Minimum common outage probability for the broadcast relay channel

In this paper the broadcast relay channel (BRC) is studied. In the BRC model, the source communicates with two destinations with the help of a single relay. The minimum common outage probability for four different transmission protocols, direct transmission (DT), multihop (MH), path selection (PS) and link combination with path selection (LCPS) is investigated under long-term power constraint for constant rate transmission. In addition, the ε-outage rate region for a fixed common outage probability is computed. Based on the cut-set bound (CSB), a lower bound on the minimum common outage probability and an upper bound on the ε-outage rate region are also found. Numerical results suggest that enforcing the relay to help both destinations simultaneously is limiting. The dominant factor in the gains obtained with respect to DT is due to path selection and link combination is not necessary when the relay is close to the source.