The problem is the detection process. The solution would be a synchronous detector.

With the conventional envelope detector, everything within the passband of the receiver beats with everything else. The AM carrier beats not only with the sidebands, but with every bit of noise. Noise components on every freqency beat with all other noise components within the passband. And every noise component beats separately with the upper sideband and the lower sideband.

A synchonous detector is basically a product detector. With the product detector, the only output signal components are the beat note products between the carrier and the sidebands, and the carrier and the noise components. Theoretically, there are no beat components between the noise and the sideband components, or between various noise components. The result is a better signal to noise ratio because of the absence of all the intermodulation of sideband, carrier and noise components that occurs with an envelope detector, such as the conventional diode detector.

The problem with attempting to copy AM using a SSB type product detector is that in order for the demodulated upper and lower sideband components to vectorially add in the proper manner, the re-inserted carrier must not only be on the exact frequency as the original AM carrier; it must be exactly in phase or exactly 180 degrees out of phase. In other words, the reinserted carrier of the BFO must be in synchronism with the original AM carrier. One way this can be accomplished is by using PLL technology.

The vectorial addition of the components of both sidebands actually gives the demodulated signal an additional 6 dB boost in amplitude. But because the DSB signal requires twice the receiver bandpass, twice the background noise (3 more dB) is admitted, so the actual boost in s/n ratio is 3 dB instead of 6. So with a product detector, the AM signal should be at least as readable in the noise, if not more, than a SSB signal of equivalent sideband power. The majority of the "advantage" that SSB is said to enjoy over AM is due to the fact that SSB is demodulated with a more efficient detector, the product detector. With a proper synchonous product detector, the SSB advantage is far less. In addition, the carrier of the AM signal can be reduced or even suppressed, since it is the re-inserted carrier that demodulates the sidebands. With the envelope detector, the original AM carrier has to do all the work. When the original carrier fades, you get selective fading distortion with the envelope detector.

A particular configuration of the synchonous detector, called the Costas Loop, can determine the frequency/phase of the original carrier strictly from phase relationships between the two coherent sidebands, without using the original carrier as a reference. Double-sideband suppressed carrier can give a 3 dB improvement in s/n ratio over single-sideband suppressed carrier, running the same total sideband power.

A PLL synchronous detector that uses the original AM carrier as reference can allow for "exalted carrier" reception which allows DSB AM to function at least at least 3 dB better, under noise conditions, as a SSB signal with equivalent total sideband power. This type of detector works with DSB reduced carrior AM. The AM carrier can be reduced without being totally suppressed, as long as the residual, or "pilot" carrier is sufficent for the synchronous detector to latch onto.
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