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 alpha 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.