Response of retrodirective array in the presence of multiple spatially separated sources

In this paper, we describe a canonical proof based on the use of multiport scattering parameters which shows that in the presence of multiple coupling paths between elements that is not possible to individually control the power returned to each transmitter in a retrodirective array which is responding to stimulation by multiple transmitters. It is proven that it is not possible to maximize retransmission to only one of the transmission elements at the expense of the others if more than one transmitter is broadcasting, nor is it possible to simultaneously equalize the signal sent to all k broadcasting antennas when they each transmit unequal power levels.