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 investigate the coordinated multi-point noncoherent joint transmission (JT) in dense small cell networks. The goal is to design beamforming vectors for macro cell and small cell base stations (BSs) such that the weighted sum rate of the system is maximized, subject to a total transmit power at individual BSs. The optimization problem is inherently nonconvex and intractable, making it difficult to explore the full potential performance of the scheme. To this end, we first propose an algorithm to find a globally optimal solution based on the generic monotonic branch reduce and bound optimization framework. Then, for a more computationally efficient method, we adopt the inner approximation (InAp) technique to efficiently derive a locally optimal solution, which is numerically shown to achieve near-optimal performance. In addition, for decentralized networks such as those comprising of multi-access edge computing servers, we develop an algorithm based on the alternating direction method of multipliers, which distributively implements the InAp-based solution. Our main conclusion is that the noncoherent JT is a promising transmission scheme for dense small cell networks, since it can exploit the densitification gain, outperforms the coordinated beamforming, and is amenable to distributed implementation.

Beamforming design for downlink coordinated multi-point (CoMP) transmission of dense small cell networks is considered. The goal is to maximize the weighted sum rate of the system subject to constraints on maximum transmit power at macro cell and small cell base stations (BSs). Here we focus on the noncoherent joint transmission technique, since it does not require tight network synchronization, and thus is more practically appealing. The considered optimization problem is intractable, thus we adopt the inner approximation (IA) to efficiently derive a locally optimal solution. Then, we develop a distributed implementation of the proposed IA based algorithm, based on the alternating direction method of multipliers (ADMM). More explicitly, in the distributed algorithm, the convex approximate subproblems obtained by the IA principles are solved by the ADMM procedure. As the result, the beamforming vectors are computed locally at the BSs. Numerical results are provided to confirm the validity of the proposed algorithms.

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 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.

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.

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.

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 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 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.

This paper studies the fairness of achievable energy efficiency (EE) in a multicell multiuser multiple-input single-output downlink. The objective is to maximize the minimum EE among all base stations (BSs) subject to per-BS power constraints. The resulting optimization problem is a max-min fractional program, and, thus, difficult to solve in general. Our goal is to develop a decentralized algorithm for the max-min EE problem which solves the problem locally. The idea behind the proposed method is to combine the framework of successive convex approximation (SCA) and alternative direction method of multipliers (ADMM). We transform the convex program obtained at each step of the SCA procedure into a form that lends itself to the ADMM. The resulting formulation is solved optimally by allowing the BSs to exchange the required information until the ADMM converges. In addition to further reduce the backhaul overhead, the proposed algorithm is modified to enhance the convergence speed. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.

We consider small-cell networks with multiple-antenna transceivers and base stations (BSs) cooperating to jointly design linear precoders to maximize the network energy efficiency, subject to a sum power and per-antenna power constraints at individual BSs, as well as user-specific quality of service (QoS) requirements. Assuming zero-forcing precoding, we formulate the problem of interest as a concave-convex fractional program to which we proposed a centralized optimal solution based on the prevailing Dinkelbach algorithm. To facilitate distributed implementations, we transform the design problem into an equivalent convex program using Charnes-Cooper's transformation. Then, based on the framework of alternative direction method of multipliers (ADMM), we develop a decentralized algorithm, which is numerically shown to achieve fast convergence. Since BSs are generally power-hungry, it may be more energy-efficient if some BSs can be shut down, while still satisfying the QoS constraints. Toward this end, we investigate the problem of joint precoder design and BS selection, which is a mixed Boolean nonlinear program, and then provide an optimal solution by customizing the branch-and-bound method. For real-time applications, we propose a greedy algorithm which achieves near-optimal performance in polynomial time. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.

A joint power splitting and beamforming design for multiuser multiple-input single-output (MISO) systems where receivers have capability of decoding information and harvesting energy simultaneously from received signals is considered. The objective is to maximize the ratio of the achieved utility to the total power consumption subject to harvested power requirements and power budget at a base station (BS). The utility function of interest combines the sum rate and the total harvested power. The design problem is nonconvex, and thus, global optimality is difficult to achieve. To solve this problem locally we first convert the problem into a more tractable form, and then propose an iterative algorithm which is guaranteed to achieve a Karush-Kuhn-Tucker solution. Numerical results are provided to demonstrate the superior performance of the proposed method.

This paper studies the problem of resource allocation for uplink multi-homing users in heterogeneous network where users can simultaneously transmit data to multiple radio access networks (RANs). The considered design problem is to optimally assign bandwidth and power to each user-RAN connection so as to maximize the overall energy efficiency of the network subject to QoS requirements and resource budgets. By the definition of energy efficiency which is the ratio of the aggregate throughput to the power consumption, the resulting problem is formulated as a fractional program. Then, we propose an energy efficient algorithm using the Dinkelback method that solves a series of convex problems to obtain the optimal design. Particularly, we derive closed-form expressions for the design parameters and provide useful insights into the proposed energy efficient resource allocation algorithm. Numerical results are presented to demonstrate that the proposed algorithm is superior to other resource allocation strategies in terms of energy efficiency.