This paper proposes multi-input physical layer network coding (multi-input PLNC) for high speed wireless communication in two-dimensional wireless multihop networks. In the proposed PLNC, all the terminals send their packets simultaneously for the neighboring relays to maximize the network throughput in the first slot, and all the relays also do the same to the neighboring terminals in the second slot. Those simultaneous signal transmissions cause multiple signals to be received at the relays and the terminals. Signal reception in the multi-input PLNC uses multichannel filtering to mitigate the difficulties caused by the multiple signal reception, which enables the two-input PLNC to be applied. In addition, a non-linear precoding is proposed to reduce the computational complexity of the signal detection at the relays and the terminals. The proposed multi-input PLNC makes all the terminals exchange their packets with the neighboring terminals in only two time slots. The performance of the proposed multi-input PLNC is confirmed by computer simulation. The proposed multi-input physical layer network coding achieves much higher network throughput than conventional techniques in a two-dimensional multihop wireless network with 7 terminals. The proposed multi-input physical layer network coding attains superior transmission performance in wireless hexagonal multihop networks, as long as more than 6 antennas are placed on the terminals and the relays.

This paper proposes relay selection techniques for XOR physical layer network coding with MMSE based non-linear precoding in MIMO bi-directional wireless relaying networks. The proposed selection techniques are derived on the different assumption about characteristics of the MMSE based non-linear precoding in the wireless network. We show that the signal to noise power ratio (SNR) is dependent on the product of all the eigenvalues in the channels from the terminals to relays. This paper shows that the best selection techniques in all the proposed techniques is to select a group of the relays that maximizes the product. Therefore, the selection technique is called “product of all eigenvalues (PAE)” in this paper. The performance of the proposed relay selection techniques is evaluated in a MIMO bi-directional wireless relaying network where two terminals with 2 antennas exchange their information via relays. When the PAE is applied to select a group of the 2 relays out of the 10 relays where an antenna is placed, the PAE attains a gain of more than 13dB at the BER of 10-3.

This paper proposes novel nonlinear precoding for XOR-physical layer network coding (XOR-PNC) to improve the performance of bi-directional MIMO relay systems. The proposed precoder comprises a pre-equalizer and a nonlinear filter, which we also propose in the paper. We theoretically analyze the performance of the XOR-PNC with the proposed nonlinear precoding. As a result, it is shown that the proposed pre-equalizer improves the distribution of the received signals at relays, while the nonlinear precoder not only improves the transmission power efficiency but also simplifies the receiver at the relays. The performance is confirmed by computer simulation. The XOR-PNC with the proposed precoding achieves almost the lower bound in BER performance, which is much better than the amplify-and-forward physical layer network coding (AF-PNC).

This paper proposes novel simplified maximum likelihood 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 superior 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 7dB better performance 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.