International Journal of Antennas and Propagation

Volume 2019, Article ID 4196513, 12 pages

https://doi.org/10.1155/2019/4196513

## Energy-Efficient Hybrid Precoding Scheme Based on Antenna Selection Technology in Massive Multiple-Input Multiple-Output Systems

College of Communication and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shanxi, China

Correspondence should be addressed to Jing Jiang; nc.ude.tpux@gnijgnaij

Received 31 August 2018; Accepted 4 March 2019; Published 2 May 2019

Guest Editor: Raed A. Abd-Alhameed

Copyright © 2019 Jian Jun Ding and Jing Jiang. 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

Hybrid precoding is a promising technology for massive multiple-input multiple-output (MIMO) systems. It can reduce the number of radio frequency (RF) chains. However, the power consumption is still very high owing to the large-scale antenna array. In this paper, we propose an energy-efficient precoding scheme based on antenna selection technology. The precoding scheme greatly increases the energy efficiency (EE) of the system. In the first step, we derive an exact closed-form expression of EE. Meanwhile, we further study the relationship between the number of transmit antennas and EE on the basis of the exact closed-form expression of EE. We prove that there exists an optimal value. When the number of transmit antennas equals to the value, the EE of the system can reach the maximum by a proper hybrid precoding scheme. Then, we propose an antenna selection algorithm to select antennas from the transmit antennas. And the number of selected antennas equals to the optimal value. Subsequently, we design the analog precoder based on a codebook to maximize the equivalent channel gain. At last, we further improve the EE by baseband digital precoding. The precoding algorithm we proposed offers a compromise between spectral efficiency (SE) and EE in millimeter wave (mmWave) massive MIMO systems. Finally, simulation results validate our theoretical analysis and show that a substantial EE gain can be obtained over the precoding scheme we proposed without large performance loss.

#### 1. Introduction

Millimeter wave band communication recently acquires more and more attention owing to its great advantages [1–4]. A beneficial feature of mmWave is that many antenna arrays can be packed into a small dimension owing to the small wavelength [5–11]. However, the problem is that the availability of multiantennas causes high interference between different users and high hardware complexity. Fortunately, precoding can eliminate interference between different users and reduce hardware complexity. Precoding is therefore more favored over mmWave MIMO communication systems. Simple linear precoding schemes, for example, zero forcing (ZF) and minimum mean square error precoding (MMSE), are virtually optimal. However, the digital processing in the MIMO system requires a dedicated base-band and radio frequency (RF) chain for every antenna element. Owing to the large amount of antennas deployed in mmWave massive MIMO systems, the costs are very huge and it is impossible to popularize in practice [12]. Researchers have widely studied on the reduction of the hardware cost. A hybrid precoding scheme comprising both digital and analog processing is capable of reducing the number of RF chains greatly. Therefore, the hybrid precoding scheme is widely used in mmWave MIMO systems. In consideration of a single-user scenario, a fully connected architecture-based hybrid precoding scheme is proposed in [13, 14], where each RF chain is connected to all antennas by analog phase shifters (APSs) and RF adders. The number of RF chains is greatly reduced in the fully connected architecture. However, in the fully connected architecture, the number of APSs is equal to the product of the number of RF chains and the number of antennas. The cost of hardware is still excessive owing to the large amount of antenna elements. Different from the fully connected architecture, a partially connected architecture-based hybrid precoding scheme is proposed in [15–19], where each RF chain only connected to an antenna subarray and the number of APSs equals to the number of antennas. Compared with the fully connected architecture, the number of phase converters and energy consumption is greatly reduced. In the partially connected precoding scheme, the mapping relationship between the antennas and RF chains is predetermined, but the channel condition is time-varying. Thus, the partially connected architecture cannot guarantee that the mapping relationship is optimal under different channel conditions. A dynamic subarray architecture-based hybrid precoding scheme is proposed in [20], where an adaptive antenna selection network is added between RF chains and antenna elements to enhance spectral efficiency (SE). All the previous work is aimed at improving the SE of the system. In the fully connected architecture-based and partially connected architecture-based architecture hybrid precoding schemes, all the transmitted antennas are activated. In this paper, we propose an energy-efficient precoding scheme with considerably reduced energy consumption and assume that not all transmitting antennas are activated. We jointly optimize the number of activated antennas, analog precoding matrix, and digital precoding matrix to maximize the of the system. Firstly, instead of designing the digital and analog precoder directly, we perform an antenna selection procedure before digital and analog precoding. Then, we further optimize the performance in terms of by digital and analog precoding.

The contributions existing in this paper are summarized as follows: (1)An exact closed-form expression of was derived in this paper, and we derived an optimum number of antennas for maximizing the EE according to the exact closed-form expression of (2)In previous precoding schemes, all the antennas are activated. In this paper, not all the transmit antennas are activated (an antenna is activated, which means the antenna is used to transmit message). Based on channel state information and the exact closed-form expression of , we select antennas from the transmitting antennas to activate and the remaining antennas will be temporarily closed(3)In the prior hybrid precoding scheme, we design the analog precoder and the digital precoder according to the channel state information which was obtained by channel estimation to improve the sum rate and reduce the interference between different users. The hybrid precoding scheme we proposed differs from the prior hybrid precoding scheme. The transmitter first performs an antenna selection process according to the channel state information and then optimizes system performance in terms of by analog and digital precoding. Through the scheme, the number of antennas and power consumption is reduced, and the is improved(4)An energy-efficient hybrid precoding scheme for a single user in mmWave systems is developed in this paper. First, we calculate the optimal number of transmit antennas and then the antenna selection algorithm is used to select the subset of transmit antennas. Then, we use the analog precoding scheme to maximize the gain of the equivalent channel between BS and objective users. Furthermore, we use the digital precoding scheme to maximize the of the system

The rest of this paper is organized as follows: Section 2, Section 3, and Section 4 introduce the system model, channel model, and power consumption model of the system, respectively. In Section 5, we introduce the optimization problem and propose an antenna selection algorithm. In Section 6, we proposed a hybrid beamforming algorithm. Computer simulation results are shown in Section 7. Finally, conclusions are drawn in Section 8.

Notations: we use the following notation throughout the paper. denotes a matrix; is a vector; denotes a scalar; denotes the transpose of . denotes the conjugate of . denotes the inversion of . denotes the -th element of . We express as . is an identity matrix. The acronym denotes “subject to,” and denotes “independent and identically distributed.” denotes the mathematical expectation of , and denotes complex Gaussian distribution.

#### 2. System Model

In this paper, we consider a downlink SU-MIMO mmWave system where a base station (BS) is equipped with antennas and RF chains to serve a single user which has RF chains and antennas. The number of RF chains satisfies to guarantee multistream transmission.

First, transmit data streams at the BS are processed by a digital precoder in the baseband and then processed by an analog precoder (RF precoder using analog circuitry). of size denotes the transmitting analog beam former. denotes the base band digital precoder satisfying , and denotes the total transmit power. Notably, the RF precoder can realize only phase changes because of phase-only control. For hybrid precoding systems as shown in Figure 1, the received signal vector of the objective user can be expressed by where denotes the received signal vector. denotes the channel matrix with denoting the channel vector between the BS and the -th receiving antenna. denotes the transmitted signal vector, satisfying . And represents the number of data streams. is the vector of additive complex Gaussian noise with zero mean and variance . denotes the power of noise.