# How to implement path loss in wireless communications?

I would like to implement path loss propagation model in a cellular network scenario.

I know that the path loss can be modeled as follows:

$$\mathrm{PL}(d)\propto\left(\dfrac{d_{ij}}{d_0}\right)^\alpha,$$ where $d_0$ is a reference distance and $d_{ij}$ is the distance between transmitter $i$ and receiver $j$.

My question is how to scientifically choose the value of $d_0$? I read a lot of papers that say typical values of $d_0$ are $10, 100$. I do not really get what does $d_0$ mean in real scenario?

Let say I generate randomly the position of my transmitter $i$ and receiver $j$, is there a constraint on $d_0$ that has to be met? What happens if $i$ and $j$ are very close to each others, i.e., $d_{ij} < d_0$?

Can anyone suggest to me a paper or a chapter in a book that I can read to understand the theory and the implementation of path loss models?

Thank you.

• I'm not an expert, but from what I've seen, those values are calculated emprirically, not theoretically. What you do is perform channel measurements in the environment you're interested in, and then fit your results to your model. This gives you the values of your constants. There is a section on this on Andrea Goldsmith's book, but I don't have it with me now. It's on an early chapter, either 2 or 3 IIRC. – MBaz Apr 29 '15 at 21:17