Next Article in Journal
Multi-Frame Super-Resolution of Gaofen-4 Remote Sensing Images
Previous Article in Journal
An Improved Evidential-IOWA Sensor Data Fusion Approach in Fault Diagnosis
Article Menu
Issue 9 (September) cover image

Export Article

Open AccessArticle

Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System

Department of Electronics and Information Engineering, Chonbuk National University, Jeonju 54896, Korea
School of Information Science and Technology, Donghua University, Shanghai 201620, China
Author to whom correspondence should be addressed.
Sensors 2017, 17(9), 2139;
Received: 15 August 2017 / Revised: 11 September 2017 / Accepted: 14 September 2017 / Published: 18 September 2017
(This article belongs to the Section Sensor Networks)
PDF [934 KB, uploaded 21 September 2017]


In this paper, we examine the robust beamforming design to tackle the energy efficiency (EE) maximization problem in a 5G massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) downlink system with imperfect channel state information (CSI) at the base station. A novel joint user pairing and dynamic power allocation (JUPDPA) algorithm is proposed to minimize the inter user interference and also to enhance the fairness between the users. This work assumes imperfect CSI by adding uncertainties to channel matrices with worst-case model, i.e., ellipsoidal uncertainty model (EUM). A fractional non-convex optimization problem is formulated to maximize the EE subject to the transmit power constraints and the minimum rate requirement for the cell edge user. The designed problem is difficult to solve due to its nonlinear fractional objective function. We firstly employ the properties of fractional programming to transform the non-convex problem into its equivalent parametric form. Then, an efficient iterative algorithm is proposed established on the constrained concave-convex procedure (CCCP) that solves and achieves convergence to a stationary point of the above problem. Finally, Dinkelbach’s algorithm is employed to determine the maximum energy efficiency. Comprehensive numerical results illustrate that the proposed scheme attains higher worst-case energy efficiency as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme. View Full-Text
Keywords: energy efficiency; beamforming; user pairing; power allocation; 5G; worst-case; massive MIMO; NOMA energy efficiency; beamforming; user pairing; power allocation; 5G; worst-case; massive MIMO; NOMA

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Chinnadurai, S.; Selvaprabhu, P.; Jeong, Y.; Jiang, X.; Lee, M.H. Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System. Sensors 2017, 17, 2139.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Sensors EISSN 1424-8220 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top