A general upper bound for FSO channel capacity with input-dependent Gaussian noise and the corresponding optimal input distribution

In this paper we derive a new upper bound for the input-output mutual information of FSO channels with input-dependent Gaussian noise by using a simple mathematical inequality. Then, by maximizing the obtained upper bound over all the discrete input distributions with equally spaced mass points, and approximating, we reach to a third order equation for the optimum input distribution. Our equation (i) determines the optimum input distribution directly in contrary to the Farid-Hranilovic (FH) work where it is found numerically, and also, (ii) gives a previously derived second order equation for the optimum input distribution of FSO channels with input-independent Gaussian noise in a special case. Using numerical illustrations, we compare our input distribution with previous works.