Thanks for your help and your time Mathurathan. Totally appreciated here. The information that you’ve shared is incredibly useful already. I purchased your ebook the other day. Very nice material in it. Amazing effort you put into it. Also, thanks for letting me know how the 64-QAM ties with the IFFT side of things. It was something that I didn’t understand before — not from your material, but just in general. I found there was some kind of lack of basic run-down by other people (other sources), where people have a hard time grasping the theory due to gaps missing. But the detail that you provide appears to be far better than what I’ve seen elsewhere. For example, I didn’t know whether the input to the IFFT (for 64-QAM) was merely a sequence of 6 unipolar binary bits, or a sequence of 6 bipolar bits. I think I incorrectly thought that the input to the IFFT was just 6 plain bits….like [1 0 1 0 0 1] or bipolar form [-1 1 -1 1 1 -1]. Then I noticed that the IFFT of these 6 bit sequences can have IFFT output sequences containing some values of zero (ie. 0 + j0)…. ie. some ‘zero’ elements. I figured that wasn’t going to down well with using the real and imaginary parts to modulate cos and sin waves (respectively). So I then focused on the definition of ‘constellation mapper’ for 64-QAM, which doesn’t seem to be clear from sources that I’ve found so far. I guessed that the mapper not only had the function of grabbing 6 consecutive data bits at a time, but the output would be a complex number (representing a vector) that is able to represent those 6 particular bits. But after that, I wondered — if the mapper only outputs one complex number (a single vector), then we’d be doing an IFFT of 1 single complex value. So this didn’t make sense to me. But then, I figured that maybe the real case is multiple 64-QAM mappers all operating in parallel. Each mapper taking in 6 bits at a time, and each one outputting a complex number. So if we had 5 mappers working in parallel, then we’d get 5 complex numbers coming out of this parallel system, where each complexer number is associated with 1 QAM symbol (and 1 QAM symbol is representing 6 particular binary bits). The input to the IFFT would be these 5 complex values for example. The IFFT output would also be 5 complex values, all in parallel. However, since the IFFT outputs are going to be tied to a time-changing ‘sequence’, then the parallel IFFT output (eg. 5 complex values) would then be pushed out (one at a time) in a time sequence fashion. In order to preserve the real and imaginary values of each complex value, we split each complex value into real and imaginary value, and operate on the real and imaginary values in a parallel fashion. The real value can be used to modulate a cos wave ( ie. multiply the real value with cos(wt) ), and the imaginary value can be used to modulate a sin wave. And since the modulated cos wave is a real-valued signal, just like the modulated sin wave, those two waveforms can be added together by summation. The summed modulated cos and sin waves (as a function of time) is the OFDM signal. I may still have the wrong idea about certain aspects of generating OFDM from IFFT. But this was the kind of thought-process that I was going through. The information you’ve provided seems to be the most user/student/scholar friendly —- as it really makes a tremendous attempt to teach and explain the details properly. Thanks Mathuranathan!

The easiest way to generate square QAM constellation is to use Karnaugh map walks (see link below).

Yes, you are right. For 64 qam, 6 bits are needed for each QAM symbol. OFDM is constructed by collecting n such QAM symbols. I accept that the diagram is not straightforward.

https://www.gaussianwaves.com/2014/11/constructing-a-rectangular-constellation-for-m-qam-using-karnaugh-map-walks/

Thanks for the possibility to discuss with you.

Can we say that the “coding QAM” is integrated, included in the IFFT process of OFDM?… Or, is it a separated operation.

I’m not expert of that.

I would suppose it is included in the IFFT process. Is it possible to have some words, to allow a better understanding of how it is done?

Best regards,
Michel

yes. absolutely. Thanks

Many thanks Mathuranathan,

Can I correct this usual point of view?

DMT is used by G.fast, a wire DSL technology, see ITU-T G.9701(12/2014). We have 2 048/4 096 subcarriers with 51.75 kHz subcarrier spacing.

G.9700, table 7-2, to mix several technologies we have possible bandwidths: 2 or 30 or 106 MHz – 106 or 212 MHz. It’s passband channels.

OFDM is used by EPoC, a wire coaxial cable technology, see IEEE 802.3bn-2016. The bandwidth is 258 MHz – 1218 MHz splitted in 5 channels.

I would say that we traditionnaly use:
– The term OFDM for wireless,
– The terms DMT and OFDM for wire (OFDM for large bandwidth > 250 MHz, DMT otherwise).

But OFDM and DMT are similar (today).

Thanks for your new advice,
Michel

DMT is a real-valued multiplexing whereas, OFDM is a complex valued multiplexing.

DMT is for baseband channels (no need for carrier translation) hence found in wired applications like ADSL. OFDM is for passband channels.

https://uploads.disquscdn.com/images/53da7f322bd10b44b9c652cfef7d3dbdad54a074fcc559aeefb3b23f39ff359f.png

DMT/OFDM transmitters are very similar, except for that fact that in DMT, there is no carrier translation. Rest of the blocks like IFFT, cyclic prefix addition, will remain the same.

https://uploads.disquscdn.com/images/3f5e1a41757bc8fe82638942748570fc8ffbf3942603f3c6a5730b1582a43768.png https://uploads.disquscdn.com/images/5dc14e0b45bae81616285d9c2dee68e7a916a958f6f818aad64d1e3864c04ee4.png

Source: http://www.eit.lth.se/fileadmin/eit/courses/eit140/ofdm_system.pdf

Is there really a difference between DMT and OFDM modulations. DMT is used for ADSL and G.fast for example. OFDM is not only used for wireless. We can find it for coaxial cable technologies, as DOCSIS and EPoC (a new IEEE specification based on DOCSIS).
DMT and OFDM are both orthogonal with IFFT and FFT.
Best regards, Michel