Interference Alignment in Cellular Networks: Theory, Algorithms, and System Design

Degrees-of-freedom (DoF) is a useful yet tractable metric in characterizing the capacity of wireless multi-antenna cellular networks. DoF provides a first-order approximation (pre-log factor) to capacity and reflects capacity scaling at high signal-to-noise ratios. Interference alignment is a concept that is used to design linear beamformers that achieve the optimal DoF of multi-antenna wireless networks. This thesis focuses on the role of interference alignment in establishing the maximal DoF of multi-antenna cellular networks and its relevance in practical cellular network optimization. The primary focus is on studying the symmetric DoF of cellular networks that consist of $G$ mutually interfering cells with $K$ users/cell, having $N$ antennas at each base station and $M$ antennas at each user. The first part of this thesis investigates the achievable DoF using two different strategies for interference alignment. The first is an asymptotic alignment scheme that is typically used in single-antenna networks and relies on symbol extensions in time, and the second is a linear beamforming strategy that exploits overlap of transmission subspaces in multi-antenna receivers. It is shown that there are distinct regimes of $G$, $K$, $M$, and $N$, where one technique outperforms the other. Using a set of outer bounds on the sum-DoF, conditions for optimality of the DoF achieved using the two techniques is established. Studying the optimal DoF highlights the importance of developing algorithmic techniques for interference alignment. The second part of this thesis focuses on the design of linear beamformers for interference alignment. Conditions for interference alignment are formulated as a rank minimization problem and insights from compressive sensing are used to develop algorithms that can efficiently solve this problem. The proposed algorithms are shown to be more effective in designing aligned beamformers for interference alignment than other existing algorithms. The final part of this thesis explores the value of interference alignment in practical cellular network optimization. Using a two-stage optimization framework, it is established that interference alignment is valuable in dense cellular networks where interference alignment provides an altered interference landscape that subsequent network utility maximization algorithms can take advantage of, but is otherwise difficult to reach.Ph.D