Multiple-input Multiple-output Interference Channel Research Articles

Robust Transceiver Design for Correlated MIMO Interference Channels in the Presence of CSI Errors under General Power Constraints

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel.

Full-Duplex MIMO Relay-Assisted Interference Alignment Algorithm in K-user Interference Channels

In this paper, we investigate the transceiver design schemes for the full-duplex multiple-input multiple-output relay-assisted K-user single-input multiple-output interference channels. Firstly, we propose an iterative optimized reference vector for IA (IORV-IA) algorithm in the perfect channel state information (CSI) scenario. The proposed IORV-IA algorithm not only achieves the alignment of interference signals at each receiver, but also iteratively optimizes the IA reference vector by orthogonalizing the directions of the interference signals and the desired signal. With the optimized IA reference vector, the relay processing matrix and the receiving filter vectors are designed to further improve the system performance. Considering that the relay cannot obtain perfect CSIs in practice due to many factors, and the performance of the IA scheme is very sensitive to this error. Furthermore, we propose a robust transceiver design scheme based on mean square error (MSE) in the imperfect CSI scenario, which minimizes the sum of MSEs in the worst case through iteration. The proposed algorithms are evaluated in terms of the average sum rate and bit error rate performance and the simulation results show the advantages of the proposed algorithms over existing centralized IA and centralized zero-forcing algorithms.

Relay Assisted Max-SINR Transceiver Optimization Design for MIMO Interference Channels

Signal to interference plus noise ratio maximization (Max-SINR) algorithm are designed to increase the transmission rate of multiple-input multiple-output interference channels (MIMO IC). The algorithms are sensitive to channel estimation error, which makes the rate performance under imperfect channel state information (CSI) conditions become unsatisfactory. To deal with this, a relay assisted signal to interference plus noise ratio maximization (Relay-Max-SINR) algorithm is proposed in this work to improve the robustness of Max-SINR in MIMO ICs. Different from the traditional relay assisted using beamforming and forward transmission, we mathematically equivalent the signal processing process of relay to the receive filtering and transmit precoding, and design the relay processing matrix. In real communication process, the relay processing matrix is directly used for the signal processing at relay. Using the channel reciprocity, the receive filtering matrix at relay, the transmit precoding matrix at relay, the relay processing matrix, the receive filtering matrix at destination and the transmit precoding matrix at source are optimized iteratively according to the nature of generalized Rayleigh quotient. With the help of additional transmission links provided by the relay, interference is more effectively suppressed and the power loss of the desired signal is reduced. Simulations show that the proposed Relay-Max-SINR algorithm can significantly increase the capacity and the robustness of MIMO ICs.

Stream level rank constrained transceiver design in MIMO interference channel networks

An interference leakage minimisation transceiver design for multiple-input multiple-output Interference Channel networks is proposed by making use of the full rank constraint of the desired signal, the low rank constraint and low power constraint of the interference signal. The objective is to suppress interference leakage caused by not only the signal from other users, but also the other streams from the same user. To do so, the transmit precoding matrix and the receive filtering matrix are iteratively optimised through convex optimisation tools at stream level. Furthermore, a Min–Max interference leakage algorithm is also proposed to suppress the maximum interference from user, with the purpose of guaranteeing the fairness among users. Simulation results demonstrate that taking inter-stream interference into consideration can significantly improve the effectiveness of multiple-input multiple-output Interference Channel networks, while the Min–Max method can slightly increase the system capacity under certain conditions. It can be also confirmed that the trade-off among effectiveness, fairness and robustness exists in the transceiver optimisation of multiple-input multiple-output Interference Channel networks.

On the Synergistic Benefits of Reconfigurable Antennas and Partial Channel Knowledge for the MIMO Interference Channel

Author(s): Yuan, Bofeng; Ismailoglu, Nilab; Jafar, Syed A | Abstract: Blind Interference Alignment (BIA) schemes create and exploit channel coherence patterns without the knowledge of channel realizations at transmitters, while beamforming schemes rely primarily on channel knowledge available to the transmit- ters without regard to channel coherence patterns. In order to explore the compatibility of these disparate ideas and the possibility of synergistic gains, this work studies the Degrees of Freedom (DoF) of the 2-user (?1 × ?1)(?2 × ?2) Multiple- Input Multiple-Output (MIMO) Interference Channel (IC) where Transmitter 1 is equipped with reconfigurable antennas and has no channel knowledge, while Transmitter 2 has partial channel knowledge but no reconfigurable antennas. Taking a fundamental dimensional analysis perspective, the main question is to identify which antenna configurations allow synergistic DoF gains. The main results of this work are two-fold. The first result identifies antenna configurations where both reconfigurable antennas and partial channel knowledge are individually beneficial, as those where ?1 l ?1 l min(?2,?2). The second result shows that synergistic gains exist in each of these settings, over the best known solutions that rely on either reconfigurable antennas or partial channel knowledge alone. Coding schemes that jointly exploit partial channel knowledge and reconfigurable antennas emerge as a byproduct of the analysis.

On Secure Degrees of Freedom of the MIMO Interference Channel With Local Output Feedback

This article studies the problem of Sum-secure Degrees of Freedom (SDoF) of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(M,M,N,N)$ </tex-math></inline-formula> multiple-input–multiple-output (MIMO) interference channel with local output feedback, so as to build an information-theoretic foundation and provide practical transmission schemes for 6G-enabled Vehicles-to-Vehicles (V2V). For this problem, we propose two novel transmission schemes, i.e., the interference decoding scheme and the interference alignment scheme, and thus establish a sum-SDoF lower bound. In particular, to optimize the phase duration, we analyze the security and decoding constraints and formulate a linear-fractional optimization problem. Furthermore, we show that the derived sum-SDoF lower bound is the sum-SDoF for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M \le N/2$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N=M$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2N \le M$ </tex-math></inline-formula> antenna configurations, and reveal that for a fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> to maximize the sum-SDoF is not less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2N$ </tex-math></inline-formula> . Through simulations, we examine the secure sum-rate performance of proposed transmission schemes and reveal that using local output feedback can lead to a higher secure sum-rate than that by using delayed channel state information at the transmitter (CSIT).

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.

The Interference Channel Revisited: Aligning Interference by Adjusting Antenna Separation

It is shown that, in a line-of-sight setting, a receiver equipped with two antennas may approximately null an arbitrary large number of spatial directions to any desired degree, while maintaining the interference-free signal-to-noise ratio, by judiciously adjusting the distance between the antenna elements, provided that the spacing can be made sufficiently large. The main theoretical result builds on ergodic theory. The practicality of the scheme at moderate signal-to-noise values is demonstrated for a scenario where each transmitter is equipped with a single antenna and each receiver has two receive chains and where the desired spacing between antenna elements is achieved by selecting the appropriate antennas from a large enough linear antenna array. We further extend the proposed scheme to show that interference can be nearly eliminated also in specular multipath channels as well as multiple-input multiple-output interference channels where a single additional receive antenna suffices to approximately align all interferers into a one-dimensional subspace. To demonstrate the performance of the scheme, we show significant gains for interference channels with four as well as six users, at low to moderate signal-to-noise ratios ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0\text{--}20$</tex-math></inline-formula> dB). The robustness of the proposed technique to small channel estimation errors is also explored.

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.

Achievable Secure Degrees of Freedom of MIMO Interference Channel With a Cooperative Jammer

In this letter, the secure degrees of freedom (SDoF) of 2-user multiple-input multiple-output (MIMO) interference channel with an external N-antenna cooperative jammer (CJ) is considered. In this model, each transmitter intends to send confidential messages to the corresponding receiver and keep secret with unintended receiver. Different from the previous studies on interference channels, our model has an external cooperative jammer, which can improve the SDoF by transmitting interference signals. We derive the converse and give the corresponding achievable schemes to determine the exact SDoF, and study the influence of CJ on the SDoF of this system. We find that adding one CJ antenna has the same effect as adding one transmitting antenna, and has a better effect than adding one receiving antenna. The converse is given by using vector extensions of the role of a helper and secrecy penalty lemmas. For arbitrary values of N and M, we provide different achievable schemes for the corresponding regimes by making use of the symbol extension and spatial alignment techniques.

Improper Gaussian Signaling for the $K$-User MIMO Interference Channels With Hardware Impairments

This paper investigates the performance of improper Gaussian signaling (IGS) for the K-user multiple-input, multiple-output (MIMO) interference channel (IC) with hardware impairments (HWI). HWI may arise due to imperfections in the devices like I/Q imbalance, phase noise, etc. With I/Q imbalance, the received signal is a widely linear transformation of the transmitted signal and noise. Thus, the effective noise at the receivers becomes improper, which means that its real and imaginary parts are correlated and/or have unequal powers. IGS can improve system performance with improper noise and/or improper interference. In this paper, we study the benefits of IGS for this scenario in terms of two performance metrics: achievable rate and energy efficiency (EE). We consider the rate region, the sum-rate, the EE region and the global EE optimization problems to fully evaluate the IGS performance. To solve these non-convex problems, we employ an optimization framework based on majorization-minimization algorithms, which allow us to obtain a stationary point of any optimization problem in which either the objective function and/or constraints are linear functions of rates. Our numerical results show that IGS can significantly improve the performance of the K-user MIMO IC with HWI and I/Q imbalance, where its benefits increase with the number of users, K, and the imbalance level, and decrease with the number of antennas.

Signal-Aligned Network Coding for Multicell Processing With Limited Cooperation

In this paper, we propose a signal-aligned network coding (SNC) scheme for K-user time-varying multiple-input multiple-output (MIMO) interference channels with limited receiver cooperation. We assume that the receivers are connected to a central processor via wired cooperation links with individual limited capacities. Our SNC scheme determines the precoding matrices of the transmitters so that the transmitted signals are aligned at each receiver. The aligned signals are then decoded into noiseless integer combinations of messages, also known as network-coded messages, by physical-layer network coding. The key idea of our scheme is to ensure that independent integer combinations of messages can be decoded at the receivers. Hence the central processor can recover the original messages of the transmitters by solving the linearly independent equations. We prove that our SNC scheme achieves full degrees of freedom (DoF) by utilizing signal alignment and physical-layer network coding. Simulation results show that our SNC scheme outperforms the compute-and-forward scheme in the finite SNR regime of the two-user and the three-user cases. The performance improvement of our SNC scheme mainly comes from efficient utilization of the signal subspaces for conveying independent linear equations of messages to the central processor.

Secure Degrees of Freedom of Rank-Deficient BCCM and Rank-Deficient ICCM

The secure degrees of freedom (SDoF) of two-user rank-deficient multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and two-user rank- deficient MIMO interference channel with confidential messages (ICCM) are studied respectively in this paper. In the systems, each transmitter has $M$ antennas, and each receiver has $N$ antennas. We consider that each transmitter intends to send secure messages to the corresponding receiver, and another receiver can receive the messages but cannot decode them, which ensures that the messages are confidential. Comparing with previous studies on two-user broadcast channel and interference channel, we explore the case that channel matrices are rank-deficient, and the rank of channel matrices can take arbitrary value, $D \leq \text{min} (M,N)$ . For the two rank-deficient channels, BCCM and ICCM, we divide the problem into several regimes according to the different configurations of the rank of channel matrices and the number of antennas at each node. The outer bound of rank-deficient BCCM is inferred from information theoretic methods and the achievable schemes are given by zero forcing techniques. We derive the outer bound of rank-deficient ICCM by taking the minimum region of the three outer bounds, where the first outer bound is the result of rank-deficient interference channel model without secrecy constraints, the second outer bound is obtained by considering secrecy constraints, and the third outer bound is achieved by transmitters cooperation. Then we present the achievable schemes by combining zero-forcing, real interference alignment, and spatial alignment. Finally, we determine the exact SDoF of the rank-deficient BCCM and the rank-deficient ICCM.

Optimal Transceiver Design for SWIPT in Interference Alignment Network

This paper studies simultaneous wireless information and power transfer in a K-user multiple-input multiple-output interference channel. A new scheme jointly designing interference ali ...

Majorization-Minimization Aided Hybrid Transceivers for MIMO Interference Channels

The potential of deploying large-scale antenna arrays in future wireless systems has stimulated extensive research on hybrid transceiver designs aiming to approximate the optimal fully-digital schemes with much reduced hardware cost, and signal processing complexity. Generally, this hybrid transceiver structure requires a joint design of analog, and digital processing to enable both beamsteering, and spatial multiplexing gains. In this paper, we develop various weighted mean-square-error minimization (WMMSE) based hybrid transceiver designs for ${K}$ -user multiple-input multiple-output (MIMO) interference systems, which are applicable to both millimeter wave (mmWave) channels, and Rayleigh fading channels. Firstly, a heuristic joint design of hybrid precoder, and combiner using alternating optimization is proposed, in which the majorization-minimization (MM) method is utilized to design the analog precoder, and combiner under unit-modulus constraints. It is demonstrated that this scheme achieves comparable performance to the fully-digital WMMSE solution. To further reduce the computational complexity, a phase projection based two-stage scheme is proposed to decouple the designs of the analog, and digital precoder/combiner. Secondly, inspired by the fully-digital solutions based on the block-diagonalization zero-forcing (BD-ZF), and signal-to-leakage-plus-noise ratio (SLNR) criteria, the low-complexity MM-based BD-ZF, and SLNR hybrid designs are proposed, respectively, for approximating the corresponding fully-digital solutions. Thirdly, the partially-connected hybrid structure conceived for reducing system hardware cost, and power consumption is considered, for which the MM-based alternating optimization algorithm still works. Our numerical results characterize the sum rate performance of all proposed hybrid designs in comparison to the existing benchmarks.

Transceiver Design for Energy-Efficiency Maximization in mmWave MIMO IoT Networks

Millimeter wave (mmWave) communications have been regarded as a fundamental enabling technology for future 5G Internet of Things (IoT) networks. This paper studies a hybrid transceiver design problem considering both perfect and imperfect channel state information to maximize the energy-efficiency (EE) of a mmWave multiple-input multiple-output (MIMO) interference channel involving multiple hardware impaired IoT devices. Since the original hybrid transceiver design problem is intractable, we propose a low-complexity two-stage algorithm, both of which are proven to converge. In the first stage, we transform the multivariate problems into their univariate equivalents and exploit the well-known relationship between rate and mean squared error to solve them in an alternating fashion. In the second stage, using the results from stage one, we separate the joint transceiver optimization problems into hybrid precoders and combiners sub-problems and apply orthogonal matching pursuit algorithm to obtain the optimal solution for each sub-problem. Finally, through numerical simulations it is shown that the proposed hybrid algorithms achieve near-optimal EE performance to support power constrained IoT devices with lower complexity than univariate designs.

Secure Degrees of Freedom of Rank-Deficient MIMO Interference Channel

This letter investigates the secure degrees of freedom (SDoF) for a 2-user rank-deficient $(M, D)$ interference channel with confidential messages (ICCM) in which each node is equipped with $M$ antennas. In this model, each transmitter intends to send a confidential message to the corresponding receiver while ensuring that the messages are kept secret against the unintended receiver. Unlike the existing studies on 2-user multiple-input multiple-output (MIMO) interference channel models, channel matrices in this letter do not need to be full rank, and they can take arbitrary rank, $D\le M$ . According to different configurations of ranks and number of antennas, the problem is divided into two regimes, and the exact SDoF is given by $\text {min}\left({2D,\frac {4M-2D}{3}}\right)$ . Then, we propose a converse proof, in which the outer bound is proved by using information theoretic methods. Finally, we propose different achievable schemes for the corresponding regimes by utilizing the spatial alignment, symbol extension, and zero-forcing techniques. It can be obviously seen that the full rank situation on ICCM can be regarded as a special case when $D=M$ .

On the Secure Degrees of Freedom for Two-User MIMO Interference Channel With a Cooperative Jammer

We investigate the secure degrees of freedom (SDoF) for the two-user multiple-input multiple-output (MIMO) interference channel with a cooperative jammer, where each transmitter is equipped with $M$ antennas, each receiver is equipped with $N$ antennas, and the jammer is equipped with $K$ antennas. For each one of the four regions of parameters $(M,N)$ , i.e., $1\leq \frac {N}{M} , $\frac {N}{M} \geq 2$ , $\frac {1}{2}\le \frac {N}{M} , and $\frac {N}{M} , we provide both upper and lower bounds on the SDoF of the system which depend on the value of $K$ . In particular, the upper bound is the union of three upper bounds that are based on the DoF of the MIMO interference channel, the SDoF of the MIMO wiretap channel with a jammer, and the Secrecy Penalty Lemma and the Role of A Helper Lemma for the interference channel, respectively. For the lower bound, we provide achievability schemes that make use of signal alignment, zero forcing, cooperative jamming, and multi-slot transmission. Our results indicate that the SDoF of the system under consideration improves with respect to the no jammer case in all regimes, especially when $N>2M$ . Moreover, we quantify the SDoF gap of the network and reveal it as a function of the number of the antennas. For large $K$ , the upper and lower bounds coincide in all regimes, and the exact SDoF can be achieved.

Max–Min Fairness Design for MIMO Interference Channels: A Minorization–Maximization Approach

We address the problem of linear precoder (beamformer) design in a multiple-input multiple-output interference channel (MIMO-IC). The aim is to design the transmit covariance matrices in order to achieve max-min utility fairness for all users. The corresponding optimization problem is non-convex and NP-hard in general. We devise an efficient algorithm based on the minorization-maximization (MM) technique to obtain quality solutions to this problem. The proposed method solves a second-order cone convex program (SOCP) at each iteration. We prove that the devised method converges to stationary points of the problem. We also extend our algorithm to the case where there are uncertainties in the noise covariance matrices or channel state information (CSI). Simulation results show the effectiveness of the proposed method compared with its main competitor.

Energy Efficient Transceiver Design in MIMO Interference Channels: The Selfish, Unselfish, Worst-Case, and Robust Methods

This paper is concerned with the energy efficiency maximization problem in multiple-input multiple-output interference channels. In the first part of this paper, we design the transmit beamforming matrices based on three approaches. In the first approach, each user tries to maximize their own energy efficiency, resulting in what we call the selfish method. The maximization problem corresponding to the selfish method can be implemented in a distributed manner with a semi-closed-form solution. The second approach aims to maximize the weighted sum-energy efficiency; we refer to it as the unselfish method. The proposed unselfish method has the following advantages. 1) It is easily implementable as the problem can be divided into several sub-problems and solved in a distributed manner. 2) It results in a quadratically constrained quadratic program with a semi-closed-form solution. Also, we consider fairness with the minimum-energy efficiency maximization problem, an approach that results in what we call the worst-case method. In the second part, general energy efficiency maximization in the presence of norm-bounded channel uncertainty is investigated which leads to a semi-definite program; the resulting method is called the robust method. Finally, the effect of the system parameters is evaluated through simulations.