--- title: "Coherent vs non-coherent detection; carrier recovery" subject: "Communication Systems" chapter: 2 key: "semester_6/communication_systems:coherent-noncoherent-carrier-recovery" source: https://www.bctengineer.com/q/semester_6/communication_systems/coherent-noncoherent-carrier-recovery site: BCT Engineering --- # Coherent vs non-coherent detection; carrier recovery Communication Systems · Chapter 2: Amplitude Modulation - Asked in: 2077 Chaitra (CS I), 2+6 marks - Video: [Coherent and Noncoherent Digital Modulation Techniques/Coherent and Noncoherent Detection [HD]](https://www.youtube.com/watch?v=Aji2hqHG5zs) — Engineering Made Easy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/coherent-noncoherent-carrier-recovery - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2 ## Question What do you mean by coherent and non-coherent detections? Describe anyone of the carrier recovery methods. ## Short answer Coherent detection multiplies signal by a phase-locked local carrier then low-pass filters; needs carrier recovery but gives optimal performance. Non-coherent detection uses envelope/energy without carrier phase; simpler but poorer noise performance. Costas loop: I and Q channels multiply signal by cos and sin of VCO output; phase discriminator multiplies I and Q outputs, loop filter drives VCO to lock phase, tracking drifts with 180° ambiguity. ## Answer #### Coherent and non-coherent detection **Coherent (synchronous) detection** recovers the message by multiplying the received signal with a locally generated carrier that has the **same frequency and phase** as the transmitted carrier, then low-pass filtering. Example: product detector for DSB-SC and SSB, coherent PSK detector. It needs carrier recovery but gives the best performance. **Non-coherent detection** recovers the message **without** knowledge of the carrier phase, using the envelope or energy of the signal. Example: envelope detector for DSB-FC AM, non-coherent FSK. It is simpler and cheaper but has worse noise performance and works only when the carrier is present. | Point | Coherent | Non-coherent | |---|---|---| | Local carrier | Needed, phase-locked | Not needed | | Complexity | High | Low | | Performance | Better | Poorer (threshold effect) | | Examples | DSB-SC, SSB, BPSK | AM envelope detector, ASK/FSK | #### Carrier recovery: Costas loop The Costas loop extracts a phase-locked carrier from a DSB-SC signal (which has no carrier component) and demodulates it at the same time. ```text +-->(X)--> LPF --> I: (Ac/2)m(t)cos(phi) | ^ | | | cos(wc t + phi) v s(t) = Ac m(t) | VCO <---- LPF <------(X) phase cos wc t -+ | (loop filter) ^ discriminator | [-90 deg] | | | sin(wc t + phi) | +-->(X)--> LPF --> Q: (Ac/2)m(t)sin(phi) ``` **Working:** 1. The I (in-phase) channel multiplies $s(t)$ by $\cos(\omega_ct + \phi)$; after LPF: $\tfrac{A_c}{2}m(t)\cos\phi$. 2. The Q (quadrature) channel multiplies by $\sin(\omega_ct + \phi)$; after LPF: $\tfrac{A_c}{2}m(t)\sin\phi$. 3. The phase discriminator multiplies I and Q: $$ e(t) = \frac{A_c^2}{4}m^2(t)\cos\phi\sin\phi = \frac{A_c^2}{8}m^2(t)\sin2\phi $$ 4. The loop filter averages $m^2(t)$, giving a DC control voltage proportional to $\sin2\phi \approx 2\phi$ for small $\phi$. 5. This voltage adjusts the VCO so that $\phi \to 0$. Then the Q output is zero and the I output is the message $\tfrac{A_c}{2}m(t)$. The loop tracks small phase and frequency drifts automatically. It has a $180^\circ$ phase ambiguity (sign of $m(t)$), which does not matter for audio. Other methods: squaring loop (square the signal, PLL at $2f_c$, divide by 2) and pilot carrier transmission. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What defines coherent detection? A. Following the envelope of the signal B. Multiplying by a local carrier of the same frequency and phase, then low-pass filtering C. Using no local oscillator D. Squaring the signal and filtering Answer: B. This is synchronous detection, e.g. for DSB-SC, SSB, BPSK. (Key point: Coherent detection) 2. Which detector is non-coherent? A. Product detector for SSB B. Costas loop C. Coherent BPSK detector D. Envelope detector for DSB-FC Answer: D. It does not need carrier phase and works only when the carrier is present. (Key point: Non-coherent example) 3. In the Costas loop, what drives the VCO control voltage? A. The product of the I and Q outputs, proportional to sin(2 phi) B. The I output alone C. The input carrier amplitude D. The Q output squared Answer: A. e = (Ac^2/8) m^2 sin 2phi, which is about proportional to phi for small phi. (Key point: Costas loop signal) 4. What happens when the Costas loop locks (phi = 0)? A. I output is zero B. Both outputs are zero C. Q output is zero and I output is the message (Ac/2)m(t) D. Q output is the message Answer: C. sin 0 = 0 and cos 0 = 1. (Key point: Locked condition) ## Related in Communication Systems - [BFSK generation, non-coherent detection and signal space](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Abfsk-noncoherent-signal-space) — Communication Systems, chapter 7 - [Threshold effect in non-coherent FM detection and its correction](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Athreshold-noncoherent-fm-correction) — Communication Systems, chapter 9 - [Phase error in coherent DSB-SC detection; AM demodulation by PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aphase-error-dsbsc-am-pll) — Communication Systems, chapter 2 - [Noise performance of coherent DSB-FC detection](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbfc-noise-coherent-100pct) — Communication Systems, chapter 9 - [SNR gain of non-coherent FM detector](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anoncoherent-fm-gain) — Communication Systems, chapter 9, asked 2× - [Figure of merit of non-coherent FM; threshold effect](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afom-noncoherent-fm-threshold) — Communication Systems, chapter 9 ## Related in other subjects - [Hartley vs Colpitts for FM carrier](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ahartley-vs-colpitts-fm) — Electronics Devices and Circuit, chapter 5 - [Restriking voltage vs recovery voltage](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Arestriking-vs-recovery-voltage) — Switchgear and Protection, chapter 6 - [Recovery from log: deferred vs immediate](https://www.bctengineer.com/question.md?key=semester_6%2Fdatabase_management_system%3Alog-recovery-deferred-immediate) — Database Management System, chapter 8 - [Unique vs non-unique address decoding](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Aunique-vs-nonunique-decoding) — Instrumentation II, chapter 2