# Sampling frequency and oversampling factor

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.

• Is this for a simulation or real system implementation? – Deve May 26 '15 at 12:35
• This is for a simulation in Matlab. – smyslov May 26 '15 at 12:37

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.