# Coded system interference

1. Jun 30, 2015

### S_David

Hello all,

The following question is related to digital communication systems.

I am studying two systems operating at the same time and on the same frequency. Each system consists of one transmitter and one receiver. However, one of them, let us say system 1, is using channel coding with code rate Rc, while the other one (system 2) is not. Let SNR1 and SNR2 denote the signal-to-noise ratio (SNR) per uncoded symbol at system 1's and system 2's receivers, respectively, when no interference is present.

I want to quantify SINR1 and SINR2, where SINRi is the signal-to-interference-plus-noise ratio (SINR) at system i's receiver. Is the following correct:

$$SINR_1=\frac{SNR_1\,R_c}{1+SNR_2}$$

and

$$SINR_2=\frac{SNR_2}{1+SNR_1\,R_c}$$
?

Thanks

2. Jul 5, 2015

### tech99

I am not sure about your approach here. For instance, why does the coding gain of RX1 influence the performance of RX2? Are both systems occupying the same bandwidth? Would it not be clearer to work out the performance of each channel using signal powers, noise powers, interfering powers and coding gains?

3. Jul 5, 2015

### S_David

That is right, both are operating at the same frequency and at the same time.

I thought that is what I am doing, isn't it?

Thanks

4. Jul 5, 2015

### S_David

I think I know what you meant.

$$SNR_1=\frac{P_1}{P_2\,R_c+N_0\,W_1}$$

and

$$SNR_2=\frac{P_2\,R_c}{P_1+N_0\,W_2}$$

where W1 and W2 are the bandwidth of system 1 and 2, respectively. Right?

5. Jul 6, 2015

### tech99

In case 1, I think the interfering power P2 is reduced by the coding gain Rc, not increased. Also notice that the two bandwidths are different and this might not be representative of the real world where all the spectrum must be shared.

6. Jul 6, 2015

### tech99

Also, second equation, not sure why you show coding gain for RX2 when this system does not employ coding? P1 is wider band than W2 so I think you can reduce P1 by the coding gain Rc.

7. Jul 6, 2015

### S_David

My mistake. I meant to write
$$SNR_1=\frac{P_1R_c}{P_2+N_0\,W_1}$$

and

$$SNR_2=\frac{P_2}{P_1R_c+N_0\,W_2}$$

Is it correct now?

Last edited: Jul 6, 2015
8. Jul 6, 2015

### tech99

I think SNR1 looks OK. With SNR2, I am thinking that the interfering power P1 is divided by Rc, because the bandwidth of channel 1 is wider, so the interference into channel 2 is reduced.

9. Jul 6, 2015

### S_David

Yes, the interfering power is reduced from system 1, and this reduction is due to coding. Remember Rc is not the coding gain, it is the code rate which is less than 1, hence P1*Rc<P1.

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