Random Thoughts on Stochastic Geometry
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
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
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
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
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?
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
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.”
It has been established (for example, here) that the standard two-dimensional homogeneous PPP is not an adequate model for vehicular networks, since vehicles are mostly confined to streets. The Poisson line Cox process (PLCP) has naturally emerged as the model of choice. In this process, one-dimensional PPPs are placed on a street system formed by … Continue reading A case for T junctions
Let us consider a cellular network with Poisson distributed base stations (BSs). We assume that in each Voronoi cell, one user is located uniformly at random (and independently across cells), and, naturally, the user is connected to the nucleus of that cell. This is the user point process of type I defined in this article. … Continue reading The typical user and her malfunctioning base station
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