Spatial Network Calculus and Performance Guarantees in Wireless Networks

This work develops a novel approach towards performance guarantees for all links in arbitrarily large wireless networks. It introduces spatial regulation properties for stationary spatial point processes, which model transmitter and receiver locations, and develops the first steps of a calculus for this regulation. This spatial network calculus can be seen as an extension to space of the initial network calculus which is available with respect to time. Specifically, two classes of regulations are defined: one includes ball regulation and shot-noise regulation, which upper constraint the total power of interference generated by other links; the other one includes void regulation, which lower constraints the signal power. Notable examples satisfying the first class of regulation are hardcore processes, and a notable counter-example is the Poisson point process. These regulations are defined both in the strong and weak sense: the former requires the regulations to hold everywhere in space, whereas the latter, which relies on Palm calculus, only requires the regulations to hold at the atoms of a jointly stationary observer point process. Using this approach, we show how to derive performance guarantees for various types of device-to-device and cellular networks. We show that, under appropriate spatial regulation, universal bounds hold on the SINR for all links. The bounds are deterministic in the absence of fading and stochastic in the case with fading, respectively. This leads to service guarantees for all links based on information theoretic achievability when treating interference as noise. This can in turn be combined with classical network calculus to provide end-to-end latency guarantees for all packets in queuing processes taking place in all links of a large wireless network. Such guarantees do not exist in networks that are not spatially regulated, e.g., Poisson networks.