Although the threedimensional (3D) channel model considering the elevation factor has been used to analyze the performance of multiuser multipleinput multipleoutput (MUMIMO) systems, less attention is paid to the effect of the elevation variation. In this paper, we elaborate the sum rate of MUMIMO systems with a 3D base station (BS) exploiting different elevations. To illustrate clearly, we consider a highrise 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 highrise buildings in modern city and used as a reference for infrastructure.
Currently, most research about multiuser multipleinput multipleoutput (MUMIMO) is taken with twodimensional (2D) channel model, which only considers the horizontal dimension while ignoring the effect of elevation in the vertical dimension [
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 [
The contributions of this paper can be summarized as follows:
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.
For uniform user distribution, we analyze the sum rate performance of MUMIMO 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.
Since the radiation pattern for the antenna elements at the BS tremendously influences the radiation gain and pathloss 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.
The sum rate of 3D MIMO systems for different tilt angle is investigated, which shows that elevation has a significant effects on system performance.
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
In the following, we consider an uplink singlecell MUMIMO system with a 3D MIMO BS. There are
Schematic illustration of a DMIMO system.
We now give the system model for the previously defined BS and UTs. The received signal vector
Channel matrix
The simplified 3D channel model which appeared in [
In order to obtain largescale fading
All these model parameters are obtained based on the practical antenna Kathrein 742215 [
The pathloss consists of indoortooutdoor (I2O) and outdoor components which are defined according to the 3GPP standard model in [
For shadowing fading, the lognormal shadowing fading model is adopted, which has been the prevalent model in the characterization of shadowing effects in wireless and satellite communications environments [
Motivated by the previous discussion, we can conclude that largescale fading function
In the following, we focus on the ergodic sum rate of 3D MIMO MMSE receivers. The equalization output of
Combining (
Substituting (
As discussed in Section
In practice, the performance of MIMO systems is affected not only by the fading but also by the user distributions [
For horizontal plane, uniform distribution, Gaussian distribution, and linear are considered. For the first case, we assume all users (desired and interfering users) are independently and uniformly distributed on the circular floor. The typical cases are dormitories and residential buildings. The PDF of uniform distribution is represented by
For the second case, most users are concentrated in the center of the floor and the density of users along the radius tends to be a Gaussian curve. Typical scenes are “hotspots” such as city centers, shopping malls, and office areas. The PDF of Gaussian distribution is represented by
As for the last case, users are distributed in the floor and the density of users along the radius tends to be a linear curve. The PDF of linear distribution is represented by
Generally in a
We investigate the sum rate of different user distribution schemes using Monte Carlo simulation. In the simulation, the simulation parameter settings are given in Table
Systme parameters.
Parameter  Details  Value 


Number of floors  3 

Number of UTs  24 

Number of BS antennae  50 

Number of UT antennae  2 

Distance between BS and the center of the building  200 m/1000 m 

Radius of building  100 m 

Height of BS  30 m 

Height of UT  1.5 m 

Height of floor  5 m 

Shadowing fading mean  4 dB 

Shadowing fading standard deviation  4 dB 

Pathloss exponent  4 

Wall penetration loss  0.01 (−20 dB) 

Inside loss 


Maximum antenna gain  18 dBi 

Halfpower beamwidth in the azimuth pattern 


Halfpower beamwidth in the elevation pattern 


Azimuth fronttoback ratio  30 dB 

Tilt side love level  −18 dB 

Fixed orientation angle 

For all the following simulation, we consider two configurations with
In the following, we investigate the performance of four different schemes as follows:
For uniform user distribution, we assess the sum rate against the SNR for different tilt angle.
The sum rate corresponding to uniform, normal (Gaussian), and linear distribution with 3D MIMO is provided.
The sum rate of each floor for the three user distributions with the same parameter configuration as in (
The impact of vertical user distribution on the sum rate for different floors is shown.
Since
We first analyze the performance of the sum rate against different average SNR for tilt angle
Simulated sum rate against the SNR for uniform distribution (
In terms of system performance in Figure
Simulated sum rate against the tilt angle for three user distributions (
Figure
Simulated sum rate against tilt angle for three user distributions (
From Figures
In this part, we focus on the influence of the optimal tilt angle and distance between BS and UTs on the sum rate for each floor. To this end, we investigate the sum rate of each floor for the three user distributions with the same parameters as in Section
Simulated sum rate against tilt angle for three user distributions (
Simulated sum rate against the tilt angle of each floor for three user distributions (
In Figures
We now study the impact of vertical user distribution on the sum rate for
The sum rate considering vertical user distribution is illustrated in Figures
Simulated sum rate against the tilt angle for three user distributions (
Simulated sum rate against the tilt angle for three user distributions (
With 3D BS exploiting elevation features, we deduce the exact analytical expression of the sum rate for single cell MUMIMO uplink system. The impacts of antenna tilt angle on the sum rate for both the whole building and the single floor are investigated. We find that appropriate tilt angle can compensate for the sum rate gain lost by the pathloss. Therefore, this paper can be used to analyze and optimize the performance. Furthermore, the functions of each floor and the related user distributions can be designed with reference to these results. This can be an important topic in the future design for wireless system.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National 863 Project (no. 2014AA01A705), the National Science and Technology Major Project (no. 2015ZX03001034), the Doctoral Scientific Funds of Henan polytechnic University (no. 60907013), the National Natural Science Foundation of China (Grant no. 61501404), Fundamental and Advanced Research Project of Henan Province of China under Grant (no. 132300410461), and the Fundamental Research Funds for the Universities of Henan Province. (no. NSFRF140125).