Feasibility Conditions For Interference Alignment Research Articles

Feasibility Analysis and Clustering for Interference Alignment in Full-Duplex-Based Small Cell Networks

With the capability of bidirectional communications on a single frequency band, the full-duplex (FD) operation can potentially double the spectral efficiency in physical layer. In network layer, nevertheless, it may cause severe mutual interference to the system. In this paper, we exploit interference alignment (IA) to address the interference in small cell networks, where some of the base stations simultaneously serve both uplink and downlink users on the same frequency via FD. Under such scenario, we first derive the feasibility condition for IA from Bezout’s theorem and find that IA can be feasible only if a certain size constraint of the network is satisfied. On this basis, we then propose two clustering methods, i.e., minimized spectrum consumption clustering (MSCC) and minimized interference leakage clustering (MILC), both of which can perfectly eliminate the intra-cluster interference with IA. The difference between them is that MSCC aims at minimizing the number of clusters through allocating orthogonal resource blocks (RBs) for each cluster to avert inter-cluster interference, while MILC tries to minimize the aggregated inter-cluster interference with all clusters sharing the same RB. Extensive simulations verify that MSCC can achieve higher system sum rate, but MILC works better in terms of spectral efficiency.

On Feasibility of Interference Alignment in Full-Duplex-Based Small Cell Networks

As an appealing interference management approach, interference alignment (IA) has not been intensively studied in full-duplex (FD)-based multi-cells. In this letter, based on Bezout’s theorem, we explore the feasibility conditions of IA in small cell networks, where base stations are equipped with FD hardware. The comparison of IA performance between FD and traditional half-duplex small cells in terms of the total degrees of freedom (DoFs) is also conducted. We find that the IA performance with FD is limited by the number of antennas at users. Furthermore, we verify that IA with opportunistic FD can be implemented to achieve higher total DoFs of the network.

The Feasibility of Interference Alignment for MIMO Interfering Broadcast—Multiple-Access Channels

The feasibility conditions of interference alignment (IA) are analyzed for interfering broadcast-multiple-access channels in which one cell operates as downlink but the other cell operates as uplink. Under a general multiple-input and multiple-output antenna configuration, a necessary condition and a sufficient condition for one-shot linear IA are established, i.e., linear IA without symbol or time extension. In various example networks of interest, the optimal sum degrees of freedom (DoFs) are characterized by the derived necessary condition and sufficient condition. For symmetric DoF within each cell, a sufficient condition is established in a more compact expression, which yields the necessary and sufficient condition for a class of symmetric DoFs. An iterative construction of transmit and receive beamforming vectors is further proposed, which provides a specific beamforming design satisfying one-shot IA. Simulation results demonstrate that the proposed IA not only achieves larger DoF, but also significantly improves the sum rate over the single-cell operation in the practical signal-to-noise ratio regime.

Precoder Designs for the Relay-Aided X Channel Without Source CSI

In this paper, precoder designs are proposed for the wireless X networks aided by a relay and with no or very limited channel state information at the transmitters (CSIT). First, we derive the general feasibility conditions for interference alignment (IA) for a relay-aided symmetric multi-input-multi-output X channel (also called the X relay channel or XRC) without any CSI at the source transmitters. Next, we propose an IA-based joint beamforming approach with very limited feedback to the transmitters (referred to as “IA-LFB” in this paper), which can attain the maximum degrees of freedom (DoF) of the network under arbitrarily low relay power. Finally, we propose an iterative minimum-sum mean-square-error (MMSE) precoder design for the single-input-single-output XRC for throughput improvement in the finite signal-to-noise ratio (SNR) region. The proposed MMSE precoder also shows better bit error rate results than the IA precoder over a wide SNR range. Since the MMSE precoder can achieve only locally optimal solutions, we propose to initialize the iterative MMSE algorithm with the IA-LFB precoder which, unlike random initializations, not only improves the throughput in the finite SNR regions but also preserves the network DoF even under limited relay power.

Interference Alignment With Partial CSI Feedback in MIMO Cellular Networks

Interference alignment (IA) is a linear precoding strategy that can achieve optimal capacity scaling at high SNR in interference networks. However, most existing IA designs require full channel state information (CSI) at the transmitters, which would lead to significant CSI signaling overhead. There are two techniques, namely CSI quantization and CSI feedback filtering, to reduce the CSI feedback overhead. In this paper, we consider IA processing with CSI feedback filtering in MIMO cellular networks. We introduce a novel metric, namely the feedback dimension, to quantify the first order CSI feedback cost associated with the CSI feedback filtering. The CSI feedback filtering poses several important challenges in IA processing. First, there is a hidden partial CSI knowledge constraint in IA precoder design which cannot be handled using conventional IA design methodology. Furthermore, existing results on the feasibility conditions of IA cannot be applied due to the partial CSI knowledge. Finally, it is very challenging to find out how much CSI feedback is actually needed to support IA processing. We shall address the above challenges and propose a new IA feasibility condition under partial CSIT knowledge in MIMO cellular networks. Based on this, we consider the CSI feedback profile design subject to the degrees of freedom requirements, and we derive closed-form trade-off results between the CSI feedback cost and IA performance in MIMO cellular networks.

The Feasibility Conditions for Interference Alignment in MIMO Networks

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.

Feasibility Condition for Interference Alignment With Diversity

This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M × N) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general.