Capacity Scaling of Ad Hoc Networks with Spatial Diversity

This paper derives the exact outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques. The analysis enables a direct comparison of the number of simultaneous transmissions achieving a certain data rate under different diversity techniques. Preliminary results derive the outage probability and transmission capacity for a general class of signal distributions which facilitates quantifying the gain for fading or non-fading environments. The transmission capacity is then given for uniformly random networks with path loss exponent alpha > 2 in which nodes: (1) perform maximal ratio transmission/combining on M antennas with Theta(M 2/alpha ) gains; (2) various antenna selection combining schemes which give appreciable but rapidly diminishing gains; and (3) orthogonal space-time block coding, for which there is only a small gain due to channel hardening. It is concluded that in ad hoc networks, beamforming performs best, selection combining performs well for smaller numbers of antennas, and that space-time block coding offers only marginal gains.