Closed-Form Solutions for Minimizing Sum MSE in Multiuser Relay Networks

A scenario consisting of single antenna source- destination node pairs communicating using multiple single antenna relays is considered. A transmission scheme utilizing two subsequent time-slots assuming a time invariant channel throughout the transmission period is applied to this scenario. In the first time-slot, the source nodes transmit to both the relays and the destination nodes. Both the source nodes and the relays retransmit to the destination nodes in the second time-slot. As the relays can not decode the received signals, amplify and forward relaying is used. By exploiting the direct links between the source and the destination nodes, each destination node observes a two dimensional signal space. In the present paper, the sum mean square error can be written as a convex quadratic function of the relays´ gain and part of the temporal filters at the source and the destination nodes. Moreover, closed form solutions for the minimum sum mean square error with interference zero forcing constraints and a total energy constraint are obtained. The results show that the proposed schemes outperform the interference alignment scheme at low and moderate SNRs.