Thats because you have 3 Tx all transmitting on the exact same frequency, and creating interference with each other. Then each Rx will see overlapped signals from all three Tx & it'll output garbage. What did you expect to happen ?
You have to shift the frequencies of each tx/Rx pair so that it is different from all others, (Freq Div Multiplex or FDM)
OR
Switch on only one Tx/ Rx pair at a time. (Time Div Multiples or TDM). I don't see an easy way to do this in a distributed system without quite complicated protocol implementations. You could try implementing some simply form of CSMA/CD ?