the relationship between the SNR and the transmission range

Dear all,

Im searching about the relationship between the SNR and the transmission range.

in my thesis , in cognitive radio network, I am going to increase the transmission range of some nodes to connect the network ,taking into account the constraints related to the CRN ( primary user interference ,...etc)

now I have to build this equation :

SNR=transmission range * factor ;

as the transmission range increase , then the transmission power will be increased too, so the SNR will also be increased, so what is the value of the "factor" ?

Why do you think that this is the case?

you can improve SNR by increasing the transmitter power with caution,as unscrupulous indulgence in increased power to multiple transmitters may cause more noise than the noise you are trying to avoid.

In a wireless link system, increasing the receiver SNR by increasing the TX output power is the ultimate solution.
First try to improve the receiver sensitivity, and decrease the receiver frequency bandwidth to exactly value that the RF system needs.
Second, try to improve the antenna gains on both sides, RX and TX.
And third, try to minimize all the cable losses that you have between antennas and receiver/transmitter.
Losses[dB] and antenna gain[dB] affect one-to-one the SNR[dB].

Dear,
Once all the mention notations improved
Such as cable losses and antenna gain ...etc

Now I need an equation .

Snr =transmission range * factor

What is the factor value if all the improvement occurred

the easy answer is that received power decreases with distance based on the Friis equation, but thermal noise is the same, so there is your SNR vs distance:

https://en.wikipedia.org/wiki/Friis_...ssion_equation

the reality though is that propagation path loss, especially near the earth and near objects, can deviate from the Friis equation.