Stability of slotted ALOHA with spatial diversity

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a general packet reception model to incorporate multiple packet receptions since the collision channel model is no longer valid in such a scenario.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 also provide a sufficient condition for stability of slotted ALOHA for the N > 2 case, Finally, we apply our results to a simple system in which two users communicate with a base station equipped with a linear antenna array. Using stability region as a performance measure, we compare four different receivers/beamformers viz. matched filter, zero forcing, pseudo-MMSE and true MMSE employed by the base station to receive information from the users.