Simplified maximum likelihood detection with unitary precoding for XOR physical layer network coding

This paper proposes novel simplified maximum likeli- hood detection for XOR physical layer network coding (XOR-PNC) in bi-directional wireless relay systems with Quaternary phase shift keying (QPSK). The proposed detection applies unitary precoding to achieve su- perior performance without computationally prohibitive exhaustive search. The performance of the XOR employing the proposed simplified MLD with the precoding is analyzed in relay systems with orthogonal frequency division multiplexing (OFDM). The performance of the XOR-PNC with the proposed techniques is also evaluated by computer simulation. The XOR-PNC with the proposed techniques achieves about 7 dB better perfor- mance than the amplify-and-forward physical layer network coding in the 5-path fading channel at BER= 10^-4. It is also shown that the XOR-PNC with the proposed techniques achieves better performance than that without precoding.