  The uplink from a very small aperture terminal (VSAT) towards multiple
satellites is considered, in this paper. VSATs can be equipped with multiple
antennas, allowing parallel transmission to multiple satellites. A
low-complexity precoder based on imperfect positional information of the
satellites is presented. The probability distribution of the position
uncertainty and the statistics of the channel elements are related by the
characteristic function of the position uncertainty. This knowledge is included
in the precoder design to maximize the mean signal-to-leakage-and-noise ratio
(SLNR) at the satellites. Furthermore, the performance w.r.t. the
inter-satellite distance is numerically evaluated. It is shown that the
proposed approach achieves the capacity for perfect position knowledge and
sufficiently large inter-satellite distances. In case of imperfect position
knowledge, the performance degradation of the robust precoder is relatively
small.
