[Ronja] Multiple receivers and transmitters

[Karel Kulhavy]

I have been thinking how to divide multiple heads between receivers and transmitters optimally, i. e. if we want to build N heads, how to get the maximum range.

Let´s assume there is no absorption in the atmosphere here.

The answer is make 2/3 transmitters and 1/3 receivers. Example: 1 receiver
and 2 transmitters, 2 receivers and 4 tx, 3 rx and 6 tx etc.

Making 4 TX instead of 1 increases the signal nd the noise stays the same, the range is double. Making 4 RX increases the signal 4x and the noise 2x
(each RX generates statistically independent noise) with resulting sqrt(2)=1.4x increase in distance.

If we try to maximize 4th power of the distance (which is the same as maximizing the distance) and mark t the percentage of transmitter heads (between 0 and 1), the maximized function is t^2*(1-t)=t^2-t^3. Derivative
is 2t-3t^2=0. 2-3t=0, t=2/3.

Karel