Shannon capacity in poisson wireless network model

We consider a realistic model of a wireless network where nodes are dispatched in an infinite map with uniform distribution. Signals decay with distance according to attenuation factor $\alpha$. At any time we assume that the distribution of emitters is $\lambda$ per square unit area. From an explicit formula of the Laplace transform of a received signal, we derive an explicit formula for the information rate received by an access point at a random position, which is $\frac\alpha2(\log 2)^{-1}$ per Hertz. We generalize to network maps of any dimension.