On the Time Dynamics of Optical Communication Through Atmospheric Turbulence With Feedback

In the turbulent atmosphere, wavefront predistortion based on receiver-to-transmitter feedback can significantly improve the performance of optical communication systems that employ sparse aperture transmit and receive spatial diversity. The time evolution of the atmosphere, as wind moves turbulent eddies across the propagation path, can limit any improvement realized by wavefront predistortion with feedback. The improvement is especially limited if the latency is large or the feedback rate is small compared to the time it takes for turbulent eddies to move across the link. In this paper, we develop a physics based channel model that describes the time evolution of atmospheric turbulence. Based on that channel model, we derive theoretical expressions relating latencies - such as feedback latency and channel state estimate latency - and feedback rate to optimal performance. Specifically, we find the theoretical optimal average bit error rate as a function of fundamental parameters such as wind speed, atmospheric coherence length, feedback rate, feedback latency, and channel state estimate latency. Further, we describe a feedback strategy to achieve the optimal bit error rate. We find that the sufficient feedback rate scales linearly with the inverse of the atmospheric coherence time and sub-linearly with the number of transmitters. Under typical turbulence conditions, low-rate feedback, of the order of hundreds of bits per second, with associated latencies of less than milliseconds is sufficient to achieve most of the gain possible from wavefront predistortion.