To obtain a full picture of potential applications for propagation-delay based X channels, it is important to obtain all feasible schemes of cyclic interference alignment including the encoder, channel instance, and decoder. However, when the dimension goes larger, theoretical analysis about this issue will become tedious and even impossible. In this letter, we propose a computer-aided solution by searching the channel space and the scheduling space, which can find all feasible schemes in details. Examples are given for some typical X channels. Computational complexity is further analyzed.

Compared with the unicast scenario, X channels with multicast messaging can support richer transmission scenarios. The transmission efficiency of the wireless multicast X channel is an important and open problem. This article studies the degrees of freedom of a propagation-delay based multicast X channel with two transmitters and arbitrary receivers, where each transmitter sends K different messages and each receiver desires K - 1 of them from each transmitter. The cyclic polynomial approach is adopted for modeling and analysis. The DoF upper bound is analyzed and shown to be unreachable. Then a suboptimal scheme with one extra time-slot cycle is proposed, which uses the cyclic interference alignment method and achieves a DoF of K - 1. Finally, the feasibility conditions in the Euclidean space are derived and the potential applications are demonstrated for underwater acoustic and terrestrial radio communications.

We propose to use clustered interference alignment for the situation where the backhaul link capacity is limited and the base station is cache-enabled given MIMO interference channels, when the number of Tx-Rx pairs exceeds the feasibility constraint of interference alignment. We optimize clustering with the soft cluster size constraint algorithm by adding a cluster size balancing process. In addition, the CSI overhead is quantified as a system performance indicator along with the average throughput. Simulation results show that cluster size balancing algorithm generates clusters that are more balanced as well as attaining higher long-term throughput than the soft cluster size constraint algorithm. The long-term throughput is further improved under high SNR by reallocating the capacity of the backhaul links based on the clustering results.

In this paper, hierarchical interference coordination is proposed that suppresses both intra- and inter-cluster interference (ICI) in clustered wireless networks. Assuming transmitters and receivers are equipped with multiple antennas and complete channel state information is shared among all transmitters within the same cluster, interference alignment (IA) is performed that uses nulls to suppress intra-cluster interference. For ICI mitigation, we propose a null-steering precoder designed on the nullspace of a principal eigenvector of the correlated ICI channels, which eliminates a significant amount of ICI power given the exchange of cluster geometry between neighboring clusters. However, as ICI is negligible for the system in which the distance between clusters are large enough, the proposed scheme may not improve the system performance compared with the pure IA scheme that exploits all spatial degrees of freedom (DoF) to increase multiplexing gain without ICI mitigation. For the efficient interference management between intra- and inter-cluster, we analyze the decision criterion that provides an adaptive transmission mode selection between pure IA and proposed ICI reduction in given network environments. Moreover, a low computational complexity based transmission mode switching algorithm is proposed for irregularly distributed networks.

Heterogeneous networks (HetNets) technology is expected to be applied in next generation cellular networks to boost system capacity. However, applying HetNets introduces a significant amount of interference among different tiers within the same cell. In this paper, we propose a weighted rank constrained rank minimization (WRCRM) based interference alignment (IA) approach for three-tier HetNets. The concept of RCRM is applied in a different way to deal with the basic characteristic of different tiers: their different interference tolerance. In the proposed WRCRM approach, interference components at different tiers are weighted with different weighting factors (WFs) to reflect their vulnerability to interference. First, we derive an inner and a loose outer bound on the achievable degrees of freedom (DoF) for the three-tier system that is modeled as a three-user mutually interfering broadcast channel (MIBC). Then, the derived bounds along with the well-known IA feasibility conditions are used to show the effectiveness of the proposed WRCRM approach. Results show that there exist WF values that maximize the achievable interference-free dimensions. Moreover, adjusting the required number of DoF according to the derived bounds improves the performance of the WRCRM approach.

Interference alignment (IA) in temporal domain is important in the case of single-antenna vehicle communications. In this paper, perfect cyclic IA based on propagation delay is extended to the K×2 X channels with two receivers and arbitrary transmitters K≥2, which achieves the maximal multiplexing gain by obtaining the theoretical degree of freedom of 2K/(K+1). We deduce the alignment and separability conditions, and propose a general scheme which is flexible in setting the index of time-slot for IA at the receiver side. Furthermore, the feasibility of the proposed scheme in the two-/three- Euclidean space is analyzed and demonstrated.

For the three-user X channel, its degree of freedom (DoF) 9/5 has been shown achievable theoretically through asymptotic model with infinite resources, which is impractical. In this article, we explore the propagation delay (PD) feature among different links to maximize the achievable DoF with the minimum cost. Since perfect interference alignment (IA) is impossible for 9 messages within 5 time-slots, at least one extra time-slot should be utilized. By the cyclic polynomial approach, we propose a scheme with the maximum achievable DoF of 5/3 for 10 messages within 6 time-slots. Feasibility conditions in the Euclidean space are also deduced, which demonstrates a quite wide range of node arrangements.

For general multiple-input multiple-output (MIMO) interference networks, determining the feasibility conditions of interference alignment (IA) to achieve the maximum degree of freedom (DoF), is tantamount to accessing the maximum spatial resource of MIMO systems. In this paper, from the view of antenna configuration, we first explore the IA feasibility in the K-user MIMO interference channel (IC), G-cell MIMO interference broadcast channel (IBC) and interference multiple access channel (IMAC). We first give the concept of the equalized antenna, and all antenna configurations are divided into two categories, equalized antennas and non-equalized ones. The feasibility conditions of IA system with equalized antennas are derived, and the feasible and infeasible regions are provided. Furthermore, we study the correlations among IC, IBC and IMAC. Interestingly, the G-cell MIMO IBC and IMAC are two special ICs, and a systemic work on IA feasibility for these three interference channels is provided.

Based on Bezout's theorem, the feasibility condition for interference alignment (IA) is established in a two-way small cell network where part of cells transmit in downlink while the others in uplink. Moreover, the sufficient and necessary condition for the two-way network to achieve as many degrees of freedom (DoFs) as the traditional one-way network is presented. We find that in certain cases every small cell can independently decide to work in either downlink mode or uplink mode as needed without causing performance degradation of IA.

In heterogenous networks (HetNets), the deployment of small cells with the reuse of limited frequency resources to improve the spectral efficiency results in cross- and co-tier interference. In addition, the excessive power usage in such networks is also a critical problem. In this paper, we propose precoding and postcoding schemes to tackle interference and energy efficiency (EE) challenges in the two-tier downlink multiple-input-multiple-output (MIMO) HetNets. We propose transmission strategies based on hierarchical partial coordination (HPC) of the macro cell and small cells to reduce channel state information (CSI) exchange and guarantee the quality of service (QoS) in the upper tier with any change of network deployment in the lower tier. We employ the interference alignment (IA) scheme to cancel cross- and co-tier interference. Additionally, to maximize the EE, power allocation schemes in each tier are proposed based on a combination of Dinkelbach's method and the bisection searching approach. To investigate insights on the optimization problem, a theoretical analysis on the relationship between the maximum achievable EE and the transmit power is derived. Simulation results prove the superior EE performance of the proposed EE maximization scheme over the sum rate maximization approach and confirm the validity of our theoretical findings.

In this paper, we propose two secure multiuser multiple-input multiple-output (MIMO) transmission approaches based on interference alignment (IA) in the presence of an eavesdropper. To deal with the information leakage to the eavesdropper as well as the interference signals from undesired transmitters (Txs) at desired receivers (Rxs), our approaches aim to design the transmit precoding and receive subspace matrices to minimize both the total inter-main-link interference and the wiretapped signals (WSs). The first proposed IA scheme focuses on aligning the WSs into proper subspaces while the second one imposes a new structure on the precoding matrices to force the WSs to zero. In each proposed IA scheme, the precoding matrices and the receive subspaces at the legitimate users are alternatively selected to minimize the cost function of a convex optimization problem for every iteration. We provide the feasible conditions and the proofs of convergence for both IA approaches. The simulation results indicate that our two IA approaches outperform the conventional IA algorithm in terms of the average secrecy sum rate.

Interference alignment (IA) is a promising technology for eliminating interferences while it still achieves the optimal capacity scaling. However, in practical systems, the IA feasibility limit and the heavy signaling overhead obstructs employing IA to large-scale networks. In order to jointly consider these issues, we propose the feedback overhead-aware IA clustering algorithm which comprises two parts: adaptive feedback resource assignment and dynamic IA clustering. Numerical results show that the proposed algorithm offers significant performance gains in comparison with conventional approaches.

In this paper, we investigate the degrees of freedom (DoF) of a MIMO cellular interfering network (CIN) with L (L≥3) cells and K users per cell. Previous works established the DoF upper bound of LK(M+N)/(LK+1) for the MIMO CIN by analyzing the interference alignment (IA) feasibility, where M and N denote the number of antennas at each base station (BS) and each user, respectively. However, there is still a gap between the DoF upper bound and the achievable DoF in existing designs. To address this problem, we propose two linear IA schemes without symbol extensions to jointly design transmit and receive beamforming matrices to align and eliminate interference. In the two schemes, the transmit beamforming vectors are allocated to different cluster structures so that the inter-cell interference (ICI) data streams from different ICI channels are aligned. The first scheme, named fixed cluster structure (FCS-IA) scheme, allocates ICI beamforming vectors to the cluster structures of fixed dimension and can achieve the DoF upper bound under some system configurations. The second scheme, named dynamic cluster structure IA (DCS-IA) scheme, allocates ICI beamforming vectors to the cluster structures of dynamic dimension and can get a tradeoff between the number of antennas at BSs and users so that ICI alignment can be applied under various system configurations. Through theoretical analysis and numerical simulations, we verify that the DoF upper bound can be achieved by using the FCS-IA scheme. Furthermore, we show that the proposed schemes can provide significant performance gain over the time division multiple access (TDMA) scheme in terms of DoF. From the perspective of DoF, it is shown that the proposed schemes are more effective than the conventional IA schemes for the MIMO CIN.

Interference alignment (IA) is a method to improve the capacity of cell-edge users and thus attracts an intense research interest. We focus on the IA extended to the multiple-input multiple-output (MIMO) interference network. In this method, each coordinated transmitter generates beamforming vectors to align interference from different transmitters into confined subspace at each receiver. Then, using singular value decomposition (SVD) with the relative magnitude coefficients, transmitters calculate the beamforming vectors and the received vectors. However, in this method it is difficult to determine the value of the relative magnitude coefficients so that the system capacity is improved, because it is necessary to solve the non-linear function of multivariable. In this paper, we propose a design method of the relative magnitude coefficients of interference channels to improve system capacity using Brent's method on the K-User MIMO interference channel (MIMO-IFC). The proposed method can improve system capacity, though the system complexity increases due to Brent's method that requires multiple SVD calculation to calculate the null space. Thus, instead of using SVD, we introduce the complexity reduction method to calculate the null space of the matrix. Furthermore, we extend the proposed method to be applicable for more common systems where all base stations have the same number of transmit antennas. Through simulation, we show that the proposed method achieves a higher system capacity than the conventional one. We also show that the method that calculates the null space needs much lower complexity than SVD. In addition, we show that the proposed design method reduces the degradation of the system capacity caused by the interference not eliminated, and achieves the fairness of capacities among users for an increase of the number of design coefficients.

The feasibility condition of interference alignment (IA) for multiple-input multiple-output two-way interference channel is studied in this paper. A necessary condition and a sufficient condition on the IA feasibility are established and the sum degrees of freedom (DoF) for a broad class of network topologies is characterized. The numerical results demonstrate that two-way operation with appropriate IA is able to achieve larger sum DoF than the conventional one-way operation.

In this paper, we introduce a promising iterative interference alignment (IA) strategy for multiple-input multiple-output (MIMO) multi-cell downlink networks, which utilizes the channel reciprocity between uplink/downlink channels. We intelligently combine iterative beamforming and downlink IA issues to design an iterative multiuser MIMO IA algorithm. The proposed scheme uses two cascaded beamforming matrices to construct a precoder at each base station (BS), which not only efficiently reduce the effect of inter-cell interference from other-cell BSs, referred to as leakage of interference, but also perfectly eliminate intra-cell interference among spatial streams in the same cell. The transmit and receive beamforming matrices are iteratively updated until convergence. Numerical results indicate that our IA scheme exhibits higher sum-rates than those of the conventional iterative IA schemes. Note that our iterative IA scheme operates with local channel state information, no time/frequency expansion, and even relatively a small number of mobile stations (MSs), unlike opportunistic IA which requires a great number of MSs.

This paper presents a downlink interference mitigation framework for two-tier heterogeneous networks, that consist of spectrum-sharing macrocells and femtocells*. This framework establishes cooperation between the two tiers through two algorithms, namely, the restricted waterfilling (RWF) algorithm and iterative reweighted least squares interference alignment (IRLS-IA) algorithm. The proposed framework models the macrocell-femtocell two-tier cellular system as an overlay cognitive radio system in which the macrocell system plays the role of the primary user (PU) while the femtocell networks play the role of the cognitive secondary users (SUs). Through the RWF algorithm, the macrocell basestation (MBS) cooperates with the femtocell basestations (FBSs) by releasing some of its eigenmodes to the FBSs to do their transmissions even if the traffic is heavy and the MBS's signal to noise power ratio (SNR) is high. Then, the FBSs are expected to achieve a near optimum sum rate through employing the IRLS-IA algorithm to mitigate both the co-tier and cross-tier interference at the femtocell users' (FUs) receivers. Simulation results show that the proposed IRLS-IA approach provides an improved sum rate for the femtocell users compared to the conventional IA techniques, such as the leakage minimization approach and the nuclear norm based rank constraint rank minimization approach. Additionally, the proposed framework involving both IRLS-IA and RWF algorithms provides an improved total system sum rate compared with the legacy approaches for the case of multiple femtocell networks.

In this paper, we address the issue of interference alignment (IA) in a two-cell network and consider both inter-cell and intra-cell interferences. For cell one, a linear processing scheme is proposed to align the inter-cell interference to the same signal dimension space of intra-cell interference. For cell two, we propose a distributed interference alignment scheme to manage the interference from the nearby cell. We assume that the relay works in an amplify-and-forward (AF) mode with a half-duplex and MIMO relaying. We show that the composite desired and interfering signals aggregated over two time slots can be aligned such that the interfering signal is eliminated completely by applying a linear filter at the receiver. The precoding matrix of the relay is optimized jointly with the precoding matrix of the base station (BS). The number of data streams is optimized jointly for every user terminal (UT). The degree of freedom (DoF) performance of the proposed scheme as well as the conventional cooperation scheme are derived for multiple antennas at both base stations, relay station and user terminals. Simulation results show that the proposed alignment scheme can achieve a better DoF performance.

Underlay cognitive radio (CR) permits unlicensed secondary users (SUs) to transmit their own data over the licensed spectrum unless the interference from the SUs on the licensed primary user (PU) exceeds an acceptable level. This paper proposes two generalized interference alignment (IA)-based distributed optimization designs for multiple secondary transceivers in the underlay CR case with channel uncertainty under assumption that the actual channel error norm is below a certain bound. One of the designs is an extension to an existing method and the other one is a new design. In these methods, the precoding and power allocation matrices for each SU are either independently or jointly optimized for imperfect channel knowledge to maximize the secondary rates and to hold the secondary interference on the primary receiver under an acceptable limit that is determined by the primary receiver. Numerical results prove the ability of the proposed methods to support significant secondary rates provided that the PU is protected from extra interference from SUs, even in presence of channel uncertainty.

The multiple-input-multiple-output (MIMO) Gaussian wireless network with K users and an intermediate relay is investigated. In this network, each user with available local channel state information (CSI) intends to convey a multicast message to all other users while receiving all messages from other users via the relay. This model is termed the MIMO K-way relay channel with distributed CSI. For this channel, the sum capacity is shown as MK/(K-1)log(SNR)+o(SNR) where each user and the relay is equipped with M antennas. Achievability is based on the signal space alignment strategy with a K-1 time slot extension. A most general case is then considered, in which each user intends to recover all messages required within T time slots. We provide an improved scheme called fractional signal space alignment which achieves MK/(K-1) degrees of freedom in the general case and the feasibility condition is also explored.