International Journal of Antennas and Propagation

Volume 2015, Article ID 318123, 9 pages

http://dx.doi.org/10.1155/2015/318123

## Sum Rate Analysis of MU-MIMO with a 3D MIMO Base Station Exploiting Elevation Features

^{1}College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China^{2}State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100786, China^{3}Beijing Institute of Computer Technology and Application, Beijing 100854, China

Received 28 August 2015; Accepted 26 November 2015

Academic Editor: Wei Xiang

Copyright © 2015 Xingwang Li 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

Although the three-dimensional (3D) channel model considering the elevation factor has been used to analyze the performance of multiuser multiple-input multiple-output (MU-MIMO) systems, less attention is paid to the effect of the elevation variation. In this paper, we elaborate the sum rate of MU-MIMO systems with a 3D base station (BS) exploiting different elevations. To illustrate clearly, we consider a high-rise building scenario. Due to the floor height, each floor corresponds to an elevation. Therefore, we can analyze the sum rate performance for each floor and discuss its effect on the performance of the whole building. This work can be seen as the first attempt to analyze the sum rate performance for high-rise buildings in modern city and used as a reference for infrastructure.

#### 1. Introduction

Currently, most research about multiuser multiple-input multiple-output (MU-MIMO) is taken with two-dimensional (2D) channel model, which only considers the horizontal dimension while ignoring the effect of elevation in the vertical dimension [1, 2]. However, the assumption of the 2D propagating waves is no longer valid in the environments when the elevation spectrum is significant. Typical scenarios are indoors [3, 4] and in vehicles [5]. To make the channel model more applicable, several studies have taken the elevation factor into consideration [6–9]. The Wireless Initiative New Radio Project Phase II (WINNER II) releases the enhanced channel model which models the elevations of arrival and departure with parameters drawn from real channel sounding measurement [10]. Thus, WINNER II supports both indoor and outdoor scenarios, which is a significant improvement compared with the previous spatial channel model (SCM) of the 3rd Generation Partnership Project (3GPP) [11]. In [12], a simplified three-dimensional (3D) model is developed. This model assumes that the electrical wave still transmits on the 2D plane from the base station (BS). Only when the waves go through the scatters and arrive at the user, a significant elevation spread is present. This model is proved to perform well in indoor an in vehicle scenarios. Literature [13] proposes an approximated 3D antenna radiation pattern that combines the two principal cuts for azimuth (horizontal) and elevation (vertical) planes. The combination of [13] shows a tolerable approximation deviation. In [14], the 3D antenna pattern is similar to [13], but it assumes that the gains of horizontal and vertical directions are equally weighted, which makes the model more practical.

Though the elevation effect in channel modeling and performance analysis has gradually caught the researchers’ attention, the exploiting of elevation variations has not yet been definitely discussed. The effect of elevation variation on communication performance is obvious in 3D channel model especially when the base station is close to the users and the users are distributed at different heights [14]. Nowadays, most buildings in modern cities have about twenty floors or even more. Thus, users in different floors have different elevations. Exploiting 3D MIMO at the BS covering the building enables us to make use of the distribution of users in elevation domain to improve the performance such as capacity. So how to deploy the users in the building or how to adjust the tilt angle of transmit antennas of the BS to achieve the best performance becomes a valuable problem. Several literatures like [15–19] have previously investigated the effects of user distribution on system performance. However, the common characteristic of [15–19] is that they consider user distributions in a single horizontal plane. More importantly, the 3D MIMO featured BS is not considered. In this paper, we mainly contribute to the sum rate derivation and analysis for uplink MU-MIMO scenario with a 3D MIMO BS considering 3D user distribution, which consists of both horizontal distribution for each floor and vertical distribution for different floors due to 3D MIMO receiving.

The contributions of this paper can be summarized as follows:(1)We build the system model with 3D MIMO BS and introduce a building with several floors. In this paper, the deterministic sum rates of 3D MIMO system with minimum mean square error (MMSE) receivers both for the single floor and the whole building with consideration of elevation factor are deduced.(2)For uniform user distribution, we analyze the sum rate performance of MU-MIMO system versus entire SNR with different tilt angles. It is demonstrated that the sum rate increases logarithmically with SNRs, and there is an optimal tilt angle for the sum rate.(3)Since the radiation pattern for the antenna elements at the BS tremendously influences the radiation gain and path-loss of the user on different floors, the simulation results of the sum rate are numerically analyzed to obtain the optimal tilt angle. The optimal tilt angle can be used to adjust the antennas of BS to achieve the best performance, which is of great value.(4)The sum rate of 3D MIMO systems for different tilt angle is investigated, which shows that elevation has a significant effects on system performance.(5)We consider and analyze the impact of 3D user distribution in the building for different number of floors, which has very realistic significance. Since there is little research about the 3D user distribution, the result can be used as a reference for practical design.

The remainder of the paper is organized as follows. The system model and 3D MIMO channel model are presented in Section 2. Section 3 gives the derivation of the ergodic sum rate with a 3D MIMO BS exploiting variable elevation considering 3D user distribution. We present some numerical results and corresponding analysis in Section 4 before we conclude the paper in Section 5.

#### 2. 3D MIMO System Model

In the following, we consider an uplink single-cell MU-MIMO system with a 3D MIMO BS. There are antenna elements for the 3D MIMO receiver. user terminals (UTs) each with transmit antenna elements are considered. All users are located in a building with floors. We define , , , as the index of the th UT on th floor. The th floor has UTs which satisfies . A schematic illustration of the 3D MIMO system under consideration is depicted in Figure 1. In this paper, it is assumed that the BS has perfect channel state information (CSI), while all UTs have no CSI. Thus, the optimum transmission strategy is to transmit independent and equal power signal from each UT.