Discussion For Homework7

Question: In question 1, we are supposed to plot the error as a function of n. What is n? Is it the total number of symbols which we need to vary? Because the first line of the question says that n goes from 1 to 10.

Answer: n is the time index for the samples. I want you to plot the output of the matched filter sampled at time nT for all n. If there is no ISI, you should see that these are exactly the same as that of the data sequence that you transmitted and hence the error should be very small for all n (except at the edges because of poor truncation).

Question: In question 2, what is meant by "worst case" snr? Since we are taking an expectation of z_n, shouldn't the snr be deterministic given Tau and the pulse shape?

Answer: I agree this is a bit confusing. What I have defined in the write up should be seen as the average SNR where the average is over the ISI. However, the worst case SNR corresponds to the worst case Es/(N_0+z_n) over all $z_n$. Now the expectation over $z_n$ should not be there.

There is another subtle point which I missed. If the sampling time is off, then the desired signal component will also be affected and it will be multiplied by $sinc(\tau/T)$. To be exact we should take this in to account also. For the purpose of this homework, if you dont it is okay. But if it is not too much effort, please take this in to account as well.

Question: How deeply are we supposed to answer question number 5? We could get as high or low level as we want to with this.

Answer: A high level description is enough, but it should be clear.

Question: In question 4 do we consider non-coherent noise too? As all the derivations seem to have been done considering the noise to be coherent?

Answer: What is the meaning of non-coherent noise and why does it matter? remember if $n$ is a complex Gaussian random variable with independent real and imaginary parts, then $e^{j\phi} n$ is also complex Gaussian with independent real and imaginary parts.

Question: In question 2 how many symbols are we sending in one sequence?
Answer: It doesnt matter, think about it.

Question: In question 2, when the pulse used is a sinc and the sampling is done at the correct time, I am still not able to get 0 ISI. Has anyone else faced the same issue? Any idea what might be the reason for this?

Question: In question 2, It was mentioned in the above questions that the worst case SNR corresponds to the worst case Es/(N_0+z_n) over all $z_n$. Is that true? think it should be Es/(N_0 + Z_n^2).

Questin: In problem 6, The second optimization problem is just the euclidian distance after the whitening filter which should be the optimum detector as the noise is white after the filter. Is that the required proof or what should we do?

Question: About problem 7, should we do it or not?

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