A study on antenna pointing for a cluster of users

Pointing a space station antenna for the coverage of a cluster of users is studied. Suppose a single antenna located on a space station is mechanically steerable for the coverage of a few users, and the goal of the antenna pointing is to minimize the maximum pointing loss among the users. Mathematically, this is a nonlinear optimization problem. Assuming that all the users are within the mainbeam coverage, it is shown that there exists a unique global optimum pointing and any local optimum is also a global optimum. Therefore, a basic two-dimensional line search algorithm can be applied to find the global optimum pointing. For antenna patterns which are circularly symmetric, a one-dimensional search algorithm, which can be more efficient when the number of active users is small is also presented