International Journal of Antennas and Propagation

Volume 2018, Article ID 7218471, 12 pages

https://doi.org/10.1155/2018/7218471

## Line-Of-Sight Interference Statistics and User Scheduling with 3D Angular Separation

Beijing University of Posts and Telecommunications, Beijing 100876, China

Correspondence should be addressed to Jianhua Zhang; nc.ude.tpub@gnahzhj

Received 27 November 2017; Accepted 3 June 2018; Published 8 July 2018

Academic Editor: Shiwen Yang

Copyright © 2018 Yawei Yu 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 interference statistical metrics of matched filter transmission over line-of-sight (LoS) downlink channels. The exact moments of the interference are derived, which can be used to make approximations for user rates and gain insights into the effects of system parameters such as angle spread (AS), antenna numbers, and array spacings. As the interference decreases with larger AS, we propose a user scheduling scheme by grouping users into different subspaces with corresponding orthogonal fraction of resource blocks, aiming to maximize the 3D angular separation among multiusers within each group; thus, a lower interference and higher sum rate would be expected. By performing this user scheduling scheme with 3D angular separation, a large sum rate gain is observed, which provides us a promising method in interference control and management.

#### 1. Introduction

The growing importance of massive MIMO [1], small cell [2], and millimeter wave [3] communications is motivating an increased interest in line-of-sight (LoS) channels [4] and simple transmission schemes such as matched filter (MF) precoding [5]. However, interference will arise in such multiuser systems with MF transmission [6], which will degrade the system performance [7], thus drawing the researchers’ attention [8].

Considering a single-cell massive MIMO system where single-antenna users are evenly distributed around the base station (BS) in the horizontal plane, the favorable propagation conditions of LoS channels, which are defined as mutual orthogonality among the vector-valued channels to the terminals with no mutual interference, are well investigated in [9]. As the mutual orthogonality among LoS channels is closely related to the antenna array at BS, the impact of different antenna parameters on asymptotic orthogonality, including the array geometries [10], antenna spacings [11], and antenna numbers [12], was studied. Using a uniform rectangular array (URA) at BS for the LoS MIMO system, results in [13] show that the ergodic rate is maximized for antenna spacing equal to integer multiples of one-half wavelength while the achievable sum rate with other antenna arrays can be found in [14]. In LoS channels, the phase of the received signal is determined by the relative location of the user (to BS); the work in [15] demonstrates that the user interference is partially determined by the LoS angle of arrival of signals. The deterministic dependence of interference on locations poses a significant challenge in modelling the interference distribution; the authors in [16] show that the main lobe distribution of LoS interference can be approximated by a beta mixture in the uplink LoS channel. As interference distribution can be used to compute signal-to-noise-plus-interference ratio (SINR) metrics such as outage probability and average throughput, prior work on LoS interference modeling is summarized in [17] and the interference model based on SINR is proposed and emphasized. The authors in [18] propose a statistical-eigenmode space-division multiple-access downlink transmission scheme based on the ergodic SINR and present the achievable sum rate of the multiuser system. This work also studies, for a different reason, the interference variables considered here.

As the sum rate of the multiuser MIMO system with interference is closely related to the SINR at each user, optimizing the SINR is key to improve the system performance [19]. Framework on transceiver (precoder and decoder) designing for interference alignment (IA) is presented [20], and different IA schemes based on resource allocation in multiuser MIMO systems are summarized [21]. By grouping users with different mobilities to have different coherence times, the interference signal only occupies limited dimensions and the degrees of freedom for the LoS interference channel are improved due to this blind IA scheme [22]. Furthermore, IA via a time-indexed interference graph for LoS channels is studied in [23], a maximal independent set is presented via dynamic programing, and orthogonal interference subspaces are designed to combat the interference at each user. Considering the MIMO downlink channel in a multiuser system, an efficient suboptimal algorithm of user scheduling is given by assigning the coordinates of transmission space to different users, aiming to achieve the best performance in terms of the sum rate throughput [24]. By allocating various resource blocks (e.g., time, frequency, and power) to users in different groups, the multiuser interference would remain within acceptable limits [25].

As we can summarize, all of the above work is closely related to the statistic characteristics of LoS interference; however, the derivation of a multiuser interference is difficult due to integrations of complicated components such as different elevation angle distributions and exponential antenna radiation patterns; thus, work on exact expressions of the interference moments is rare. Furthermore, conventional work all assumes that multiusers are evenly or randomly distributed around BS in the azimuth domain with no consideration of the elevation counterpart, which is not that realistic especially for 3D propagation scenarios with multiusers in high-rise buildings. For a 3D LoS propagation channel, the interference model is lacking and the effects of system parameters including the angle spread (AS), antenna spacing, and antenna numbers on the interference still remain unknown. Till now, there are various IA schemes such as resource allocations in the time, frequency, and power domains; the utilization of the degree of freedom in 3D space is rarely reported. The overall performance of multiuser MIMO systems is a complex joint multiobjective optimization problem since many variables and parameters have to be optimized, including the selection of users, the number and interval spacing of antennas, power allocation, and transmission technique. Based on the prior work, we make the following contributions: (1)Considering the LoS downlink channel with a simple MF transmission scheme and multiusers are distributed in the 3D space, we derive the exact expressions of the interference moments and present the simulative interference results under different antenna numbers, antenna spacings, and AS values. As usual, the multiusers are assumed as evenly distributed around the BS in the azimuth domain and von Mises (VM) distribution in the elevation counterpart [26].(2)Comparative results of the interference against AS, antenna numbers, and antenna spacings demonstrate that the averaged interference decreases rapidly when the elevation angle spread (EAS) increases (or the antenna number decreases, antenna spacing increases), which enables us to reduce the interference once users are scheduled to maintain decent angular separations (or finite antenna activation, antenna configuration optimization). While the mean interference level falls with increasing AS, there remains large variability (see the results of interference variance), especially in the super dense area with , which poses a severe challenge to simple MF processing.(3)Except IA schemes achieved by user scheduling in time, frequency, and power domains as mentioned above, we present the user scheduling via 3D space utilization as well. On the criteria of maximizing the angular separations among users within each group, multiusers are divided into different groups and occupy corresponding orthogonal fraction of wireless resource blocks. By performing the user scheduling scheme via 3D angular separation, a large sum rate gain is obtained and will be further enhanced by larger EAS and antenna spacing.(4)We conclude that by performing the user scheduling scheme via 3D angular separation, a significant system sum rate gain can be achieved, which ensures the promising future of 3D space utilization in interference management.

The remainder of this article is outlined as follows: in Section 2, we give the system model and performance metrics. In Sections 3 and 4, we derive the interference moments and present the results of interference against AS and antenna spacing. In Section 5, the user scheduling scheme is put forwarded along with the simulative results of the system sum rate. Then, conclusions are drawn in Section 6.

#### 2. System Model and Performance Metrics

Given the typical URA at BS, as shown in Figure 1, there are *M* vertical elements spaced by wavelength and horizontal elements with wavelength spacing. For simplicity, we assume single-antenna users (UEs) being served in a pure LoS environment within a single cell and the LoS angle of UE is denoted by (). The channel impulse response (CIR) between UE and the URA, , is given by [27]
where