Imagine you are playing with a ball and you throw it to a friend who is far away from you. The farther your friend is, the harder it is for the ball to reach them. It's kind of like your voice when you talk to someone far away. The farther away they are, the harder it is for them to hear you.
Now, let's imagine that instead of a ball, we are talking about radio waves or signals that are sent from one place to another. The farther away the signal travels, the weaker it becomes. This is because the signal is being absorbed by things like trees, buildings, and air molecules as it travels through the air.
The log-distance path loss model is a way to calculate how much weaker the signal will become as it travels from one place to another. It takes into account things like the distance between the transmitter (the place where the signal is sent from) and the receiver (the place where the signal is received), the frequency of the signal, and any obstacles that might be in the way.
The formula for the log-distance path loss model looks like this:
PL(dB) = 10log(d) + 10nlog(f) + C
PL stands for Path Loss, which is a measure of how much weaker the signal is compared to when it was transmitted. dB stands for decibels, which is a way of measuring the strength of a signal. d is the distance between the transmitter and the receiver, f is the frequency of the signal, n is a constant that depends on the environment (like how many obstacles there are), and C is a constant that represents any additional losses (like losses from cables or connectors).
Basically, what this formula is saying is that the farther away the receiver is from the transmitter, the weaker the signal will be. The higher the frequency of the signal (like for WiFi or Bluetooth), the more it will be absorbed by obstacles like walls and buildings. And the more obstacles there are between the transmitter and receiver, the weaker the signal will be.
So, the log-distance path loss model is a way for engineers and scientists to predict how much weaker a signal will be as it travels from one place to another. By understanding this model, they can design wireless systems (like cell phone networks or WiFi) that can work reliably over long distances and in a variety of environments.