# Question regarding digital communications and bit error probability.

1. Nov 26, 2008

### breakshift

1. The problem statement, all variables and given/known data

I am having trouble understanding the bit error probability equation. I need to determine the bit error probability for a coursework. I am given a noise sample and asked to determine the SNR and bit error probability for a signal voltage of 0.5 V. The noise is given as an oscilloscope screenshot and 250 values sampled over 100us. In the equation, I understand that delta V is the difference between the two voltage's used for 0 and 1, but sigma confuses me. Obviously it is related to the level of noise present in the channel, but I am unsure how to determine it. From the sampled values of noise, I have determined that the average rms voltage is 14.92 mV (rms).

2. Relevant equations

SNR(dB) = 10log(S/N), where S/N = A^2/2*sigma^2, where A = delta V
bit error probability, p = 1/2 * erfc{deltaV/2*sigma*sqrt(2)}

3. The attempt at a solution

A is simply 0.5V, and I gather from worked examples (which are not clear, so I may be wrong) that sigma is equal to the rms voltage of the noise present in the channel. I have worked through the calculations assuming this, and I get a probability of 0.4943585 which is why I am posting this; this value seems wrong to me because the signal voltage of 0.5V is much greater than the noise voltage, which shouldn't result in a probability of bit error of roughly 1/2.

So my question is what does sigma represent and how do I find it?

Thanks a lot.