Max-min Fractional Program Research Articles

Secrecy energy efficiency optimization in heterogeneous networks with simultaneous wireless information and power transfer

In this paper, we investigate the secrecy energy efficiency (SEE) optimization for a heterogeneous network with simultaneous wireless information and power transfer, where multiple femtocell base stations (FBSs) are deployed under the coverage of one macrocell base station (MBS). Meanwhile, the MBS serves multiple macrocell users (MUs) in the presence of a malicious multiple-antenna eavesdropper (Eve) while each FBS serves a pair of information receiver (IR) and energy receiver (ER), where the ER with multiple antennas acts as a potential Eve to wiretap the information transmitted to IR in the same femtocell. Then, to promote the secrecy performance, artificial noise (AN) is injected into the downlink transmit signal at the MBS and FBSs. Furthermore, with the aim of achieving green and secure communications in 5G, the problem of maximizing average SEE performance of the whole network is reformulated while considering cross-tier multi-cell transmit beamforming (TBF) design. To obtain the optimal design, we resort to the successive convex approximation (SCA) and semi-definite relaxation (SDR) techniques to reformulate this nonconvex max–min fractional program problem into a series of solvable forms. Subsequently, an iterative algorithm is proposed to arrive at provably convergent design. Finally, simulation results validate the effectiveness and security of the proposed AN-aided TBF design.

Secrecy Energy Efficiency in Wireless Powered Heterogeneous Networks: A Distributed ADMM Approach

This paper investigates the physical layer security in heterogeneous networks (HetNets) supported by simultaneous wireless information and power transfer (SWIPT). We first consider a two-tier HetNet composed of a macrocell and several femtocells, where the macrocell base station (BS) serves multiple users in the presence of a malicious eavesdropper, while each femtocell BS serves a couple of Internet-of-Things (IoT) users. With regard to the energy constraint of IoT users, SWIPT is performed at the femtocell BSs, and IoT users accomplish the reception of information and energy in a time-switching manner, where information secrecy is to be protected. To enhance the secrecy performance, we inject artificial noise (AN) into the transmit beam at both macrocell and femtocell BSs, and for the sake of achieving green communications, we formulate the problem of maximizing secrecy energy efficiency while considering the fairness in a cross-tier multi-cell coordinated beamforming (MCBF) design. To handle this resulting nonconvex max–min fractional program problem, we propose an iterative algorithm by applying successive convex approximation method. Then, we further develop a decentralized solution based on alternative direction multiplier method (ADMM), which reduces the overhead of information exchange among coordinated BSs and achieves good approximation performance. Finally, simulation results demonstrate the performance of the proposed AN-aided cross-tier MCBF design and verify the validity of distributed ADMM-based approach.

Distributed Solutions for Energy Efficiency Fairness in Multicell MISO Downlink

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.

Joint Video Packet Scheduling, Subchannel Assignment and Power Allocation for Cognitive Heterogeneous Networks

In this paper, a joint video scheduling, subchannel assignment, and power allocation problem in cognitive heterogeneous networks are modeled as a mixed integer non-linear programming (MINLP), which maximizes the minimum video transmission quality among different secondary mobile terminals (MTs) subject to the total available energy at each secondary, the total interference power at each primary base station, the total available capacity at each radio interface of each secondary MTs, and the video sequence encoding characteristic. In order to solve it, we decompose the original MINLP as joint subchannel and power allocation problem and video packet scheduling problem. Then, we model the joint subchannel and power allocation problem as a max–min fractional programming, and transform it as a convex optimization problem. Finally, we utilize dual decomposition method to design a joint subchannel and power allocation algorithm, and propose a video packet scheduling scheme based on auction theory to maximize the video quality for each secondary MT. Simulation results demonstrate that the proposed framework not only improves the video transmission quality significantly, but also guarantees the fairness among different secondary MTs.

Achieving Energy Efficiency Fairness in Multicell MISO Downlink

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.

Distributed Energy-Efficient Power Optimization for CoMP Systems With Max-Min Fairness

This letter considers the power optimization problem for downlink transmission in coordinated multi-point (CoMP) systems. We aim to maximize the minimum weighted energy efficiency (EE) with QoS constraint and limited intercell coordination. The established optimization problem is converted to the standard form of max-min fractional programming problem first. Then we discuss feasibility of the Dual Dinkelbach-type Algorithm (DDA). A distributed algorithm is proposed to solve the subproblem in DDA with limited intercell coordination, where only a small number of positive scalars are shared between base stations. Simulation results show that the proposed algorithm outperforms previous schemes in terms of both the minimum EE of all the BSs' EE and fairness.