Stability of slotted ALOHA access with capture provided by an adaptive array

We study slotted ALOHA multiple access when a satellite contains an on-board antenna array to attenuate interference. This leads to a capture phenomenon in slotted ALOHA that is provided by the adaptive array. As expected, and as earlier reported in the literature, the adaptive array can improve system throughput. We find that it also improves system robustness. That is, the probabilities of new packet generation and retransmission can vary over a wider range than for slotted ALOHA and still maintain nearly maximum throughput. The same is true for the average packet delay and average system backlog. As in the earlier literature the adaptive beamforming capability on-board the satellite is taken to be ideal. For a system with two uplink and two downlink beams the throughput increase relative to slotted ALOHA is 128% for a wide range of system parameters