International Journal of Antennas and Propagation

Volume 2015, Article ID 873134, 9 pages

http://dx.doi.org/10.1155/2015/873134

## Energy-Efficient Resource Allocation in Uplink Multiuser Massive MIMO Systems

^{1}School of Information Science and Engineering, Southeast University, Nanjing 210096, China^{2}Institute of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang, China^{3}Information Engineering College, Henan University of Science and Technology, Luoyang, China^{4}State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

Received 15 July 2014; Revised 7 November 2014; Accepted 12 November 2014

Academic Editor: Xiang Cheng

Copyright © 2015 Ying Hu et al. 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.

#### Abstract

Energy-efficient communications, namely, green communications, has attracted increasing attention due to energy shortage and greenhouse effect. Motivated by this, we consider the uplink energy-efficient resource allocation in multiuser massive multiple-input multiple-output (MIMO) systems. Specifically, we consider that both the number of antenna arrays at the base station (BS) and the transmit data rate at UE are adjusted adaptively to maximize the energy efficiency. Firstly, we demonstrate the existence of a unique resource allocation solution that is globally optimal by exploiting the properties of objective function. Then we develop an iterative algorithm to solve it. By transforming the originally fractional optimization problem into an equivalent subtractive form using the properties of fractional programming, we develop another efficient iterative resource allocation algorithm. Simulation results have validated the effectiveness of the proposed two algorithms and have shown that both algorithms can fast converge to a near-optimal solution in a small number of iterations.

#### 1. Introduction

The amount of energy consumption for information and communication technology (ICT) increases dramatically with the exponential growth of service requirement [1], which directly impact on global greenhouse gas emissions. Therefore, as opposed to traditional spectral efficiency resource allocation [2–6], dynamic resource allocation is designed to maximize energy efficiency [7–13]. On the other side, MIMO technology has been proposed to substantially increase the system performance. Basically, the more antennas the transmitter/receiver are equipped with, the more degrees of freedom the propagation channel can provide, the better the performance in terms of data rate or link reliability is [14–17]. Massive MIMO (also known as large-scale antenna systems, very large MIMO, hyper-MIMO, full-dimension MIMO, and ARGOS) makes a clean break with current practice through the use of a large excess of service antennas over active terminals and time-division duplex operation [18]. Recently, multiuser massive MIMO gains more and more attention, where “massive MIMO” usually means the arrays comprising a few hundred antennas simultaneously serving tens of users in the same time-frequency resource [19]. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-square error (MMSE) detection in massive multiuser MIMO systems are derived in [19]. Whereas it is pointed out in [20] that although MIMO techniques have been shown to be effective in improving capacity and spectral efficiency (SE) of wireless communication systems, energy consumption also increases.

Recently energy-efficient design has emerged as a new trend in wireless communications. The tradeoff between EE (energy efficiency) and SE (spectral efficiency) in downlink multiuser DAS (distributed antenna systems) is addressed in [1]. They first transformed the multicriteria optimization problem with high complexity into a simple single objective optimization problem and proposed a novel power allocation algorithm to achieve maximum EE. In [7], the authors consider the energy-efficient power optimization for a general signal cell SISO-OFDM downlink system where subcarriers are allowed to be shared among users. They first proved that OFDMA is optimal for energy-efficient design of the SISO-OFDM system and then turned the nonconvex energy-efficient power allocation problem into a quasiconvex optimization problem and proposed an efficient power allocation algorithm. In [9], link adaptive transmission for maximized energy efficiency is addressed. The authors demonstrated the existence of a unique globally optimal link adaptation solution and developed iterative binary search assisted ascent (BSAA) algorithm to obtain it. In [10], the authors address the energy-efficient design of uplink MU-MIMO in a single cell environment. They demonstrated that a unique globally optimal power allocation always exists and gave energy-efficient MU-MIMO power allocation (EMMPA) algorithm to obtain it. In [11], we considered energy-efficient design of resource allocation for a multiuser OFDMA and developed schemes of user selection, rate allocation, and power allocation under QoS requirement to maximize the energy efficiency. In [13], resource allocation for energy-efficient communication in multicell OFDMA downlink network with cooperative base stations is studied. They transformed the considered problem in fractional form into an equivalent optimization problem in subtractive form, which enables the derivation of an efficient iterative resource allocation algorithm.

It is worth mentioning that all the above works only consider energy-efficient resource in single-antenna or fixed-beam OFDM system. There exist few works on the energy-efficient design concerning antenna selection for the massive MIMO system. In [21], we consider energy-efficient resource allocation in very large multiuser MIMO single cell systems, in which the effect of large-scale fading is ignored for the sake of simplicity. In [22], an energy-efficient iterative resource allocation scheme is proposed for the OFDMA downlink network with a large number of transmit antennas at the BS, which involves multiple-layer iterations and thus is computationally inefficient. Motivated by this, in this paper, we consider uplink energy-efficient resource allocation in multiuser massive MIMO systems. Specifically, in our problem formulation, the number of antenna arrays at BS and the transmit data rate vector at the user are jointly optimized to maximize the energy efficiency, in which the power consumption includes both transmit power and circuit power. Using the energy efficiency lower bound as the optimization criterion, we propose two iterative solutions. We first demonstrate the existence of a unique globally optimal solution by exploiting the properties of objective function; then we develop an iterative algorithm to solve the resource allocation problem. It is proved that the convergence of this iterative algorithm can be guaranteed, but the convergence rate and the performance are sensitive to initial conditions and step length. Herein, we further propose a more efficient iterative algorithm by transforming the considered nonconvex optimization problem in fractional form into an equivalent optimization problem in subtractive form. Its convergence property is also proved. The numerical results show that the proposed algorithms converge to a near-optimal point with a small number of iterations.

The remainder of this paper is organized as follows. In Section 2, the multiuser massive MIMO system model is described, and the optimization problem for the energy-efficient resource allocation is formulated. In Section 3, we provide two iterative algorithms to obtain the optimal solution. Then, we present numerical results in Section 4. Finally, we conclude the paper in Section 5.

#### 2. System Model

As shown in Figure 1, a massive MIMO system consisting of one BS equipped with antennas and users each equipped with single antenna is investigated in this paper. The received signal at the BS can be expressed aswhere and is the transpose operator. is channel matrix between the BS and the users. is the power allocation matrix, where is the transmit power of user . is transmit signal matrix. is additive white Gaussian noise (AWGN). Channel matrix is given bywhere is matrix of fast fading coefficients between the BS and the users and ; the component denotes the large-scale channel factor for user .