Upper bound on the ergodic rate density of ALOHA Wireless Ad-Hoc networks

We present a novel upper bound on the Ergodic Rate Density (ERD) of ALOHA wireless ad-hoc networks. Our analysis uses a proper model of the physical layer together with an abstraction of higher communication layers. The novel bound is very general and supports various system models including for example, beamforming, spatial multiplexing, different fading models and different power control schemes. We also derive a closed form expression for the maximal gap between the novel bound and a known lower bound on the ERD. This maximal gap holds for any network that operates below the optimal density. This expression is simple to evaluate and only depends on the path loss factor. For example, for a path loss factor of $\alpha=3$ the novel upper bound is proved to be at most 31% higher than the lower bound (and hence also from the actual ERD). The usefulness and the generality of the novel bound is demonstrated by applications in multiple-antenna schemes. In particular, we study the optimization of the number of transmitted spatial streams in a MIMO network and derive the scaling of the ERD as the number of antennas grows. The results are further demonstrated using extensive simulations.