International Journal of Antennas and Propagation

Volume 2017, Article ID 4302950, 9 pages

https://doi.org/10.1155/2017/4302950

## Joint Antenna Selection and Precoding Optimization for Small-Cell Network with Minimum Power Consumption

^{1}The School of Electronic and Information, Nantong University, Nantong 226019, China^{2}The National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China^{3}The Nantong Research Institute for Advanced Communication Technologies, Nantong 226019, China

Correspondence should be addressed to Chen Xu; nc.ude.utn@nehcux

Received 7 July 2016; Accepted 15 March 2017; Published 28 March 2017

Academic Editor: Sotirios K. Goudos

Copyright © 2017 Qiang Sun 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

We focus on the power consumption problem for a downlink multiuser small-cell network (SCN) considering both the quality of service (QoS) and power constraints. First based on a practical power consumption model taking into account both the dynamic transmit power and static circuit power, we formulate and then transform the power consumption optimization problem into a convex problem by using semidefinite relaxation (SDR) technique and obtain the optimal solution by the CVX tool. We further note that the SDR-based solution becomes infeasible for realistic implementation due to its heavy backhaul burden and computational complexity. To this end, we propose an alternative suboptimal algorithm which has low implementation overhead and complexity, based on minimum mean square error (MMSE) precoding. Furthermore, we propose a distributed correlation-based antenna selection (DCAS) algorithm combining with our optimization algorithms to reduce the static circuit power consumption for the SCN. Finally, simulation results demonstrate that our proposed suboptimal algorithm is very effective on power consumption minimization, with significantly reduced backhaul burden and computational complexity. Moreover, we show that our optimization algorithms with DCAS have less power consumption than the other benchmark algorithms.

#### 1. Introduction

Power consumption has increased considerably with the explosive rise of mobile data traffic demand over the past decade. Base stations have to consume much power to transmit a large amount of data traffic to meet the higher quality of service (QoS) required by the users. As pointed out in [1], base stations consume much more than sixty percent of the total power in the cellular networks. However, this is not in conformity with the lower power consumption and higher energy efficiency (EE) advocated by the green communications.

Spurred by growing environmental and economic concerns about how to sustain the exponential traffic growth, it is important to design energy saving wireless networks. The small-cell network (SCN) and massive MIMO are recognized as the key technologies for the decrease of power consumption because they have a great potential to enhance the EE [2, 3]. However, massive MIMO improves the EE, but at the cost of deploying more hardware infrastructure which means high power consumption. Besides, SCN achieves higher EE than massive MIMO in whatever crowded or sparse areas [4]. Unlike massive MIMO, SCN consists of a number of small-cell access points (SAPs), where each SAP is connected to a central processing unit (CPU) through a limited-capacity backhaul. SCN has less propagation losses and higher spatial reuse due to the short access distance provided [5], thereby resulting in higher EE.

So far, methods of improving the SCN’s EE have been focused on in many related investigations such as communication mode [6], hardware improvement [7], and network deployment [8, 9]. All the above literature provides comprehensive insights into how the EE can be improved, while the optimization for power consumption minimization of the SCN has also been well investigated in [10–12]. However, the optimization methods in [10–12] are all based on coherent joint transmission, which requires full channel state information (CSI) of all jointly processed SAPs, a strict synchronization across the SAPs, and large backhaul capacity for information exchange [13]. Since the overhead of exchanging all information and computational complexity of joint processing is usually prohibitive for practical implementations, it is not suitable for coherent joint transmission in the SCN. Facing these challenges, we aim at designing efficient transmission schemes on the coordination and loosening the backhaul requirements for the SCN.

In addition, it is well known that antenna selection can significantly reduce the complexity and power consumption to improve the spectral efficiency (SE) [14] and the EE [15, 16], which has been extensively studied for MIMO systems. However, most of these previous works for enhancing the SE and the EE ignored the fact that increasing the number of antennas is not always the best choice because of more power consumed in the circuits part [17]. Therefore, we believe that antenna selection is also an efficient approach to further reduce power consumption for the SCN.

To the best knowledge of the authors, the power consumption optimization, which combines the antenna selection and transmission scheme design for the SCN, is not presented before. Therefore, it is attractive to analyze and optimize this issue. In this work, we aim to minimize the power consumption under the quality of service (QoS) constraint per user and the power constraint per antenna of each SAP. First, we transform the initial power consumption minimization problem into a convex problem by using semidefinite relaxation (SDR) to obtain the system power consumption minimization and find the relationship among power consumption, the number of users, and the number of antennas per SAP. However, we know that it is difficult for this optimal algorithm to implement precoding in real-time due to heavy backhaul burden and high computational complexity when the number of SAPs is large. Then we propose a suboptimal algorithm which is on the basis of noncoherent joint transmission, for example, multi-SAP minimum mean square error (MMSE) precoding, to reduce the backhaul overhead and computational complexity. In addition, SAPs equipped with redundant antennas would consume a large amount of power consumption. In this case, we propose joint antenna selection and precoding optimization algorithms to further reduce power consumption. The simulation results show that there exists a small performance gap between the optimal algorithm and our proposed suboptimal algorithm. Moreover, our optimization algorithms with distributed correlation-based antenna selection (DCAS) are effective ways to minimize power consumption when the number of antennas is larger than the number of users per SAP.

The rest of this paper is organized as follows. In Sections 2 and 3, we present the system model and formulate the power consumption minimization problem, respectively. In Section 4, we propose a low overhead and complexity suboptimal algorithm. In Section 5, we propose the DCAS algorithm to further reduce the power consumption. The simulation results are presented in Section 6. Finally, the paper is concluded in Section 7.

*Notation.* Capital and small bold letters represent matrices and vectors, respectively; and stand for conjugate transpose and transpose of matrix , respectively. is the set of complex matrix with rows and columns, is the trace of matrix , is an identity matrix, and denotes correlation of and . stands for a multivariate circularly symmetric complex Gaussian distribution and we use and to denote the Euclidean norm and absolute value, respectively. The basic notations are given in the Notations.

#### 2. System Model

As shown in Figure 1, we consider a downlink multiuser SCN consisting of small cells, where each small cell deploys a SAP with antennas and all the SAPs are connected to the CPU through the high-speed backhaul, via which some critical information, such as the CSI, is shared among all SAPs. There are single-antenna users simultaneously being served on the same frequency band. We assume the following aspects for the SCN:(i)*Constant User Number.* Each SAP serves users and the number of users being served stays constant in each small cell.(ii)*Uniform Network Topology.* SAPs are deployed uniformly and randomly in the SCN and the users are distributed uniformly and randomly in the coverage area of each SAP.(iii)*Perfect CSI.* Perfect CSI is globally available at all SAPs and users.