  Efficient and low-complexity beamforming design is an important element of
satellite communication systems with mobile receivers equipped with phased
arrays. In this work, we apply the simultaneous perturbation stochastic
approximation (SPSA) method with successive sub-array selection for finding the
optimal antenna weights that maximize the received signal power at a uniform
plane array (UPA). The proposed algorithms are based on iterative gradient
approximation by injecting some carefully designed perturbations on the
parameters to be estimated. Additionally, the successive sub-array selection
technique enhances the performance of SPSA-based algorithms and makes them less
sensitive to the initial beam direction. Simulation results show that our
proposed algorithms can achieve efficient and reliable performance even when
the initial beam direction is not well aligned with the satellite direction.
