I am a bit confused about QAM modulation. In wikipedia, I found this:

It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves of the same frequency are out of phase with each other by 90°, a condition known as orthogonality or quadrature.

So for example, I can imagine having two carrier signals, lets say one sine wave and one cosin wave, which are modulated either by an analog baseband message signal (analog QAM), or by a digital message signal (digital QAM).

However, in another article, I found this:

The QAM transmitter first encodes bits into complex QAM symbols, which become the complex amplitudes of baseband pulses. The baseband QAM signal then modulates a digital RF subcarrier. The digital QAM signal is finally converted to an analog drive signal by a high-speed DAC.

Also, I could also find several references linking QAM to two PAM modulations. So here are my questions:

1. Are these two different things which happen to have the same name? My understanding is that, in the wikipedia definition, QAM has nothing to do with pulses.
2. What exactly is the meaning of "baseband QAM signal" in the second quote? Are PAM signals also baseband? My understanding is that we want to modulate a signal in order to transfer it to a higher (carrier's frequency) and to allow better communication (multiplexing, less interference, etc.).

EDIT

Link to paper where I took the second reference.

Link of following quote about PAM and QAM. What confuses me is that PAM is a pulsed signal, and QAM is a sinusoid. How exactly are they associated?

To simplify the basic concept, one can think of a 16-QAM signal as being the Cartesian product of two PAM4 signals.

• Two views of the same concept. Jan 26 '21 at 13:21

QAM is generated from a complex baseband signal, which can only be represented as two separate baseband signals for real and imaginary part.

The first paragraph you quoted directly modulates those onto the RF carrier, by converting real and imaginary part to analog separately, modulating them onto two carrier waves with 90 degrees offset and mixing them.

The second quote describes a method where the signal is digitally modulated onto an intermediate frequency carrier (by creating two sines at 90 degrees offset in a numerically controlled oscillator (NCO), multiplying real and imaginary part of the signal separately and adding them digitally, before converting the combined signal to analog, and mixing the analog signal with an RF carrier that has been shifted by the NCO frequency.

In both cases, the mixing step uses two carrier waves of equal frequency, 90 degrees apart, and the difference is whether that step is in the analog or digital domain.

Analog mixing:

• (+) output signal directly usable
• (+) cheap to build
• (-) RF paths need to be well matched in gain and delay
• (-) DAC DC offset shifts symbols around

Digital mixing:

• (+) real and imaginary parts combined perfectly
• (+) DC of IF signal carries no information and can be filtered
• (-) faster DAC needed for higher frequency components of mixed signal
• (-) upmixing to RF creates mirror images that need to be filtered out, usually with multiple mixer/filter stages

On the receiver side, the same issues apply, and there are also two ways to build them, "direct" and "superheterodyne."

• I am still having difficulty understanding the second quote. Could you explain the reference to "baseband pulses"? Also, what does it mean by "digital RF carrier"? Aren't carrier waves supposed to be analog signals? Jan 26 '21 at 19:47
• @NickG, the QAM baseband signal is a series of individual symbols, with sharp transitions between them, so each symbol can be seen as a separate pulse with a specific complex amplitude. This is then low pass filtered as the higher frequencies do not carry additional information, and this filtering step causes the smooth transitions you normally see in a QAM signal. Jan 27 '21 at 10:26
• @NickG, modulation can be entirely digital (it's just a multiplication), as long as the sampling rate of the system is high enough that all frequency components of the combined signal can be represented accurately. You normally wouldn't upmix to 2 GHz in this way though, because that requires a bit more than 4 GHz sampling rate, but modulating a 5 MHz wide baseband signal onto a 100 MHz carrier is doable with 250 or so MHz of sampling rate, this can then be converted, upmixed to 500/700 MHz with a 600 MHz carrier, filtered, upmixed again and filtered again for a clean RF signal. Jan 27 '21 at 10:34

PAM is basically baseband Sample & Hold for some pulse period that is a fraction of the shortest wavelength.

QAM is 4 bits encoded into a matrix of 4 amplitudes and 4 phases into a constellation of 16 stages using a coding method to scramble data with the shortest path to the next differential state using 2 signals in Quadrature than can be modulated with the following.

Wiki gives more details how this encoder works which is then used to modulate a carrier frequency. The advantage is bandwidth compression at the expense of requiring a slightly higher SNR to decode than binary according to Shannon-Hartley’s Law for the same BER. I believe you refer to Wiki - Quadrature amplitude modulation in your question.

I can imagine having two carrier signals, lets say one sine wave and one cosin wave, which are modulated either by an analog baseband message signal (analog QAM), or by a digital message signal (digital QAM).

Nearly correct. There are two carriers of the same frequency but are at 90 ° to each other and each carrier is amplitude modulated by a digital baseband signal. Hence there are two bits modulating two carriers at any one moment in time.

Each bit amplitude modulates its respective carrier by multiplying it by +1 or -1. This of course is the digital version of the story. In effect, each carrier is either inverted in amplitude or not inverted in amplitude by its digital bit. This is the same as advancing the carrier by 180 ° or leaving the carrier unaffected.

The two modulated carriers are then summed to produce a composite modulated carrier where the phase and amplitude of that carrier are defined by the two digital baseband signals.

In effect, you are taking two carriers at 90 ° to each other but, each has an phase (180 ° or 0 °) defined by the bit stream that modulated it. Then you sum them together to produced a combined modulated carrier: - So, if you look at the constellation diagram above for 0, 0 it has a phase angle of +45 °. Then if both digital inputs become 1, 1 then, the combined carrier phase angle shifts by 180 ° to 225 °. Maybe this might help: - This is digital 4-QAM.

If the carriers are analogue modulated, in effect there would be many more "circles" in the picture above because, for each carrier, it can be truly varied in amplitude by its baseband signal and also inverted in phase as the baseband signal passes from a positive value to a negative value (or vice versa). There wouldn't be constellations either because the combined effect of two carriers (each amplitude modulated) produces a "dot" at any one instant in time that is anywhere within a circle of a defined maximum radius.

I don't recognize your other reference.

• Thank you for the explanation. I have also added a link of the paper that I took the second quote, to the original post, in case it helps you provide more information about it. I have also added a reference to a site where PAM is associated with QAM, which confuses me, since PAM is a pulsed signal, and QAM is a sinuosid. Jan 26 '21 at 19:52
• @NickG I’m done now with this answer unless you have something more specific and direct to ask. Jan 26 '21 at 21:07