Sampling frequency and oversampling factor

Question

A quite naïve question. I need some clarification regarding choosing the sampling frequency and oversampling factor. The scenario is as follows:

I have an OQPSK modulated sequence with symbol rate 2 M Symbols/sec. In order to transmit this through an AWGN channel, I am trying to half sine pulse shape this modulated sequence. I have read from a couple of online resources that before pulse shaping the sequence should be oversampled. I am currently confused by the factor that I need to oversample the sequence.

Regarding the sampling frequency, at Baseband I am confused as to what I should take as the sampling frequency. I assume that at passband of 2.4 GHz, I am considering the sampling frequency of 6 GHz but I am not sure if this is right and how should I decide on the sampling frequency if I do not consider the passband and just the baseband frequency.

Answer 1

The rule you must remember when deciding on your sampling frequency is: it must be at least double the highest frequency signal that will ever appear in your simulation.

Consider your baseband signal. The highest frequency signal is the half-sine pulse (its bandwidth is infinite in theory). We know, from the Fourier series of a full-wave rectified sine, that its spectrum decays with frequency as $$\frac{1}{\pi(4n^2-1)}.$$ I would go with $n=3$, which corresponds to a frequency of $3f_0$. If your pulse rate is 2 Mpulses per second, then $f_0=2$ MHz, the pulse bandwidth is 6 MHz, and your sampling rate must be 12 MHz.

Regarding passband: If you must simulate this system at a high carrier frequency, you know that the bandwidth now will be 2.4 GHz plus 6 MHz, or 2.406 GHz, so your sampling frequency needs to be double that. However, before doing this, please learn about the complex envelope. There is nothing to be gained by simulating the passband system, and you can lose a lot of time.