SINR calculation

I would like to calculate the total SINR of a IQ modulation system in time domain. $$SINR = \frac{P}{N+I}$$ The blocks of the system are.

• Bit generation
• QAM modulation
• pulse shaper (sq root raised cosine f)
• IQ mod
• IQ dem
• filter (root raised)
• QAM demodulation

I made a simulation of a IQ modulation system in time domain, with a recovery of the signal, but unfortunately I dunno how to calculate the SNIR.

Here is the file, thanks for your help.

The main file is my_modem.m.

Here you can see the outputs! http://matlabonline.p.ht/

• – Deve
Aug 30, 2013 at 11:22
• Christian: Welcome to DSP.SE! Please do not cross-post to multiple SE sites. Choose one. If another is more appropriate, the mods will migrate it. Also, please take some time to format your question. Cutting and pasting without sensible editing makes it look bad. Better editing usually results in better answers.
– Peter K.
Aug 30, 2013 at 12:31
• If this is a simulation, then the only noise and interference should be noise and interference that you have added. I'm not quite sure what you are asking for. Aug 30, 2013 at 18:15
• Dear Jim, even though I haven't add noise or interference to the simulation, I am just trying to find a way to measure them at the receiver. Please check the code with functions here Sep 1, 2013 at 16:54
• @JimClay, please check the simulation here Sep 1, 2013 at 20:55

1 Answer

If there was intersymbol interference or additive noise in your simulation you could calculate the noise term by taking the difference of the transmit signal $x(k)$ (before pulse shaper) and the received signal $r(k)$ (after sampler): $$n(k) = r(k) - x(k),$$

where $k$ is the discrete time and is omitted in the following. Computation of the signal to interference and noise ratio (SINR) is then straightforward: $$\gamma_\mathrm{SINR} = \frac{\mathrm E[|x|^2]}{\mathrm E[|n|^2]} = \frac{\sum_{k} |x|^2}{\sum_{k} |n|^2}$$

$\mathrm E[]$ is the expectation operator.

In your simulation, $x$ corresponds to input signal and $r$ to filtered signal.