Smart Antennas, Dumb Scheduling for Medium Access Control

We consider the problem of stability of slotted ALOHA for a system consisting of N users communicating with a common receiver, which employs spatial diversity to receive multiple transmissions simultaneously. We introduce a general packet reception model to incorporate multiple packet receptions since the collision channel model is no longer valid in such a scenario. We characterize the stability region of slotted ALOHA for the two user case explicitly. We find that the relaxation of the collision channel model introduces a distinct change in the structure of the stability region. We show that the stability region undergoes a phase transition from a concave region to a convex region bounded by lines. We show that after this phase transition slotted ALOHA is optimal in the sense that slotted ALOHA can stabilize any rates that can be stabilized by any MAC protocol. Not only that, we find that after the phase transition, the best strategy is for both users to transmit with probability one which is an extreme case of slotted ALOHA with retransmission probability one. This significant finding suggests that if the physical layer is even reasonably good there is no need for sophisticated Medium Access Control protocols.