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Free space optical (FSO) communication links experience different fading for longer terrestrial links, which may result in lognormal, Gamma-Gamma or exponentially distributed signals under weak, modarate and strong turbulence. Channel estimation is also corrupted by background and electrical noise. In this paper, we measure the FSO fading distribution from experimental data collected from a 1550nm, 12 km long terrestrial link. Background and electrical noise statistics are found from collected noise data. We also consider the estimation of unknown parameters from FSO channel samples considering the background and electrical noise which are the sum of fading plus Gaussian noise. We determine the root mean square estimation errors (RMSE) using various methods including the Method of Moments (MOM) and iterative Maximum Likelihood (ML) estimations. We evaluate the Cramer-Rao Bounds (CRB) for these problems. We compare our estimation technique performance with existing methods of estimation which ignore Gaussian noise. The new estimation technique which takes noise into account shows significant performance improvement in the low signal to noise ratio (SNR) region. We also compare the estimation performance under varying number of channel samples. We use a single dimension approach where only one parameter is estimated at once.