To assess the coherent detection of an optical signal perturbed by atmospheric turbulence, the loss in the mean signal-to-noise ratio (SNR) is usually invoked although it constitutes a limited description of the signal fluctuations. To produce statistical distributions of the SNR, we generate random optical fields. A 5∕3-power law for the phase structure function is considered. The benefit of a wavefront tilt correction is assessed. Based on the 1%-probability fade, an optimum receiver size is found. For phase fluctuations only, a similarity between the signal distribution and the beta distribution is observed. Phase and amplitude are assumed independent, and the influence of amplitude perturbations is assessed with a scintillation index of 2. Turbulence impairments are compared for a coherent receiver and a direct-detection receiver.