Abstract-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.Index Terms-Energy efficiency, max-min fractional programming, inner approximation algorithm.

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This paper aims at guaranteeing the achievable energy efficiency (EE) fairness in a multicell multiuser multipleinput 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 successive convex approximation (SCA) framework and alternating direction method of multipliers (ADMM). 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 small-cell networks with multipleantenna 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-andbound 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.Index Terms-Small-cell networks, energy efficiency, MIMO, joint design, ADMM, branch-and-bound.

We proposed several energy-efficient resource allocation algorithms for the downlink of an orthogonal frequencydivision-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 delaysensitive (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.