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.

Recent works on MIMO interference channels have shown that interference alignment can significantly increase the achievable degrees of freedom (DoF) of the network. However, most of these works have assumed a fully connected interference graph. In this paper, we investigate how the partial connectivity can be exploited to enhance system performance in MIMO interference networks.We propose a novel interference mitigation scheme which introduces constraints for the signal subspaces of the precoders and decorrelators to mitigate "many" interference nulling constraints at a cost of "little" freedoms in precoder and decorrelator design so as to extend the feasibility region of the interference alignment scheme. Our analysis shows that the proposed algorithm can significantly increase system DoF in symmetric partially connected MIMO interference networks.We also compare the performance of the proposed scheme with various baselines and show via simulations that the proposed algorithms could achieve significant gain in the system performance of randomly connected interference networks.

Abstract-In contrast to its wired counterpart, wireless communication is highly susceptible to eavesdropping due to the broadcast nature of the wireless propagation medium. Recent works have proposed the use of interference to reduce eavesdropping capabilities in wireless wiretap networks. However, the concurrent effect of interference on both eavesdropping receivers (ERs) and legitimate receivers (LRs) has not been thoroughly investigated, and carefully engineering the network interference is required to harness the full potential of interference for wireless secrecy. This two part paper addresses this issue by proposing a generalized interference alignment (GIA) technique, which jointly designs the transceivers at the legitimate partners to impede the ERs without interfering with LRs. In Part I, we have established a theoretical framework for the GIA technique. In Part II, we will first propose an efficient GIA algorithm that is applicable to large-scale networks and then evaluate the performance of this algorithm in stochastic wireless wiretap network via both analysis and simulation. These results reveal insights into when and how GIA contributes to wireless secrecy.

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Interference alignment (IA) has attracted enormous research interest as it achieves optimal capacity scaling with respect to signal to noise ratio on interference networks. IA has also recently emerged as an effective tool in engineering interference for secrecy protection on wireless wiretap networks. However, despite the numerous works dedicated to IA, two of its fundamental issues, i.e., feasibility conditions and transceiver design, are not completely addressed in the literature. In this two part paper, a generalized interference alignment (GIA) technique is proposed to enhance the IA's capability in secrecy protection. A theoretical framework is established to analyze the two fundamental issues of GIA in Part I and then the performance of GIA in large-scale stochastic networks is characterized to illustrate how GIA benefits secrecy protection in Part II. The theoretical framework for GIA adopts methodologies from algebraic geometry, determines the necessary and sufficient feasibility conditions of GIA, and generates a set of algorithms that can solve the GIA problem. This framework sets up a foundation for the development and implementation of GIA.

Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of the qubits to the other agent through a quantum channel. In this process, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. To address this challenge, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. This paper puts forth two recurrence QED algorithms that adapt to the quantum channel to tackle the efficiency issue. The proposed algorithms have guaranteed convergence for quantum channels with two Kraus operators, which include phase-damping and amplitude-damping channels. Analytical results show that the convergence speed of these algorithms is improved from linear to quadratic and one of the algorithms achieves the optimal speed. Numerical results confirm that the proposed algorithms significantly improve the efficiency of QED.