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If OFDM did not have a cyclic prefix or zero padding would have equalization of the individual sub-carriers been possible in the frequency domain?

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Since the goal of the CP is to remove or prevent ISI and ISCI, you would need a form of DFE with feedback from several neighbouring subcarriers of the previous symbol.

That can be expanded into a multi-symbol MMSE with feedback.

So yes it's possible.

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  • \$\begingroup\$ Inspite of the fact that frequency domain equalization relies on cyclic convolution which is ensured by the cyclic prefix? \$\endgroup\$ – ali khalil Sep 3 '20 at 13:25
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    \$\begingroup\$ @alikhalil, there's a lot in your comment that depends on semantics, so I won't answer it literally, but maybe this helps: the CP enables ISI-free matched filtering for each sub-carrier. If there were no or negligible ISI, you wouldn't need a CP. The FEQ generally takes care of gain and phase rotation, not interference. The cyclic-convolution is not a requirement for FEQ, but a way to take advantage of a CP where needed. \$\endgroup\$ – P2000 Sep 3 '20 at 17:23
  • \$\begingroup\$ Interesting, so does that mean that the one tab channel inversion or zero forcing FEQ per sub-carrier can be done with a formula corresponding to linear convolution? \$\endgroup\$ – ali khalil Sep 3 '20 at 17:48
  • \$\begingroup\$ @alikhalil FFT + FEQ, for one subcarrier, = I&D matched filter + inversion. The linear convolution happens in the I&D matched filter. Cycl. convolution is just a fancy name for shifting the I&D window into the CP. \$\endgroup\$ – P2000 Sep 3 '20 at 18:07
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To extend on P2000's answer:

So yes it's possible.

and he even tells you what kind of equalizer might be worth looking into.

However, in almost all cases (there's a few sparse signal speciality channels out there), you do OFDM to avoid having such a complicated equalizer.

So, when using a long (and thus, complex) equalizer, why still use OFDM? If you've done your equalizer right, your channel is flat afterwards. If you do (classical) OFDM right, you don't need the equalizer.

There's a few corner cases (and those are very real) that could benefit from a combination, but seriously, reading your questions, you're not designing one of these. You're trying to understand what OFDM is about. And OFDM is mostly about not needing an equalizer.

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    \$\begingroup\$ Agreed. I was never tempted to design an OFDM system without CP. I even avoid channel shortening TDEQ where possible, and pay a bit extra overhead for the CP. \$\endgroup\$ – P2000 Sep 3 '20 at 16:33

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