  Slotted ALOHA (SA) algorithms with Successive Interference Cancellation (SIC)
decoding have received significant attention lately due to their ability to
dramatically increase the throughput of traditional SA. Motivated by increased
density of cellular radio access networks due to the introduction of small
cells, and dramatic increase of user density in Machine-to-Machine (M2M)
communications, SA algorithms with SIC operating cooperatively in multi base
station (BS) scenario are recently considered. In this paper, we generalize our
previous work on Slotted ALOHA with multiple-BS (SA-MBS) by considering users
that use directional antennas. In particular, we focus on a simple randomized
beamforming strategy where, for every packet transmission, a user orients its
main beam in a randomly selected direction. We are interested in the total
achievable system throughput for two decoding scenarios: i) non-cooperative
scenario in which traditional SA operates at each BS independently, and ii)
cooperative SA-MBS in which centralized SIC-based decoding is applied over all
received user signals. For both scenarios, we provide upper system throughput
limits and compare them against the simulation results. Finally, we discuss the
system performance as a function of simple directional antenna model parameters
applied in this paper.
