Analytical expression and optimization of spatial acquisition for intersatellite optical communications

In intersatellite optical communications it is important to obtain the most efficient performance of acquisition system with respect to acquisition time for a given probability. In this paper a novel approach to the analytical optimization of spatial acquisition is presented as an alternative of the conventional Monte Carlo simulation. First, an analytical expression of estimating mean acquisition time (MAT) is derived as a function of the desired acquisition probability, taking into account the distribution function of satellite position, field of uncertainty (FOU), beam divergence angle and dwell time. Accordingly, the analytical expression of multi-scan, which is always adopted by practical optical terminals to ensure the acquisition success, is also presented. Then, by minimizing the MAT of multi-scan, the optimum ratio of the FOU θU to the pointing error deviation σis obtained, which is θU/σ=1.3. An example for a practical intersatellite acquisition between a Low Earth Orbit Satellite and a Geostationary Earth Orbit Satellite is given. And the theoretical result calculated by the proposed analytical expression is approximately equal to the result by Monte Carlo simulation. The results can be used in designing acquisition system for the intersatellite optical communications.