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Hummm actually is more about the distance (in the radio topology) between the nodes and the gateway. Closer are the gateway to the nodes less power you need.

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Yes, so if you have a uniform distribution of nodes and gateways over space, a node's nearest gateway gets closer as network density increases.

Definitely, but the philosophy that I usually see is that once your gateway cover an area you may want to add a second one (to cover in case of failure) but no more.

So the distribution is not uniform... On the other way, once an area is covered, more and more nodes are added.

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