Scaling Laws for Two-Dimensional Random Ad-Hoc Wireless Networks

We derive an information theoretic scaling law for the maximum achievable rate per communication pair in a two-dimensional random ad-hoc wireless network. Our scaling law holds for non-absorptive media and when the path loss exponent (describing the decay of the amplitude of the signal) is between 1 and 2. The key ingredient of our result is the recently established information theoretic scaling law for one-dimensional ad-hoc wireless networks in the attenuation regime of interest