DSB-SC vs SSB; synchronous demodulation of DSB-SC

Comparison of DSB-SC and SSB

Both suppress the carrier and need coherent detection; they differ in the number of sidebands sent.

Similarity: both save carrier power, both give the same output SNR as baseband for the same transmitted power.

Synchronous (coherent) demodulation of DSB-SC

The received wave is multiplied by a locally generated carrier of exactly the same frequency and phase, and the product is low-pass filtered.

 s(t) ----->( X )----- v(t) ----> LPF ----> vo(t)
              ^                  (0 to W)
              |
        Local oscillator
        cos(wc t + phi)

Let $s(t) = A_cm(t)\cos\omega_ct$ and local carrier $\cos(\omega_ct + \phi)$:

$$\begin{aligned} v(t) &= A_cm(t)\cos\omega_ct\cos(\omega_ct + \phi) \\ &= \frac{A_c}{2}m(t)\cos\phi + \frac{A_c}{2}m(t)\cos(2\omega_ct + \phi) \end{aligned}$$

The LPF removes the $2\omega_c$ term:

$$v_o(t) = \frac{A_c}{2}\cos\phi\; m(t)$$

With $\phi = 0$: $v_o(t) = \tfrac{A_c}{2}m(t)$, the message is recovered exactly.

Requirements

• The local oscillator must be synchronised in frequency and phase with the transmitter carrier.
• LPF cut-off at $W$, and $f_c \gg W$ so spectra do not overlap.
• A carrier-recovery circuit (pilot carrier, squaring loop or Costas loop) is needed because no carrier is transmitted.

Limitations

• Phase error: output scales by $\cos\phi$. At $\phi = 90^\circ$ the output is zero (quadrature null effect). A slowly varying $\phi$ causes fading.
• Frequency error $\Delta\omega$: output becomes $\tfrac{A_c}{2}m(t)\cos(\Delta\omega t)$, a beating distortion.
• Receiver is costlier and more complex than an envelope detector.