Relay selection in bidirectional relay communication

We consider the problem of relay selection in a scenario with N relay nodes. A half-duplex relay node enables bidirectional communication between two nodes with a spectral efficient two phase protocol. In the first phase, both nodes transmit a message to a relay node, which decodes the messages and broadcasts a composition in the succeeding phase. The relay selection criteria decides for any bidirectional rate pair on the boundary of the achievable rate region for the relay node which achieves the largest weighted rate sum. With time-sharing between the usage of relay nodes the achievable rate region can be further increased. In a iid Rayleigh fading scenario relay selection realizes multi-user space diversity so that the sum-rate of any rate pair on the boundary of the ergodic rate region scales like O(log(log(N))).