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This paper proposes coded modulation for physical layer network coding in multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) bi-directional wireless relay systems where precoding is applied. The proposed coded modulation enables the relays to decode the received signals, which improves the transmission performance. Soft input decoding for the proposed coded modulation is proposed. Furthermore, we propose two precoder weight optimization techniques, called “per subcarrier weight optimization” and “total weight optimization”. This paper shows a precoder configuration based on the optimization with the lattice reduction or the sorted QR-decomposition. The performance of the proposed network coding is evaluated by computer simulation in a MIMO-OFDM two-hop wireless relay system with the 16 quadrature amplitude modulation (QAM) or the 256QAM. The proposed coded modulation attains a coding gain of about 2 dB at the BER of 10−4. The total weight optimization achieves about 1 dB better BER performance than the other at the BER of 10−4. key words: relaying, coded modulation, network coding, soft input decoding, non-linear precoding, quadrature amplitude modulations

Precoded Physical Layer Network Coding with Coded Modulation in MIMO-OFDM Bi-Directional Wireless Relay Systems