International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 840142, 11 pages

http://dx.doi.org/10.1155/2015/840142

## Outage-Constrained Beamforming for Two-Tier Massive MIMO Downlink with Pilot Reuse

^{1}The State Key Laboratory of Advanced Optical Communication Systems and Networks, Peking University, Beijing 100871, China^{2}Department of Electrical and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong

Received 20 August 2014; Revised 14 February 2015; Accepted 22 February 2015

Academic Editor: Ahmed T. Mobashsher

Copyright © 2015 Guozhen Xu 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

Massive multiple-input multiple-output (MIMO) systems and small cell networks are both regarded as promising candidates to meet the exponential growth of mobile data traffic for the next generation (5G) wireless communications. Hence, a new kind of multitier networks which combine massive MIMO macro cells with a secondary tier of small cells is proposed to resolve the contradiction of large network coverage and high data rate. In such multitier networks, it is inevitable to allocate nonorthogonal uplink pilot sequences to user equipment (UE) due to the large number of users. We propose a pilot reuse scheme by exploiting the unique architecture of this networks and analyse the special mixed channel state information (CSI) yielded by the pilot reuse scheme. Based on the mixed CSI, we formulate a downlink transmit beamforming problem of minimizing the total power consumption while satisfying the quality of service (QoS) requirements with outage constraints. After decomposing the original problem into simpler subproblems, we provide an efficient algorithm to combine these subproblems and solve them iteratively for generating the beamforming vectors. Monte Carlo simulations show that the average power consumption of the proposed pilot reuse scheme and its associated beamforming algorithm is close to that of the perfect CSI case.

#### 1. Introduction

With the advent of the fifth generation (5G) cellular wireless communications, an ever-increasing demand of substantially higher throughput is a quite pressing task laid in front of us and drives the researchers to find new technology for wireless communications. Massive MIMO is a potential technology for meeting this demand and also taken as an attractive solution for 5G systems [1]. By implementing a large number of antennas at the BS, massive MIMO systems offer a high spatial and multiplexing resolution which can drastically improve the communication systems’ performance in terms of data rate and reliability [2]. However, a critical issue for such massive MIMO systems is the excessive energy cost for their large number of antennas. How to provide higher data rates with lower energy consumption for such massive MIMO systems is a critical problem in front of us.

An innovative solution to this problem is a densified network with a multitier network architecture as stated in [3]. Sometimes, such multilayer and multiarchitecture networks are also called heterogeneous networks (HetNets). In [4], the authors have made further discussions about two-tier massive MIMO networks. The fundamental architecture of such networks is based on a deployment of a macro cell with very large antenna arrays in combination with a secondary tier of small cells (SCs) with a few antennas each. Macro cells are deployed for the coverage of large areas and capable of handling low data traffic or the users with a relative high mobility, and SCs with a reduced coverage range of tens of meters are designed for providing localized higher data rate communications.

However, there still exist some implicit obstacles to put such two-tier massive MIMO networks into practice. One problem is how to fulfill the channel estimation. In time division duplexing (TDD) cellular systems, channel estimation is obtained via the uplink training based on the channel reciprocity property. In other words, each user in the cell would be assigned a specific pilot sequence and these pilot sequences would be transmitted to the base station (BS) via the uplink. Acquiring perfect CSI inherently asks for sufficient numbers of orthogonal pilot sequences, which may not be possible for massive MIMO cellular systems. Hence, the pilot reuse is inevitable in massive MIMO systems, and the imperfect uplink training due to reusing the same pilot sequences tends to be a critical problem (referred to as “pilot contamination” problem [5]).

It is critical to design an appropriate pilot reuse scheme for mitigating the interference due to the pilot contamination. In [6–8], a time-shifted pilot reuse scheme was proposed to combat pilot contamination by symmetrically rearranging the uplink pilot transmission order for different cells and the system performance for such scheme with zero-forcing beamforming and a large number of BS antennas is also studied. Reference [9] studied the optimal pilot reuse factor for sum-rate maximization in massive MIMO systems. In [10], the authors proposed a pilot reuse scheme in homogenous multicell networks based on the degree of the spatial orthogonality in greedy fashion. In [11], the authors partitioned each cell into sectors and assigned the reused pilot sequences in a symmetrical way in order to perform pilot contamination precoding (PCP). Recently, a novel pilot reuse scheme is proposed in [12] which exploits the channel spatial localization property to reduce the number of orthogonal pilots for uplink channel estimation in single cell massive MIMO systems. However, the pilot reuse scheme in [12] requires restrictive assumptions such as high channel spatial correlation and uniform linear array at the BS. In summary, all the works mentioned above focused on either homogenous multicell networks or single cell systems. As a result, they cannot be directly applied to (or are not optimized for) HetNets with asymmetrical system architecture.

Another problem is how to tackle the intercell interference. With limited spectral resources, a cochannel deployment of macro cell and secondary tier SCs is the only viable solution, and this in turn requires a sophisticated interference management scheme across the tiers. The cross-tier interference is even thought to be one of the bottlenecks for designing high-performance HetNets [13].

Now, a tough problem of proposing a high-performance and low-complexity interference management scheme to guarantee the system’s QoS requirements with limited uplink pilot resources is in front of us.

For this problem, robust transmit beamforming methods which take the CSI errors into consideration are in need for the reason that “pilot contamination” causes imperfect CSI. In [14, 15], a sum-rate maximization problem with imperfect CSI was investigated. However, these methods mainly focused on the worst case approach under the assumption of norm-bounded uncertainty which is not suitable for the considered system. Furthermore, a more efficient conservative formulation is presented which involves solving a semidefinite programming (SDP) in [16]. By using the Bernstein-type inequality, a chance constrained beamforming problem in cognitive radio networks is also provided in [17]. The kernel of these methods is to transform the original problem to a tractable SDP problem conservatively. However, the huge computation complexity of SDP, , makes these methods unattractive in massive MIMO systems [18].

Compared with the previous works, we propose a pilot reuse scheme by exploiting the unique architecture of this HetNet. A “mixed CSI” is achieved at the BS due to our pilot reuse scheme. Based on the mixed CSI, we formulate the energy-efficient beamforming problem as a chance constraint programming and decompose it into simpler subproblems. Then, an efficient iterative algorithm is provided to combine these subproblems and solve them iteratively for obtaining the beamforming vectors.

The rest of this paper is organized as follows. In Section 2, the system model is provided. How to compress the number of the uplink pilot sequences and how to design the energy-efficient beamformer with the mixed CSI are presented and solved in Section 3. Section 4 presents the numerical results and Section 5 concludes this paper.

#### 2. System Model

We consider the downlink of a TDD orthogonal frequency division multiplexing (OFDM) system. Different from the traditional systems with single base station, one macro base station (MBS) and low range small cell base stations (SBSs) separately serve their intended single antenna users in the same frequency band shown as in Figure 1. The MBS has antennas and each SBS has antennas, where is assumed to be a large number which is known as massive MIMO. We consider that the total number of the served users is ; since the total number of transmit antennas is , the downlink channel propagation matrix between the antennas and users can be described by a matrix, . The base stations can exploit channel reciprocity to obtain channel state information at the transmitter (CSIT) based on uplink training. Here we denote the macro cell as cell and the th SC is denoted as cell . The channel of the th user is represented as , where and . Let , denote the entries of , and describes the channel between the th antenna in cell and the th user. We consider a composite fading channel; that is, , where is the path gain between antenna in cell and user , and is the small scale fading with i.i.d. ~ entry. Here, we assume a time block fading model. Thus path fading vectors , stay constant during each coherence interval and these vectors are assumed to be independent in different coherence blocks. Since all the transmit antennas of MBS are considered to be center collected, is satisfied, where , are independent random variables describing the path loss fading.