# Information content of amplitude modulation versus single-sideband transmission

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.

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.

• What are the relative advantages and disadvantages of independent sideband modulation versus QAM? I would think QAM would be simpler to implement. Commented Aug 29, 2011 at 17:51

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.

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.

• I first encountered the term QAM in a description of 2400-baud modems, which indicated that while 1200 baud modems just modulated phase, 2400-baud modems modulated both phase and amplitude. I'd thus associated the term QAM as being a combination of phase and amplitude modulation, even though it would be in many ways more natural to think of it in terms of amplitude modulation of two orthogonal signals at the same frequency. QAM sounds a lot like NTSC color modulation, though I've don't recall ever hearing it described as such. Commented Aug 29, 2011 at 17:42
• My familiarity with sine and cosine components comes from some work I did with DTMF and tone detection in a DSP. What I did there was compute the dot products of 64-sample pieces of incoming audio with sine- and cosine reference waves and run those through symmetric FIR filters. In addition to running sine and cosine through (IIRC) a six-stage filter, and computed the sum of the squares. I also took the sine and cosine values at the third tap, computed sum-of-squares, and ran that through a three-tap filter so the net response would match the six-tap filter. Commented Aug 29, 2011 at 17:46
• For a signal to be considered DTMF, the sum-of-squares of the sixth-tap outputs had to be within a certain margin of the output from the third tap of the pre-summed value. I've not done anything with RF, but I would think that one could use today's technology to process things at 250KHz using techniques much like I used years ago at 8KHz. In any case, for whatever reason I never made the connection between the term QAM, and the concept of modulating two signals at the same carrier frequency 90 degrees apart, even though I'd seen such things used (e.g. in NTSC video). Commented Aug 29, 2011 at 17:49
• Incidentally, in a different project I had to measure the signal strength of some sine waves in the low Khz range (2-8Khz, IIRC) using a PIC. Rather than using quadrature, I sampled at 6x the frequency of interest, and then did sum-of-squares on p0+p1-p3-p4, p1+p2-p4-p5, and p2+p3-p5-p0. Square-wave based demodulation will pick up all odd harmonics of the input signal; the approach I used served to cancel out every third harmonic. Commented Aug 29, 2011 at 17:58

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.

• I've been pondering a number of things. Among them, from what I understand, TDMA generally works on a macroscopic time scale--using more bandwidth (transmitting data faster) for a short amount of time, and sitting idle the rest of the time, while CDMA works on a microscopic time scale (transmitting data over a wide bandwidth, but being able to selectively grab data within that bandwidth). What would be the implications of e.g. increasing the data rate 8x, but having the transmitter idle a "random" 80+% of the time. Figure that some transmissions will get 'splatted', but use... Commented Aug 30, 2011 at 15:06
• ...forward error correction to deal with that? Commented Aug 30, 2011 at 15:09
• TDMA and CDMA are multiple-access methods; they allow multiple users to share a channel, divided either by time or by coding of their transmissions. I'm not sure what "implications" you're asking about. Bit-error performance is always going to be a function of the signal-to-noise ratio at the receiver. I would recommend a textbook on digital communications theory if you're interested in how these schemes actually work. There is a good text by Sklar that may help. Commented Aug 30, 2011 at 16:03