Slotted Aloha for networked base stations with spatial and temporal diversity

We consider framed slotted Aloha where m base stations cooperate to decode messages from n users. Users and base stations are placed uniformly at random over an area. At each frame, each user sends multiple replicas of its packet according to a prescribed distribution, and it is heard by all base stations within the communication radius r. Base stations employ a decoding algorithm that utilizes the successive interference cancellation mechanism, both in space-across neighboring base stations, and in time-across different slots, locally at each base station. We show that there exists a threshold on the normalized load G = n/(τm), where τ is the number of slots per frame, below which decoding probability converges asymptotically (as n, m, τ → ∞, r → 0) to the maximal possible value-the probability that a user is heard by at least one base station, and we find a lower bound on the threshold. Further, we give a heuristic evaluation of the decoding probability based on the and-or-tree analysis. Finally, we show that the peak throughput increases linearly in the number of base stations.