Interference alignment for MIMO cellular networks : degrees of freedom analysis and performance improvement in limited feedback

다국어 초록 (Multilingual Abstract)

Analyzing the degrees of freedom(DoF) for MIMO interference channels(IFC) or MIMO mutually interfering broadcast channels(IFBC) with finite dimension(i.e. without symbol extension) has been unsolved problem in general, even for SISO case. In \cite{Yetis:2009}, Yetis et al. relate the feasibility issue of MIMO interference alignment for IFC in vector signal space to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry. They use Bezout's Theorem that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables. However, multiple beams transmission case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic.
In this dissertation, at first, we analyze the DoF for two cell IFBC(2IFBC) without symbol extension. In contrast to IFC, there are two type of interferences in the IFBC: intercell interference and intracell interference, which make harder to analyze the DoF performance than the IFC. We set up two stage precoder:intercell and intracell precoder. We formulate interference free equations as function of the precoders and receive beamformers. By checking solvability of these polynomial equations, we prove that $min(M+N-1,2M)$ DoF can be achieved for 2cell MIMO IFBC almost surely, where $M$ is the number of transmit antennas and $N$ is the number of receiver antennas. These polynomial equations are not generic, thus Yetis's approach gives us only a necessary condition. To prove sufficient condition, we use Implicit Function Theorem and Chevalley Theorem in algebraic geometry. Using these theorems, we can show that any antenna combination satisfying $d \leq (M+N-1)/2$, $d \leq M$ is almost surely feasible for any generic channel realization, for instance, when $d=4$, $(M,N)=(4,5),(5,4),(6,3),(7,2),(8,1)$ are feasible for 2IFBC.
We also propose several transceiver design methods to achieve $M+N-1$. This results show that the DoF of 2cell IFBC is better than that of 2cell IFC.
At the second part, IA with limited feedback is studied. Conventional IA for MIMO interference channel (IFC) requires \emph{global} and \emph{perfect} channel state information at transmitter(CSIT) to achieve the optimal DoF. These assumptions, however, are much burden to implement practical system. In order to alleviate global CSIT assumption, a single feedback based IA scheme for three node MIMO IFC is proposed.
The main feature of the proposed scheme is to reduce $\alpha$ number of data streams at first transmitter so as to decouple equations of the original IA. The decoupled IA solution results in \emph{single} feedback structure. Using a random codebook assumption, the upper bound of the average throughput loss caused by imperfect channel knowledge as a function of feedback bits is derived. Based on the analysis, the proposed scheme provides better sum rate performance than that of the conventional IA and much less feedback overhead.
At the third part, to avoid feedback inaccuracy and alleviate feedback overhead, we propose a blind interference alignment (B-IA) for two-cell single-input multiple-output (SIMO) mutually interfering multiple access channels (IFMAC) and a multimode blind interference alignment for multiple-input single-output (MISO) broadcast channels (BC).
The B-IA schemes do not require CSIT, but require reconfigurable antennas at receivers. We analyze the achievable DoF of B-IA for two-cell IFMAC and propose a mode adaptation method to enhance the sum rate of B-IA for MISO BC.