Capacity of Simple Multiple-Input-Single-Output Wireless Networks over Uniform or Fractal Maps

We want to estimate the average capacity of MISO networks when several simultaneous emitters and a single access point are randomly distributed in an infinite fractal map embedded in a space of dimension D. We first show that the average capacity is a constant when the nodes are uniformly distributed in the space. This constant is function of the space dimension and of the signal attenuation factor, it holds even in presence of non i.i.d. fading effects. We second extend the analysis to fractal maps with a non integer dimension. In this case the constant still holds with the fractal dimension replacing D but the capacity shows small periodic oscillation around this constant when the node density varies. The practical consequence of this result is that the capacity increases significantly when the network map has a small fractal dimension.