Question regarding digital communications and bit error probability.

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Homework Statement

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).

Homework 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)}

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.

 

[KataKoniK]

Thank you for reaching out for help with understanding the bit error probability equation. I am happy to assist you in understanding this concept.

Firstly, let me clarify that sigma represents the standard deviation of the noise present in the channel. In other words, it is a measure of the variability or spread of the noise values. This value is important in determining the bit error probability because it affects the accuracy of the received signal.

To determine the value of sigma, you can use the formula sigma = sqrt(sum((x-mean)^2)/n), where x is the noise values, mean is the average rms voltage (14.92 mV), and n is the total number of noise values (250 in this case). This will give you the standard deviation of the noise present in the channel.

Once you have the value of sigma, you can plug it into the bit error probability equation and calculate the probability of bit error. It is important to note that the value of delta V should also be determined from the noise values, rather than assuming it to be the signal voltage of 0.5V.

I hope this helps clarify the concept for you. If you have any further questions or need assistance with the calculations, please do not hesitate to ask. Best of luck with your coursework!

 

[Mene]

The bit error probability is an important metric in digital communications, as it represents the likelihood of a bit being received incorrectly due to noise in the channel. In the equation, sigma represents the standard deviation of the noise present in the channel. This value can be determined by taking the square root of the mean square voltage value of the noise sample, which in this case is 14.92 mV. It is important to note that the noise sample should be taken over a sufficient period of time to accurately represent the noise in the channel.

Based on the given information, the SNR can be calculated as 10log(0.5/14.92) = -34.9 dB. This indicates that the signal voltage is significantly higher than the noise voltage, which is why the resulting bit error probability of 0.49 seems unexpected. It is possible that there may be other factors at play, such as signal distortion or interference, that could affect the bit error probability.

I would recommend double-checking your calculations and also considering any other potential sources of error in the channel. If you are still unsure, it may be helpful to consult with your instructor or a classmate for clarification or assistance. Additionally, conducting further research on the topic of bit error probability and digital communications may also provide helpful insights.