Multiple-input Single-output Interference Channel Research Articles

Distributed Beamforming and Power Allocation for Heterogeneous Networks with MISO Interference Channel.

To address the limitations of centralized resource allocation, i.e., high computational complexity and signaling overhead, a distributed beamforming and power allocation strategy is proposed for heterogeneous networks with multiple-input-single-output (MISO) interference channels. In the proposed scheme, each secondary user transceiver pair (SU TP) determines the beamforming vector and transmits power to maximize its own spectral efficiency (SE) while keeping the interference to the primary user below a predetermined threshold, and such resource management for each SU TP is updated iteratively without any information sharing until the strategies for all SU TPs converge. The simulation confirms that the proposed scheme can achieve a performance comparable to that of a centralized approach with a much lower computation time, e.g., less than 5% degradation in SE while improving computation time by more than 10 times.

Achievable Rate Region of MISO Interference Channel Aided by Intelligent Reflecting Surface

This paper investigates the achievable rate region of the multiple-input single-output (MISO) interference channel aided by intelligent reflecting surfaces (IRSs). We exploit the additional design degree of freedom provided by the coordinated IRSs to enhance the desired signal and suppress interference so as to enlarge the achievable rate region of the interference channel. To this end, we jointly optimize the active transmit beamforming at the transmitters and passive reflective beamforming at the IRSs, subject to the constant modulus constraints of reflective beamforming vectors. To address the non-convex optimization problem, we propose an iterative algorithm to optimize the transmit beamforming via second-order cone program (SOCP) and the reflective beamforming via the semi-definite relaxation (SDR). Numerical results demonstrate that the performance of the IRS-aided interference channel with the proposed algorithm can significantly outperform the conventional interference channel without IRS.

Optimizing Efficient Energy Transmission on a SWIPT Interference Channel Under Linear/Nonlinear EH Models

In this paper, we consider simultaneous wireless information and power transfer (SWIPT) in a multiple-input single-output interference channel (IC) system where the power-splitting (PS) receivers utilize linear/nonlinear energy-harvesting (EH) models. The functions that express the relationship between the input radio frequency power and the output direct current harvested energy of the EH circuits are usually assumed to be linear in recent SWIPT works, while the nonlinear function is suitable for practical data. In a SWIPT IC system, two important targets are sum harvested energy maximization and harvested energy efficiency maximization at the PS receiver, and they are investigated under linear/nonlinear EH models. Thus, some nonconvex resource allocation problems with the two targets and linear/nonlinear EH models are formulated to jointly optimize beamforming vectors at the transmitters and the PS ratios at the receivers. By exploiting a successive convex approximation method and a semidefinite relaxation (SDR) technique, iterative algorithms are proposed to obtain local optimal solutions. Interestingly, the optimal solution to the subproblem is proven to satisfy the rank-1 constraint of the SDR technique. Finally, numerical experiments illustrate effective performance from the proposed solutions, in comparison with some special schemes.

On the Two-User MISO Interference Channel With Single-User Decoding: Impact of Imperfect CSIT and Channel Dimension Reduction

This paper examines the Rayleigh fading multiple-input single-output interference channel with single-user decoding and limited channel state information (CSI) feedback. Its contribution is twofold. First, the achievable rate-region with imperfect CSI at the transmitters due to channel quantization errors is analyzed for the two-user case. An analytically tractable inner bound on that region is derived, which provides insights into the problem. Similarly to the case of perfect CSI at the transmitters, it can be shown that beamforming constitutes an optimal strategy for achieving the boundary points of the inner bound. Second, we present a novel CSI feedback scheme that reduces the cross-link CSI feedback overhead, and enhances throughput for any rate-limited feedback scheme. This feedback reduction is crucial when control channels for sharing information between transmitters and unintended receivers are rate limited. A distinguishing feature of the proposed scheme is that feedback is taken into account already at the channel estimation stage. While maintaining a high array gain in the direct channel towards the intended user, the scheme induces an effective low-dimensional cross-link channel, which can be quantized more accurately than the full-dimensional channel. This eventually leads to enhanced performance while maintaining a low CSI feedback overhead. Finally, the proposed feedback scheme is extended to the case of $N>2$ users and shown to provide a significant reduction in CSI feedback overhead in a practically oriented setting.

Linear Algebraic Beamforming Design for Multiuser MISO Interference Channels: A Reduction in Search Space Dimension.

Near-optimal transmit beamformers are designed for multiuser multiple-input single-output interference channels with slowly time-varying block fading. The main contribution of this article is to provide a method for deriving closed-form solutions to effective beamforming in both low and high signal-to-noise ratio regimes. The proposed method basically leverages side information obtained from the channel correlation between adjacent coding blocks. More specifically, our methodology is based on a linear algebraic approach, which is more efficient than the optimal scheme based on the Gaussian input in the sense of reducing the average number of search space dimensions for designing the near-optimal transmit beamformers. The proposed method is shown to exhibit near-optimal performance via computer simulations in terms of the average sum-rate.

Transceiver Design of Optimum Wirelessly Powered Full-Duplex MIMO IoT Devices

In this paper, we investigate the energy harvesting (EH) technique and accordingly design transceivers for a K link multiple-input multiple-output interference channel. Each link consists of two full-duplex (FD) Internet of Things (IoT) nodes exchanging information simultaneously in a bi-directional communication channel. All the nodes suffer from interference, in particular strong self-interference and inter-node interference, due to operating in FD mode and simultaneous transmission at each link, respectively. Further, we divide the received signal at each node into two parts. While one part of the signal is used for information decoding, the other part is used for EH. We jointly design the transmit and receive beamforming vectors and receiver power splitting ratios by minimizing the total transmission power of the system, subject to both signal-to-interference-plus-noise ratio and EH threshold constraints. Furthermore, the case of multiple-input single-output interference channel is also included for the sake of comparison. We also revisit the above problems for the case when the available channel state information (CSI) at the transmitters is imperfect, where the errors of the CSI are assumed to be norm bounded. Simulation results show that the EH technique can harvest enough energy to support power consumption limited IoT devices by aiding in recharging their respective batteries.

Decentralized Robust Transceiver Designs for MISO SWIPT Interference Channel

This paper considers a $K$ -user multiple-input single-output interference channel for simultaneous wireless information and power transfer, where each multi-antenna transmitter serves a single-antenna receiver per user pair. All receivers perform simultaneously information processing and energy harvesting (EH) based on the receive power-splitting (PS) architectures. Assuming imperfect channel state information (CSI) at the transmitters, we develop a near-optimal robust transceiver design scheme that minimizes the total transmission power under the worst-case signal-to-interference-plus-noise ratio (SINR) and EH constraints at the receivers, by jointly optimizing transmit beamforming and receive PS ratio per receiver. When the CSI uncertainties are bounded by ellipsoidal regions, it is shown that the worst-case SINR and EH constraints per receiver can be recast into quadratic matrix inequality forms. Leveraging semidefinite relaxation technique, the intended robust beamforming and PS (BFPS) problem can be relaxed as a tractable (centralized) semidefinite program. More importantly, relying on the state-of-the-art alternating direction method of multipliers in convex optimization, we propose a decentralized algorithm capable of computing the robust BFPS scheme with local CSI and limited information exchange among the transmitters. It is shown that the proposed decentralized algorithm is guaranteed to converge to the centralized solution. Numerical results are provided to demonstrate the merits of the proposed approaches.

Optimality Properties, Closed-Form Parameterizations and Distributed Strategy of the Two-User MISO Interference Channel

In this paper, the closed-form parameterizations to the Pareto boundary for the two-user multiple-input single-output interference channel are studied. Firstly, for the equivalent channel model with each transmitter having only two antennas, the weighted sum-rate maximization (WSRMax) problem is reformulated with newly defined angle variables. Then, a centralized weighted leakage-plus-noise-to-signal ratio minimization (WLNSRMin) algorithm is proposed to find a locally optimal weighted sum-rate point. Each step of the algorithm is solved by evaluating closed-form expressions. A distributed algorithm is also given to avoid the exchange of the channel state information (CSI) between transmitters. Numerical results show that the centralized WLNSRMin algorithm converges to a local optimum of the WSRMax problem after a few iterations and the distributed algorithm achieves a performance very close to that of the centralized algorithm with only local CSI.

Robust Beamforming Design for Secure Multiuser MISO Interference Channel

In this letter, we investigate the secure beamforming design for multiuser multiple-input single-output interference channel with an eavesdropper. The robust secrecy rate optimization problem is studied with the imperfect channel state information. We consider the beamforming design to maximize the minimum worst case secrecy rate subject to the transmit power constraints with norm-bounded channel uncertainty. The problem is non-convex and hard to solve. We propose an effective method to reformulate this non-convex problem as a series of tractable convex program problems with linear matrix inequality and second-order cone constraints by exploiting the conservative approximation and the sequential convex approximation methods. The simulation results demonstrate the effectiveness of the proposed algorithm.

Linear Degrees of Freedom for $K$ -user MISO Interference Channels With Blind Interference Alignment

In this paper, we characterize the degrees of freedom (DoF) for $K$ -user $M \times 1$ multiple-input single-output interference channels with reconfigurable antennas, which have $N$ -preset modes at the receivers, assuming linear coding strategies in the absence of channel state information at the transmitters, i.e., blind interference alignment. Our linear DoF converse builds on the lemma that if a set of transmit symbols is aligned at their common unintended receivers, those symbols must have independent signal subspace at their corresponding receivers. This lemma arises from the inherent feature that channel state’s changing patterns of the links towards the same receiver are always identical, assuming that the coherence time of the channel is long enough. We derive an upper bound for the linear sum DoF, and propose an achievable scheme that exactly achieves the linear sum DoF upper bound when both of the ${n^{*}}/{M}=R_{1}$ and ${MK}/{n^{*}}=R_{2}$ are integers, where $n^{*}$ denotes the optimal number of preset modes out of $N$ preset modes. For the other cases, where either $R_{1}$ or $R_{2}$ is not an integer, we only give some guidelines how the interfering signals are aligned at the receivers to achieve the upper bound. As an extension, we also show the linear sum DoF upper bound for downlink/uplink cellular networks.

A MIMO Relay With Delayed Feedback Can Improve DoF in $K$- User MISO Interference Channel With No CSIT

This paper studies the impact of a multiple-input-multiple-output (MIMO) relay on the K-user multiple-input-single-output (MISO) interference channel (IC) when the relay has delayed feedback (i.e., delayed channel state information (CSI) or delayed channel output feedback) from each receiver, yet each transmitter has no knowledge about CSI. We first develop a new relay-aided retrospective interference alignment (r-RIA) and characterize the optimal sum degrees of freedom (DoFs) for the K-user MISO IC with a MIMO relay by providing a new matching outer bound. It is shown that the sum DoF does not decrease, even in the absence of direct links between transmitters and receivers, as long as K is sufficiently large. We next show that a MIMO relay can provide a sum-DoF gain in the K-user MISO IC with delayed feedback to the relay in the absence of CSI at transmitter (CSIT), whereas relaying is shown to be not useful with instantaneous CSIT from the DoF perspective.

Distributed energy efficiency beamforming design in multiple‐input‐single‐output interference channels

Coordinated beamforming designs based on energy efficiency of multiple-user interference channels have attracted much attention. The optimisation problem has a fractional form, and is coupled among users, which makes it difficult to be solved directly. A beamforming design for energy-efficient communication in multiple-input–single-output interference channels is studied, and proposes an efficient distributed approach to solve it. A novel method is developed to transform the optimisation problem into a DC (difference of two convex/concave functions) structure. The transformed optimisation problem is approximated by using a separable structure across the users, and this approximated version is solved iteratively. Numerical results show the effectiveness of the authors’ proposed algorithm.

Robust Beamforming for Simultaneous Wireless Information and Power Transfer in MISO Interference Channels

Taking the channel uncertainty into account, we investigate the robust beamforming design for simultaneous wireless information and power transfer in multiple-input single-output interference channels, where multiple multi-antenna transmitters communicate with their targeted single-antenna receivers and simultaneously interfere with all other receivers. Under quality-of-service and energy harvesting constraints at the receivers which adopt power splitting scheme, we aim to minimize the total transmit power at the transmitters when the channel uncertainty is modeled as the norm-bounded. The robust optimization is non-convex and the global optimal solution is challenging. With the help of the extension of the S-Procedure and rank-one relaxation, the robust beamforming is transformed into a semidefinite programming . We develop an novel method to recover a rank-one feasible and locally optimal solution, which is based on difference of convex programming and sequential parametric convex approximation method. Simulations show that our proposed algorithm outperforms the well-known Gaussian randomization method and has much lower computational complexity.

Robust beamforming based on transmit power analysis for multiuser multiple‐input–single‐output interference channels with energy harvesting

In this study, the authors study the robust transmit beamforming and receive power splitting design for simultaneous wireless information and power transfer in multiuser multiple-input–single-output interference channel with imperfect channel-state information at the transmitter. Following the worst-case model, they minimise the average total transmit power subject to a set of energy harvesting constraints and signal-to-interference-and-noise ratio constraints. On the basis of the Lagrangian multiplier method, they propose a robust design method based on tight bounds that is able to achieve an approximate optimum. To reduce the complexity, they transform this original problem into a relaxed semi-definite programming problem based on loose bounds, which can be solved efficiently. It is shown from simulation results that their proposed methods outperform the non-robust scheme.

Sum-Rate Maximization Schemes for <inline-formula> <tex-math notation="LaTeX">$K$</tex-math></inline-formula>-User MISO Interference Channels With a Cognitive Relay

In this paper, we consider $K$ -user multiple-input single-output interference channels with a cognitive relay. Assuming that data of all transmitters and channel state information are known at the cognitive relay, we design a linear precoder for the cognitive relay with the aim of maximizing the sum-rate without changing the transmitter operations at all transmitters. We first define the receiver set as a set which contains a part of the receivers, and then introduce a performance metric called “partial signal-to-interference-plus-noise ratio” (PSINR) based on the receiver set. Then, we can obtain a precoder at the cognitive relay by solving the PSINR maximization problem. The optimal receiver set which yields the maximum sum-rate can be identified by checking all possible receiver sets. Since this exhaustive search has prohibitive complexity, we develop a low complexity set search method by utilizing the properties of the optimal receiver set. Combining the PSINR maximization problem and the low complexity search method, we finally propose a precoder design scheme for the sum-rate maximization. Numerical simulation results confirm that the proposed scheme shows performance close to the projected gradient method with much reduced complexity.

Optimal Beamforming Designs for Wireless Information and Power Transfer in MISO Interference Channels

This paper investigates the optimal transmit beamforming designs for simultaneous wireless information and power transfer (SWIPT) in multiple-input single-output interference channels (IFC). Based on cooperation level among transmitters and receivsers, we classify the SWIPT IFC systems into two categories. First, we consider the IFC with partial cooperation , where only channel state information (CSI) is available at transmitters and receivers, but not the signal waveform. Second, we examine the IFC with signal cooperation , where both the CSI and the signal waveforms are known to transmitters and receivers. Then, for the both scenarios, we identify the Pareto boundary of the achievable rate-energy (R-E) region which characterizes the optimal tradeoff between the information rate and the harvested energy. To this end, the problems for maximizing the information rate are formulated with minimum required harvested energy constraint. To solve these non-convex problems, we introduce parameterization techniques for characterizing the R-E region. As a result, the original problem is separated into two subproblems, for which closed-form solutions are obtained by addressing the line search method. Finally, we provide numerical examples for the Pareto boundary of the R-E region through simulations.

Multicell Coordinated Beamforming With Rate Outage Constraint—Part I: Complexity Analysis

This paper studies the coordinated beamforming (CoBF) design in the multiple-input single-output interference channel, assuming only channel distribution information given a priori at the transmitters. The CoBF design is formulated as an optimization problem that maximizes a predefined system utility, e.g., the weighted sum rate or the weighted max-min-fairness (MMF) rate, subject to constraints on the individual probability of rate outage and power budget. While the problem is non-convex and appears difficult to handle due to the intricate outage probability constraints, so far it is still unknown if this outage constrained problem is computationally tractable. To answer this, we conduct a computational complexity analysis of the outage constrained CoBF problem. Specifically, we show that the outage constrained CoBF problem with the weighted sum rate utility is intrinsically difficult, i.e., NP-hard. Moreover, the outage constrained CoBF problem with the weighted MMF rate utility is also NP-hard except the case when all the transmitters are equipped with single antenna. The presented analysis results confirm that efficient approximation methods are indispensable to the outage constrained CoBF problem.

Multicell Coordinated Beamforming With Rate Outage Constraint—Part II: Efficient Approximation Algorithms

This paper studies the coordinated beamforming (CoBF) design for the multiple-input single-output interference channel, provided that only channel distribution information is known to the transmitters. The problem under consideration is a probabilistically constrained optimization problem which maximizes a predefined system utility subject to constraints on rate outage probability and power budget of each transmitter. Our recent analysis has shown that the outage-constrained CoBF problem is intricately difficult, e.g., NP-hard. Therefore, the focus of this paper is on suboptimal but computationally efficient algorithms. Specifically, by leveraging on the block successive upper bound minimization (BSUM) method in optimization, we propose a Gauss-Seidel type algorithm, called distributed BSUM algorithm, which can handle differentiable, monotone and concave system utilities. By exploiting a weighted minimum mean-square error (WMMSE) reformulation, we further propose a Jocobi-type algorithm, called distributed WMMSE algorithm, which can optimize the weighted sum rate utility in a fully parallel manner. Both algorithms are shown to converge to the stationary points of the original NP-hard problems. To further provide a performance benchmark, a relaxed approximation method based on polyblock outer approximation is also proposed. Simulation results show that the proposed algorithms are significantly superior to the existing successive convex approximation method in both performance and computational efficiency, and can yield promising approximation performance by comparing with the performance benchmark.

Robust Transceiver Design for MISO Interference Channel With Energy Harvesting

In this paper, we consider multiuser multiple-input single-output (MISO) interference channel where the received signal is divided into two parts for information decoding and energy harvesting (EH), respectively. The transmit beamforming vectors and receive power splitting (PS) ratios are jointly designed in order to minimize the total transmission power subject to both signal-to-interference-plus-noise ratio (SINR) and EH constraints. Most joint beamforming and power splitting (JBPS) designs assume that perfect channel state information (CSI) is available; however CSI errors are inevitable in practice. To overcome this limitation, we study the robust JBPS design problem assuming a norm-bounded error (NBE) model for the CSI. Three different solution approaches are proposed for the robust JBPS problem, each one leading to a different computational algorithm. Firstly, an efficient semidefinite relaxation (SDR)-based approach is presented to solve the highly non-convex JBPS problem, where the latter can be formulated as a semidefinite programming (SDP) problem. A rank-one recovery method is provided to recover a robust feasible solution to the original problem. Secondly, based on second order cone programming (SOCP) relaxation, we propose a low complexity approach with the aid of a closed-form robust solution recovery method. Thirdly, a new iterative method is also provided which can achieve near-optimal performance when the SDR-based algorithm results in a higher-rank solution. We prove that this iterative algorithm monotonically converges to a Karush-Kuhn-Tucker (KKT) solution of the robust JBPS problem. Finally, simulation results are presented to validate the robustness and efficiency of the proposed algorithms.

On the Effect of Different Grips of Handsets on Data Rate in the Measured Channels

The investigation on the achieved data rate of the cellular system considering different grips of handsets at different frequencies using measurement results of the measurement campaign—which was carried out in the city of Aalborg—is presented in this paper. The achieved data rate of the multiple-input single-output (MISO) interference channel is investigated. A typical propagation environment using two BSs and four handsets, like smart phones, held by four to eight different users was designed and multiple-input multiple-output (MIMO) channels in different scenarios were measured. In this paper, two BSs and two handsets at each measurement time are considered. The impact of the different parameters like correlation, different grips of handsets, and different long term evolution (LTE) frequency bands on the achieved data rate is investigated for different measurements. It could be concluded that the variations in the values of data rate are weakly associated with the different grips of handsets but more correlated with different frequencies.