Interference Alignment with Partially Coordinated Transmit Precoding

In this paper, we introduce an efficient interference alignment (IA) algorithm exploiting partially coordinated transmit precoding to improve the number of concurrent interference-free transmissions, i.e., the multiplexing gain, in multicell downlink. The proposed coordination model is such that each base-station simultaneously transmits to two users and each user is served by two base-stations. First, we show in a K-user system operating at the information theoretic upper bound of degrees of freedom (DOF), the generic IA is proper when $K \leq 3$, whereas the proposed partially coordinated IA is proper when $K \leq 5$. Then, we derive a non-iterative, i.e., one shot, IA algorithm for the proposed scheme when $K \leq 5$. We show that for a given latency, the backhaul data rate requirement of the proposed method grows linearly with K. Monte-Carlo simulation results show that the proposed one-shot algorithm offers higher system throughput than the iterative IA at practical SNR levels.Comment: 19 pages, 8 figure

Degrees of Freedom of MIMO Cellular Networks: Decomposition and Linear Beamforming Design

This paper investigates the symmetric degrees of freedom (DoF) of MIMO cellular networks with G cells and K users per cell, having N antennas at each base station and M antennas at each user. In particular, we investigate achievability techniques based on either decomposition with asymptotic interference alignment (IA) or linear beamforming schemes, and show that there are distinct regimes of (G,K,M,N) where one outperforms the other. We first note that both one-sided and two-sided decomposition with asymptotic IA achieve the same degrees of freedom. We then establish specific antenna configurations under which the DoF achieved using decomposition based schemes is optimal by deriving a set of outer bounds on the symmetric DoF. For linear beamforming schemes, we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios. Packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference. Such a structured beamforming design can be shown to achieve the optimal spatially normalized DoF (sDoF) of two-cell two-user/cell network and the two-cell three-user/cell network. For larger networks, we develop an unstructured approach to linear interference alignment, where transmit beamformers are designed to satisfy conditions for IA without explicitly identifying the underlying structures for IA. The main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sDoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition, and a significant portion of sDoF elsewhere. Remarkably, polynomial identity test appears to play a key role in identifying the boundary of the achievable sDoF region in the former case.Comment: 25 pages, 14 figures, submitted to IEEE Transactions on Information Theor

Signal Processing and Optimal Resource Allocation for the Interference Channel

In this article, we examine several design and complexity aspects of the optimal physical layer resource allocation problem for a generic interference channel (IC). The latter is a natural model for multi-user communication networks. In particular, we characterize the computational complexity, the convexity as well as the duality of the optimal resource allocation problem. Moreover, we summarize various existing algorithms for resource allocation and discuss their complexity and performance tradeoff. We also mention various open research problems throughout the article.Comment: To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Interference Exploitation Precoding for Multi-Level Modulations: Closed-Form Solutions

In this paper, we study closed-form interference-exploitation precoding for multi-level modulations in the downlink of multi-user multiple-input single-output (MU-MISO) systems. We consider two distinct cases: first, for the case where the number of served users is not larger than the number of transmit antennas at the base station (BS), we mathematically derive the optimal precoding structure based on the Karush-Kuhn-Tucker (KKT) conditions. By formulating the dual problem, the precoding problem for multi-level modulations is transformed into a pre-scaling operation using quadratic programming (QP) optimization. We further consider the case where the number of served users is larger than the number of transmit antennas at the BS. By employing the pseudo inverse, we show that the optimal solution of the pre-scaling vector is equivalent to a linear combination of the right singular vectors corresponding to zero singular values, and derive the equivalent QP formulation. We also present the condition under which multiplexing more streams than the number of transmit antennas is achievable. For both considered scenarios, we propose a modified iterative algorithm to obtain the optimal precoding matrix, as well as a sub-optimal closed-form precoder. Numerical results validate our derivations on the optimal precoding structures for multi-level modulations, and demonstrate the superiority of interference-exploitation precoding for both scenarios

Interference Alignment for Multicell Multiuser MIMO Uplink Channels

This paper proposes a linear interference alignment (IA) scheme which can be used for uplink channels in a general multicell multiuser MIMO cellular network. The proposed scheme aims to align interference caused by signals from a set of transmitters into a subspace which is established by the signals from only a subset of those transmitters, thereby effectively reducing the number of interfering transmitters. The total degrees of freedom (DoF) achievable by the proposed scheme is given in closed-form expression, and a numerical analysis shows that the proposed scheme can achieve the optimal DoF in certain scenarios and provides a higher total DoF than other related schemes in most cases.Comment: Submitted to IEEE Transactions on Signal Processing, Jan., 201

The Feasibility of Interference Alignment for Reverse TDD Systems in MIMO Cellular Networks

The feasibility conditions of interference alignment (IA) are analyzed for reverse TDD systems, i.e., one cell operates as downlink (DL) but the other cell operates as uplink (UL). Under general multiple-input and multiple-output (MIMO) antenna configurations, a necessary condition and a sufficient condition for one-shot linear IA are established, i.e., linear IA without symbol or time extension. In several example networks, optimal sum degrees of freedom (DoF) is 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 DoF. An iterative construction of transmit and received beamforming vectors is further proposed, which provides a specific beamforming design satisfying one-shot IA. Simulation results demonstrate that the proposed IA not only achieve lager DoF but also significantly improve the sum rate in the practical signal-to-noise ratio (SNR) regime.Comment: 12 pages; 5 figure

Sum-rate Maximization in Sub-28 GHz Millimeter-Wave MIMO Interfering Networks

MIMO systems in the lower part of the millimeter-wave spectrum band (i.e., below 28 GHz) do not exhibit enough directivity and selectively, as their counterparts in higher bands of the spectrum (i.e., above 60 GHz), and thus still suffer from the detrimental effect of interference, on the system sum-rate. As such systems exhibit large numbers of antennas and short coherence times for the channel, traditional methods of distributed coordination are ill-suited, and the resulting communication overhead would offset the gains of coordination. In this work, we propose algorithms for tackling the sum-rate maximization problem, that are designed to address the above limitations. We derive a lower bound on the sum-rate, a so-called DLT bound (i.e., a difference of log and trace), shed light on its tightness, and highlight its decoupled nature at both the transmitters and receivers. Moreover, we derive the solution to each of the subproblems, that we dub non-homogeneous waterfilling (a variation on the MIMO waterfilling solution), and underline an inherent desirable feature: its ability to turn-off streams exhibiting low-SINR, and contribute to greatly speeding up the convergence of the proposed algorithm. We then show the convergence of the resulting algorithm, max-DLT, to a stationary point of the DLT bound. Finally, we rely on extensive simulations of various network configurations, to establish the fast-converging nature of our proposed schemes, and thus their suitability for addressing the short coherence interval, as well as the increased system dimensions, arising when managing interference in lower bands of the millimeter wave spectrum. Moreover, our results also suggest that interference management still brings about significant performance gains, especially in dense deployments.Comment: 16 page

Linear Transceiver Design for Interference Alignment: Complexity and Computation

Consider a MIMO interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize system throughput. The recent work [1] suggests that optimal beamformers should maximize the total degrees of freedom and achieve interference alignment in high SNR. In this paper we first consider the interference alignment problem in spatial domain and prove that the problem of maximizing the total degrees of freedom for a given MIMO interference channel is NP-hard. Furthermore, we show that even checking the achievability of a given tuple of degrees of freedom for all receivers is NP-hard when each receiver is equipped with at least three antennas. Interestingly, the same problem becomes polynomial time solvable when each transmit/receive node is equipped with no more than two antennas. Finally, we propose a distributed algorithm for transmit covariance matrix design, while assuming each receiver uses a linear MMSE beamformer. The simulation results show that the proposed algorithm outperforms the existing interference alignment algorithms in terms of system throughput

MIMO Precoding in Underlay Cognitive Radio Systems with Completely Unknown Primary CSI

This paper studies a novel underlay MIMO cognitive radio (CR) system, where the instantaneous or statistical channel state information (CSI) of the interfering channels to the primary receivers (PRs) is completely unknown to the CR. For the single underlay receiver scenario, we assume a minimum information rate must be guaranteed on the CR main channel whose CSI is known at the CR transmitter. We first show that low-rank CR interference is preferable for improving the throughput of the PRs compared with spreading less power over more transmit dimensions. Based on this observation, we then propose a rank minimization CR transmission strategy assuming a minimum information rate must be guaranteed on the CR main channel. We propose a simple solution referred to as frugal waterfilling (FWF) that uses the least amount of power required to achieve the rate constraint with a minimum-rank transmit covariance matrix. We also present two heuristic approaches that have been used in prior work to transform rank minimization problems into convex optimization problems. The proposed schemes are then generalized to an underlay MIMO CR downlink network with multiple receivers. Finally, a theoretical analysis of the interference temperature and leakage rate outage probabilities at the PR is presented for Rayleigh fading channels.We demonstrate that the direct FWF solution leads to higher PR throughput even though it has higher interference "temperature (IT) compared with the heuristic methods and classic waterfilling, which calls into question the use of IT as a metric for CR interference.Comment: 11 page

A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends

Multiple antennas have been exploited for spatial multiplexing and diversity transmission in a wide range of communication applications. However, most of the advances in the design of high speed wireless multiple-input multiple output (MIMO) systems are based on information-theoretic principles that demonstrate how to efficiently transmit signals conforming to Gaussian distribution. Although the Gaussian signal is capacity-achieving, signals conforming to discrete constellations are transmitted in practical communication systems. As a result, this paper is motivated to provide a comprehensive overview on MIMO transmission design with discrete input signals. We first summarize the existing fundamental results for MIMO systems with discrete input signals. Then, focusing on the basic point-to-point MIMO systems, we examine transmission schemes based on three most important criteria for communication systems: the mutual information driven designs, the mean square error driven designs, and the diversity driven designs. Particularly, a unified framework which designs low complexity transmission schemes applicable to massive MIMO systems in upcoming 5G wireless networks is provided in the first time. Moreover, adaptive transmission designs which switch among these criteria based on the channel conditions to formulate the best transmission strategy are discussed. Then, we provide a survey of the transmission designs with discrete input signals for multiuser MIMO scenarios, including MIMO uplink transmission, MIMO downlink transmission, MIMO interference channel, and MIMO wiretap channel. Additionally, we discuss the transmission designs with discrete input signals for other systems using MIMO technology. Finally, technical challenges which remain unresolved at the time of writing are summarized and the future trends of transmission designs with discrete input signals are addressed.Comment: 110 pages, 512 references, submit to Proceedings of the IEE