Abstract-Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

Interference alignment is degree of freedom optimal in K-user MIMO interference channels and many previous works have studied the transceiver designs. However, these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology. In this paper, we consider a limited feedback system with heterogeneous path loss and spatial correlations, and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency. We propose a novel spatial codebook design, and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology. We bound the system throughput under the proposed dynamic scheme in terms of the transmit SNR, feedback bits and the interference topology parameters. It is shown that when the number of feedback bits scales with SNR as C s ·log SNR, the sum degrees of freedom of the network are preserved. Moreover, the value of scaling coefficient C s can be significantly reduced in networks with asymmetric interference topology.

Interference is a major performance bottleneck in Heterogeneous Network (HetNet) due to its multi-tier topological structure. We propose almost blank resource block (ABRB) for interference control in HetNet. When an ABRB is scheduled in a macro BS, a resource block (RB) with blank payload is transmitted and this eliminates the interference from this macro BS to the pico BSs. We study a two timescale hierarchical radio resource management (RRM) scheme for HetNet with dynamic ABRB control. The long term controls, such as dynamic ABRB, are adaptive to the large scale fading at a RRM server for co-Tier and cross-Tier interference control. The short term control (user scheduling) is adaptive to the local channel state information within each BS to exploit the multi-user diversity. The two timescale optimization problem is challenging due to the exponentially large solution space. We exploit the sparsity in the interference graph of the HetNet topology and derive structural properties for the optimal ABRB control. Based on that, we propose a two timescale alternative optimization solution for the user scheduling and ABRB control. The solution has low complexity and is asymptotically optimal at high SNR.Simulations show that the proposed solution has significant gain over various baselines.