Threshold effect in non-coherent FM detection and its correction

Threshold effect in FM

In FM with non-coherent detection (limiter + discriminator), the output SNR follows

$$(SNR)_O = \tfrac32\beta^2 (SNR)_C \quad (\text{tone modulation})$$

only when the carrier-to-noise ratio (CNR) at the detector is high. When the CNR falls below a certain value, called the threshold (about 10 dB, often quoted as 10 to 13 dB), the output SNR drops much faster than the input SNR. This sharp breakdown is the threshold effect.

Cause. The received signal is the resultant phasor of the carrier $A_c$ and the noise $r(t)$:

            noise r(t)
           ,--->
          /
 0 ------+------> Ac (carrier)
     resultant phase = phi(t) + noise angle

• High CNR ($A_c \gg r$): noise only slightly perturbs the phase; the output noise is small and smooth (parabolic PSD).
• Near or below threshold ($r \approx A_c$ occasionally): the resultant phasor can swing around the origin, so its phase changes suddenly by $\pm 2\pi$. The discriminator output (the derivative of the phase) then contains sharp impulses ("clicks") of area $2\pi$.
• The click rate rises rapidly as the CNR falls; the clicks carry large power and make the output SNR collapse. At very low CNR the signal is "captured" by the noise (the message is mutilated).

 (SNR)o dB
     |                    /
     |                  /   above threshold: straight line,
     |                /     (SNR)o = (SNR)c + FM gain (in dB)
     |              /
     |            * <- threshold (~10 dB CNR)
     |           /
     |          |   below threshold: output SNR
     |          |   falls off steeply
     +----------+----------------- (SNR)c dB

A wider deviation (larger $\beta$) increases the noise bandwidth and so raises the threshold point.

Correction (threshold extension)

The aim is to lower the CNR at which threshold occurs, i.e. to reduce the effective noise bandwidth seen by the detector:

1. FM demodulator with feedback (FMFB): the VCO output, driven by the demodulated signal, is mixed with the input, compressing the deviation; the IF filter can then be narrow, so noise is reduced and the threshold is lowered by about 5 to 7 dB.
2. Phase-locked loop (PLL) demodulator: the loop bandwidth only needs to follow the message, so it rejects much of the noise; this gives a threshold extension of a few dB over a discriminator.
3. Pre-emphasis and de-emphasis: boosts the high message frequencies before modulation and cuts them after detection, reducing high-frequency output noise and improving SNR (about 13 dB for broadcast FM); it improves performance above threshold.
4. Practical measures: increase transmitter power or antenna gain, or use a smaller deviation where bandwidth allows, to keep the CNR above threshold.