Coherent vs non-coherent detection; carrier recovery

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.

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.

                 +-->(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.