Effects of directivity on wireless network complexity

We study the effect of anisotropic radiation on wireless network complexity. To this end, we model a wireless network as a random geometric graph where nodes have random antenna orientations as well as random positions, and communication is affected by Rayleigh fading. Complexity is quantified by computing the Shannon entropy of the underlying graph model. We use this formalism to develop analytic scaling results that describe how complexity can be controlled by varying key system parameters such as the transmit power and the directivity of transmissions in large-scale networks. Our results point to striking contrasts between power scaling and directivity scaling in the large connection range regime.