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The authors investigate error performance and an optimum power allocation scheme for Multiple-Input Multiple-Output (MIMO) channel Physical layer Network Coding (PNC) based two-way relay system. Zero forcing pre-coding technique is used at source nodes to facilitate PNC operations at the relay node. First, system error performance is investigated by introducing upper and lower bounds for BPSK modulation system. They are validated with numerical results and bounds provide accurate results at high SNR regime. Then, they consider sum rate maximization under a total power constraint to obtain the optimum power allocation scheme.
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