Iterative Interference Alignment Research Articles

Iterative interference alignment with spatial hole sensing in MIMO cognitive radio networks

Iterative interference alignment with spatial hole sensing in MIMO cognitive radio networks

Alignment Chain-Based Closed-Form IA Solution for Multiple User MIMO Interference Networks

As a potential interference management technique, interference alignment (IA) can enormously improve the system capacity in the future mobile communication networks. However, the general closed-form IA solution in the multiple user scenario is still an open problem, which hinders the implementation due to the high complexity of iterative IA design. In this paper, a alignment chain-based closed-form IA solution scheme is proposed for generalized $K (K > 3)$ -user multiple-input multiple-output (MIMO) interference channel. The alignment chains are sophisticatedly designed, on the basis of compressing the interference subspace and improving the degree of freedom (DoF) as much as possible. Then based on the alignment chains, the alignment chain equations are built, and the least-squares IA solution with optimal DoF or the exact IA solution with reduced DoF is provided, by using the theory of matrices. A series of simulation experiments are carried out to verify the proposed closed-form IA solution, and simulation results demonstrate its effectiveness and low computational complexity.

Interference alignment in two‐hop multiple‐input multiple‐output interference channel under various CSI and antenna correlation

In this paper, the problem of interference management is investigated in the downlink of multi-user multiple-input multiple-output two-hop interference channel under various scenarios of channel state information (CSI) and antenna correlation. Interference alignment (IA) in the space dimension is a powerful tool to solve this problem. Iterative IA algorithms are adopted in both the first and the second hops transmissions independently. After aligning interfering signals, the recovery of the transmitted signal vector is performed based on zero-forcing and semi-definite relaxation detectors. Furthermore, the impacts of the imperfect CSI and antenna correlation on sum-rate are investigated for decode-and-forward (DF) and amplify-and-forward relaying protocols. When the system is proper but IA is not completely feasible, the performance of minimum interference leakage (MIL) is compared with rank-constrained rank minimisation (RCRM) algorithm in DF protocol. RCRM algorithm is more sensitive to CSI such that the channel uncertainty easily leads to an increase in the interference matrix rank. According to the simulation results, for the case of perfect CSI, RCRM makes further interference-free dimensions which leads to better performance than MIL, but for the case of imperfect CSI, close performance is observed.

Optimal IA design and performance analysis for MIMO–OFDM systems with imperfect CSI

Both multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) are key technologies for the fifth-generation mobile communication systems. However, interference is one of the critical challenges in MIMO–OFDM systems that degrades the overall performance. In this study, a novel interference alignment (IA) design-based diagonal-block channel charter to mitigate the interference for MIMO–OFDM systems is proposed. The proposed IA scheme can be used in physical layer security, e.g. anti-location. Based on the diagonal-block charter of the channel matrix, the optimal degree of freedom, i.e. the maximum number of multiple data streams concurrently transmitted interference-free can be achieved by IA. Correspondingly, the authors present the closed-form IA design scheme for some special scenarios, and two iterative IA ones for general scenarios in detail. Furthermore, the performance analysis of IA systems with diagonal-block channel error is provided, where the imperfect channel state information case is considered. The simulation results show that the IA design based on the diagonal-block channel can improve the sum-rate performance effectively, by sufficiently exploiting the spatial and frequency resources.

Interference Subspace Alignment in Multiple-Multicast Networks

In the traditional interference channel (IC), each transmitter works in the mode of one-to-one. For serving more user terminals (UTs), a multiple-multicast network is proposed, in which there are multiple transmitters, and each transmitter works in the mode of one-to-many. Thus, each UT would suffer from both the intra-transmitter and inter-transmitter interference. Given the transmitting and receiving degrees of freedom, the desired signal would be more difficult to be separated from the numerous interference signals. For managing the interference, an interference subspace alignment (ISA) algorithm is proposed to decrease the dimension of the interference subspace. Different from the traditional iterative interference alignment (IA) algorithms, which iteratively calculate the precoding and receiving combining matrices to minimize the strength of interference, the ISA algorithm directly aligns the interference subspace spanned by the $T-N$ transmitters within that spanned by the residual $N$ transmitters, in which $T$ denotes the number of all the transmitters, and $N$ is the cardinality of the transmitter set used for IA. Now, the dimension of each UT's interference subspace is determined via $N$ transmitters ( $N ). During the subspace alignment, we, respectively, construct the composite IC state matrices for the $T-N$ and $N$ transmitters, and the composite precoding vector, which lies in the null space of the composite IC matrices. Thus, all the precoding matrices can be obtained once. After the subspace alignment, each UT's receiving combining matrix can be designed to lie in the null space of the aligned interference subspace. According to the simulation results, the proposed ISA algorithm can effectively suppress the interference and improve the system sum rate compared with the traditional interference management algorithms.

An Iterative Interference Alignment Algorithm for the General MIMO X Channel

Interference alignment (IA) has been shown as an important technique to achieve a linear capacity scaling in wireless communications. However, the IA scheme over finite signaling dimensions for a general multiple-input-multiple-output (MIMO) X channel is still rarely studied. The main challenge of MIMO X channels is that the two sets of conditions for IA, namely the interference nulling conditions and the rank preservation conditions, get coupled. The usual IA methods for the interference channel and the broadcasting channel cannot be applied anymore. In this paper, we show that the rank preservation conditions can be replaced by a group of specific rank conditions, under which the IA problem is simplified. Then, based on this technique, an iterative algorithm of IA is designed for the MIMO X channel. The algorithm is designed with limited signaling dimensions. From the simulation results, we find that the algorithm has good performances even under limited signal-to-noise ratio.

Joint interference alignment and power allocation for NOMA-based multi-user MIMO systems

Interference alignment (IA) and non-orthogonal multiple access (NOMA) are key technologies for achieving the capacity scaling required by next generation networks to overcome the unprecedented growth of data network traffic. Each of these technologies was proved to present excellent performance for MIMO systems. In this article, we propose a joint IA and power allocation (PA) framework for NOMA-based multi-user MIMO (MU-MIMO) systems. Different approaches for applying IA in downlink NOMA-based MU-MIMO systems will be addressed while implementing a PA technique that fully exploits the characteristics of NOMA-based systems. The proposed framework aims to maximize the sum-rate of the NOMA-based MU-MIMO system through combining IA with PA. The process begins by initially grouping the system users into clusters for optimum implementation of NOMA. The sum-rate maximization is carried out under cluster power budget, user quality-of-service (QoS), and robust successive interference cancellation (SIC) constraints. Meanwhile, it uses the power domain multiplexing strategy to allow the users within each cluster to share the data streams without exerting interference to one another. Three iterative joint IA and PA algorithms are proposed for NOMA-based MU-MIMO systems. Moreover, these algorithms are compared with orthogonal multiple access (OMA)-based MU-MIMO counterpart as well as the state-of-the-art techniques presented for NOMA-based MU-MIMO systems. Numerical simulations verify that the proposed framework can greatly improve the performance of NOMA-based MU-MIMO systems in terms of the achievable sum-rate when compared with OMA-based MU-MIMO and the state-of-the-art NOMA-based MU-MIMO systems.

Interference alignment based on adaptive eigenmodes in a multiple-input, multiple-output cognitive radio network

This article aims to optimize the information rate of a cognitive radio network with multiple secondary users. A primary user rate optimization approach based on dichotomy of the degree of freedom is proposed, where the primary users’ eigenmodes are adjusted according to its rate requirement. In order to provide a higher sum rate of secondary users, two interference alignment schemes are presented. The first one is an interference sub-space alignment scheme, which aims to align the sub-spaces spanned by interference from other secondary users with the sub-space spanned by interference from primary user. However, interference sub-space alignment may not be favorable in low signal-to-interference ratio region due to the negligence of the influence of noise. Thus, an iterative interference alignment scheme which maximizes the secondary system sum rate based on Grassmann manifold is developed. To accelerate the convergence speed, the objective function in Grassmann manifold is transformed into two parts without the inversion operation using the extensions of the Minkowski inequality. Simulation results show that interference sub-space alignment is more effective than Grassmann manifold to mitigate interference in the system with more secondary users. We further validate the effectiveness of Grassmann manifold and interference sub-space alignment in comparison with the existing schemes employing a water filling algorithm.

Joint Iterative Interference Alignment and Energy Harvesting for Multi-User Networks

In a wireless network with multiple users, interferences cause performance degradation as well as provide extra opportunities for harvesting RF energies. In this work, a new joint design of interference alignment (IA) and energy harvesting (EH) that aims to reduce interferences to the desired user and harvest energies from the interferences when IA is inefficient is studied. Two iterative IA schemes, distributed IA (DIA) and IA via alternating minimization (IAAM) are considered. Based on a tradeoff decision criterion, the operation switches between IA and EH. Numerical results show that there is a tradeoff between information rate and harvested energy for both DIA and IAAM. The scheme with higher information rate often has smaller harvested energy.

Distributed Real-Time Implementation of Interference Alignment with Analog Feedback

Interference alignment (IA) is a precoding technique that aligns interfering signals at receivers. It is known that IA achieves the maximum degrees of freedom over an interference channel under ideal assumptions. The real-world performance of IA depends on a range of practical issues, such as imperfect synchronization, channel estimation, and feedback. Practical issues have been studied in simulations and prototypes, but fully distributed operation of IA network nodes has not been considered. In this paper, we present the first investigation of real-time IA performance on a fully distributed 2 $\times$ 2 multiple-input–multiple-output (MIMO) prototype system with three physically independent user pairs. Over-the-air algorithms for time and frequency synchronization, as well as analog feedback, are studied and implemented. Sum rates are illustrated as a function of complexity and accuracy of different alignment, synchronization, and feedback algorithms. Corresponding tradeoffs are evaluated using an iterative IA method, the injection of residual frequency offset into synchronization, and analog versus quantization-based limited feedback approaches. We demonstrate that, while considering all possible error sources in estimation, synchronization, and feedback, the theoretical multiplexing gain of IA can be reached in practical systems with a constant sum rate loss that remains within 5 bits/Hz/s compared with an ideal simulation.

Antenna Configurations for MIMO Interference Alignment in Three-User Heterogeneous Systems

Recently, heterogeneous network (HetNet) has been introduced as an appropriate strategy to cope with the explosive growth of wireless traffic. To address the issue of severe interference in the HetNet, we can consider interference alignment (IA), which achieves the maximum degrees of freedom (DOFs) in multiple-input-multiple-output (MIMO) interference channels (ICs). However, an anticipated performance of the MIMO IA is difficult to be clarified, particularly with different numbers of antennas across the nodes when designing an appropriate system. In this paper, we thus study antenna configurations for the three-user MIMO IA with respect to the intended data stream tuple, i.e, DOF. For simple analysis, we consider two-tier network with two types of data stream numbers in a system. First, the dimension of the subspace occupied by interference is derived by aligning the interference in the signal space of the MIMO IA. After this, the suitable numbers of antennas are computed depending on the transmitted data stream numbers. Our obtained results provide an insight on how the performance of the MIMO IA is affected as the system configurations change. Furthermore, we discuss how to maximize the performance of such systems when the available numbers of antennas are finite. The actual simulations with an iterative IA confirm the validity of our derived results.

Robust Iterative Interference Alignment for Cellular Networks With Limited Feedback

In theory coordinated multi-point transmission (CoMP) promises vast gains in spectral efficiency. But industrial field trials show rather disappointing throughput gains, whereby the major limiting factor is proper sharing of channel state information. Many recent papers consider this so-called limited feedback problem in the context of CoMP. Usually taking the assumptions: 1) infinite SNR regime, 2) no user selection and 3) ideal link adaptation; rendering the analysis too optimistic. In this paper we make a step forward towards a more realistic assessment of the limited feedback problem by introducing an improved metric for the performance evaluation which better captures the throughput degradation. We find the relevant scaling laws (lower and upper bounds) and how that they are different from existing ones. Moreover, we provide a robust iterative interference alignment algorithm and corresponding feedback strategies achieving the obtained scaling laws. The main idea is that instead of sending the complete channel matrix each user fixes a receive filter and feeds back a quantized version of the effective channel. Finally we underline our findings with simulations for the proposed system.

Iterative reweighted least squares interference alignment approach for multicell MIMO networks

In this paper, we investigate iterative interference alignment (IA) approaches for multi-input multi-output (MIMO) multicell communication systems. We proposed an iterative reweighted least square (IRLS) approach for MIMO interference channel in single-cell scenario. The basic contribution of this paper is to extend the proposed IRLS algorithm to the more practical case of aligning co-channel interference signals in orthogonal frequency division multiple access (OFDMA) based cellular systems. The simulation results show that the proposed approach achieves a superior total system sum-rate than both the conventional Orthogonal-Minimum Leakage (OR-ML) and the Orthogonal-Maximum Signal to Interference Noise Ratio (OR-MSINR) approaches.

Iterative Equalization and Interference Alignment for Multiuser MIMO HetNets with Imperfect CSI

In this paper we consider a scenario, where several small-cells work under the same coverage area and spectrum of a macrocell. The signals stemming from the small-cell (macrocell) users if not carefully dealt with will generate harmful interference into the macrocell (small-cell). To tackle this problem interference alignment and iterative equalization techniques are considered. By using IA all interference generated by the small-cell (macrocell) users is aligned along a low dimensional subspace, at the macrocell (small-cells). This reduces considerably the amount of resources allocated, to enable the coexistence of the two systems. However, perfect IA requires the availability of error-free channel state information (CSI) at the transmitters. Due to CSI errors one can have substantial performance degradation due to imperfect alignments. Since in this work the IA precoders are based on imperfect CSI, an efficient iterative space-frequency equalization is designed at the receiver side to cope with the residual aligned interference. The results demonstrate that iterative equalization is robust to imperfect CSI and removes efficiently the interference generated by the poorly aligned interference. Close to matched filter bound performance is achieved, with a very few number of iterations.

Generic Iterative Downlink Interference Alignment

Generic Iterative Downlink Interference Alignment

EIV-Based Interference Alignment Scheme with CSI Uncertainties

A novel interference alignment (IA) scheme based on the errors-in-variables (EIV) mathematic model has been proposed to overcome the channel state information (CSI) estimation error for the MIMO interference channels. By solving an equivalently unconstrained optimization problem, the proposed IA scheme employing a weighted total least squares (WTLS) algorithm can obtain the solution to a constrained optimization problem for transmit precoding (TPC) matrices and minimizes the distortion caused by imperfect CSI according to the EIV model. It is shown that the design of TPC matrices can be realized through an efficient iterative algorithm. The convergence of the proposed scheme is presented as well. Simulation results show that the proposed IA scheme is robust over MIMO interference channels with imperfect CSI, which yields significantly better sum rate performance than the existing IA schemes such as distributed iterative IA, maximum signal-to-interference-plus-noise ratio (Max SINR), and minimum mean square error (MMSE) schemes.

A distributed interference alignment algorithm using min‐maxing strategy

AbstractInterference alignment is a joint‐transmission strategy that significantly increases the sum rate of interference channels at high signal‐to‐noise ratios (SNRs). The recent iterative interference alignment approaches are incapable of guaranteeing the best sum‐rate performance with the increase of the SNR amongst different K‐user interference channels, especially at high SNR regime. In this paper, a new interference alignment algorithm is developed to improve the sum‐rate performance of K‐user multi‐input multi‐output (MIMO) and multi‐carrier interference channels by minimising the interference leakage and maximising the desired power concurrently, which is called by min‐maxing strategy. For a K‐user MIMO interference channel, we design transmit precoding matrices and receive decoding matrices through an efficient iterative algorithm based on min‐maxing strategy in a distributed way, in which each receiver maximises the desired signal power, whereas it preserves the minimum leakage interference as a constraint. This optimisation problem is reformulated and relaxed into a standard semidefinite programming form. The convergence of the proposed algorithm is proved as well. Furthermore, a simplified min‐maxing algorithm is proposed for rank‐deficient interference channels to achieve the targeted performance with less complexity. The numerical simulations show that the proposed algorithm proffers significant sum‐rate improvement in K‐user MIMO interference channels compared with the existing algorithms at high SNR regime. Moreover, the simplified algorithm matches the optimal performance in the systems of rank‐deficient channels. Finally, the developed min‐maxing algorithm has been extended to K‐user multi‐carrier interference channels, which outperform the previous approaches in terms of sum rate in several scenarios. Copyright © 2014 John Wiley & Sons, Ltd.

A Large-Scale MIMO Precoding Algorithm Based on Iterative Interference Alignment

Abstract The performance of Large-scale MIMO system is degraded by Pilot Contamination. In order to reduce Pilot Contamination, a downlink precoding algorithm is put forward, based on Interference Alignment (IA). The main idea of this algorithm is aligning the pilot contamination and inter-cell interference to the same null space in order to acquire the maximal degrees of freedom. Then the downlink receiving precoding matrix is solved with respect to a maximal SINR (Signal Interference Noise Ratio) criterion. Exploiting the channel reciprocity and an iterative process, Base station and User Equipment switch transmitting and receiving roles in the uplink and downlink, the precoding matrices of the Base station and User Equipment is gradually updated until convergence. Finally, the simulation results have shown that the algorithm proposed can efficiently mitigate the impact of pilot contamination and outperform some popular precoding algorithms, e.g., MF precoding algorithm and MMSE precoding algorithm. When the number of antennas increases, the performance of the proposed algorithm will be greatly improved.

On feasibility of linear interference alignment for single‐input–single‐output multi‐frequency interference channel

This study explores the feasibility of linear interference alignment (IA) for a ( M × M , 1) K system with multi-frequency independent channels. The authors prove that number of users K ≤ 2 M - 2 is a necessary condition for ( M × M , 1) K multi-frequency IA system, which is less than that of ( M × M , 1) K multiple-input-multiple-output system (i.e. K ≤ 2 M - 1). The conclusion can be extended to all cases with the diagonal channel matrix. They also reveal that the traditional frequency division multiplexing method is inefficient in spectrum utilisation. They apply max-SINR (signal to interference plus noise ratio) and iterative IA algorithms and the author's simulation results verify that IA algorithms work well in ( M × M , 1) 2M-2 IA system.

Distributed Iterative Interference Alignment for Three-user MIMO Interference Channels

Distributed Iterative Interference Alignment for Three-user MIMO Interference Channels