# Typical number of samples per symbol

Assuming a pulse shaping of a source of symbols (like $s=\{3,-i,2+5i\}$), and a SRRC waveform (or any other waveform). I know that it depends on many factors like modulation scheme, but, in practice, are there any typical value or range of "number of samples per symbol" required for the pulse shaping process?

• 2 to 4 samples per symbol is common in my experience. The incentive for using fewer samples per symbol is an overall lower sample rate (and thus less processing load). It depends what point in the system you're talking about, but you also need to take the excess bandwidth of your pulse shape into account to ensure that the sample rate is high enough to avoid aliasing. – Jason R Nov 28 '17 at 16:57
• It isn't really insufficient (mostly for 2)? How one can represent a SRRC with 2 samples only? Can't it be confusing with other waveforms? – Sofiane Nov 28 '17 at 19:37
• It depends on where you are in the processing chain. If the signal is perfectly synchronized, then you can in some cases get away with fewer samples per symbol. In the literature you'll find 2 samples per symbol as a target rate that you often would like techniques to use, because it's really the smallest that you're realistically going to achieve. – Jason R Nov 28 '17 at 19:56
• In some cases, can we go up to 20? In other words, in which cases we can set this parameter to higher values? Any examples for these "higher values"? – Sofiane Nov 28 '17 at 22:01
• You can always go higher if you need to. It just results in a higher sample rate (so more computational work). – Jason R Nov 28 '17 at 22:08

## 1 Answer

2 to 4 samples per symbol is common in my experience. The incentive for using fewer samples per symbol is an overall lower sample rate (and thus less processing load). It depends what point in the system you're talking about, but you also need to take the excess bandwidth of your pulse shape into account to ensure that the sample rate is high enough to avoid aliasing.

In some parts of the processing chain, you can get away with fewer samples per symbol than you might expect given the Nyquist rate and the signal's bandwidth. If the signal is perfectly synchronized, for example, then you don't need additional oversampling. In that case, you can use just one sample per symbol (basically, the symbol values themselves). You can then use that and the known pulse shape to reconstruct the signal to whatever fidelity you desire.

In the absence of perfect synchronization (for example, in the various receiver blocks that perform frequency, phase, and/or timing synchronization), you'll have some amount of oversampling. In the literature you'll find 2 samples per symbol as a desirable target rate, because it's really the smallest that you're realistically going to achieve. You can always go higher if you need to. It just results in a higher sample rate (so more computational work)

• Thanks Jason. But the main issue is at the transmitter and not the receiver, it's about the typical "number of samples per symbol" required for the pulse shaping at the transmitter. We don't yet have any idea about the synchronization. – Sofiane Nov 29 '17 at 11:12
• In that case, then you can use the aliasing criterion. Based on your pulse shape, you know what the total bandwidth of the shaped signal will be. Select an oversampling factor that yields a sample rate that is above the Nyquist rate and you will be fine. – Jason R Nov 29 '17 at 12:03