Analytical curve not matching with simulation curve.

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.