Research On Degrees Of Freedom Of Wireless Networks Based On Interference Alignment

Exploring the fundamental capacity limit of wireless networks is a hot issue for a long time in the request for understanding various performances of the wireless communications, and pointing to the development direction of practical techniques. Considering the intricate relationships between difference capacity determinants of multi-user interference network, the degrees-of-freedom(Do F) approach as an effective mean to describe the capacity of wireless networks whose accuracy approaches 100% in the high signal-to-noise ratio(SNR) regime has been adopted widely. Following the further investigations of Do F, there are many fundamental ideas have been generated such as interference alignment(IA) which caused wide attention of academia. Through IA, the interference signal spaces can be significantly compressed and the influence of interferences on the desired signal can be maximized eliminated, so that the interference network could achieve the maximum Do F. A main research direction of IA is the research on Do F of the multi-user interference network, which can be summed up in the following two major aspects: first, the research on the Do F outer bound, which is the proof for the maximum Do F of the multi-user interference network; second, the research on the Do F inner bound, which is to design the achievable scheme to approach the Do F outer bound at the largest extent. Following the development of IA, the research on the Do F of various wireless networks has been further d eveloped. The dissertation mainly focus on three typical interference networks, including heterogeneous two-tier interference networks, cognitive relay assisted interference networks and multi-cell cellular networks. By proving the Do F outer bound and the associated Do F inner bound through designing the achievable schemes based on IA, the dissertation has found out some important tight Do F results. The research results for the further exploring the capacity of wireless networks and increasing the transmission rate of wireless communication tec hnology have a certain application value. Based on the latest research results, the dissertation conducted research work in the following three aspects.Firstly, to solve the severe interference problems between the small cell u sers and the macro cell users, the dissertation studies the cooperative transmission problem of the heterogeneous two-tier interference network. A general network model for the heterogeneous network has been established, which includes one multi-antenna macro cell base station(BS), K single antenna small cell BSs and K single antenna users. A tight Do F result of this network has been shown by proving the Do F outer bound and inner bound respectively. Specially, to simplify the Do F inner bound proof the reciprocity of linear beamfoming based alignment is utilized. Meanwhile, in the achievable scheme construction, the precoding m atrixes are jointly designed at all the transmitters according to the difference a ntenna numbers of BSs, so that one-to-one alignment and many-to-many alignment are realized at all the small cell BSs and macro cell BS respectively. In o rder to show the correctness of achievable scheme, the independence of the desired signal space and the interference signal space at BSs is further proved.Secondly, to further improve the capacity of the multi-user interference networks, we analyze the Do F improvement with the help of co gnitive relay. First, 2-user MIMO interference channel with a cognitive relay is analyzed. A Do F i nner bound achievable scheme is set up which is based on the interference neutralization idea. Through this scheme we can improve the Do F of 2-user MIMO interference channel about 50% compared with conventional relay assisted scheme. Second, K-user interference network assisted by a multi-antenna cognitive relay is mainly analyzed. The Do F outer bound is proposed and the detailed proof is also showed. The achievable scheme of the Do F outer bound is also given which is based on channel diagonalization, interference neutralization and interference alignment. At last, through the comparison with the conventional relay and no relay assisted network on the aspects of the Do F and average sum rate, the result showed that cognitive relay can effectively improve the average sum rate and the Do F of the network.Finally, we consider the topological interference management problem(TIM) for a downlink hexagonal cellular network where the channel state information at the transmitters is limited to just the network topology. Recent work by Jafar showed that if interference is limited to only near the cell boundary then an aligned frequency reuse pattern achieves the optimal val ue of 6/7 Do F per cell, as opposed to the conventional frequency reuse baseline of 1/3 Do F per cell. We generalize the setting to include interference from multiple layers of adjacent cells, and characterize how the gains of the optimal solution over basic frequency reuse diminish with increasing number of interference layers. Next we focus on single layer interference and explore the sensitivity of the idealized assumptions behind the connectivity model of Jafar, which achieves higher Do F but only at the cost of a higher effective noise floor than the baseline, and under idealized placements of users. A modified connectivity model that operates at a comparable noise-floor to the baseline is then studied and its Do F are shown to be bounded above by 6/11 and below by 1/2. Through numerical simulations we compare the solutions that achieve 6/7, 1/2 and 1/3 Do F per cell and find that while both the 6/7 and the 1/2 Do F solutions beat the baseline 1/3 figure, between them the 1/2 Do F aligned frequency reuse pattern is more robust for small cell networks especially for random users’ distribution on the cell boundaries.