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The OFDM signal I'm interested in is rated for a 204.8MHz sampling rate!

I'm limited to sampling at 20MHz to give me just enough resolution into the range of subcarriers I'm interested in, but I just want to see if I can recover the QAM constellation from the sub-carriers I'm interested in.

I understand OFDM very well, but I'm used to having the full sample rate! Thanks for any insider comments.

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  • $\begingroup$ Are you referring to the IEEE paper by Nikos Petrellis: Information Recovery Using Undersampling in Orthogonal Frequency Division Multiplexing Systems? $\endgroup$ – penguin359 Jul 20 '18 at 18:54
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    $\begingroup$ Are you planning to filter the signal before sampling to remove the subcarriers you don’t care about? That would be an option. $\endgroup$ – Jason R Jul 20 '18 at 19:05
  • $\begingroup$ @penguin359 no, I'm not. Only observing a small sub-set of sub-carriers in a larger OFDM symbol. $\endgroup$ – ReachRF Jul 26 '18 at 17:38
  • $\begingroup$ @JasonR Essentially, yes, because at 20MHz on the sub-carrier frequency I expect to analyze, I'm automatically removing the sub-carriers I don't care about. $\endgroup$ – ReachRF Jul 26 '18 at 17:38
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Well, apply the definition of OFDM to a subcarrier range of an OFDM signal: it's still OFDM, in all letters of that acronym.

So, on a superficial level, yes, this works easily¹. Looking closer:

OFDM signals aren't usually rated for some sampling rate, the systems transmitting them just work at a specific rate, which mathematically coincides with the product of subcarrier spacing and numbers of subcarriers.

The good thing about OFDM is you don't have to worry about what the spectrum looks like in between the subcarrier "frequency points"; the orthogonality guarantees you've got no signal from other subcarriers on any subcarrier frequency, and the way perfectly synchronized OFDM works is by the DFT – which essentially samples the frequency domain.

Now, have you ever wondered why in e.g. a waterfall plot or on a spectrum analyzer, the spectrum in the unoccupied carriers at the edge doesn't actually decrease as fast as the (ideliazed) 6dB / decade of sidelobe power suggest?

LTE spectrum observed through Sylvain Munaut's *fosphor*

We often forget that yes, as you say, OFDM systems are actually discrete systems based on the DFT; often, the DACs involved are actually internally oversampling, even. This implies a "folding" imaging scenario, where sidelobe power that would fall out of the (nominal) DAC's bandwidth will be folded back – not a problem, because it just adds power from other sidelobes to sidelobes; at the transmitter, the orthogonality still stands!

Now, at the receiver, we're happy that the edge carriers are unoccupied – because the moment where we're not sampling-clock-synchronized and frequency-synchronized yet, we'll have a lot of fun with circularly shifted-in sidelobes overlaying the tentative correct subcarrier frequencies at both ends of the spectrum (assuming we critically sample).

Your subset-of-subcarrier-restricted OFDM receiver runs exactly into that hardship: No "leeway" for frequency offset and clock error to work out. Note that in this case, the frequency offset isn't "worse" to deal with than in the "normal" OFDM receiver case. It's just that you're guaranteed to have aliases from the adjacent carriers and their sidelobes also ending up in your signal – and whilst these have the same PSD as in the full OFDM signal, your processing gains on the DFT structure of the signal during synchronizations are but a fraction of what the full system has!

So, as Jason R commented:

  • Make sure the analog side of your receiver has adequate filtering. In theory, the sidelobes of adjacent channels don't matter, in practice, your sampling clock offset makes them hurtful. At any rate, you don't want other carriers to alias into your signal.
  • Make sure your receiver has plenty of dynamic range headroom. Really - OFDM has notoriously nasty PAPR, and you don't want dynamically appearing intermodulation products (hint: in many hardware SDR receivers, sampling rate and RF frequency generation are somehow coupled, so sampling rate-rationally-related intermodulation products often appear – especially bad here, because these can map "unseen" carriers to your carriers.
  • Use additional digital low-pass filtering to enforce unoccupied carriers at the edge of your observed band; yes, that'll take energy away from the carriers you want to see (remember, sidelobes in OFDM do carry information energy!), but it'll make your synchronization life easier.
  • Adapt the synchronization algorithm to your carrier subset. This might or might not be easy or even possible, considering we know nothing about how your system does synchronization.
  • Equalization might become a lot harder, if the original system was designed to interpolate channel state between neighboring carriers (and at bandwiths> 200 MHz, we can be pretty sure it does so to minimize the need for pilots), since you've got only a very partial view on things.

Astonishingly, the QAM aspect together with the last point might be a show-stopper here: QAM requires relatively good equalization, and since your part of the OFDM signal might give you less than an equivalent part of the pilot information in the overall system, you might simply be channel-coherency limited (either not enough pilots in frequency direction, or not enough pilots over time). So, make a channel model first, figure out how often you'll see pilots, and estimate whether things can work first, before spending too much time on this.


¹ assuming you can still frequency-synchronize. Since you said you understand OFDM very well, I assume you've got practical knowledge of OFDM synchronization methods – but in short: most do work on a restricted bandwidth, with slight modifications; you need to assume 0 subcarrier coarse frequency offset, anyways. Note that I'd still assume that if implementing an OFDM receiver, the synchronization would be the hardest part to get right. Timing synchronization is another challenge, but gets even more system-specific; if your system uses Schmidl&Cox to detect both freq and time, then you're more or less lucky and just need to adjust tolerances (and sample counts) to make this work.

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  • $\begingroup$ Thank you very much for your detailed reply, and I apologize about the delay I had to put work down for a little bit. Your response is adequate and verified some of my assumptions. Thank you for correcting my use of the term: rated, as it doesn't really apply to OFDM.\par In another forum I was advised to be weary of interference due to other sub-carrier because of reduced sampling. It was mentioned that there may be extra noise / distortion not expected at the full sample rate. I believe the timing and synchronization will be fine. $\endgroup$ – ReachRF Jul 26 '18 at 17:36

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