Random Thoughts on Stochastic Geometry
Q cell analysis
Coverage is a key metric in wireless networks but usually only analyzed in terms of the covered area fraction, which is a scalar in [0,1]. Here we discuss a method to analytically bound the coverage manifold 𝒞, formed by the locations y on the plane where users are covered in the sense that the probability…
Is the IRS interfering?
There is considerable interest in wireless networks equipped with intelligent reflecting surfaces (IRSs), aka reconfigurable intelligent surfaces or smart reflecting surfaces. While everyone agrees that IRSs can enhance the signal over a desired link, there are conflicting views about whether IRSs matched to a certain receiver causes interference at other receivers. The purpose of this…
Taming the meta distribution
The derivation of meta distributions is mostly based on the calculation of the moments of the underlying conditional distribution. The reason is that except for highly simplistic scenarios, a direct calculation is elusive. Recall the definition of a meta distribution 
How well do distributions match? A case for the MH distance
Papers on wireless networks frequently present analytical approximations of distributions. The reference (exact) distributions are obtained either by simulation or by the numerical evaluation of a much more complicated analytical expression. The approximation and the reference distributions are then plotted, and a “highly accurate” or “extremely precise” match is usually declared. There are several issues…
Meta visualization
In this post we contrast the meta distribution of the SIR with the standard SIR distribution. The model is the standard downlink Poisson cellular network with Rayleigh fading and path loss exponent 4. The base station density is 1, and the users form a square lattice of density 5. Hence there are 5 users per…
Realistic communication
Today’s blog is about realistic communication, i.e., what kind of performance can realistically be expected of a wireless network. To get started, let’s have a look at an excerpt from a recent workshop description: “Future wireless networks will have to support many innovative vertical services, each with its own specific requirements, e.g. End-to-end latency of…
What to expect (over)
In performance analyses of wireless networks, we frequently encounter expectations of the form 
Signal-to-interference, reversed
Interference is the key performance-limiting factor in wireless networks. Due to the many unknown parts in a large network (transceiver locations, activity patterns, transmit power levels, fading), it is naturally modeled as a random variable, and the (only) theoretical tool to characterize its distribution is stochastic geometry. Accordingly, many stochastic geometry-based works focus on interference…
Path loss point processes
Naturally the locations of wireless transceivers are modeled as a point process on the plane or perhaps in the three-dimensional space. However, key quantities that determine the performance of a network do not directly nor exclusively depend on the locations but on the received powers. For instance, a typical SIR expression (at the origin) looks…
The transdimensional approach
In vehicular networks, transceivers are inherently confined to a subset of the two-dimensional Euclidean space. This subset is the street system where cars are allowed to move. Accordingly, stochastic geometry models for vehicular networks usually consist of two components: A set of streets and a set of point processes, one for each street, representing the…
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Stogblog by M. Haenggi 