal input where the NBFM system deteriorates rapidly, whilst the SSB S/N drops as a linear function of the input.  So when the input S/N is less than about 10dB, SSB offers better performance than NBFM.  A 10dB S/N is a quite workable signal on SSB.
If we take a  -138dBm value as the "noise level"  (Note 1), SSB is superior for levels up to about 10dB above this. And for signals below -133dBm, NBFM produces no useful output at all, whilst we still get about 5dB S/N on SSB.
For a system with 5kHz deviation, the improvement at high signal levels is greater - perhaps another 2 to 3dB, whilst the threshold is correspondingly increased by 2 to 3dB.



What we are really interested in is the intelligibility or readability of the signal.  This is a major topic in its own right, and beyond the scope of this article, so I will simply demonstrate the effects with some recordings.  (The same audio source was used in each case, from the digital voice recorder on the K3.)  The first recording is made using NBFM at a level equivalent to -129dBm.  The next recording is of ssb at the same level. Finally there is ssb 9dB weaker at -138dBm.  From this it's apparent that nbfm is no use at -129 and probably below about -126dBm.  This is illustrated with a vertical line on the graph above.

The discussion above relates to a constant signal with a white noise background.  In practice other factors can be important:-

• fading and capture effect - where there is more than one station on a frequency, the stronger station tends to capture the FM demodulation process and suppress the weaker signal.  As the relative strength of the signals vary, first one then the other station can be audible, leading to confusion over the use of the channel.  
• occupied bandwidth - the advantage of FM comes at the cost of increased bandwidth and hence poorer utilisation of the allowed spectrum. Where the available band is limited, fewer stations can be accommodated.  
• distortion - whilst FM can provide a higher quality signal under ideal conditions, the wider bandwidth can lead to greater distortion when the propagation path is through a dispersive medium such as the ionosphere, or in the presence of multipath.
• muting - most people operate FM with "squelch" to mute the noise when no signal is present. So this in practice might set a higher limit to the signal level needed for useful NBFM. 

In conclusion, NBFM is best used on tropospheric paths where signals are quite strong, and on bands where adequate bandwidth is available to avoid interference.  Where a low signal level and/or fading is expected, ssb will prove more effective.

Measurement method

The method relies on using the K3's audio dB meter. The signal is generated on 70.12MHz, and fed to the K3 through an OZ2M transverter. For these measurements, the set up was:-

• ssb: Noise blanker off, AGC off, 2.4kHz b/w, 1kHz cw tone
• nbfm: 12.5kHz b/w, 2.4kHz deviation, 1kHz tone

On FM, the receiver produces a very loud noise if no signal is present, which reduces of course as the signal increases.  So I first measured this audio noise as a function of signal level with an unmodulated carrier. Then I repeated it with 1kHz tone modulation. Then subtracting  dB's I get a (S+N+D)/N ratio. That's the ratio signal plus noise plus distortion to noise.  At very low levels there is an apparent excess of signal over noise, but it's mostly distorted and crackly, and not much 1kHz tone. But that's what is measured anyway.  Finally I calculate S/N from S+N/N. S+N/N is converted to a true ratio, subtract 1 and then take logs to return to dBs.

The level of tone I've used was set up to null the carrier as seen on a spectrum analyser (actually the P3 panadaptor) - this corresponds with a modulation index of 2.4, hence I know the deviation is 2.4kHz (index=deviation/modulating frequency).

Note

1.  Thermal noise level N = kTBF = -140dBm, where k=1.38E-23, T=290K, B=2400Hz, F=0.4dB

References

RSGB VHF/UHF Handbook 2002, p4-34
http://en.wikipedia.org/wiki/Edwin_Howard_Armstrong
Frequency Modulation Noise Characteristics - M G Crosby, Proc IRE vol 25, pp472-514, 1937
Information, Transmission, Modulation and Noise  -  M Schwartz, McGraw-Hill 1959
The Paging Technology Handbook - Neil Boucher, John Wiley and Sons, 1992
Speech intelligibility papers - see http://www.meyersound.com/support/papers/speech/