Combining of physical-layer network coding (PNC) and multiple-input multiple-output (MIMO) can significantly improve the performance of the wireless TWRN. This paper proposes novel Max-Min optimization based relay antenna selection (RAS) schemes for zero-forcing (ZF) based MIMO-PNC transmission. RAS relaxes ZF’s constraints on the number of antennas and extends the applications of ZF based MIMO-PNC to more practical scenarios, where the dedicated relay has more antennas than the end-node. Moreover, RAS also brings diversity advantages to TWRN and the achievable diversity gains of the proposed schemes are theoretically analyzed. In particular, an equivalence relation is carefully built for the diversity gains obtained by 1) RAS for ZF based MIMO-PNC and 2) transmit antenna selection (TAS) for MIMO broadcasting (BC) with ZF receivers. This equivalence transforms the original problem to a more tractable form which eventually allows explicit analytical results. It is interesting to see that Max-Min RAS keeps the network diversity gain of ZF based MIMO-PNC to be the same as the diversity gain of the point-to-point link within the TWRN. This insight extends the understanding on the behaviors of ZF transceivers with antenna selection (AS) to relatively complicated MIMO-TWRN/BC scenarios.
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