—We design a model of wireless terminals, i.e. transmitters and receivers, obtained from a Poisson point process with support in an embedded fractal map. The terminals form a virtual MISO (Multiple Input Single Output) system with successful reception under SNR (signal-to-noise ratio) capture condition in a single hop transmission. We show that if we omit antennas cross sections, the energy needed to broadcast a packet of information tends to zero when the density of transmitters and receivers increases. This property is a direct consequence of the fact that the support map is fractal and would not hold if the terminal distribution were Poisson uniform, as confirmed by simulations. The result becomes invalid if the cross sections overlap or if we consider a masking effect due to antennas, which would imply an extremely large density of terminals. In the case where the cross sections of the transmitters have a non-zero value, the energy has a non-zero limit which decays to zero when the cross sections tend to zero.
55th Annual Allerton Conference on Communication, Control, and Computing https://hal.archives-ouvertes.fr/hal-01591112 55th Annual Allerton Conference on Communication, Control, and Computing, Oct 2017, Urbana-Champaign, United StatesARRAY(0x7fe6a74ea118) 2017-10-03