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I wrote a matlab code for lifetime optimization using a cost function for relay selection for data forwarding, the residual energy in each node is respresented bynormal distribution, the result which is the relation between lifetime(no.of superframes) & sigma squared is wavy, how can it be linear

I wrote the energy and needed equations, I used the cost function for relay selection and select the cost function with the minimum value to act as a relay node, I expect the result which is the relation bet. lifetime( represented in no.of superframes) and sigma squared to be linear, but it is wavy , i need the curve to increase linearly

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