Information content of amplitude modulation versus single-sideband transmission

Question

An amplitude-modulated radio signal with carrier frequency C, which includes frequencies from 0 to F, will use output frequencies in the range C-F to C+F, or a total bandwidth of 2F. A modulation approach called single-sideband modulation omits either the frequencies below C or those above C, and simply transmits the others, on the basis that the frequencies on the other side of C are "redundant".

It would seem, though, that there is information content in the seemingly "redundant" frequencies. For example, if the signal to be modulated on a 1MHz carrier was a sine waves at 100Hz, an AM signal would contain two frequencies: 999,900Hz and 1,000,100Hz. Receiving both frequencies and demodulating them would a 100Hz signal whose phase matched that of the original.

If the signal were single-sideband modulated (let's assume upper), then the modulated signal would simply be a continuous 1,000,100Hz signal. Although a receiver which was tuned to precisely 1,000,000Hz would be able to detect that the signal was a 100Hz signal, I see no means by which it could determine anything about the phase of it.

On the other hand, it would seem like it would be possible to have two signals amplitude-modulated in the same bandwidth if the carrier waves were 90 degrees out of phase, provided that the receiver could discern which carrier wave was which. If the signals to be modulated were devoid of DC content, one could obtain such a result by having the base level of one carrier substantially exceed that of the other. The receiver would be phase-locked onto the first signal when the primary (0 degrees) carrier strength was at maximum.

If one can make use of two simultaneous analog communications channels, would amplitude modulation of two signals with carrier frequencies 90 degrees out of phase provide the same level of bandwidth efficiency as single-sideband modulation? What other tricks exist?

(BTW, I'm pondering the notion of performing spread-spectrum transmission by amplitude-modulating a medium-frequency signal (e.g. 100,000-250,000Hz) on a ~900Mhz carrier. Most "spread-spectrum" receivers I've seen are limited to receiving a single channel at once, but I would think that using analog modulation and demodulation would allow for a DSP to process many channels simultaneously). To get optimal results, however, one would probably have to be able to accurately determine the relative phases of the signals one was receiving.

Answer 1

Your perfectly single-sideband suppressed-carrier modulated sinusoid certainly has a phase which can be measured. However, what you cannot tell is what the contributions of that measured phase from the audio input and the RF oscillator were.

There is another form of single-sideband modulation, in which not only one sideband but also the carrier component is transmitted. This provides a reference which can be used to synchronize the receive LO to the transmit one - normally done to insure exact tuning, but it would also give you the ability to recover the original audio phase.

It is also quite possible, especially with modern DSP gear, to transmit two separate audio channels, one on each side band. This is commonly called independent sideband modulation (ISB).

Many spread spectrum implementations are DSP based and capable of receiving multiple channels at once - GPS being a good example.

Answer 2

Are you not "just" describing quadrature (I/Q) modulation? OTOH I admire that you came to the conclusion by yourself, without (consciously) thinking about I/Q.

From the Wikipedia article

Like all modulation schemes, QAM conveys data by changing some aspect of a carrier signal, or the carrier wave, (usually a sinusoid) in response to a data signal. In the case of QAM, the amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed (modulated or keyed) to represent the data signal. Amplitude modulating two carriers in quadrature can be equivalently viewed as both amplitude modulating and phase modulating a single carrier.

Answer 3

In standard amplitude modulation, there is no additional information present in the second sideband; you can suppress either one of them with no theoretical loss. This is because the signal that is used to modulate the carrier is real-valued. Real-valued signals have a Fourier transform that is Hermitian symmetric about zero frequency; therefore, given only a one-sided spectrum, you can readily calculate what the other sideband would contain.

In your question, you seem to be concerned about determining the phase of the modulating signal by observing the phase of the upconverted component at 1 MHz + 100 Hz. There is no relationship in this case; as the name suggests, amplitude modulation results in a carrier whose amplitude varies according to the modulating signal. There is no relationship between the baseband audio signal's phase and the transmitted carrier's phase at any given time instant.

You have also correctly deduced that quadrature modulation works; two orthogonal carriers (i.e. separated in phase by 90 degrees) can carry modulated signals that can be detected independently from one another. This is used frequently in phase-shift-keyed techniques such as QPSK, as well as amplitude-and-phase-shift-keyed approaches like the various flavors of QAM.

With regard to your proposed project (I assume you're suggesting a direct-sequence spread spectrum system), spread spectrum systems are typically implemented using phase-shift keying, not amplitude-shift. Synchronization is easier for constant-envelope signals, and power amplification is typically more efficient for that case. It is also common to find spread-spectrum receivers that can simultaneously receive data from more than one co-channel transmitter, such as in CDMA.