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Information Theoretic Cut-set Bounds on the Capacity of Poisson Wireless Networks

This paper presents a stochastic geometry model for the investigation of fundamental information theoretic limitations in wireless networks. We derive a new unified multi-parameter cut-set bound on the capacity of networks of arbitrary Poisson node density, size, power and bandwidth, under fast fading in a rich scattering environment. In other words, we upper-bound the optimal performance in terms of total communication rate, under any scheme, that can be achieved between a subset of network nodes (defined by the cut) with all the remaining nodes. Additionally, we identify four different operating regimes, depending on the magnitude of the long-range and short-range signal to noise ratios. Thus, we confirm previously known scaling laws (e.g., in bandwidth and/or power limited wireless networks), and we extend them with specific bounds. Finally, we use our results to provide specific numerical examples.