In this paper, we investigate the diversity-multiplexing trade off (DMT) performance of a coherent free-space optical (FSO) communication system with multiple receive apertures over atmospheric turbulence channels. Our study builds on the recently introduced statistical model that characterizes the combined effects of turbulence-induced wave front distortion and amplitude fluctuation in coherent receivers with phase compensation. Our results provide in sight in to performance mechanisms of coherent FSO systems and demonstrate significant performance gains that can be obtained through the deployment of multiple receive apertures and phase compensation techniques.