Smart antennas are becoming one of the promising technologies to meet the rapidly increasing demands for more capacity of satellite communication systems. A main component in a smart antenna system is beamforming. Because of the limitations of analog beamforming, digital beamforming will be employed in future satellite communication systems. We evaluate the performance of various digital beamforming strategies proposed in the literature for satellite communications: 1) single fixed beam/single user, 2) single fixed beam/multiple users, 3) single adaptive beam/single user, and 4) single Chebyshev dynamic beam/multiple users. Multiple criteria including coverage, system capacity, signal-to-interference-plus-noise ratio (SINR), and computation complexity are used to evaluate these satellite communication beamforming strategies. In particular, a Ka-band satellite communication system is used to address the various issues of these beamforming strategies. For the adaptive beamforming approach, subarray structure is used to obtain the weights of a large 2D antenna array, and a globally convergent recurrent neural network (RNN) is proposed to realize the adaptive beamforming algorithm in parallel. The new subarray-based neural beamforming algorithm can reduce the computation complexity greatly, and is more effective than the conventional least mean square (LMS) beamforming approach. It is shown that the single adaptive beam/single user approach has the highest system capacity.