A Criterion for Determining the Optimal Position of the Demodulate-and-Forward (DMF) Relay

This paper considers the issue of selecting the optimal position where a Relay could be fixed to enable the communication between a Source and a Destination. Our analysis is focused on the case when Relay works on Demodulate-and-Forward (DMF) mode, due its simple nature in implementation. DMF Relay only demodulates the received signals from the Source without checking the integrity of the signals and it may happen that it forwards the erroneous signals toward the Destination. Since moving the Relay in different positions between the Source and the Destination brings different performances, we are interested to find the position at which the benefit of using the Relay is maximized. To help us find this optimal position analytically and numerically, we have introduced a criterion which relies on the trade-off between the demodulation errors on the channel S-R and the ability of the Relay to succeed on the transmission path R-D, where the theoretical analysis of the criterion matches perfectly with the simulation analysis. Moreover, in a scenario of having more than one Relay, this criterion helps us to choose the best instantaneous Relay for cooperation. The comparison of our proposed criterion with a referent criterion from the literature, has shown that our criterion outperforms the referent criterion.