Scaling laws for one- and two-dimensional random wireless networks in the low-attenuation regime

The capacity scaling of extended two-dimensional wireless networks is known in the high-attenuation regime, i.e., when the power path loss exponent a, is greater than 4. This has been accomplished by deriving information-theoretic upper bounds for this regime that match the corresponding lower bounds. On the contrary, not much is known in the so-called low-attenuation regime when 2 <= alpha <= 4. (For one-dimensional networks, the uncharacterized regime is 1 <= alpha <= 2.5.) The dichotomy,is due to the fact that while communication is highly power-limited in the first case and power-based arguments suffice to get tight upper bounds, the study of the low-attenuation regime requires a more precise analysis of the degrees of freedom involved. In this paper, we study the capacity scaling of extended wireless networks with an emphasis on the low-attenuation regime and show that in the absence of small scale fading, the low attenuation regime does not behave significantly different from the high attenuation regime.