Academic profiles:
Google scholar profile
arXiv profile (All my preprints since 2009 are here)
ORCID profile (possibly not uptodate)
Research themes
Wireless signals appear Poisson
Under the standard statistical propagation model, researchers have mathematically shown that wireless networks can appear (in terms of received signal powers) to any single observer as an inhomogeneous Poisson point process on the real line, provided there are sufficiently random propagation effects, such as multipath fading or shadowing. In other words, the signal powers form a point process on the positive real line, which is statistically close to a Poisson point process. This has been proven for a quite general propagation model with independent propagation effects and, more recently, correlated shadowing. These results imply, through the Poisson mapping theorem, that network transmitter layouts that do not appear Poisson, such as lattices or other configurations, can be modelled as realizations of Poisson processes, as a Poisson network with matching intensity measure would produce the same inhomogeneous Poisson point process on the positive real line.
The source of randomness that makes a nonPoisson network appear (or behave stochastically) more Poisson is the random propagation effects of fading, shadowing, randomly varying antenna gains, and so on, or some combination of these. These Poisson results were originally derived for independent lognormal shadowing, but then they were greatly extended so they still hold true under a propagation model with a general path loss function and (sufficiently large and independent) propagation effects, such as Rayleigh or Nakagami fading, and this behavior is more likely for the stronger signals. In the case of lognormal shadowing and a powerlaw pathloss function, this Poisson behaviour still holds true if there is correlation between the random propagation effects. More specifically, signals can still appear Poisson when the propagation effects are modelled with a correlated Gaussian field.
Coverage probability
For mobile (or cellular) phone networks and other wireless network, a very popular stochastic geometry model consists of base stations (that is, transmitters) as a Poisson process, a simple power law as the path loss function, and iid random variables as the random propagation effects such as fading and shadowing. Borrowing an expression from physics, this Poisson model could be called the "standard model" due to its popular use. Researchers have used it to derive closedform expressions, sometimes with surprisingly simple forms, for the probability distributions of the signaltointerference ratio (SIR) in the downlink, which gives the probability of a user being covered in the network. Under various models, these coverage probability expressions have been derived, where the model assumptions depend on considerations such as whether a user connects to the closest base station or the base station with the strongest signal.
Under the standard model, an expression was paper for the probability that a user can connect to k base stations in a singletier Poisson network. Using point process techniques, these kcoverage results were extended to the case of multitier Poisson network models, which are often used to model heterogeneous networks. The results can also be used to calculate the coverage probabilities under certain signal management schemes, such as successive interference cancellation, so generalizing previous results based on point process theory.
The main idea behind the kcoverage results is using the SchuetteNesbitt formula and recognizing that the symmetric sums are a simple function of the factorial moment measures of the SINR process.
The STIR process is a PoissonDirichlet process
Some of the aforementioned work in the engineering literature, namely that of deriving probability expressions for SIRbased coverage, had already been discovered years earlier in the field of probability, which is pointed out in this short article. Under the Poisson network model with (singular) power law path loss function, the SINR process of a single user is a simple transform of the STIR process, which is an example of a PoissonDirichlet process.
The twoparameter PoissonDirichlet process, also called the PitmanYor process, gives the STIR process when one of the parameters is set to zero. In other words, the STIR process is a special case. Note there are two different point processes both called the PoissonDirichlet process, where the much more wellknown one was introduced by Kingman, which is not the STIR process, but these two point processes are the two special cases of the twoparameter PoissonDirichlet/PitmanYor process.
The above special case of the PoissonDirichlet (that is, the STIR) point process is also the same point process used in Ruelle's energy model, which is studied in relation to the SherringtonKirkpatrick spin glass model; see Chapter 2 of Panchenko (Springer Verlag, 2013) or Chapter 4 of Contucci and Giardiná (Cambridge University Press, 2013).
Academic background
I originally studied physics and electronic engineering before changing over to applied mathematics and completing an honours thesis in fluid mechanics. I completed my PhD in applied mathematics at the University of Melbourne under the supervision of Peter G. Taylor whose detailed websites can be found here and here. I then spent two years, partly being funded by Orange Labs, in Paris as a postdoc in the Inria (formerly INRIA) group DYOGENE * headed by Marc Lelarge (the group was known as TREC, headed by François Baccelli, during my first few months there). Then I became a member of the Weierstrass Institute (or WIAS), Berlin, in a group headed by Wolfgang König.
Collaborators:
* DYOGENE is actually a reference to ancient Greek philosopher Diogenes of Sinope (who famously lived in a giant jar) as his name in French is pronounced the same as DYOGENE, all of which had to be explained to me.
** ł is not a Latin "l", but a Slavic letter, and it's pronounced more like a "w". The "z" also plays a different role, so in English the name "Błaszczyszyn" sounds more like "Bwashtchyshyn" with a long "a" sound.
