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# Angular Beamforming Technique for MIMO Beamforming System

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## Abstract and Figures

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 beamforming 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.
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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
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 oers 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 [15].
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 oer high channel capacity. Therefore, the
study of using AB technique is the focus of this paper.
Many works on MIMO system [69] 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 [1012] 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 dierent 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
coecients (line of sight and nonline of sight) via both
simulation and measurement results. However, they did not
discuss any analysis of correlation coecients 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 oers 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 oer 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
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
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 oered 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
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
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
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
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-o 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
transmitter. Let w
t
and w
r
be the beamforming vectors. This
requires B
=
N
t
1
i
=1
B
i
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
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 oers
better perfor mance than both QB and AB. However, the
implementation of AB is so easy that provides a very good
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
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
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 coecients 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
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 eects 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 oers 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 oers a low complexity
while oering 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
× 4MIMOsystemsisveried
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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The past decade has seen many advances in physical-layer wireless communication theory and their implementation in wireless systems. This textbook takes a unified view of the fundamentals of wireless communication and explains the web of concepts underpinning these advances at a level accessible to an audience with a basic background in probability and digital communication. Topics covered include MIMO (multiple input multiple output) communication, space-time coding, opportunistic communication, OFDM and CDMA. The concepts are illustrated using many examples from wireless systems such as GSM, IS-95 (CDMA), IS-856 (1 × EV-DO), Flash OFDM and ArrayComm SDMA systems. Particular emphasis is placed on the interplay between concepts and their implementation in systems. An abundant supply of exercises and figures reinforce the material in the text. This book is intended for use on
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This paper addresses digital communication in a Rayleigh fading environment when the channel characteristic is unknown at the transmitter but is known (tracked) at the receiver. Inventing a codec architecture that can realize a significant portion of the great capacity promised by information theory is essential to a standout long-term position in highly competitive arenas like fixed and indoor wireless. Use (nT, nR) to express the number of antenna elements at the transmitter and receiver. An (n, n) analysis shows that despite the n received waves interfering randomly, capacity grows linearly with n and is enormous. With n = 8 at 1% outage and 21-dB average SNR at each receiving element, 42 b/s/Hz is achieved. The capacity is more than 40 times that of a (1, 1) system at the same total radiated transmitter power and bandwidth. Moreover, in some applications, n could be much larger than 8. In striving for significant fractions of such huge capacities, the question arises: Can one construct an (n, n) system whose capacity scales linearly with n, using as building blocks n separately coded one-dimensional (1-D) subsystems of equal capacity? With the aim of leveraging the already highly developed 1-D codec technology, this paper reports just such an invention. In this new architecture, signals are layered in space and time as suggested by a tight capacity bound.
Article
This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99%
Article
This paper studies the performance of multiple-input multiple-output (MIMO) systems employing multichannel beamforming in the presence of unequal power cochannel interference and noise. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel, allowing for transmission on any arbitrary number of eigensubchannels, with possibly different modulation formats, and with possibly unequal powers. New exact expressions are derived for the symbol error rate (SER) of each eigensubchannel, the global SER, and the outage probability. We also present simplified closed-form expressions for the high SNR regime, and show that cochannel interference has no effect on the diversity order, but leads to a loss in array gain. Our results are based on new closed-form exact and asymptotic expressions which we derive for the marginal ordered eigenvalue distributions of a certain class of finite-dimensional complex random matrices.
Conference Paper
The knowledge of state information (CSI) is necessary to be known at transmitter in a multiple input multiple output (MIMO) system in order to improve the capacity performance. Among methods to realize CSI at transmitter, the use of reciprocity principle is the most attractive technique for implementation. This is because CSI at transmitter is easily estimated by the reverse channel where the forward and reverse channels are symmetrically considered in time, frequency and location. In frequency division duplex (FDD) mode, forward and reverse links are allocated by different frequency thus channel reciprocity fails under this condition. In this paper, the capacity performances of adaptive 4times4 MIMO system based on measured data are presented. Also the feasible method to compensate the differences between TDD and FDD channels is studied. The results reveal that the capacity of adaptive MIMO system in FDD mode can be improved by compensation technique.
Conference Paper
In this paper, the verification of using angle domain processing for Multiple Input Multiple Output (MIMO) system is presented. This paper proposes the concept of angle domain processing by applying a Butler matrix into 4 Ã 4 MIMO systems. A butler matrix is the most attractive technique for constructing angle domain due to its low cost and easy to implement. The measured results are compared with conventional MIMO system so called as array domain processing. The capacity performance indicates that the angle domain processing realized by Butler matrix outperforms the conventional system.