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We consider downlink transmission whereby a multiantenna base station simultaneously transmits data to multiple single-antenna users. We focus on slow flat fading channel where the channel state information is imperfect, the channel estimation error is unbounded and its statistics are known. The aim is to design beamforming vectors such that the sum rate is maximized under the constraints on probability of successful transmission for each user and maximum transmit power. The optimization problem is intractable due to the chance constraints. To this end, we propose an efficient solution drawn upon stochastic optimization. In particular, we first use the step function and its smooth approximation to get an approximate nonconvex stochastic program of the considered problem. We then develop an iterative procedure to solve the stochastic program based on the stochastic successive convex approximation framework. The numerical results show that the proposed solution can achieve remarkable sum rate gains compared to the conventional one.

We consider uplink multiuser wireless communications systems, where the base station (BS) receiver is equipped with a large-scale antenna array and resolution adaptive analog-to-digital converters (ADCs). The aim is to maximize the energy efficiency (EE) at the BS subject to constraints on the users’ quality-of-service. The approach is to jointly optimize both the number of quantization bits at the ADCs and the on/off modes of the radio frequency (RF) processing chains. The considered problem is a discrete nonlinear program, the optimal solution of which is difficult to find. We develop an efficient algorithm based on the discrete branch-reduce-and-bound (DBRnB) framework. It finds the globally optimal solutions to the problem. In particular, we make some modifications, which significantly improve the convergence performance. The numerical results demonstrate that optimizing jointly the number of quantization bits and on/off mode can achieve remarkable EE gains compared to only optimizing the number of quantization bits.

We consider a secure transmission including a transmitter, a receiver and an eavesdropper, each being equipped with multiple antennas. The aim is to develop a low-complexity and scalable method to find a globally optimal solution to the problem of secrecy rate maximization under a total power constraint at the transmitter. In principle, the original formulation of the problem is nonconvex. However, it can be equivalently translated into finding a saddle point of a minimax convex-concave program. An existing approach finds the saddle point using the Newton method, whose computational cost increases quickly with the number of transmit antennas, making it unsuitable for large scale antenna systems. To this end, we propose an iterative algorithm based on alternating optimization, which is guaranteed to converge to a saddle point, and thus achieves a globally optimal solution to the considered problem. In particular, each subproblem of the proposed iterative method admits a closed-form solution. We analytically show that the iteration cost of our proposed method is much cheaper than that of the known solution. As a result, numerical results demonstrate that the proposed method remarkably outperforms the existing one in terms of the overall run time.

We proposed several energy-efficient resource allocation algorithms for the downlink of an orthogonal frequency-division-multiple-access (OFDMA) based femtocell heterogeneous networks (HetNets). Heterogeneous QoS and fairness in rate are investigated in the proposed resource allocation problem. A dense deployment of femtocells in the coverage area of a central macrocell is considered and energy usage of both femtocell and macrocell users are optimized simultaneously. We aim to maximize the weighted sum of the individual energy efficiencies (WSEEMax) and the network energy efficiency (NEEMax) while satisfying the following: (1) minimum throughput for delay-sensitive (DS) users, (2) fairness constraint for delay-tolerant (DT) users, (3) required constraints of OFDMA systems. The problem is formulated in three different forms: mixed 0—1 integer programming formulation, time-sharing formulation and sparsity-inducing formulation. The proposed resource block (RB) and power optimization problems are combinatorial and highly non-convex due to the fractional form of the objective function, the integer constraint of OFDMA RBs and non-affine fairness. We adopt the successive convex approximation (SCA) approach and transform the problems into a sequence of convex subproblems. With the proposed algorithms, we show that the overall joint RB and power allocation schemes converge to suboptimal solutions. Numerical examples confirm the merits of the proposed algorithms.

We consider downlink transmission of a fronthaul-constrained cloud radio access network. Our aim is to maximize the system sum data rate via jointly designing beamforming and user association. The problem is basically a mixed integer non-convex programs for which a global solution requires a prohibitively high computational effort. The focus is thus on efficient solutions capable of achieving the near optimal performance with low complexity. To this end, we transform the design problem into continuous programs by two approaches: penalty and sparse approximation methods. The resulting continuous nonconvex problems are then solved by the successive convex approximation framework. Numerical results indicate that the proposed methods are near-optimal, and outperform existing suboptimal methods in terms of achieved performances and computational complexity.

We consider a multi-pair amplify-and-forward relay network where the energy-constrained relays adopting the time-switching protocol harvest energy from the radio-frequency signals transmitted by the users for assisting user data transmission. Both one-way and two-way relaying techniques are investigated. Aiming at energy efficiency (EE) fairness among the user pairs, we construct an energy consumption model incorporating rate-dependent signal processing power, the dependence on output power level of power amplifiers’ efficiency, and nonlinear energy harvesting (EH) circuits. Then, we formulate the max-min EE fairness problems in which the data rates, users’ transmit power, relays’ processing coefficient, and EH time are jointly optimized under the constraints on the quality of service and users’ maximum transmit power. To achieve efficient suboptimal solutions to these nonconvex problems, we devise monotonic descent algorithms based on the inner approximation (IA) framework, which solve a second-order-cone program in each iteration. To further simplify the designs, we propose an approach combining IA and zero-forcing beamforming, which eliminates inter-pair interference and reduces the numbers of variables and required iterations. Finally, extensive numerical results are presented to validate the proposed approaches. More specifically, the results demonstrate that ignoring the realistic aspects of power consumption might degrade the performance remarkably, and jointly designing parameters involved could significantly enhance the EE.

We study downlink of multiantenna cloud radio access networks with finite-capacity fronthaul links. The aim is to propose joint designs of beamforming and remote radio head (RRH)-user association, subject to constraints on users’ quality-of-service, limited capacity of fronthaul links and transmit power, to maximize the system energy efficiency. To cope with the limited-capacity fronthaul we consider the problem of RRH-user association to select a subset of users that can be served by each RRH. Moreover, different to the conventional power consumption models, we take into account the dependence of the baseband signal processing power on the data rate, as well as the dynamics of the efficiency of power amplifiers. The considered problem leads to a mixed binary integer program which is difficult to solve. Our first contribution is to derive a globally optimal solution for the considered problem by customizing a discrete branch-reduce-and-bound approach. Since the global optimization method requires a high computational effort, we further propose two suboptimal solutions able to achieve the near optimal performance but with much reduced complexity. To this end, we transform the design problem into continuous (but inherently nonconvex) programs by two approaches: penalty and ℓ0 -approximation methods. These resulting continuous nonconvex problems are then solved by the successive convex approximation framework. Numerical results are provided to evaluate the effectiveness of the proposed approaches.

We consider a cooperative non-orthogonal multiple access system with radio frequency energy harvesting, in which a user with good channel harvests energy from its received signal and serves as a decode-and-forward relay for enhancing the performance of a user with poor channel. We here aim at maximizing the weighted sum rate of the system by optimizing the power allocation coefficient used at the source and the power splitting coefficient used at the user with good channel. By exploiting the specific structure of the considered problem, we propose a low-complexity one-dimensional search algorithm, which can provide optimal solution to the problem. As a benchmark comparison, we derive analytic expressions and simple high signal-to-noise ratio (SNR) approximations of the ergodic rates achieved at the two users and their weighted sum with fixed values of the power allocation and the power splitting coefficients, from which the scaling of the weighted sum in the high SNR region is revealed. Finally, we provide representative numerical results to demonstrate the validity of our results.

We consider downlink transmission in cloud radio access networks with multiple cochannel multicasting groups served by a group of remote radio heads (RRHs), which receive information from a base band unit via finite-capacity fronthaul links. Our aim is to jointly design RRH selection and beamforming vectors such that the minimum weighted data rate among users is maximized under the constraints of maximum transmit power and fronthaul capacity at each specific RRH. The problem is intractable due to the numerical difficulties of combination and nonconvex functions. Based on a semidefinite relaxation technique, bisection search, and a branch-and-bound method, we develop an upper bound, which is also the optimal solution to the original problem if the relaxation is tight. More importantly, we propose a heuristic low-complexity iterative procedure for practical applications based on the state-of-the-art sequential convex approximation. Subsequently, we modify the proposed methods for the uncertain channel state information case. To be specific, the upper bound and its suboptimal solution are altered based on the S-lemma while the low-complexity algorithm is tailored by using two different approximations of intractable robust counterpart. The validity of the proposed methods in the region of limited fronthaul capacity is confirmed by numerical results.

A joint beamforming and remote radio head (RRH)-user association design for downlink of cloud radio access networks (CRANs) is considered. The aim is to maximize the system energy efficiency subject to constraints on users’ quality-of-service, capacity of front haul links and transmit power. Different to the conventional power consumption models, we embrace the dependence of baseband signal processing power on the data rate, and the dynamics of the power amplifiers’ efficiency. The considered problem is a mixed Boolean nonconvex program whose optimal solution is difficult to find. As our main contribution, we provide a discrete branch-reduce-and-bound (DBRnB) approach to solve the problem globally. We also make some modifications to the standard DBRnB procedure. Those remarkably improve the convergence performance. Numerical results are provided to confirm the validity of the proposed method.

This paper considers a downlink transmission of cloud radio access network (C-RAN) in which precoded baseband signals at a common baseband unit are compressed before being forwarded to radio units (RUs) through limited fronthaul capacity links. We investigate the joint design of precoding, multivariate compression and RU-user selection which maximizes the energy efficiency of downlink C-RAN networks. The considered problem is inherently a rank-constrained mixed Boolean nonconvex program for which a globally optimal solution is difficult and computationally expensive to find. In order to derive practically appealing solutions, we invoke some useful relaxation and transformation techniques to arrive at a more tractable (but still nonconvex) continuous program. To solve the relaxation problem, we propose an iterative procedure based on DC algorithms which is provably convergent. Numerical results demonstrate the superior of the proposed solution in terms of achievable energy efficiency compared to existing schemes.

This paper considers a multicell downlink channel in which multiple base stations (BSs) cooperatively serve users by jointly precoding shared data transported from a central processor over limited-capacity backhaul links. We jointly design the beamformers and BS-user link selection so as to maximize the sum rate subject to user-specific signal-to-interference-noise (SINR) requirements, per-BS backhaul capacity and per-BS power constraints. As existing solutions for the considered problem are suboptimal and their optimality remains unknown due to the lack of globally optimal solutions, we characterized this gap by proposing an globally optimal algorithm for the problem of interest. Specifically, the proposed method is customized from a generic framework of a branch and bound algorithm applied to discrete monotonic optimization. We show that the proposed algorithm converges after a finite number of iterations, and can serve as a benchmark for existing suboptimal solutions and those that will be developed for similar contexts in the future. In this regard, we numerically compare the proposed optimal solution to a current state-of-the-art, which show that this suboptimal method only attains 70% to 90% of the optimal performance.

This paper aims at guaranteeing the achievable energy efficiency (EE) fairness in a multicell multiuser multiple-input single-output downlink system. The design objective is to maximize the minimum EE among all base stations (BSs) subject to per-BS power constraints. This results in a max-min fractional program and as such is difficult to solve in general. Our goal is to develop decentralized algorithms for the max-min EE problem based on combining the successive convex approximation (SCA) framework and the alternating direction method of multipliers (ADMMs). Specifically, leveraging the SCA principle, we iteratively approximate the nonconvex design problem by a sequence of convex programs for which two decentralized algorithms are then proposed. In the first approach, the convex program obtained at each step of the SCA procedure is solved optimally by allowing the BSs to exchange the required information until the ADMM converges. The convergence of the first method is analytically guaranteed but the amount of backhaul signaling can be noticeable in some realistic settings. To reduce the backhaul overhead, the second method performs an abstract version of the ADMM where only one variables update is carried out. Numerical results are provided to demonstrate the effectiveness of the two proposed decentralized algorithms.

We consider multicell downlink transmission where multi-antenna base stations (BSs) collaborate in transferring data to multiple cochannel multicast groups. Our aim is to design a joint transmitter selection and cooperative precoding scheme which maximizes the minimum received data rate among all receivers under constraints on the individual BS transmit power budgets as well as backhaul link capacity. The problem is naturally cast as a mixed Boolean nonconvex program whose global optimal solution is difficult to achieve. To solve this problem locally, we first use difference-convex (DC) functions to represent the Boolean variables, and further transform the problem into an equivalent but more tractable formulation. We then propose an iterative algorithm which provably converges to stationary solutions. Numerical results are provided to demonstrate the superior performance of the proposed method.

We investigate the fairness of achievable energy efficiency in a multicell multiuser multiple-input single-output (MISO) downlink system, where a beamforming scheme is designed to maximize the minimum energy efficiency among all base stations. The resulting optimization problem is a nonconvex max-min fractional program, which is generally difficult to solve optimally. We propose an iterative beamformer design based on an inner approximation algorithm which aims at locating a Karush-Kuhn-Tucker solution to the nonconvex program. By novel transformations, we arrive at a convex problem at each iteration of the proposed algorithm, which is amendable for being approximated by a second order cone program. The numerical results demonstrate that the proposed algorithm outperforms the existing schemes in terms of the convergence rate and processing time.