# Random Thoughts on Stochastic Geometry

## What to expect (over)

In performance analyses of wireless networks, we frequently encounter expectations of the form called average (ergodic) spectral efficiency (SE) or mean normalized rate or similar, in units of nats/s/Hz. For networks models with uncertainty, its evaluation requires the use stochastic geometry. Sometimes the metric is also normalized per area and called area spectral efficiency. The … Continue reading What to expect (over)

## 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 … Continue reading Signal-to-interference, reversed

## 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 … Continue reading Path loss point processes

## 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 … Continue reading The transdimensional approach

## To be connected or not to be

These days, “connectivity” is a very popular term in wireless networking. Related to 5G, typical statements include “5G will be the main driver of wireless connectivity.” “5G is designed to provide more connectivity.” “5G provides 1 million connected devices per square km.” There is also talk about “massive connectivity”, “poor connectivity”, “intermittent connectivity”, “high-speed connectivity”, … Continue reading To be connected or not to be

## Wishful thinking

Today we are listening in to a conversation between Achill and the Turtle. Achill: I have been conducting research on the performance of wireless links for a while now, and I learnt that analyzing a fixed deterministic channel does not lead to insightful and general results. To capture a variety of channel conditions and obtain … Continue reading Wishful thinking

## Randomness decreases correlation – does it?

Intuition may tell us that increasing the randomness in the system (e.g., by increasing the variance of some random variables relative to their mean) will decrease the correlation between some random quantities of interest. A prominent example is the interference or SIR in a wireless network measured at two locations or in two time slots. … Continue reading Randomness decreases correlation – does it?

## Rayleigh fading and the PPP – part 2

The previous blog highlighted that the Rayleigh fading channel model and the Poisson deployment model are very similar in terms of their tractability and in how realistic they are. It turns out that Rayleigh fading and the PPP are the neutral cases of channel fading and node deployment, respectively, in the following sense: For Rayleigh … Continue reading Rayleigh fading and the PPP – part 2

## Rayleigh fading and the PPP

When stochastic geometry applications in wireless networking were still in their infancy or youth, I was frequently asked “Do you believe in the PPP model?”. I usually answered with a counter-question:“Do you believe in the Rayleigh fading model?”. This “answer” was motivated by the high likelihood that the person askingwas familiar with the idea of … Continue reading Rayleigh fading and the PPP

## Stochastic geometry (is) fun – part 3

This is a true story. Not 100% comic but also showing an interesting point of view.

Reviewer 2:*“This is a well-written paper. But it uses probability theory.”*

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