Spectral Efficiency in Single-Hop Ad-Hoc Wireless Networks with Interference Using Adaptive Antenna Arrays

Receivers with N antennas in single-hop, ad-hoc wireless networks with nodes randomly distributed on an infinite plane with uniform area density are studied. Transmitting nodes have single antennas and transmit simultaneously in the same frequency band with power P that decays with distance via the commonly-used inverse-polynomial model with path-loss- exponent (PLE) greater than 2. This model applies to shared spectrum systems where multiple links share the same frequency band. In the interference-limited regime, the average spectral efficiency of a representative link E[C] (b/s/Hz/link) is found to grow as log(N) and linearly with PLE, and its variance decays as 1/N. The average signal-to-interference-plus-noise-ratio (SINR) on a representative link is found to grow faster than linearly with N. With multiple-input-multiple-output (MIMO) links where transmit nodes have multiple antennas without Channel- State-Information, it is found that E[C] in the network can be improved if nodes transmit using the optimum number of antennas compared to the optimum selfish strategy of transmitting equal-power streams from every antenna. The results are extended to random code-division-multiple-access systems where the optimum spreading factor for a given link length is found. These results are developed as asymptotic expressions using infinite random matrix theory and are validated by Monte-Carlo simulations.