Writing an OFDM modem - subcarriers are interferring

Question

I am trying to write an OFDM modem. I've already written a QAM modem, which I'm using as a basis for this project. The way I'm doing this currently is by spinning up several QAM modulators, each with a carrier frequency corresponding to a different DFT bin, and adding the waves together. On the decode side, I'm spinning up a QAM demodulator for each frequency and feeding the samples into each one.

For instance, I'm trying to use 52 carriers. My DFT has a bin size of 46.875 Hz. I use a symbol rate of 31.25 Hz, because I only process 2/3 of each symbol. My subcarriers are on the following frequencies: 1242.1875 Hz, 1289.0625 Hz, 1335.9375 Hz, etc.

Even though the QAM modem works fine on a clear channel, multiple QAM modems spaced apart as mentioned seems to cause problems. Here is a constellation from one of the demodulators:

Also, here is the output audio file from the OFDM modulator.

I am reasonably confident that the QAM modem is not the issue, as I have tested that it behaves properly with regards to synchronization and noisy channels.

Answer 1

To emulate OFDM with QAM modems with each carrier spaced by $1/T$ where $T$ is the QAM symbol duration, it will be critical that the QAM transmitter does not use any pulse shaping (meaning that it must send rectangular pulses without any tight filtering) and the receiver also has no tight filtering and either demodulates continuously or on even symbol boundaries. Under this condition, the individual QAM waveforms will have a spectral envelope as given by the Fourier Transform of the rectangular pulse (a Sinc function, or as a power spectral density, a Sinc-squared), with (importantly!) nulls spaced by $1/T$ in frequency, and thus required to ensure orthogonality of the subcarriers. With pulse shaping (as would typically be done in any QAM modem operating independently due to bandwidth efficiency requirements), the spectrum will be inevitably wider and thus will cause inter-carrier interference.

Any other subsequent filtering if not done carefully can also degrade the orthogonality for the same reason. Frequency (and time as Marcus mentions in the comments) offsets can also be a factor, but I am assuming the QAM modem has no issue with determining accurate carrier and time recovery-- however we must be certain that the transmitter modems and receiver modems are tightly synchronized in frequency and time (the tx components share a common clock, and the rx components share a common, possibly different than tx clock).