Configuration of Base Station Antennas inMillimeter Wave MU-MIMO Systems

Lu Liu, Yafei Tian and Yifan Xue

School of Electronics and Information Engineering, Beihang University, Beijing, China

Email: {luliu, ytian, yfxue}@buaa.edu.cn,

Abstract—Millimeter wave (mmWave) communication is a sig-nificantly enabling technology in the fifth-generation (5G) cellularsystem to promote the capacity. In recent years, people havefocused on studying the propagation characteristics of mmWave.However, the impact of mmWave channel on the system capac-ity, especially in multi-user multi-input and multi-output (MU-MIMO) scenarios, has not been fully investigated. In this paper,we first study a low-complexity numerical calculation method ofthe sum-capacity in MU-MIMO downlink scenarios, and theninvestigate the effect of base station (BS) antenna configurationson the system capacity. The antenna spacing, deployment positionand array shape are respectively studied, and the cumulativedistribution functions (CDFs) of user correlations are analyzed.We find insights to achieve higher channel capacity and to guidethe deployment of BS antennas in practical cellular scenarios.

Index Terms—antenna array, array configuration, channelcapacity, millimeter-Wave, MU-MIMO.

I. INTRODUCTION

One of the primary technique in next generation cellular

system is milimeter wave (mmWave) communications, which

is the spectral frontier for wireless communication systems

nowadays [1]. The mmWave band can provide much wider

bandwidth comparing to today’s cellular networks, and can

promise much smaller base station (BS) antenna arrays due

to its short wavelength [2]. The propagation characteristic of

mmWave channel is different from the microwave channel.

Due to the larger penetration loss, less scattering and diffrac-

tion, mmWave channel is more sparse both in time domain

and space domain [3]–[5].

Channel capacity not only depends on the propagation

characteristics, but also depends on the antenna configurations.

The sub-channel correlation greatly circumscribes the capacity

of MIMO system [6]. One way to decrease the correlation is

to equip antennas with different polarizations and radiation

patterns. In [7], the author investigates MIMO systems where

antenna arrays are composed of different number of dipoles

in three axes (X,Y,Z) and then introduce diverse radiation

patterns to reduce correlation. The result demonstrated that

MlMO systems exploiting antenna pattern diversity allow for

performance improving. In [8], genetic algorithm (GA) are

utilized to design the antenna spacing of the linear array. Op-

timized results show that minute modification of the element

positions can improve the array pattern, especially for the

fewer elements case.

In cellular system, the space constraint of BS antenna

make it infeasible to deploy hundreds of antenna elements

in one horizontal or vertical dimension. In order to cope with

this limitation, people extend the line antenna array to two-

dimensional (2D) antenna arrays. The full-dimension MIMO

(FD-MIMO) system was proposed in [9], where 2D active

antennas are equipped on BSs. To accommodate the intro-

duction of 2D antenna arrays, the channel model is extended

to three dimensions (3D), where the azimuth and elevation

angles are both taken into account. The simulation results show

that the number or spacing of elements in two dimensions

can impact the throughput gain. Referring to the factors of

antennas, the geometry of antenna array has significant impact

on the eigenvalues of single-user MIMO (SU-MIMO) channel

[10], and thus influences channel capacity. In addition, there

are other studies on the formation, spacing and polarization of

antenna arrays [11]–[13].

In this paper, we study the relationship between array

factors and system performance in 3D mmWave multiple-

user MIMO (MU-MIMO) channels. We first study a low-

complexity numerical calculation method of the sum-capacity

in MU-MIMO downlink scenarios. Then combining MU-

MIMO with mmWave propagation, we analyze the impact of

BS antenna factors in detail, including the spacing between

antenna elements, the position of antennas, and the number

of elements on the horizontal or vertical dimensions. The

antenna spacing is changed with multiples of the wavelength

from 18λ to 32λ to find the effect of different array spacing

on the system performance. When BS antennas are deployed

indoors, we considered two positions, such as the ceiling

and the side wall, which are representative for the indoor

layout. Changing the number of elements on the horizontal

and vertical dimensions, we develop antenna arrays with kinds

of configurations and then find their difference on the capacity

as well as the user correlation coefficients.

Since the relationship between each factor and the system

capacity is complicated, it is intractable to derive a rigorous

mathematical formula. Hence, Monte Carlo simulations are

employed to observe cumulative distribution function (CDF)

of channel correlation coefficients and the sum-capacity. After

comprehensive study, we will obtain some general rules to

guide the deployment and configuration of the BS antenna

array in practical 5G systems.

The rest of this paper is organized as follows. In Section II,

we introduce channel models for two BS deployment position-

s. Then we formulate the calculation of channel capacity in

Section III. In section IV, we investigate the impact of various

antenna factors on the system performance in detail. Finally,

Section V concludes the paper.

II. CHANNEL MODEL

We consider a downlink MU-MIMO transmission scenario,

where multiple users are randomly distributed in an indoor

environment. Due to severe path losses, the mmWave environ-

ment is well characterized by a clustered channel model, i.e.,

the Saleh-Valenzuela model [14]. The channel matrix between

the BS and one user is defined as

H =

√NtNr

NclNray

Ncl∑i=1

Nray∑l=1

αilar(φril, θ

ril)a

Ht (φt

il, θtil). (1)

In (1), Nt = Nth ×Ntv is the number of transmitter antennas

on the BS, and Nr = Nrh × Nrv is the number of receiver

antennas on the user end. Nxh and Nxv represent the number

of antenna elements on the horizontal and vertical dimensions

respectively, where x ∈ {t, r} denotes the transmitter or

receiver. When Nxh = 1 or Nxv = 1, the array is linear,

otherwise it is planar. Ncl and Nray denote the number of

clusters and the number of rays in each cluster. Generally,

all of the clusters are consumed to be uniformly distributed,

while the rays in one cluster follow Laplace distribution in

their own angel spread. αil represents the gain of the l-th ray

in the i-th cluster. We suppose that it is i.i.d. and follows the

distribution CN (0, σ2α,i) where σ2

α,i is the average power of

the i-th cluster.ax(φ

xil, θ

xil) is the array response vector in which φx

il is the

azimuth angle and θxil is the elevation angle. The angles with

superscript t denote AoDs and that with superscript r denote

AoAs. The array response vector can be formulated as

ax(φxil, θ

xil) =

1√Nx

[1, e−jvxil , . . . , e−j(Nxh−1)vx

il ]T

⊗[1, e−juxil , . . . , e−j(Nxv−1)ux

il ]T ,

(2)

where uxil and vxil are the phase difference between adjacent el-

ements on the vertical and horizontal dimensions. The symbol

⊗ denotes Kronecker product. While establishing the channel

model, we found that the array response vector ax(φxil, θ

xil) is

different in two kinds of antenna deployments, which will be

shown in detail in the next two subsections.

A. The Array Deployed on the Side WallIf the antenna array is on the side wall, we introduce the

system schematic as shown in Fig. 1 and take the link between

the BS and one user as an example.In Fig. 1, φ is the angle between the ray and the positive

x-axis while θ is the angle between the ray and the x-y

plane. Then the phase difference between adjacent elements

on vertical and horizontal dimensions are

uxil =

2πdxvλ

sin θxil, (3)

vxil =2πdxhλ

cos θxil cosφxil, (4)

where dv and dh are antenna spacing on the vertical and

horizontal dimensions, and λ is the signal wavelength.

X

Y

Z

d1

d2

V

H

User

Fig. 1: The system model with the array on the side wall.

B. The Array Deployed on the Ceiling

If the antenna array is on the ceiling, we establish the

coordinate system as shown in Fig. 2. The definitions of angles

keep the same, and the two kinds of phase difference are

respectively

uxil =

2πdxvλ

cos θxil cosφxil, (5)

vxil =2πdxhλ

cos θxil sinφxil. (6)

X

Y

Z

d1

d2

V

H

User

Fig. 2: The system model with the array on the ceiling.

III. CAPACITY ANALYSIS

In the analysis of data rate, different precoding approaches

could lead to different results. Considering that we mainly

concentrate on the relationship between antenna factors and

the system performance, to avoid the influence of specific

precoding method, we directly analyze the channel sum-

capacity.

It is well known that dirty paper coding (DPC) can achieve

the capacity region of MIMO broadcast channel (BC) [15],

but the implementation of DPC has very high complexity.

According to the duality between MIMO-BC and MIMO

multiple-access channel (MAC), the capacity region of a

MIMO-BC is the same as the capacity region of its dual

MIMO-MAC [16]. Considering a K-user Gaussian MIMO-

BC, the capacity region is represented as

Cunion(P,HH)

�⋃

∑Ki=1 Pi�P

CMAC(P1, . . . , PK ;HH)

=⋃

∑Ki=1 Tr(Pi)�P

{(R1, . . . , RK) :

∑i∈S

Ri

� log∣∣∣I+∑

i∈SHH

i PiHi

∣∣∣, ∀S ⊆ {1, . . . ,K}}. (7)

In (7), H is the channel matrix between the BS and

users where H = [H1, . . . ,HK ]T

. Hi is the channel matrix

of the i-th user. We assume H is constant and is known

perfectly at the transmitter and at all receivers. Pi is individual

power constraint for each transmitter in the dual MAC, and∑Ki=1 Pi ≤ P is the sum power constraint. The positive

semidefinite matrix Pi = ViVHi represents every set of MAC

covariance matrix, where Vi denotes the precoding matrix for

the i-th user equipment (UEi). Ri is the achievable rate of

UEi.

The calculation of capacity region involves a series of

optimization problem of the sum-rate in any possible user set

S . If we are interested in the sum-capacity instead of the whole

capacity region, the problem will be much simplified. Consider

a BS equipped with Nt = Nth × Ntv antennas and UEs

equipped with single antenna. Then, the matrix Hi degrades

to a vector hi. To find the sum-capacity of this MU-MIMO

channel, (7) can be converted as the following optimization

problem

maxP

|I+HHPH|s.t. Tr(P) ≤ P, (8)

where P = diag(P1, . . . , PK) and H = [h1, . . . ,hK ]T

. Note

that the sum-capacity optimization problem of MU-MIMO

is different with the capacity optimization problem of SU-

MIMO. In (8), if P is the covariance matrix of a single

user precoding matrix, the optimal result will be obtained by

singular value decomposition of HH and water filling power

allocation. But for the MU-MIMO case, P is a diagonal matrix

and only involves transmit power of each user. It has no rule

on how to allocate the powers according to the channel matrix

H, which is the combination of channel vectors of different

users.

The problem (8) is convex, which can be solved by standard

convex optimization algorithm, like interior-point method [17].

However, the computational complexity of the interior-point

method is still high for this specific problem. Furthermore, we

cannot find the condition when the sum-capacity is achieved.

Observing the optimization problem (8), we can recognize

that the objective function is a quadratic form whose maximum

value will increase along with the increasing of sum transmit

power. Therefore, the optimal result should be obtained when

the sum power reaches the constraint. In other words, the

optimization problem (8) is the same as

maxP

|I+HHPH|s.t. Tr(P) = P. (9)

We propose a gradient based method to solve problem (9).

Define L = |I+HHPH|, then the gradient over P is

∂L

∂P= |HHPH| (H(I+HHPH)−1HH

)T. (10)

The diagonal element of ∂L∂P is the derivative of L with respect

to the diagonal elements of P.

Theorem 1. In a K-user dual MIMO-MAC channel, whereeach user is equipped with single antenna, the maximum of itssum-capacity is achieved when the transmit powers of someusers are zero and the gradients over the transmit powers ofother users are equal.

Proof. Assume that P has random initial values, P(0) =

diag(P(0)1 , P

(0)2 , . . . , P

(0)K ), where Tr(P(0)) = P . Then, we

can get

diag

(∂L

∂P

)∣∣∣∣P=P(0)

=

[∂L

∂P1,∂L

∂P2, . . . ,

∂L

∂PK

]∣∣∣∣P=P(0)

.

(11)

Note that the partial derivative over one transmit power ∂L∂Pi

actually depends on itself and all other transmit powers.

When P(0) is not the optimal one to get the maximum of

sum-rate, there exists m and n leading to

∂L

∂Pm�= ∂L

∂Pn

∣∣∣∣P=P(0)

, (12)

where m,n ∈ {1, 2, . . . ,K}. It means that the data rate grows

with different speed over Pm and Pn. If ∂L∂Pm

> ∂L∂Pn

, L grows

more rapidly over Pm than over Pn. In other words, adding

a small amount of power ε to Pm will be more effective to

increase data rate than adding ε to Pn. Considering that ∂L∂Pm

and ∂L∂Pn

are continuous, when ε is small enough, we can

always get higher data rate by setting

P(1) = diag[P

(0)1 , . . . , P (0)

m + ε, . . . , P (0)n − ε, . . . , P

(0)K

].

(13)

In this way, the sum-rate can keep increasing and the sum-

power constraint is always satisfied.

Since the transmit power cannot be less than 0, when

one variable Pi approaches 0, it will stay at 0 and other

variables keep to change. Finally, the gradients over all non-

zero transmit powers will be equal, and the achieved sum-

rate is the sum-capacity of the given K-user MIMO-MAC

channel.

The proposed optimization algorithm follows the proof. At

first, set initial values for P, for example Pi = PK for all

i. Then calculate the gradient matrix ∂L∂P using (10). Find

the transmit power Pm with the maximal gradient component∂L∂Pm

, and the transmit power Pn with the minimal gradient

component ∂L∂Pn

. Update P using (13). If one transmit power

Pi approaches 0, find the second minimal gradient component

and keep updating the transmit power matrix. The algorithm

terminates when the gradients over all non-zero transmit

powers are equal (within a given precision). In our statistics,

the proposed algorithm can be about 100 times faster than the

interior-point method used in CVX toolbox, while simulation

results of the two methods are almost the same.

IV. FACTORS AFFECTING CAPACITY

In this section, we strive to find factors of antenna arrays that

affecting MU-MIMO system capacity in mmWave propagation

environments. We simulate in a typical indoor office scenario

described in 3GPP TR38.900 R14 [5], where the length is

120 m, the width is 50 m and the height is 3 m. There are 16

users uniformly distributed at the height of 1 m, and the BS

antennas are 3 m high. The channel parameters are given by

Ncl = 8, Nray = 10 and σ2α,i = 1. The large scale pathloss is

calculated according to [5] in the indoor-office scenario with

28 GHz center frequency .

About the parameters of angles, in the cluster level, the

angle spread of AoDs in line-of-sight (LOS) is 15◦ in the

azimuth and is 7.5◦ in the elevation, in which central AoDs

of each cluster in azimuth and elevation follow the uniform

distribution. The central AoAs of each cluster in azimuth

and elevation follow the uniform distribution varying from 0◦

to 360◦. In the ray level, the AoDs and AoAs in azimuth

and elevation of rays follow the Laplacian distribution. The

angle spread of rays in each cluster is 5◦. Other simulation

parameters are listed in Table I and II for various scenarios.

A. The Antenna Spacing and Deployment Position

If we enlarge or reduce the spacing between antenna ele-

ments such as dh and dv , the phase difference in (3)-(6) will

change. Then the array response and the channel matrix will

also change according to (2) and (1). Therefore, the correlation

of users and the channel capacity may be influenced. We want

to find the relationship between the antenna spacing and the

system performance.

When the BS is at the side wall with 50 m width, the layout

of indoor office scenario is shown in Fig. 3. The antenna

array of the BS is square with Ntv = 8, Nth = 8, totally 64

elements, while the antenna of the user is single. We change

the BS antenna spacing by multiple of wavelength and study

its influence on sum data rate. Set the simulation parameters

as those in Table I. The sum-capacity is calculated with the

proposed gradient algorithm, and is shown in Fig. 4. As a

comparison, the sum data rate achieved by the zero-forcing

(ZF) precoding method is also provided. The simulation results

demonstrate that as the antenna spacing increases, the data rate

continues to rise and eventually reaches a plateau. Therefore,

in practical systems, when the antenna array is placed on the

side wall, we can greatly improve the system capacity through

increasing the antenna spacing appropriately.

When the BS is at center of the ceiling, we set antenna

arrays as those in the side wall scenario and apply the same

method to study the effect of antenna spacing on the sum data

rate. Fig. 5 displays the simulation results with the parameters

in Table I. The trend of lines is similar to that in Fig. 4, but the

achieved data rate is higher. When the antenna spacing is less

than 4λ, the data rate increases more rapidly. In this scenario,

when the antenna spacing is small, even though we enlarge

it a little, the data rate can remarkably get higher. Therefore,

widening antenna spacing will be more effective for the BS

antennas on the ceiling than those on the side wall. In Fig. 4

and Fig. 5, we can also see that, there is a large gap between

the sum-capacity and the achieved sum-rate of ZF precoding

when the BS antenna array is on the side wall, while the gap

greatly shrinks when the BS antenna array is deployed on the

ceiling.

TABLE I: Simulation Parameters

BS array Nth = 8, Ntv = 8Receiver array Nrh = 1, Nrv = 1

Antenna spacing 18λ, 1

4λ, 1

2λ, λ, 2λ, 4λ, 8λ, 16λ, 32λ

50m

Nth

Ntv

BS

User

1m

3m

120m

Fig. 3: Layout of the indoor office scenario.

0 5 10 15 20 25 300

10

20

30

40

50

60

Antenna Spacing (λ)

Dat

a R

ate

(bps

/Hz)

Sum−CapacityZF−Precoding

Fig. 4: Data rate with different antenna spacing when the BS

antenna array is on the side wall.

B. The Configuration of the Antenna Array

The BS antennas we considered are all 2D planar arrays

which can be divided into horizontal and vertical dimensions.

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

Antenna Spacing (λ)

Dat

a R

ate

(bps

/Hz)

Sum−CapacityZF−Precoding

Fig. 5: Data rate with different antenna spacing when the BS

antenna array is on the ceiling.

In this part, we change the number of antenna elements

on these two dimensions to form different kinds of array

configurations. For example, in the above subsections, the BS

antenna arrays are square, and each array has 8 elements on

both dimensions. However, what will happen on the system

performance if the number of elements on vertical and hori-

zontal dimensions are not equal?

Firstly, take the BS array on the side wall as an example.

When Nth > Ntv , we call it “fat array”. Otherwise, if

Nth < Ntv , we call it “thin array”. Each array has 64 elements.

Other parameters are listed in Table II. In Fig. 6, the sum-

capacities are shown for seven kinds of array configurations. In

general, when the array is on the side wall and the total number

of elements is constant, the more elements are put on the

horizontal dimension, the higher capacity that can be achieved.

Additionally, the gap of the capacity curves of fat arrays is

wider than that of thin arrays. Therefore, it will be more

effective to increase the elements on horizontal dimension.

Moreover, we plot the CDF of correlation among users in Fig.

7 when the antenna spacing is 4λ. It can be seen that when the

array is fat, the correlation among users is smaller than that of

the thin array, so the inter-user interference is weaker and the

capacity is higher. Hence, if the antenna array is arranged on

the side wall, we should increase elements on the horizontal

dimension as much as possible.

Then consider that the BS array is at the center of the

ceiling. When Nth > Ntv , we call it “wide array”. Otherwise,

if Nth < Ntv , we call it “long array”. We take the same

method to get simulation results of capacity and correlation

coefficients which are shown in Fig. 8 and Fig. 9. As can

be seen from Fig. 8, the difference of capacity is most

recognizable when the antenna spacing is 12λ. Thus, in Fig.

9 we assume the antenna spacing as 12λ to see the CDF of

channel correlation coefficients. We can see that the wide

arrays have advantages over the long arrays, so it is more

effective to add elements on the horizontal dimension (parallel

to the long side wall). But if the long array configuration has

to be used, putting all elements on a vertical line (parallel to

the short side wall) can achieve the highest capacity.

TABLE II: Simulation Parameters

BS array

Nth Ntv

64 132 216 48 84 162 321 64

Receiver array Nrh = 1, Nrv = 1

Antenna spacing Side 12λ, λ, 2λ, 4λ, 8λ, 16λ

Ceiling 18λ, 1

4λ, 1

2λ, λ, 2λ, 4λ

0 2 4 6 8 10 12 14 16Antenna Spacing ( )

20

25

30

35

40

45

50

55

Cap

acity

(bps

/Hz)

Nth=64 Ntv=1 (Fat)

Nth=32 Ntv=2 (Fat)

Nth=16 Ntv=4 (Fat)

Nth=8 Ntv=8 (Square)

Nth=4 Ntv=16 (Thin)

Nth=2 Ntv=32 (Thin)

Nth=1 Ntv=64 (Thin)

Fig. 6: Capacity of BS antennas with various configurations

on the side wall.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Correlation Coefficient

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

Nth=64 Ntv=1 (Fat)

Nth=32 Ntv=2 (Fat)

Nth=16 Ntv=4 (Fat)

Nth=8 Ntv=8 (Square)

Nth=4 Ntv=16 (Thin)

Nth=2 Ntv=32 (Thin)

Nth=1 Ntv=64 (Thin)

Fig. 7: CDF of users correlation for BS arrays on the side

wall with various configurations and antenna spacing = 4λ.

0 0.5 1 1.5 2 2.5 3 3.5 4Antenna Spacing ( )

40

45

50

55

60

65

70

75

Cap

acity

(bps

/Hz)

Nth=64 Ntv=1 (Wide)

Nth=32 Ntv=2 (Wide)

Nth=16 Ntv=4 (Wide)

Nth=8 Ntv=8 (Square)

Nth=4 Ntv=16 (Long)

Nth=2 Ntv=32 (Long)

Nth=1 Ntv=64 (Long)

Fig. 8: Capacity of BS antennas with various configurations

on the ceiling.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Correlation Coefficient

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

Nth=64 Ntv=1 (Wide)

Nth=32 Ntv=2 (Wide)

Nth=16 Ntv=4 (Wide)

Nth=8 Ntv=8 (Square)

Nth=4 Ntv=16 (Long)

Nth=2 Ntv=32 (Long)

Nth=1 Ntv=64 (Long)

Fig. 9: CDF of users correlation for BS arrays on the ceiling

with various configurations and antenna spacing = 12λ.

V. CONCLUSION

In this paper, we study how the array factors of BS

antennas affect the system performance in millimeter-wave

MU-MIMO systems. We first study the property of optimal

power allocation when the sum-capacity is achieved, and then

propose a low-complexity calculation method for the sum-

capacity. Then we simulate the system performance under

different kinds of deployments and configurations of the BS

array in an indoor office scenario. In an appropriate range,

with the antenna spacing increasing, the channel capacity will

gradually increase. With a fixed height, deploying the BS

antennas on the ceiling can achieve higher capacity. If the

total number of elements in the array is constant, allocating

more number of elements on the horizontal dimension is more

effective. The channel correlation properties among users are

also demonstrated. In a given propagation environment, the

guidance of BS antenna configuration is trying every aspect

to reduce the channel correlation among users.

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science

Foundation of China under Grant 61371077.

REFERENCES

[1] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellularwireless networks: Potentials and challenges,” Proceedings of the IEEE,vol. 102, no. 3, pp. 366–385, March 2014.

[2] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G. N.Wong, J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter wavemobile communications for 5G cellular: It will work!” IEEE Access,vol. 1, pp. 335–349, May 2013.

[3] T. S. Rappaport, G. R. MacCartney, M. K. Samimi, and S. Sun, “Wide-band millimeter-wave propagation measurements and channel modelsfor future wireless communication system design,” IEEE Transactionson Communications, vol. 63, no. 9, pp. 3029–3056, Sept 2015.

[4] S. Hur, S. Baek, B. Kim, Y. Chang, A. F. Molisch, T. S. Rappaport,K. Haneda, and J. Park, “Proposal on millimeter-wave channel modelingfor 5G cellular system,” IEEE Journal of Selected Topics in SignalProcessing, vol. 10, no. 3, pp. 454–469, April 2016.

[5] 3GPP, “Study on channel model for frequency spectrum above 6 GHz,”in TR 38.900 V14.0.0, June 2016.

[6] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fadingcorrelation and its effect on the capacity of multielement antennasystems,” IEEE Transactions on Communications, vol. 48, no. 3, pp.502–513, Mar 2000.

[7] L. Dong, H. Ling, and R. W. J. Heath, “Multiple-input multiple-outputwireless communication systems using antenna pattern diversity,” inIEEE Global Telecommunications Conference, vol. 1, Nov 2002, pp.997–1001.

[8] Y.-B. Tian and J. Qian, “Improve the performance of a linear arrayby changing the spaces among array elements in terms of geneticalgorithm,” IEEE Transactions on Antennas and Propagation, vol. 53,no. 7, pp. 2226–2230, July 2005.

[9] Y. H. Nam, B. L. Ng, K. Sayana, Y. Li, J. Zhang, Y. Kim, andJ. Lee, “Full-dimension MIMO (FD-MIMO) for next generation cellulartechnology,” IEEE Communications Magazine, vol. 51, no. 6, pp. 172–179, June 2013.

[10] A. A. Abouda, H. M. El-Sallabi, and S. G. Haggman, “Impact ofantenna array geometry on MIMO channel eigenvalues,” in IEEE16th International Symposium on Personal, Indoor and Mobile RadioCommunications, vol. 1, Sept 2005, pp. 568–572.

[11] C. B. Dietrich, K. Dietze, J. R. Nealy, and W. L. Stutzman, “Spatial,polarization, and pattern diversity for wireless handheld terminals,” IEEETransactions on Antennas and Propagation, vol. 49, no. 9, pp. 1271–1281, Sep 2001.

[12] K. Sulonen, P. Suvikunnas, L. Vuokko, J. Kivinen, and P. Vainikainen,“Comparison of MIMO antenna configurations in picocell and microcellenvironments,” IEEE Journal on Selected Areas in Communications,vol. 21, no. 5, pp. 703–712, June 2003.

[13] L. Dong, H. Choo, R. W. Heath, and H. Ling, “Simulation of MIMOchannel capacity with antenna polarization diversity,” IEEE Transactionson Wireless Communications, vol. 4, no. 4, pp. 1869–1873, July 2005.

[14] T. S. Rappaport, R. W. Heath, R. Daniels, and J. N. Murdock, MillimeterWave Wireless Communications. Prentice Hall: Pearson Education,2014.

[15] H. Weingarten, Y. Steinberg, and S. S. Shamai, “The capacity region ofthe Gaussian multiple-input multiple-output broadcast channel,” IEEETransactions on Information Theory, vol. 52, no. 9, pp. 3936–3964,Sept 2006.

[16] S. Vishwanath, N. Jindal, and A. Goldsmith, “Duality, achievable rates,and sum-rate capacity of Gaussian MIMO broadcast channels,” IEEETransactions on Information Theory, vol. 49, no. 10, pp. 2658–2668,Oct 2003.

[17] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge:Cambridge University Press, 2004.