Transmission Capacity of Ad Hoc Networks with Spatial Diversity

Abstract

This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or non-fading environments. The transmission capacity is given for interference-limited uniformly random networks on the entire plane with path loss exponent \(\alpha>2\) in which nodes use: (1) static beamforming through \(M\) sectorized antennas, for which the increase in transmission capacity is shown to be \(\Theta(M^2)\) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigen-beamforming (maximal ratio transmission/combining), in which the increase is shown to be \(\Theta(M^{\frac{2}{\alpha}})\); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal space-time block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagami-\(m\) fading for increasing \(m\). It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that space-time block coding offers only marginal gains.