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.

翻译：本文提出了一种新颖方法，用于在任意大规模无线网络中实现所有链路的性能保证。该方法引入了针对平稳空间点过程的空间调控性质（这些点过程用于建模发射机与接收机位置），并建立了该调控微积分的初步框架。这一空间网络微积分可视为经典时间网络微积分在空间维度的扩展。具体而言，定义了两类调控：第一类包括球调控与散粒噪声调控，用于约束其他链路产生的总干扰功率的上界；第二类包括空隙调控，用于约束信号功率的下界。满足第一类调控的典型实例为硬核过程，而典型反例为泊松点过程。这些调控分别以强形式和弱形式定义：前者要求调控在空间各处均成立，后者则依赖于Palm微积分，仅要求调控在联合平稳观测者点过程的原子处成立。基于该方法，我们展示了如何推导各类设备到设备及蜂窝网络的性能保证。研究表明，在适当空间调控下，所有链路的信干噪比均存在普适界。无衰落情况下该界为确定性，存在衰落情况下则为随机性。这进而可在将干扰视为噪声时，基于信息论可达性为所有链路提供服务保证。进一步地，该结果可与经典网络微积分相结合，为大型无线网络中所有链路的排队过程提供端到端时延保证。此类保证在未实施空间调控的网络（如泊松网络）中并不存在。