3. Killing the Carrier: DSB-SC and SSB

The carrier in AM contains no information yet eats two-thirds of the power. The first "obvious" optimization is to skip transmitting it.

3.1 Double-sideband suppressed carrier (DSB-SC)

Multiply the message by the carrier with no DC offset:

$s_\text{DSB-SC}(t) = m(t)\cos(2\pi f_c t)$

The spectrum is the two sidebands of conventional AM, but the carrier impulse at $f_c$ is gone. All transmitted power goes into the sidebands. Bandwidth is still $2W$, the same as AM. Power efficiency is, in principle, 100% for the modulation step itself.

The catch: there is no carrier to envelope-detect. The envelope of $m(t)\cos(2\pi f_c t)$ is $|m(t)|$, not $m(t)$. Whenever $m(t)$ crosses zero, the envelope dips to zero and the carrier flips phase by 180 degrees. An envelope detector would output a half-wave-rectified message, which is wildly distorted.

The only viable detection is synchronous detection: multiply received signal by a locally-generated $\cos(2\pi f_c t)$ that is exactly in phase with the transmitted carrier, then low-pass filter. The output is $\tfrac{1}{2}m(t)$. Beautiful, except you now have to figure out, at the receiver, what the transmitted carrier's phase actually is (since you are no longer transmitting it). This is the carrier recovery problem, and the standard solution is the Costas loop (next subsection).

Generation of DSB-SC. Two flavors:

The balanced modulator uses two AM-modulator paths driven by carriers in antiphase. Both paths produce $[A_c + m(t)]\cos(2\pi f_c t)$ and $[A_c - m(t)]\cos(2\pi f_c t)$ respectively (with appropriate signs). Sum them and the carrier components cancel, leaving $2 m(t)\cos(2\pi f_c t)$.

The ring modulator uses four diodes in a ring driven by a strong carrier:

              carrier
                │
       ┌────────┴────────┐
       │                 │
    ──>│──D1   D4─<──    │
       │                 │
   m(t)                  output
       │                 │
    ─<─│──D2   D3─>──    │
       │                 │
       └────────┬────────┘
                │
              ground

The carrier drives the diodes alternately on and off, effectively multiplying the message by a $\pm 1$ square wave. The fundamental component of that switching is $\cos(2\pi f_c t)$, and the bandpass filter at the output keeps only the desired DSB-SC term. Ring modulators were workhorses of 1950s telephony (used in single-sideband carrier systems that crammed thousands of voice channels onto coaxial cables across the Atlantic) and they survive in analog music synthesizers as a "ring modulator" effect that produces clangorous metallic timbres. The reason it sounds metallic: you are multiplying two sinusoids at unrelated frequencies, producing sum-and-difference tones that are inharmonic, hence not a pleasant musical interval.

3.2 The Costas loop, briefly

The receiver needs a local oscillator phase-locked to a carrier that is not being transmitted. The Costas loop achieves this by exploiting that DSB-SC has even symmetry under sign flip: if your local oscillator is in phase, the I-channel output is $\tfrac{1}{2}m(t)$; if you are 90 degrees off, the Q-channel output is $\tfrac{1}{2}m(t)$ (but wrong-signed); if you are at some other phase $\theta$, you get a mix of both with $\cos\theta$ and $\sin\theta$ weighting. Multiply I and Q together and you get a signal proportional to $\sin(2\theta)\cdot m^2(t)$, whose long-term average is zero exactly when $\theta = 0$ (or $\pi$, which still gives valid demodulation). Feed that error signal into a VCO control, and the loop drives itself to lock.

We will see Costas loops again in Chapter 12 (digital communications) where they recover BPSK and QPSK carriers. The principle is identical to what we just described for DSB-SC voice.

3.3 Single sideband (SSB)

Both sidebands of DSB-SC carry the same information (one is the mirror of the other in the spectrum). Why send both? Drop one and you halve the bandwidth: an SSB signal occupies $W$ Hz instead of $2W$. The same message in half the spectrum is twice the spectral efficiency. SSB also turns out to perform well on the noisy HF bands where every dB of efficiency matters.

Filter method. Generate DSB-SC, then bandpass-filter one sideband out. Easy if the carrier is low (so the filter only needs a moderate Q to separate two sidebands separated by $2W$ at frequency $f_c$, where $W \ll f_c$ but the relative gap is still large enough for a real filter). Hard if the carrier is high. At HF carriers around 10 MHz with audio bandwidth of 3 kHz, the lower sideband ends at $f_c - 0$ and the upper sideband begins at $f_c + 0$; you need a filter that transitions from passband to stopband in essentially zero frequency span, an impossibility. The real trick is to do the SSB filtering at a low IF (typically 10 kHz to 500 kHz) where filters with crystal lattices or mechanical resonators have ridiculous Q, then mix the result up to the final carrier frequency.

Phasing method (Hilbert transform). Recall from Chapter 3 that the Hilbert transform $\hat{m}(t)$ of $m(t)$ shifts every frequency by $-90°$. The identity

$s_\text{USB}(t) = m(t)\cos(2\pi f_c t) - \hat{m}(t)\sin(2\pi f_c t)$

produces only the upper sideband; substitute a plus sign and you get the lower sideband. The proof is most easily seen in the frequency domain: $m(t)\cos$ shifts the spectrum to $\pm f_c$, and $\hat{m}(t)\sin$ shifts the spectrum to $\pm f_c$ with a 90-degree phase rotation that, when subtracted, cancels exactly the lower sideband and doubles the upper.

The phasing method needs four ingredients: a 90-degree-shifted copy of the message ($\hat{m}$), two mixers, a 90-degree-shifted copy of the carrier, and a summer. The challenging part historically was the audio Hilbert transform; analog implementations approximated it with all-pass filter networks (typically 6 to 8 cascaded stages) that achieved 90 degrees plus or minus a degree across the audio band. Modern radios do the Hilbert with one line of DSP and the rest is trivial.

Demodulation. Coherent product detection. Multiply received SSB by a locally-generated carrier and low-pass filter:

$s_\text{USB}(t)\cdot\cos(2\pi f_c t) = \tfrac{1}{2}m(t) + \text{HF terms}$

If the local carrier has a frequency or phase error, the recovered audio is shifted in frequency. This is why SSB voice sounds like Donald Duck when you tune it slightly off. In an AM signal the carrier provides a built-in reference, but in SSB you tune until the voice sounds natural. HF amateur radio operators do this all day.

3.4 Vestigial sideband (VSB)

VSB is a compromise between full DSB-LC AM and pure SSB: send one full sideband plus a "vestige" of the other. The vestige is small but enough that an envelope detector still works (with some distortion), or that the filter at the transmitter does not need impossibly steep skirts.

The classic application is analog NTSC television (and PAL and SECAM). The luma video signal is 4 to 5 MHz wide, so DSB would consume 8 to 10 MHz of channel; pure SSB filters are impractical at MHz video bandwidths around hundreds-of-MHz carriers; VSB hits the sweet spot at about 6 MHz channel width while still allowing simple receivers. ATSC digital TV (the US OTA digital standard from 1998 onward) inherited 8-VSB for the same reason: VSB filtering hardware was already in place across every TV station and consumer.

3.5 Summary table