Joint Relay Antenna Selection and Zero-Forcing Spatial Multiplexing for MIMO Two-Way Relay with Physical-Layer Network Coding

We consider a multiple-input multiple-output (MIMO) two-way relay network with two N_T-antenna (N_T ≥ 2) end nodes and one dedicated NR-antenna (N_R >; N_T) relay node. A physical-layer network coding (PNC) based joint relay antenna selection and zero-forcing (ZF) spatial multiplexing scheme is proposed to support N_T streams of bidirectional data exchanging with the help of N_T out of N_R selected antennas at the relay node. The optimum relay antennas are selected by a Max-Min criterion with respect to the post-processing SNR of the whole system and then the linear ZF based MIMO two- way relay transmission is achieved with the help of the selected relay antennas. The optimum relay antenna selection not only fulfills the ZF based scheme´s requirement on the number of effective relay antennas but also provides an end-to-end diversity advantage to the N_T streams of bidirectional data exchanging with linear transceiver at each end node. The diversity order of the proposed scheme is analyzed. Explicit diversity order d = N_R - 1 is obtained theoretically for N_T = 2 streams of bidirectional data exchanging. For N_T ≥ 2 cases, a conjecture that d = N_R - N_T + 1 is obtained based on simulation results.