# A dense debate

In recent years, many research efforts were dedicated towards modeling and analyzing denser and denser wireless networks, in terms of the number of devices per km2 or m2. The terminology used ranges from “ultradense” to “hyperdense”, “massively dense”, and “extremely dense”.

IEEE Xplore lists more than 500 journal papers on “ultradense” networks, 25 on “hyperdense” networks (generally published more recently than the ultradense ones), and about 90 on “extremely dense” networks. There even exist 15 on “massively dense” networks. The natural question is how they are ordered. Is “ultradense” denser than “hyperdense” or vice versa? How does “extremely dense” fit in? Are there clear definitions what the different levels of densities mean? And what term do we use when networks get even denser?

Perhaps we can learn something from the terminology used for frequency bands. There is “high frequency” (HF), “very high frequency” (VHF), “ultrahigh frequency” (UHF), followed by “super high frequency” (SHF), “extremely high frequency” (EHF), and “tremendously high frequency” (THF). The first five each span an order of magnitude in frequency (or wavelength), while the last ones spans two order of magnitude, from 300 GHz to 30 THz.
So how about we follow that approach and classify network density levels as follows:

HD: 1-10 km-2
VHD: 10-100 km-2
UHD: 100-1’000 km-2
SHD: 1’000-10’000 km-2
EHD: 10’000-100’000 km-2
THD: 0.1-10 m-2

So, who will be the first to write a paper on tremendously dense networks?

What comes after THD? Not unexpectedly, there is a mathematical answer to that question. A dense set has a well-defined meaning. So in the super tremendously extreme case, we can just say that the devices are dense on the plane, without further qualification. This is achieved, for instance, by placing a device at each location with rational x and y coordinates. This is a dense network model, and almost surely there is no denser one.

## 2 thoughts on “A dense debate”

1. Jeff Andrews says:

It might be better to think about it in terms of behaviors rather than arbitrary density numbers? The first main density regime is the “normal” one, which is where the single slop path loss model more or less is a reasonable approximation as far as average received power. And then you could call the next one “Dense”, which is where you need at least a two-slope or some other appropriate model to capture the behavior. For me “Ultra dense” is the behavior as lambda -> infinity. But I agree, there should ideally be some standardization of these terms!

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1. Thanks for the comment. I agree that the definitions of the different density regimes could (probably should) be tied to the propagation characteristics. Wavelength should probably be included, too. While \lambda\to\infty may be appropriate for some networks (e.g., cellular), it may not be the right regime for others, such as M2M or D2D, where the performance keeps decreasing as the density increases.
Certainly the suggestion of borrowing the terminology from frequency bands is more “tongue-in-cheek” than it’s meant to be the final word on this topic.

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