Capacity calculation for a specific channel

Computing a complex formula for a channel capacity using Matlab

I am having trouble obtaining viable results for the capacity of this channel. I am provided with 2 vectors (elements_constallation and prob), which correspond to the y and the p in the formula. I have to compute the formula shown in the image. Although my code generates results, I am not convinced by them due to the fact that for low noise variance values (sigma variable in my code) the capacity should increase logarithmically, but it grows exponentially. Any help would be appreciated.