Capacity of MIMO wireless networks in fractal maps

We want to estimate the average capacity of MIMO network when several simultaneous emitters and an access point are randomly distributed in an innite fractal map embedded in a space of dimension D. We rst 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 veries.