| With the rapid development of wireless technologies, interference has become the bottleneck of wireless systems. Among several interference management schemes, interference alignment(IA) has attracted a lot of attention since it can provide the optimum degrees of freedom(DOF) or multiplexing gain for interference channels. In multi-user systems, each user’s signal space can be divided into two non-overlapping subspaces:desired signal subspace and interference subspace. The key idea of IA is to align all interference into a small subspace as much as possible, and thus make the DOF optimal.Besides IA, two-way relay communications(or generalized multi-way relay communications) and physical layer network coding(PLNC) also have received significant interest for they can further improve the spectrum utilization efficiency. How to integrate these technologies with IA to achieve higher DOF and sum rate, has become a hot topic in network information theory recent years.This dissertation has systematically studied the theory and key technology of IA in various wireless channels under different topological models and channel state information at the transmitter(CSIT) assumptions. The focus is the achievable DOF characterization for wireless channels and the corresponding achievable scheme design. The contribution of this dissertation can be summarized as follows:1. Under the assumption that each user has delayed CSIT, Chapter III investigates the achievable DOF for MIMO Y channel. First, Chapter III considers a three-user case and proposes two schemes: physical layer network coding multi-stage transmission(PLNC-MST) scheme and retrospective network coding alignment(RNCA) scheme. The key idea of PLNC-MST is to divide the broadcast(BC) phase into three smaller stages to transmit PLNC vectors and utilize IA by using delayed CSIT. Compared with Abdoli scheme and conventional time division multiple access(TDMA) scheme, PLNC-MST can achieve significant DOF gain. RNCA is an improved scheme of PLNC-MST, which uses two smaller stages to transmit PLNC vectors. By efficient construction and selection of high order vectors or symbols, RNCA can achieve higher DOF than PLNC-MST.Then, Chapter III generalizes RNCA to K-user case and derive the closed-form expression for achievable DOF. In the end, Chapter III proposes a new model for three-user case named ‘semi-blind users’ for each user has no CSIT in the multiple access(MAC)phase. In such model, three scenarios were considered: relay has perfect CSIT, relay has delayed CSIT and relay has no CSIT. It was found that, if the number of antenna of each user is sufficiently large, this model can achieve the same DOF with the case that each node(include each user and the relay) has perfect CSIT. Chapter 3 proposes a new joint PLNC and antenna selection(PLNC-AS) algorithm, which can achieve significant power gain over conventional signal space alignment for network coding(SSA-NC) scheme.2. Under the assumption of each node has delayed CSIT, Chapter IV studies the achievable DOF of MIMO two-way X relay channel. Specifically, a two-stage transmission(TST) scheme was proposed, which is a non-trivial generalization of RNCA.Compared with four-user MIMO Y channel with delayed CSIT, the dis-connectivity in two-way X relay channel leads to DOF loss. Both analytical and simulation results show that, the proposed scheme can provide significant DOF gain and power gain over conventional TDMA scheme.3. Under the asumption that each node has delayed CSIT, Chapter V investigates the achievable DOF of K-pair-user MIMO two-way relay interference channel. Chapter V derives the closed-form expression of the achievable DOF and proposes a new twostage transmission scheme(New TST). Interestingly, when K = 2, the achievable DOF of MIMO two-way relay interference channel is equal to which of MIMO two-way X relay channel. That means, four cross links in the later provide no DOF gain when delayed CSIT exists, which is in contrast with the perfect CSIT case.
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