I have a time domain OFDM signal and to this I need to apply different linear filter however I am not sure on the cut off frequency. I am simulating for multiple symbols where each symbol has 1200 central subcarriers in a 2048 FFT/IFFT bin. The samp freq is 30.72MHz. While designing filters in MATLAB using commands like "fir1", I am not sure how to set cut off freq.


In a real hardware implementation, you always needs to implement additional filtering to an OFDM signal, in digital sometimes and then in analogue. The same is true in fact for all digital signals.

In a simulation, the filtering is realized in digital. The issue is so select the cut-off frequency effectively. It has to be slightly higher than the maximum signal frequency to avoid performance degradation, and short enough to be effective in suppressing the sidelobes.

Concerning performance degradation, the point is so have a cyclic prefix large enough to handle the time response of the filter, and to have a receiver able to equalize the transmission chain correctly. This transmission chain include the different filters, but also the multipath channel.

In my experience, the degradation brought by the filters are negligible compared to the degradation brought by the channel.

  • $\begingroup$ Having written real-world OFDM implementations, aside from the anti-aliasing filter of the baseband ADC: Nope. That's simply not true. And you say why it's not true yourself: all the effects of the filter can be reversed by the OFDM system itself. So, if that OFDM system can and will do that by itself, your filter is "compensated" the moment you add it and doesn't do anything useful. What's the benefit of the digital filter you're proposing as necessary? $\endgroup$ – Marcus Müller Jan 4 at 12:50
  • $\begingroup$ @MarcusMüller I think there is a little confusion in the terms. In a real system, analogue filtering is absolutely necessary to respect the spectrum masks, and not only for ADC anti-aliasing. In simulation, all filters are digital. Therefore, we implement digital filter (associated with oversampling of course) to simulate these analogue filters. This is mainly necessary for some particular types of simulations. Nowadays, this is generally performed by increasing the number of FFT points, for the same number of "useful" subcarriers. This is a way to perform oversampling. $\endgroup$ – Damien Jan 4 at 13:11
  • $\begingroup$ In the past, with very expensive memory, we associated FFT with FIR oversampling ... I participated in a first OFDM hardware development in 1988 ... $\endgroup$ – Damien Jan 4 at 13:13
  • $\begingroup$ Spectral mask is a TX issue, this is RX :) so that's where my confusion stems from! So, yeah, oversampling is typically one way (typically even a necessary way, barring a priori frequency sync) (and, especially long-haul broadcasting standards mandate things like "2048-FFT with 1536 occupied carriers in the center"). I mean, yeah, sure, if I simulate something, then the simulated filter will be implemented digitally; but isn't OP's question revolving on how to build a digital RX filtering process to deal with OOB,which doesn't even exist in the digital domain(or is aliased anywhere)? $\endgroup$ – Marcus Müller Jan 4 at 13:17
  • $\begingroup$ @MarcusMüller OP mentioned sidelobes. This is a typical transmission issue. I may have misunderstood the question anyway. Such a digital filtering in the receiver has no interest indeed $\endgroup$ – Damien Jan 4 at 13:21

You don't need that filter. Your previous questions still indicate you shouldn't be using a filter. OFDM is a filterbank in itself, and applying a filter beforehand will increase delay spread, and thus you get ISI¹.

Sure, with a filter, you'll save on the noise power you'd get in carrier sidelobes, but that should typically be lower than what you lose in ISI.

So, no, you don't apply a different linear filter. You simply ignore the FFT bins that don't contain signal.

¹ you'll get ISI under the assumption that your OFDM system is designed with the minimum amount of subcarriers needed to compensate the maximum expectable delay spread on the channel. That makes a lot of sense because using significantly more subcarriers has no advantage, but makes your system depend on a longer coherency time. If you convolve the channel output with your receive filters, you get a "convolved channel-filter", with a length that is thus longer than your channel, and thus worse than your OFDM system can deal with.

  • $\begingroup$ Thank you for your insight dear Marcus however it is part of my study to do such observation. I had to window the IFFT'ed signal and now I need to filter as well and see respective changes. Good or bad alike $\endgroup$ – samz12 Jan 3 at 16:28
  • $\begingroup$ That makes no sense. Windowing the IFFT'ed signal is something you would never do, because it breaks OFDM. That's nothing you need to "see respective changes" of, that's just three lines of 1. writing down the DFT as formula 2. Writing down the IDFT as formula 3. Applying DFT(window(IDFT(data))) and seeing that it breaks. Are you sure you've understood OFDM well enough to model deterioriations? $\endgroup$ – Marcus Müller Jan 3 at 16:46
  • $\begingroup$ The Out of band emissions of the signal/transmission under study are pretty high. My job is to window and filter it to see the reduction in OOBs and the corresponding BER it produces. Does that help $\endgroup$ – samz12 Jan 3 at 17:02
  • $\begingroup$ The OOB of an OFDM signal is either part of the signal, or due to amplifier/ mixer nonlinearities. You would not combat that with filters, but with predistortion! $\endgroup$ – Marcus Müller Jan 3 at 17:06
  • $\begingroup$ If it's part of your signal, then the OFDM design was bad; if it's result of nonlinearities: 1. predistortion 2. If filtering is necessary, you haven't even described what those radiations look like, what suppression of OOB you need! so how on earth should we know where to put your cut-off frequency? $\endgroup$ – Marcus Müller Jan 3 at 17:10

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