# Wireless radio reception power vs distance

I found a PDF online that says:

The diagram shows that one unit of power is required to achieve a given data rate over one unit of distance. But to maintain the same data rate over x the distance, a traditional wireless network requires not x but rather 16x the power.

It refers to this diagram:

Shouldn't it have been 9X the power (instead of 16X) or 4X the distance (instead of 3X)?

• calculate the surface area of a sphere that has a radius of 1 meter, then calculate the same for a radius of 2m and 3m .... what is the ratio of areas? – jsotola Jun 1 '18 at 16:18
• It all depends on what link loss formula they assumed. Does the pdf tell you that? – Andy aka Jun 1 '18 at 16:36
• @Andyaka they didn't – Luís Marques Jun 1 '18 at 16:45
• Can you link the pdf please – Andy aka Jun 1 '18 at 16:46
• motorola.com/innovators/pdfs/mesh-ntwks-wp-7.24.06.pdf – Luís Marques Jun 1 '18 at 16:48

But, conceivably they could have used an exponent of 2.53 and $3^{2.53}$ = 16.1.