Analytical curve not matching with simulation curve.

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charu shree
charu shree 2021-9-2
Hello all,
I am trying to simulate the system that has a source , a receiver and M relays. To understand the problem that I am facing, I will explain it in steps.
Step I: I had obtained the SNR at the receiver as .
Step 2: At receiver , I am using MRC combining and hence the SNR becomes .
Step 3: I want to find the outage probability and so we get,
Step 4: The and are exponential random variable. And from step 3 , we observe that there is M fold summation. So, I used MGF (moment generating function) to solve the summation and obtain the answer using MATHEMATICA.
Step 5: The MGF is
Step 6: To find outage probability, we have to take the inverse laplace of MGF and it is obtained using Eq. (41) of Paper titled "Performance of Digital Modulation in Double Nakagami-m Fading Channels with MRC diversity".
The problem is that analytical is not coming properly while simulation is coming perfectly.
I am not getting what mistake I am doing for this case.
Any help in this regard will be highly appreciated.

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