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Hindawi Publishing Corporation

International Journal of Antennas and Propagation

Volume 2012, Article ID 638150, 10 pages

doi:10.1155/2012/638150

Research Article

Angular Beamforming Technique for

MIMO Beamforming System

Apinya Innok, Peerapong Uthansakul, and Monthippa Uthansakul

School of Telecommunication Engineering, Suranaree University of Technology, Muang, Nakhon Ratchasima 30000, Thailand

Correspondence should be addressed to Apinya Innok, apinya

in@hotmail.com

Received 3 August 2012; Revised 2 October 2012; Accepted 6 November 2012

Academic Editor: Ananda Sanagavarapu Mohan

Copyright © 2012 Apinya Innok 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 t he original work is properly cited.

The method of MIMO beamforming has gained a lot of attention. The eigen beamforming (EB) technique provides the best

performance but requiring full channel information. However, it is impossible to fully acquire the channel in a real fading

environment. To overcome the limitations of the EB technique, the quantized beamforming (QB) technique was proposed by

using only some feedback bits instead of full channel information to calculate the suitable beamforming vectors. Unfortunalely,

the complexity of ﬁnding the beamforming vectors is the limitation of the QB technique. In this paper, we propose a new technique

named as angular beamforming (AB) to overcome drawbacks of QB technique. The proposed technique oﬀers low computational

complexity for ﬁnding the suitable beamfor ming vectors. In this paper, we also present the feasibility implementation of the

proposed AB method. The experiments are undertaken mainly to verify the concept of the AB technique by utilizing the Butler

matrix as a two-bit AB processor. The experimental implementation and the results demonstrate that the proposed technique is

attractive from the point of view of easy implementation without much computational complexity and low cost.

1. Introduction

The multiple input multiple output (MIMO) systems pro-

vide a good quality of service such as channel capacity. In

general, for MIMO systems, the consideration of channel

capacity is based on the use of array antennas at both the

transmitter and the receiver. Many works have proposed the

eigen beamforming (EB) technique in the literature [1–5].

This technique utilizes the properties of estimated channels

by performing singular value decomposition on channel

matrix. Then the eigenvectors of the channel matrix are con-

sidered as pre- and postcoding schemes for MIMO systems.

This technique can improve the capacity performance, but

both transmitter and receiver have to have perfect knowledge

of the channel information. However, there are many issues

that make use of EB technique in practice such as a

requirement of high system complexity and many procedures

employed for channel feedback transmission. In this paper,

we propose a new technique known as angular beamforming

(AB) technique; the received channels are used to estimate

the suitable pre- and postcoding schemes at the receiver side.

Then, a little number of bits are fed back to transmitter

in order to form beam to the suitable direction according

to the channel. The pre- and postcoding schemes are low

complexity and oﬀer high channel capacity. Therefore, the

study of using AB technique is the focus of this paper.

Many works on MIMO system [6–9] have been proposed

to enhance the channel capacity in order to satisfy the user

demand for high data rate applications. Some of the studies

were focused on theoretical works, and others performed

measurements. Nevertheless, most of the paper developed

techniques to enhance the channel capacity through channel

behaviour [10–12] such as adjusting transmitted powers

according to eigenvalue of channels which is known as

water ﬁlling method. In general, it can be noticed that

the theoretical consideration of channel capacity is based

on the assumption that array antennas are employed at

both the transmitter and the receiver. However, the channel

characteristic is dependent on many angle-based parameters

of multipath such as angle of arrival, angle of departure,

and angle of spread. Therefore, it would be interesting

to investigate the performance of MIMO system using

2 International Journal of Antennas and Propagation

the angular beamforming (AB) instead of the conventional

methods.

Recently, the authors in [13, 14] developed a channel

estimation of MIMO-OFDM system based on angular

beamforming (AB) consideration. The applicability of AB

technique depends on the channel stochastic information

available at the receiver. The design of suitable pilots is pro-

posed by facilitating the direct implementation of analyzing

the performances of diﬀerent channel estimation techniques.

Although the signiﬁcant improvement on MIMO capacity

can be expected by using AB method, so far in the literature,

there is no work available that illustrates the capacity beneﬁt

of using AB method. The reason is the lack of pre- and post-

coding schemes for angle transformations that can decrease

the complexity on both transmitter and receiver. Hence, it

is challenging to ﬁnd a technique that can obtain lower

cost and lower complexity that matches with the concept

of AB method. In [15], a scheme was proposed that uses

a discrete fourier transformation (DFT) to receive a signal

vector in RF domain. This can be realized by placing a Butler

matrix between the antenna elements and the receiver switch.

However , [15] presented only the simulations results, and

no measurement result was provided. With only simulation

results, one cannot claim the practical advantages of the

system. A low proﬁle concept of angle domain processing

has been conveniently implemented in [16] by only inserting

Butler matrices before antenna array at transmitter and

receiver. The authors of [17] investigated the correlation

coeﬃcients (line of sight and nonline of sight) via both

simulation and measurement results. However, they did not

discuss any analysis of correlation coeﬃcients which was later

presentedbyusin[18]. But, in our previous work, we did not

consider the process of feedback bits for increasing channel

capacity. In this paper, the complexity analysis of how

Angular beamforming (AB) and quantized beamforming

(QB) impact on the channel matrix is provided. We also

provide reasons as to why the use of AB method for MIMO

system oﬀers a better performance over a QB method.

Further, in this paper, we perform experimental campaigns

by fabricating a Butler matrix so as to further demonstrate

the usefulness of our system for practical application. The

Butler matrix was chosen because it is just a low-complexity

hardware that can oﬀer the Angular beamforming (AB). In

general, there are inﬁnite choices to choose for the set of

orthogonal steering vectors to form an AB. Therefore, it is

hard to justify whether Butler matrix provides the best per-

formance among others. To focus on hardware complexity,

the other methods to form AB might need 16 phase shifters

to simultaneously form 4 beams whereas the Butler matrix

approach uses only one low-cost printed circuit board. This

motivated the authors to construct the 4

× 4MIMOsystem

featuring AB by employing a Butler matrix which has a

low proﬁle concept and is convenient for implementation.

This Butler matrix simultaneously forms multiple beams for

providing departure or arrival angles into four directions.

By only inserting Butler matrix into the antenna arrays, the

conventional MIMO systems can be transformed into the

MIMO systems with Angular beamforming (AB) without

Transmitter

Receiver

MIMO

encoder

Weight Weight

MIMO

decoder

Feedback bit

H

- v - b

s

- w

t

- u

t

- w

r

- u

r

Figure 1: 4 × 4 MIMO system with beamforming.

the need for additional burden on processing units at both

transmitter and receiver.

In summary, the contribution of this paper falls into

three main categories. The ﬁrst contribution is related to

the comparisons in terms of channel capacity. Secondly, we

demonstrate as to how the simulation complexity of AB

method and QB method impacts on the channel matrix

which is not available elsewhere. The main aim here is to

help the reader to understand the key beneﬁts oﬀered by AB.

The third contribution is to the implementation feasibility

of AB method for 4

× 4MIMOsystemswhichhasbeen

demonstrated using a Butler matrix. All the three contri-

butions either propose a new concept or conﬁrm the actual

beneﬁt of employing MIMO with AB. The paper is organized

as follows. In Section 2, the details of M IMO beamforming,

AB, QB, and EB techniques are described. Then in Section 3,

the simulation results and complexity analysis of using AB

and QB are explained. The implementation and feasibility of

usingaButlermatrixtoapplyforABaregiveninSection 4.

Section 5 describes the details of channel measurements.

Section 5 provides the measurement results of AB realized

by Butler m atrix in comparing with CM system. Finally in

Section 6, the conclusion of this paper is given.

2. MIMO Beamforming

2.1. Angular Beamforming (AB). Referring to Figure 1, the

transmitter, the data symbol s is modulated by the beam-

former u

t

, and then the sig nals are transmitted into a

MIMO channel. At the receiver, the signals are processed

with the beamforming vector u

r

. Then the relation between

transmitted and received signal is given by

y

= u

∗

r

[

Hu

t

s + n

]

.

(1)

The transmit beamforming vector u

t

and the receive beam-

forming vector u

r

in (1) are usually chosen to maximize

the receive SNR. Without loss of generality, we assume that

U

r

2

= 1, E{s

2

}=1. Then the received SNR is expressed

as

ρ

=

E

u

∗

r

Hu

t

s

2

E

u

∗

r

n

2

=

u

∗

r

Hu

t

2

σ

2

n

. (2)

To maximize the received SNR, the optimal transmit beam-

former is chosen as the eigenvector corresponding to the

International Journal of Antennas and Propagation 3

largest eigen-value of HH

∗

. The singular values can be

obtained form SVD technique by using MATLAB. Thus the

maximized received S NR is ρ

= (λ

max

(HH

∗

))/(σ

2

n

). The

λ

max

is the maximum eigen-value of a matrix that is formed

by identically distributed (i.i.d.) complex Gaussian random

variables with zero-mean and variance σ

2

n

in [3].

There is an arbitrary number of physical paths between

the transmitter and receiver [19]; the ith path having atten-

uation of a

i

makes an angle of φ

ti

(Ω

ti

:= cos φ

ti

) with the

transmit antenna array and angle of φ

ri

(Ω

ri

:= cos φ

ri

)

with the receive antenna array. The channel mat rix H can be

written using the following expressions:

H

=

i

a

b

i

e

r

(

Ω

ri

)

e

t

(

Ω

ti

)

∗

,

(3)

where

a

b

i

:= a

i

N

t

N

r

exp

−

j2πd

i

λ

c

,

e

t

(

Ω

)

:

=

1

N

t

⎡

⎢

⎢

⎢

⎢

⎣

1

exp

−

j

(

2πΔ

t

Ω

)

.

.

.

exp

−

j

(

N

t

− 1

)(

2πΔ

t

Ω

)

⎤

⎥

⎥

⎥

⎥

⎦

,

e

r

(

Ω

)

:

=

1

N

r

⎡

⎢

⎢

⎢

⎢

⎣

1

exp

−

j

(

2πΔ

r

Ω

)

.

.

.

exp

−

j

(

N

r

− 1

)(

2πΔ

r

Ω

)

⎤

⎥

⎥

⎥

⎥

⎦

.

(4)

Also, d

i

is the distance between transmit and receive

antennas along ith path. Note that (

·)

∗

is the conjugate

and transpose operation. The vectors e

t

(Ω)ande

r

(Ω)are,

respectively, transmitted and received unit spatial signatures

along the direction Ω,andλ

c

is the wavelength of the

center frequency in a whole signal bandwidth. Assuming

uniform linear array, the normalized separation between

the transmit antennas is Δ

t

(antenna separation/λ

c

), and

the normalized separation between receive antennas is Δ

r

(antenna separation/λ

c

). Note that the reason of normal-

ization is because this proposed system can work in any

frequency band. Hence, the normalization is made to neglect

the unused parameter. Channel state information (CSI) is

not available at the transmitter. The concept of Angular

beamforming (AB) can be represented by the transmitted

and received signals. It is convenient for implementation

by just inserting u

t

and u

r

at both transmitter and receiver

because the beamforming vectors depend on ang le of arrival

or departure. The numbers of feedback bits are deﬁned by

the angle (θ), θ

∈ [0, π). The angles are divided equally.

The angle can be expressed as N

i

= 2

B

i

, N

i

denoting

the number of angle levels. B

i

is the number of feedback

bits. When comparing with Quantized Beamforming (QB),

theproceduretoﬁndbeamformingvectorsinQBismore

complex than that of AB. The detail of QB is shown in the

next section. In general, u

t

and u

r

can be written as

u

t

=

1

N

t

exp

jlkΔ

t

cos θ

; l = 1, 2, ..., N

t

,

u

r

=

1

N

r

exp

jmkΔ

r

cos θ

; m = 1, 2, ..., N

r

,

(5)

where k

= 2π/λ

c

. We can use max u

∗

r

Hu

t

2

that will be

maximum for u

t

and u

r

. So the channel mat rix of AB can

be wr itten as

H

a

max

= u

∗

r max

Hu

t max

.

(6)

Thus, the capacity [20] of MIMO systems using AB is given

by

C

= log

2

det

I

N

r

+

P

t

P

N

N

t

H

a

max

H

a

max

∗

,

(7)

where P

t

is the transmitted power and P

N

is the noise power

in each branch of antennas at the receiver. Note that the

signal-to-noise power ratio ( SNR) is deﬁned as P

t

/P

N

. I

N

r

is

the identity matrix having N

r

× N

r

dimension, and H is the

channel matrix having N

r

× N

t

dimension with H

∗

being its

transpose conjugate. In this paper, the channel matrix H is

normalized by

H

2

F

= N

r

N

t

. H

a

max

is the channel matrix of

size N

r

× N

t

streams.

2.2. Quantized Beamforming (QB). In eigen beamforming

(EB) designs, we have assumed that the transmitter has

perfect knowledge of CSI. However, in many real systems,

having the CSI known exactly at the transmitter is hardly

possible. The channel information is usually provided by the

receiver through a bandwidth-limited ﬁnite-rate feedback

channel, and quantization method, which has been widely

studied for source coding [3], can be used to provide the

feedback information. We assume herein that the receiver

has perfec t CSI. The transmit beamforming vector w

t

for

QB is used under the uniform elemental power constraint.

The expression for transmit beamformer w

t

(θ

0

, θ

1

, ..., θ

N

t

−1

)

which is a function of N

t

parameters {θ

i

, θ

i

∈ [0, 2π)}

N

t

−1

i

=0

is

obtained using simple manipulations as

w

t

θ

0

, θ

1

, ..., θ

N

t

−1

=

1

N

t

e

jθ

0

⎡

⎢

⎢

⎢

⎢

⎢

⎣

1

e

j

¨

θ

1

.

.

.

e

j

¨

θ

N

t

−1

⎤

⎥

⎥

⎥

⎥

⎥

⎦

,(8)

where

Hw

t

(θ

0

, θ

1

, ..., θ

N

t

−1

)

2

=Hw

t

(

¨

θ

1

,

¨

θ

2

, ...,

¨

θ

N

t

−1

)

2

.

Since

Hw

t

(θ

0

, θ

1

, ..., θ

N

t

−1

)

2

=Hw

t

(

¨

θ

1

,

¨

θ

2

, ...,

¨

θ

N

t

−1

)

2

.

We can reduce one parameter and quantize w

t

(

¨

θ

1

,

¨

θ

2

,

...,

¨

θ

N

t

−1

) instead of w

t

(θ

0

, θ

1

, ..., θ

N

t

−1

). Consider

w

t

¨

θ

n

i

1

, ..., θ

n

N

t

−1

N

t

−1

=

1

N

t

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎣

1

e

j

¨

θ

n

1

1

.

.

.

e

j

¨

θ

n

N

t

−1

N

t

−1

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎦

,(9)

4 International Journal of Antennas and Propagation

Table 1: Average capacity (bps/Hz) 4 × 4 MIMO beamforming for SNR = 10 dB.

Methods

Number of feedback bits

12345678

EB 5.113 5.113 5.113 5.113 5.113 5.113 5.113 5.113

AB 2.391 4.538 5.076 5.088 5.091 5.093 5.093 5.093

QB 3.711 3.711 5.09 5.09 5.09 5.09 5.09 5.09

0

5 10 15 20

25

0

2

4

6

8

10

12

SNR (dB)

MIMO 4 × 4 (1 stream)

Average capacity (bits/s/Hz)

EB

AB 1 bit

QB 1 bit

AB 2 bits

QB 2 bits

AB 3 bits

QB 3 bits

Figure 2: Capacity versus SNR.

where

¨

θ

n

i

1

= (2πn

i

)/(N

i

), 0 ≤ n

i

≤ N

i

−1, i = 1, 2, ..., N

t

−1,

with N

i

= 2

B

i

and N

i

denoting the number of quantization

levels and feedback index of

¨

θ,respectively,andwhereB

i

is

the number of feedback bits for

¨

θ

i

.

We quantize the parameters

¨

θ

i

to the round-oﬀ grid point

¨

θ

n

i

1

, i = 1, 2, ..., N

t

− 1. Hence for this quantization scheme,

we need to send the index set n

i

from the receiver to the

transmitter. Let w

t

and w

r

be the beamforming vectors. This

requires B

=

N

t

−1

i

=1

B

i

bits. The receive beamformer w

r

can

be wr itten as

w

r

=

Hw

t

¨

θ

n

i

1

,

¨

θ

n

i

2

, ..., θ

n

N

t

−1

N

t

−1

Hw

t

¨

θ

n

i

1

,

¨

θ

n

i

2

, ..., θ

n

N

t

−1

N

t

−1

.

(10)

We can use max

w

∗

r

Hw

t

2

that will provide maximum

w

t

and w

r

. Then, the channel matrix QB when applying

the maximum transmits beamforming (w

t max

) and the

maximum receive combing vector (w

r max

)canbewrittenas

H

q

max

= w

∗

r max

Hw

t max

.

(11)

Thus, the capacity [20] of MIMO system using QB is given

by

C

= log

2

det

I

N

r

+

P

t

P

N

N

t

H

q

max

H

q

max

∗

,

(12)

1 2 3 4 5 6 7

0

5

10

15

20

25

Number of feedback bits

AB

QB

Simulation times (milliseconds)

MIMO 4 × 4

Figure 3:Simulationtimesversusnumberoffeedbackbits.

where I

N

r

is the identity matrix of size N

r

× N

r

and H

q

max

is

the channel matrix of size N

r

× N

t

.

2.3. Eigen Beamforming (EB). Considering a MIMO channel

with N

r

× N

t

channel matrix H to be known at both the

transmitter and the receiver, the eigenvectors can be found

by applying SVD technique to the channel matrix as shown

in the following:

H

= BSV

∗

,

(13)

where N

r

× N

r

matrix B and the N

t

× N

t

matrix V are

unitary matrices and S is an N

r

× N

t

diagonal matrix. The

beamforming vectors b and v can be found from unitary

matrices B and V, respectively. The beamforming vectors

are given by the ﬁrst column of the unitary matrices. These

two vectors are used as pre- and postcoding matrices at

transmitter and receiver, respectively. So the channel matrix

of EB can be written as

H

e

= b

∗

Hv.

(14)

Thus, the capacity of MIMO system using EB is given by

C

= log

2

det

I

N

r

+

P

t

P

N

N

t

H

e

H

e

∗

.

(15)

International Journal of Antennas and Propagation 5

5.14mm.

5.14 mm

2.99 mm

5.14 mm

2.99 mm

2.99 mm

14.26 mm

14.26 mm

5.14 mm

2.99 mm

2.99 mm

5.14 mm

2.99 mm

2.99 mm

14.26 mm

14.26 mm

5.14 mm

2.99 mm

2.99 mm

5.14 mm

2.99 mm

2.99 mm

14.26 mm

14.26 mm

2.99 mm

2.99 mm

5.14 mm

2.99 mm

2.99 mm

5.14 mm

2.99 mm

2.99 mm

14.26 mm

14.26 mm

2.99 mm

2.99 mm

5.14 mm

14.26 mm

12.18 mm

38.92 mm

12.18 mm

Z

0

Z

0

14.26 mm 14.26 mm

38.92 mm

Figure 4:ThedimensionsofButlermatrix.

Table 2: The process of formation of FLOP with the QB.

QB

FLOP

N

i

= 2

B

i

B − 1

B

a

1

=B/(N

t

− 1)

2

B

a

2

= B

a

1

+1

1

N

s

= B − B

a

1

(N

t

− 1)

3

¨

θ

i

=

2πn

i

N

i

;0≤ n

i

≤ N

i

− 1

2

Return loop θ

n

i

i

can ﬁnd from N

i

B − 1

w

t

¨

θ

n

i

1

, ..., θ

n

N

t

−1

N

t

−1

=

1

N

t

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

1

e

j

¨

θ

n

1

1

.

.

.

e

j

¨

θ

n

N

t

−1

N

t

−1

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

N

t

− 1

w

r

=

Hw

t

¨

θ

n

i

1

,

¨

θ

n

i

2

, ..., θ

n

N

t

−1

N

t

−1

Hw

t

¨

θ

n

i

1

,

¨

θ

n

i

2

, ..., θ

n

N

t

−1

N

t

−1

3(N

t

− 1)

h

s

=

1

N

t

w

∗

r

Hw

t

2

5

Return loop and ﬁnd maximum

channel from N

i

= 2

B

i

B − 1

Total

2B

2

+5B +4BN

t

− 4N

t

− 7

3. Simulation Results and Discussion

The simulations are performed using MATLAB, and the

capacity results are evaluated by using (7), (12), and (15).

Tx Rx

00

01

10

11

00

01

10

11

2-bits feedback

Figure 5: Illustration of applying two-bit feedback (Butler matrix)

for 4

× 4 MIMO systems.

Figure 2 shows the average capacity versus SNR. We increase

the number of feedback bits, since the range of capacity

enhancement depends on the number of feedback bits.

Also, the number of feedback bits can improve the channel

capacity. The numerical values of average capacity at SNR

=

10 dB for other bits are given in Table 1 . It can be obviously

noticed that the beneﬁt of AB is pronounced for all the

bits. It must be kept in mind that the improvement of

MIMO capacity comes with a cost of inserting u

t

and

u

r

at both transmitter and receiver and corresponding

extra implementation complexity. The optimum EB oﬀers

better perfor mance than both QB and AB. However, the

implementation of AB is so easy that provides a very good

tradeoﬀ with EB.

The method of calculating feedback bits in AB is simpler

than QB so that the operating time of AB is much shorter

6 International Journal of Antennas and Propagation

Table 3: The process of formation of FLOP with the AB.

AB FLOP

N

i

= 2

B

i

B − 1

π/2

B

1

Return loop ﬁnd θ from N

i

B − 1

u

t

=

1/

N

t

exp

jlkΔ

t

cos θ

; l = 1, 2, ..., N

t

N

t

u

r

=

1/

N

r

exp

jlkΔ

r

cos θ

; l = 1, 2, ..., N

r

N

r

h

a

=

(

1/N

t

)

u

∗

r

Hu

t

2

5

Return loop and ﬁnd maximum channel from N

i

= 2

B

i

B − 1

Total 2B

2

+2B + BN

t

+ BN

r

− N

t

− N

r

− 4

Table 4: Element phasing, beam direction, and interelement phasing for the Butler matrix shown in Figure 3 (conceptual).

b

t

, b

r

E1(l = 1) E2(l = 2)

E3(l

= 3) E4(l = 4)

Beam direction Interelement phasing

Port 1 (m = 1)

1

√

4

e

−j45

◦

1

√

4

e

−j180

◦

1

√

4

e

j45

◦

1

√

4

e

−j90

◦

138.6

◦

−135

◦

Port 2 (m = 2)

1

√

4

e

j0

◦

1

√

4

e

−j45

◦

1

√

4

e

−j90

◦

1

√

4

e

−j135

◦

104.5

◦

−45

◦

Port 3 (m = 3)

1

√

4

e

−j135

◦

1

√

4

e

−j90

◦

1

√

4

e

−j45

◦

1

√

4

e

−j0

◦

75.5

◦

45

◦

Port 4 (m = 4)

1

√

4

e

−j90

◦

1

√

4

e

j45

◦

1

√

4

e

−j180

◦

1

√

4

e

−j45

◦

41.4

◦

135

◦

Table 5: Element phasing, beam direction, and interelement phasing for the Butler matrix shown in Figure 4 (manufactured).

b

t

, b

r

E1 (l = 1) E2 (l = 2)

E3 (l

= 3) E4 (l = 4)

Beam direction Intere lement phasing (average)

Port 1 (m = 1)

1

√

4

e

j158

◦

1

√

4

e

j25

◦

1

√

4

e

−j112

◦

1

√

4

e

j118

◦

138

◦

−130

◦

Port 2 (m = 2)

1

√

4

e

−j87

◦

1

√

4

e

−j137

◦

1

√

4

e

j176

◦

1

√

4

e

j137

◦

105

◦

−42

◦

Port 3 (m = 3)

1

√

4

e

j132

◦

1

√

4

e

j178

◦

1

√

4

e

−j139

◦

1

√

4

e

−j98

◦

76

◦

50

◦

Port 4 (m = 4)

1

√

4

e

j136

◦

1

√

4

e

−j90

◦

1

√

4

e

j40

◦

1

√

4

e

j176

◦

42

◦

138

◦

LNAPower ampliﬁer

Rx

RxTx

Tx

Butler

Butler matrixButler matrix

Angular

beamforming

Butler

Conventional

MIMO (CM)

(AB)

Conventional

MIMO (CM)

Angular

beamforming

(AB)

Network analyzer

Figure 6: Block diagram of measurement setup.

International Journal of Antennas and Propagation 7

Transmitter

Receiver

4

1

2

3

Chamber room

24 m

12 m

Figure 7: Measurement scenarios.

than QB. The complexity of QB and AB can be expressed

in Tables 2 and 3, respectively. We evaluate the complexity

[21] of AB and QB in terms of FLOPs. It is clearly seen that

the Flop in Table 3 of AB is less than Flop of QB presented

in Table 2 . This implies that the lower processing time for

AB can be obtained, w hich is shown in Figure 3. Figure 3

also shows the time spent computation with feedback

information for 4

× 4 MIMO beamforming. The simulation

times versus number of feedback bits using AB and QB

technique are presented. It is demonstrated that AB requires

less processing time than QB.

4. Feasibility of Practical Implementation

The feasibility of implementing AB processing for 4 × 4

MIMO systems is explored here by using Butler matrix [22].

Butler matrix constitutes four 90

◦

hybrid couplers and two

phase shifters w ith 45

◦

phase and a crossover. Figure 4 shows

the dimensions of Butler matrix which has been calculated

by using transmission line theory. The ﬁxed beamforming

matrix is a bidirectional transmission. Hence, it can be used

for either receiver or transmitter.

It can be easily shown that the weight vectors corre-

sponding to each port presented in Ta ble 4 are mutually

orthogonal. Therefore, instead of using (5), the vector beam-

forming of applying Butler matrix can be written by the

following expressions:

b

t

=

1

N

t

exp

jlkΔ

t

cos φ

; l = 1, 2, ..., N

t

,

b

r

=

1

N

r

exp

jmkΔ

t

cos φ

; m = 1, 2, ..., N

r

,

(16)

where φ is the beam direction in Table 5 . The characteristic

of fabricated prototype is also conﬁrmed by measuring

interelement phasing and beam direction w h ich are shown

in Ta b le 5. In this table, the distributions of all interelement

phasing are similar to conceptual Butler matrix but they a re

slightly deviated by

±10 degree. However, the beam direction

is deviated only by just 0.6 degree.

Figure 5 illustrates the beam direction of applying 2-bit

feedback (Butler matrix) to both transmitter and receiver.

It is interesting to see that the concept of AB is successfully

achieved by simply adding Butler matrices next to antenna

elements. We use the beamforming vector b

t

1

representing

beam direction 00; b

t

2

, b

t

3

,andb

t

4

represent beam direction

01, 10, and 11 degrees, respectively. Then, the channel matrix

realized by Butler matrix can be written as

H

b

= b

∗

r

Hb

t

,

(17)

where b

t

and b

r

are the beamforming vectors whose rows

are the vectors in four directions for transmitter and receiver

and H is channel matrix of size N

r

× N

t

to get conventional

MIMO. Thus, the capacity of MIMO systems when applying

Butler matrix is given by

C

= log

2

det

I

N

r

+

P

t

P

N

N

t

H

b

H

b

∗

.

(18)

5. Measurement Results and Discussion

Figure 6 shows a block diagram of measurement setup for

4

× 4 MIMO system. The network analyzer is used for

measuring channel coeﬃcients in magnitude and phase. The

power ampliﬁer (PA) is used at transmitter to provide more

transmitted power. Low noise ampliﬁer (LNA) is used at the

receiver to increase the appropriate by the received signal

level [23]. Four measurements on the channel are under-

taken at each location. In each location, two modes of MIMO

operation (conventional MIMO and AB) are measured. The

Butler matrices are inserted a t both transmitter and receiver

when measuring MIMO channels w ith AB. Figure 7 shows

measurement scenarios. We chose measurements in a large

room to provide various test conditions. The location of the

transmitter is ﬁxed as shown in Figure 7 with rectangular

symbol. There are four measured locations for the receiver

represented by circular symbol in Figure 7. The antenna

is a monopole. The numbers of transmitted and received

antennas are 4

×4. The center frequency (λ

c

) is 2.4 GHz. The

normalized separation between transmit and receive anten-

nas (Δ

t

, Δ

r

) is 0.5. Distance between Tx and Rx locations

1, 2, 3, and 4 is 2.3, 6.1, 6.8, and 13.3 meters, respectively.

It is easy to measure both conventional MIMO and AB

by using switches presented in Figure 6.Themeasured

results obtained by network analyzer are used as a channel

response in MIMO systems. As seen in Figure 6,apartfrom

Butler matrix, all the other components are the same for

both conventional MIMO and AB. Therefore, the measured

channels can be directly compared to each other as presented

in the following. Figure 8 shows the photo of measurement

areas for LOS (location 1) and NLOS (location 4).

ThechannelmatricesH and H

b

can be realized from

the measured data from vector network analyzer. The

channel fading environments are measured by changing the

locations of the receiver. We also believe that the mismatches

8 International Journal of Antennas and Propagation

Tx

Rx

Network analyzer

Power ampliﬁer

(a) LOS

Tx

Network analyzer

Power ampliﬁer

Rx

(b) NLOS

Figure 8: The photo of measurement areas for LOS and NLOS.

00 01 10 11

0

1

2

3

4

5

6

Capacity(bits/s/Hz)

Feedback bits

Location 1, Tx to Rx

= 2.3 meters

The best

choice

Level of EB

(a)

00 01 10 11

0

1

2

3

4

5

6

Capacity(bits/s/Hz)

Feedback bits

Location 2, Tx to Rx

= 6.1 meters

=

The best

choice

Level of EB

(b)

00 01 10 11

0

1

2

3

4

5

6

Capacity(bits/s/Hz)

Feedback bits

Location 3, Tx to Rx

= 6.8 meters

EB

AB

QB

The best

choice

Level of EB

(c)

00 01 10 11

0

1

2

3

4

5

6

Capacity(bits/s/Hz)

Feedback bits

Location 4, Tx to Rx

= 13.3 meters

EB

AB

QB

The best

choice

Level of EB

(d)

Figure 9: Average capacity versus beam direction for two-bit feedback, locations 1, 2, 3, and 4.

International Journal of Antennas and Propagation 9

among RF circuits in transmitting/receiving components

and mutual coupling eﬀects are included in the measured

channel. We use 2 bits of feedback for QB. The simulations

are undertaken by utilizing measured data into M ATLAB

programming. We have made comparisons between EB, QB,

and AB. The capacity results are evaluated by using (12),

(15), and (18).

In Figure 9, the average capacity versus beam direction

for feedback of two bits is presented, in order to justify

the results of all locations at SNR

= 10 dB. The results

indicate that AB oﬀers a better performance than QB. It is

obviously noticed that the beneﬁt of using AB is pronounced

at all locations. The gap deviation is about 1.83 bits/s/Hz.

Please be reminded that the improvement of MIMO capacity

comes at a little expense of inserting Butler matrices at both

transmitter and receiver but without any extra complexity

when compared with EB.

6. Conclusion

This paper presents the performance of MIMO beamforming

systems using EB, QB, and AB techniques. The result reveals

that the proposed system, AB technique, is attractive to be

practically implemented because it oﬀers a low complexity

while oﬀering the similar performance as that of QB. We

have also presented the performance of MIMO systems using

AB realized by using Butler matrix. Further, the beneﬁt of

using AB technique for 4

× 4MIMOsystemsisveriﬁed

by measured results. The AB method as realized by Butler

matrix has been implemented and compared with EB and

QB. The results have revealed that the EB outperforms the

AB and QB at all locations. The reason for this is that the EB

uses the maximum eigenvalue for ﬁnding channel capacity.

It is concluded that the proposed system is very attractive to

practically implement on MIMO systems due to its low cost

and complexity.

Acknowledgments

This work is ﬁnancially supported by Suranaree Un iversity of

Technology, Thailand, and the Royal Golden Jubilee Program

of Thailand Research Fund, Thailand.

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