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In a digital communication system, is it possible to counteract the aliasing problem by properly tuning the constellation order $M$ and/or the carrier frequency?

Here is my train of thought, please correct me if I'm wrong:

The sampling rate needs to be 2 times the signal bandwidth. This is because we need to cover all the frequencies in which the signal operates. If the signal breaks the Nyquist criterion we'll only get a part of the signal. So if I look at a fix sampling rate and try to tune the constellation order $M$ up and down it won't help, because the signal will still have the same bandwidth. The only thing that will change is the transfer rate $r_b = \log_2(M)/T_s$, where $T_s$ is the sampling rate. Also tinkering around with carrier frequency will only move the signal up or down the frequency. So neither of these solutions will counteract the aliasing problem. The only solution is to somehow reduce the signal bandwidth. I'm thinking of using an RRC filter on the transmitter (to shrink the bandwidth) and then using another RRC filter on the receiver to counteract the ISI.

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    $\begingroup$ Hi! What do you (spceifically) mean by counteract ? $\endgroup$ – Fat32 Aug 21 '17 at 15:14
  • $\begingroup$ Getting the most out of your signal. From my understanding aliasing happens when we go below the Nyquist criterion ( the sampling rate goes below the 2*bandwidth of the signal). Also I have updated my questing with a possible solution. $\endgroup$ – Tilen Kavčič Aug 21 '17 at 15:29
  • $\begingroup$ ok so you want to prevent aliasing, bu tuning some parameters of the signal... under a given sampling rate. $\endgroup$ – Fat32 Aug 21 '17 at 15:47
  • $\begingroup$ This question in a "theoretical" one to see if we understand things in dsp. I want to prevent aliasing. $\endgroup$ – Tilen Kavčič Aug 21 '17 at 15:50
  • $\begingroup$ One thing: the rate is $r_b = \log_2 M / T_p$, where $T_p$ is the symbol rate (how many pulses/symbols per second are transmitted). Sampling ocurrs at the boudary between the analog front end and the digital back end; it is at this point that Nyquist must be obeyed. $\endgroup$ – MBaz Aug 21 '17 at 21:51
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If the signal breaks the Nyquist criterion we'll only get a part of the signal.

This needs to be clarified: the frequencies above Nyquist will fold back into the Nyquist band, so it's not just that you lose part of the signal; it's that the signal is corrupted (usually) beyond hope of reconstruction.

As an example, consider a 4 kHz real signal sampled at 4 kHz -- the frequencies between 2 and 4 kHz will fold back into the 0 to 2 kHz range; not a single "part" of the signal will survive.

You're correct that this can't be solved by modifying the constellation order $M$ or the carrier frequency. As you correctly assume, you have two options. You can reduce the bandwidth through pulse shaping; if the symbol rate is $R$, then the minimum bandwidth $B=R/2$ is achieved with sinc pulses. The second option is to reduce the rate.

(As a side note, recently there have been proposals to increase the rate without increasing the bandwidth (search for "Faster than Nyquist signaling"), but I think these ideas are outside the scope of your studies at the moment.)

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  • $\begingroup$ Also I would add one more thing how to solve this problem. You can oversample the signal before sampling. Also thank you for the your clarification, it helped me a lot. $\endgroup$ – Tilen Kavčič Aug 21 '17 at 17:15

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