Most of existing studies about two-way relay network rely on the assumption that two sources transmit with symmetric traffics, which is often unsatisfied in practical application. In this paper, we focus on asymmetric traffics for two-way relay network, and investigate how to minimize system outage probability. To achieve this objective, we first propose a strategy to combine relay selection (RS) and incremental relaying (IR), which is referred to as Proportional Max-Min selection plus Asymmetric Incremental Relaying (PMM-AIR). According to the expression of system outage event, we propose an Optimal-PMM (O-PMM) RS criterion that minimizes outage probability. Based on PMM-AIR strategy, we propose an optimal power allocation (OPA) scheme to achieve minimum outage probability. We also propose suboptimal alternatives for both O-PMM and OPA, i.e. Suboptimal-PMM (S-PMM) and suboptimal power allocation (SPA), to reduce overhead. Simulation results show that the suboptimal alternative for O-PMM (or OPA), i.e. S-PMM (or SPA), only causes trivial performance degradation.
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