--- title: "Threshold effect in non-coherent FM detection and its correction" subject: "Communication Systems" chapter: 9 key: "semester_6/communication_systems:threshold-noncoherent-fm-correction" source: https://www.bctengineer.com/q/semester_6/communication_systems/threshold-noncoherent-fm-correction site: BCT Engineering --- # Threshold effect in non-coherent FM detection and its correction Communication Systems · Chapter 9: Noise in Communication Systems - Asked in: 2069 Chaitra (CS II), 4+3 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/threshold-noncoherent-fm-correction - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-9 ## Question Explain the threshold effect in non coherent detection of FM signal. How can it be corrected? ## Short answer In non-coherent FM detection, below a carrier-to-noise ratio of about10 dB the output SNR drops sharply due to noise-induced phase clicks. Threshold extension uses FMFB or PLL demodulators to narrow effective noise bandwidth, or pre-emphasis/de-emphasis, lowering the threshold by several dB. ## Answer #### 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 $r(t)$: ```text 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). ```text (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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the threshold effect in non-coherent FM detection? A. Output SNR rises faster than input SNR at high CNR B. Below a critical CNR (about 10 dB) the output SNR collapses much faster than the input SNR C. The carrier disappears at low modulation D. The bandwidth doubles at low CNR Answer: B. The linear relation SNR_O = 1.5 beta^2 SNR_C holds only above threshold; below it output SNR drops sharply. (Key point: Threshold effect) 2. What causes the impulse noise (clicks) near threshold? A. Limiter saturation B. The resultant phasor swings around the origin, changing phase by 2 pi C. Carrier frequency drift D. De-emphasis Answer: B. When noise amplitude approaches the carrier, the phasor circles the origin, and the discriminator derivative gives impulses of area 2 pi. (Key point: Cause of clicks) 3. Which technique lowers the CNR at which threshold occurs? A. Increasing the frequency deviation B. FM demodulator with feedback (FMFB) or PLL demodulator C. Widening the IF filter D. Removing the limiter Answer: B. FMFB and PLL reduce the effective noise bandwidth, extending threshold by several dB. (Key point: Threshold extension method) 4. What does a larger deviation ratio beta do to the threshold point? A. Lowers it B. Raises it, because noise bandwidth increases C. Has no effect D. Eliminates it Answer: B. A larger beta needs a wider bandwidth, admitting more noise and raising the threshold point. 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