Stochastic analysis of spatial and opportunistic aloha

• Published in: IEEE journal on selected areas in communications Vol. 27; no. 7; pp. 1105 - 1119
• Main Authors: Baccelli, F., Miihlethaler, P., Blaszczyszyn, B.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Series: STOCHASTIC GEOMETRY AND RANDOM GRAPHS FOR THE ANALYSIS AND DESIGN OF WIRELESS NETWORKS
• Subjects: Access protocols; Channels; Coins; Computer Science; Exact solutions; Fading; Field theory; Geometry; MAC layer; Magnetic heads; Mobile ad hoc networks; multiple access; network design; Networking and Internet Architecture; Networks; optimization; outage; point process; Rayleigh channels; signal to interference ratio; Stations; stochastic geometry; stochastic process; Stochastic processes; Stochastic resonance; Stochasticity; Studies; Throughput; Transmitters; transport capacity; outage; optimization; point process; multiple access; transport capacity; stochastic process; throughput; network design; stochastic geometry; signal to interference ratio; MAC layer
• ISSN: 0733-8716; 1558-0008
• DOI: 10.1109/JSAC.2009.090908

Spatial Aloha is probably the simplest medium access protocol to be used in a large mobile ad hoc network: each station tosses a coin independently of everything else and accesses the channel if it gets heads. In a network where stations are randomly and homogeneously located in the Euclidean plane, there is a way to tune the bias of the coin so as to obtain the best possible compromise between spatial reuse and per transmitter throughput. This paper shows how to address this questions using stochastic geometry and more precisely Poisson shot noise field theory. The theory that is developed is fully computational and leads to new closed form expressions for various kinds of spatial averages (like e.g. outage, throughput or transport). It also allows one to derive general scaling laws that hold for general fading assumptions. We exemplify its flexibility by analyzing a natural variant of Spatial Aloha that we call Opportunistic Aloha and that consists in replacing the coin tossing by an evaluation of the quality of the channel of each station to its receiver and a selection of the stations with good channels (e.g. fading) conditions. We show how to adapt the general machinery to this variant and how to optimize and implement it. We show that when properly tuned, Opportunistic Aloha very significantly outperforms Spatial Aloha, with e.g. a mean throughput per unit area twice higher for Rayleigh fading scenarios with typical parameters.