Kun-Yu Wang

Outage Constrained Robust Transmit Optimization for Multiuser MISO Downlinks: Tractable Approximations by Conic Optimization

In this paper, we study a probabilistically robust transmit optimization problem under imperfect channel state information (CSI) at the transmitter and under the multiuser multiple-input single-output (MISO) downlink scenario. The main issue is to keep the probability of each users achievable rate outage as caused by CSI uncertainties below a given threshold. As is well known, such rate outage constraints present a significant analytical and computational challenge. Indeed, they do not admit simple closed-form expressions and are unlikely to be efficiently computable in general. Assuming Gaussian CSI uncertainties, we first review a traditional robust optimization-based method for approximating the rate outage constraints, and then develop two novel approximation methods using probabilistic techniques. Interestingly, these three methods can be viewed as implementing different tractable analytic upper bounds on the tail probability of a complex Gaussian quadratic form, and they provide convex restrictions, or safe tractable approximations, of the original rate outage constraints. In particular, a feasible solution from any one of these methods will automatically satisfy the rate outage constraints, and all three methods involve convex conic programs that can be solved efficiently using off-the-shelf solvers. We then proceed to study the performance-complexity tradeoffs of these methods through computational complexity and comparative approximation performance analyses. Finally, simulation results are provided to benchmark the three convex restriction methods against the state of the art in the literature. The results show that all three methods offer significantly improved solution quality and much lower complexity.

Distributed Robust Multicell Coordinated Beamforming With Imperfect CSI: An ADMM Approach

Multicell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the intercell interference (ICI), has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method to obtain the worst-case robust beamforming solutions in a decentralized fashion with only local CSI used at each BS and limited backhaul information exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method for solving the nonconvex centralized problem, using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Then a distributed robust MCBF algorithm is further proposed, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution. We also extend the worst-case robust beamforming design as well as its decentralized implementation method to a fully coordinated scenario. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm.

Probabilistic SINR constrained robust transmit beamforming: A Bernstein-type inequality based conservative approach

Recently, robust transmit beamforming has drawn considerable attention because it can provide guaranteed receiver performance in the presence of channel state information (CSI) errors. Assuming complex Gaussian distributed CSI errors, this paper investigates the robust beamforming design problem that minimizes the transmission power subject to probabilistic signal-to-interference-plus-noise ratio (SINR) constraints. The probabilistic SINR constraints in general have no closed-form expression and are difficult to handle. Based on a Bernstein-type inequality for quadratic forms of complex Gaussian random variables, we propose a conservative formulation to the robust single-cell beamforming design problem. The semidefinite relaxation technique can be applied to efficiently handle the proposed conservative formulation. Simulation results show that, in comparison with existing methods, the proposed method is more power efficient and is able to support higher target SINR values for receivers.

Robust {MISO Transmit} Optimization under Outage-Based QoS Constraints in Two-Tier Heterogeneous Networks

To improve wireless heterogeneous network service via macrocell and femtocells that share certain spectral resources, {this paper studies} the transmit beamforming design for femtocell base station (FBS), {equipped with multiple antennas}, under an outage-based quality-of-service (QoS) constraint at the {single-antenna} femtocell user equipment characterized by its signal-to-interference-plus-noise ratio. {Specifically}, we {focus on} the practical case of {imperfect} downlink {multiple-input single-output (MISO)} channel state information (CSI) at the FBS due to limited CSI feedback or CSI estimation errors. By characterizing the CSI uncertainty probabilistically, we formulate an outage-based robust beamforming design. This nonconvex optimization problem can be relaxed into a convex semidefinite programming problem, which reduces to a power control problem when all CSI vectors are independent {and} identically distributed. We also investigate the performance gap between the optimal transmission strategy (that allows maximum transmission degrees of freedom (DoF) equal to the number of transmit antennas) and the proposed optimal beamforming design (with the DoF equal to one) and provide some feasibility conditions, followed by their performance evaluation and trade-off through simulation results.

Worst-Case SINR Constrained Robust Coordinated Beamforming for Multicell Wireless Systems

Multicell coordinated beamforming (MCBF) has been recognized as a promising approach to enhancing the system throughput and spectrum efficiency of wireless cellular systems. In contrast to the conventional single-cell beamforming (SBF) design, MCBF jointly optimizes the beamforming vectors of cooperative base stations (BSs) (via a central processing unit (CPU)) in order to mitigate the intercell interference. While most of the existing designs assume that the CPU has the perfect knowledge of the channel state information (CSI) of mobile stations (MSs), this paper takes into account the inevitable CSI errors at the CPU, and study the robust MCBF design problem. Specifically, we consider the worst-case robust design formulation that minimizes the weighted sum transmission power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on MSs. The associated optimization problem is challenging because it involves infinitely many nonconvex SINR constraints. In this paper, we show that the worst-case SINR constraints can be reformulated as linear matrix inequalities, and the approximation method known as semidefinite relation can be used to efficiently handle the worst-case robust MCBF problem. Simulation results show that the proposed robust MCBF design can provide guaranteed SINR performances for the MSs and outperforms the robust SBF design.

Chance-constrained robust beamforming for multi-cell coordinated downlink

This paper considers robust multi-cell coordinated beamforming (MCBF) design for downlink wireless systems, in the presence of channel state information (CSI) errors. By assuming that the CSI errors are complex Gaussian distributed, we formulate a chance-constrained robust MCBF design problem which guarantees that the mobile stations can achieve the desired signal-to-interference-plus-noise ratio (SINR) requirements with a high probability. A convex approximation method, based on semidefinite relaxation and tractable probability approximation formulations, is proposed. The goal is to solve the convex approximation formulation in a distributed manner, with only a small amount of information exchange between base stations. To this end, we develop a distributed implementation by applying a convex optimization method, called weighted variable-penalty alternating direction method of multipliers (WVP-ADMM), which is numerically more stable and can converge faster than the standard ADMM method. Simulation results are presented to examine the chance-constrained robust MCBF design and the proposed distributed implementation algorithm.

Optimal transmission strategy for outage rate maximization in MISO fading channels with training

In this paper, we consider a single-user multiple-input single-output (MISO) fading channel with training, and investigate optimal training and data transmission strategies for outage rate maximization. The receiver obtains instantaneous channel estimates through training; while the transmitter knows only the statistical information of the channel. We present analytical, closed-form solutions for the optimal training power and optimal data transmit covariance matrix. In particular, explicit numbers of antennas required for optimal data transmission are analyzed. Numerical results are presented to validate our analysis.

Energy-efficient precoding matrix design for relay-aided multiuser downlink networks

This paper considers the energy-efficient precoding matrix design for relay-aided multiuser downlink multiple-input single-output wireless systems. The precoders of the base station (BS) and the relay station (RS) are designed to maximize the transmit energy efficiency, defined as the ratio between the system sum rate and the total power consumption, under the quality-of-service constraints of the users and the transmit power constraints on the BS and the RS. In view of the fact that this precoder design problem is a nonconvex fractional programming, a successive Dinkelbach and convex approximation (SDCA) algorithm is proposed to handle this problem. Simulation results are provided to demonstrate the effectiveness of the proposed SDCA algorithm, and significant EE improvement as the number of antennas at the BS and the RS increases.

A Low-Complexity Algorithm for Worst-Case Utility Maximization in Multiuser MISO Downlink

This work considers worst-case utility maximization (WCUM) problem for a downlink wireless system where a multiantenna base station communicates with multiple single-antenna users. Specifically, we jointly design transmit covariance matrices for each user to robustly maximize the worst-case (i.e., minimum) system utility function under channel estimation errors bounded within a spherical region. This problem has been shown to be NP-hard, and so any algorithms for finding the optimal solution may suffer from prohibitively high complexity. In view of this, we seek an efficient and more accurate suboptimal solution for the WCUM problem. A low-complexity iterative WCUM algorithm is proposed for this nonconvex problem by solving two convex problems alternatively. We also show the convergence of the proposed algorithm, and prove its Pareto optimality to the WCUM problem. Some simulation results are presented to demonstrate its substantial performance gain and higher computational efficiency over existing algorithms.

Outage constrained transmission optimization for MISO two-tier femtocell networks

In this paper, we consider a two-tier heterogeneous network that locally consists of a multi-antenna macrocell base station and a multi-antenna femtocell base station (FBS) each serving separate single-antenna users. We investigate an optimal transmission strategy with maximum degree of freedom for transmit power minimization of the FBS under outage-based quality-of-service (QoS) constraints for the femtocell user equipment (FUE) and macrocell user equipment (MUE). Specifically, we examine the scenario that the FBS receives no instantaneous channel estimate from the FUE, and relies on only statistical information of downlink multiple-input single-output (MISO) channels. Although the outage constrained problem has no closed-form probabilistic constraints and may not be convex in general, we propose a transmission strategy and prove its optimality under a given condition. Our simulation results also demonstrate that the proposed transmission strategy can significantly save power compared to beamforming strategies.