Physical Layer Network Coding Using Lattice

Physical layer network coding (PNC) is a technique that implementing network coding at the physical layer by making the best use of the broadcast nature of the wireless medium in wireless cooperative communication. PNC greatly improves the throughput of the wireless networks, thus it becomes a hot topic. This thesis investigates PNC using the two-way relay channel model under AWGN channel, and studies two PNC detection schemes:MAP-based PNC and MMSE-based PNC, where QPSK modulation is adopted. The simulation results verify the feasibility of the schemes.In order to improve the spectral efficiency of the wireless network further, we need to consider the PNC scheme using higher order modulation such as M-QAM, M-PAM. However, when M-QAM is adopted, the decoding problem occurs because the analog signals corresponding to several unique bit assignments may sum up to the same analog signal, making it impossible for the relay to distinguish these bit assignments from one another by simply decoding their sum. This thesis proposes one solution that,16-QAM, for example, modifying the original16-QAM modulation amplitude (unequi-spaced16-QAM) so that it becomes one-to-one map between analog signal and bit assignments. And theoretical symbol error rate at the relay node is derived, which matches the simulation results. However, this scheme has high decoding complexity and poor performance because the points in the constellation at relay increases and the minimum Euclidean distance decreases.In order to find a better solution, this thesis studies the joint design of the lattice and PNC. The third chapter introduces the definition as well as performance parameters of lattice, and focuses on its application in AWGN channel. By introducing the minimum mean square error (MMSE) coefficient and dithering techniques, the capacity of the AWGN channel can be achieved using a good Nested Lattice code, the coarse lattice for shaping, the fine lattice for channel coding. The fourth chapter analyzes the PNC scheme using nested lattice. The thesis shows that the capacity of the two-way relay channel can also be approached. In addition, the decoding problem of PNC when adopting M-QAM is solved based on nested lattice. And both the theoretical results and simulation results show that the performance of the new scheme is significantly better than the one using unequi-spaced16-QAM. Meanwhile, the schemes with different coding rates of Nested Lattice code have been analysized and simulated, which further improve the error performance. Finally, the square M-QAM constellation is modified to improve the effective coding gain.