# 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

## 1 Answer

A good text is by WIlliam Y. C. Lee. He did alot of the original work on propagation models. There are many others, just google "path loss model". This equation you selected is a very basic one for a cellular network. It doesn't take into account many of the fActors like environment(urban, suburban, rural), clutter or morphology, line of sight propagation or non line of sight, statistical factors and others. There are empirical models for various environments that have been used and modified (Hata, Okumura cost 231 etc) and can be iteritively adjusted with real field data.

With regard to your question about the reference distance. I'm sure you can find the answer in the references I mentioned above and the Goldsmith reference mentioned by ...

There might be a relationship to that distance and the far field or it may be justa standard reference, I'm not sure. In any case you could use a different model if the user is too close if necessary.

The path loss exponent is also a very important parameter(alpha in your equation)

Hope this helps