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Simulation of MIMO channel capacity with antenna polarization diversity

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Liang Dong at Baylor University
Liang Dong
Hosung Choo
Hosung Choo
Hosung Choo
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Robert W. Heath at University of California, San Diego
Robert W. Heath
Hao Ling at University of Texas at Austin
Hao Ling
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A simulation study of the channel capacity of a multiple-input multiple-output (MIMO) antenna system exploiting multiple polarizations is carried out. We focus on a simple yet realistic trimonopole antenna structure, taking into account all the mutual coupling and casing effects using the computational electromagnetics solver-numerical electromagnetics code. Simulation results show that, with a special transmit geometry, using the collocated trimonopole antennas at a size-constrained receiver can offer channel capacity that approaches the capacity of an uncorrelated MIMO Rayleigh channel. In addition, it is shown that the capacity increase is mainly attributed to polarization diversity instead of pattern diversity. Furthermore, we find that the mutual coupling and casing effects in the trimonopole system can actually provide a large capacity increase with less constraint on the antenna configurations than the idealized tridipole system.
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY 2005 1869
Simulation of MIMO Channel Capacity With
Antenna Polarization Diversity
Liang Dong, Member, IEEE, Hosung Choo, Member, IEEE,
Robert W. Heath, Jr., Member, IEEE, and Hao Ling, Fellow, IEEE
Abstract—A simulation study of the channel capacity of a
multiple-input multiple-output (MIMO) antenna system exploit-
ing multiple polarizations is carried out. We focus on a simple
yet realistic trimonopole antenna structure, taking into account
all the mutual coupling and casing effects using the computational
electromagnetics solver—numerical electromagnetics code. Simu-
lation results show that, with a special transmit geometry, using
the collocated trimonopole antennas at a size-constrained receiver
can offer channel capacity that approaches the capacity of an
uncorrelated MIMO Rayleigh channel. In addition, it is shown
that the capacity increase is mainly attributed to polarization
diversity instead of pattern diversity. Furthermore, we find that
the mutual coupling and casing effects in the trimonopole system
can actually provide a large capacity increase with less constraint
on the antenna configurations than the idealized tridipole system.
Index Terms—Channel capacity, fading correlation, multiple-
input multiple-output (MIMO) systems, multiple polarizations.
I. INTRODUCTION
A
PROMISING way of achieving high data rate in wireless
communications is to use multiple antennas at both the
transmitter and the receiver, forming a multiple-input multiple-
output (MIMO) system [1], [2]. Parallel subchannels can be
established between the transmitter and the receiver antennas if
the fading of the transmitter–receiver pairs is uncorrelated [3].
Correlated fading can pose a serious problem, typically at the
mobile handset where the spacing of antenna elements is highly
constrained. Polarization diversity and pattern diversity have
been exploited to decrease the signal correlation of local anten-
nas at mobile handsets [4]. The performance of a MIMO system
employing dual-polarized antennas has been investigated in [5]
and [6].
Recently, many researchers have examined the multiple
polarizations for a MIMO antenna system. Andrews et al. [7]
argued for a wireless MIMO link that provides six uncorrelated
signals with three electric dipoles and three magnetic dipoles
Manuscript received August 26, 2003; revised January 14, 2004; accepted
May 11, 2004. The editor coordinating the review of this paper and approving it
for publication is R. Valenzuela. This work was supported by the Texas Higher
Education Coordinating Board under the Texas Advanced Technology Program
and by the Office of Naval Research.
L. Dong is with the Department of Electrical and Computer En-
gineering, Western Michigan University, Kalamazoo, MI 49008 USA
(e-mail: liang.dong@wmich.edu).
H. Choo is with the School of Electronic and Electrical Engineering, Hongik
University, Seoul, 121-791, Korea (e-mail: hschoo@hongik.ac.kr).
R. W. Heath, Jr. and H. Ling are with the Department of Electrical and
Computer Engineering, University of Texas at Austin, Austin, TX 78712 USA
(e-mail: rheath@ece.utexas.edu; ling@ece.utexas.edu).
Digital Object Identifier 10.1109/TWC.2005.850318
at the transceiver. They assumed an antenna model with ideal
polarizations and a rich scattering environment, and verified
their analysis experimentally using three orthogonal electric
dipoles. Svantesson [8] studied the effect of multipath angular
spread on the channel capacity of such a system, and showed
that the capacity increase is due to a combination of polarization
and pattern diversity. Stancil et al. [9] presented experimental
results verifying that collocated electric and magnetic dipoles
can be used to realize independent channels. Andersen and
Getu [10] proposed an antenna cube with an electric dipole on
each of the 12 edges. The diversity among the antennas is a
combination of space and polarization diversity.
In this paper, we present a simulation study to investigate
the capacity of a multipolarized MIMO channel. The capacity
increase is affected by various system parameters, such as
antenna configurations, propagation environments, and system
assumptions. For the mobile handset, we use a realistic antenna
structure consisting of three collocated monopole antennas
mounted on a small box (to simulate the handheld unit). The
numerical electromagnetics code (NEC) [11], a full-wave com-
putational electromagnetic solver, is used to simulate the an-
tenna radiation patterns and polarizations taking into account
all the mutual coupling and casing effects. The antenna pat-
tern from the NEC model is verified by measured data from
an experimental prototype. Based on the simulation results,
we examine the effect of different propagation environments,
pinpoint the channel capacity increase from polarization and
pattern diversity, and compare the performance to idealized
dipole-antenna systems.
II. MIMO C
HANNEL CAPACITY WITH ANTENNA
POLARIZATION DIVERSITY
We assume a MIMO downlink with n
T
transmit antennas
at the base transceiver station (BTS) and n
R
receive antennas
at the mobile station (MS), where the channel is known to the
receiver but not to the transmitter. When the transmitted signals
are independent with equal power at each antenna, the ergodic
channel capacity taken over the probability distribution of G is
given by [1]
C = E
log
2
det
I
n
R
+
P
n
T
N
GG
†

(1)
where G is an n
R
× n
T
transfer matrix of the flat-fading
channel, P is the total transmitted power, and N is the variance
1536-1276/$20.00 © 2005 IEEE
1870 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY 2005
Fig. 1. MS prototype with three quarter-wavelength monopoles (polarization diverse antennas). (a) NEC model. (b) Experimental model. (c) X–Z section of
antenna radiation patterns from NEC simulation and measurement.
of the independent Gaussian noise at each receive antenna.
Both the signal strength and the channel correlation can affect
the capacity [5]. Focusing on the effect of channel correlation
on the capacity, we normalize the channel in the sense that
E[G
F
]=(n
T
n
R
)
1/2
, where ·
F
denotes the Frobenius
norm. This normalization has been used in other work such as
[12]. A deeper study of normalization issues, along the lines of
[13], is a topic for future work.
The elements of G are correlated by an amount that depends
on the propagation environment as well as the polarization of
the antenna elements and the spacing between them. One model
for G that takes the fading correlation into account splits the
correlation into two independent components as receive corre-
lation and transmit correlation G = Ψ
1/2
r
G
w
Ψ
1/2
t
[14], [15].
Ψ
r
and Ψ
t
are respectively the covariance matrices of the re-
ceive and transmit antennas, and G
w
has uncorrelated complex
Gaussian entries. Suppose receive antennas i and j, with field
patterns A
i
and A
j
, respectively, are exposed to the incident
wave represented by electric field E. We assume that the phase
angles of E
θ
and E
φ
are independent and uniformly distributed
in [0, 2π), and they are independent for waves arriving from
different directions. Thus, the (i, j)th entry of Ψ
r
is [16]
Ψ
(i,j)
r
=
1
σ
i
σ
i
E
[A
i
(Ω) · E(Ω)]
A
∗
j
(Ω) · E
∗
(Ω)

dΩ
(2)
where σ
i
and σ
j
are the variances of signals received by an-
tennas i and j, respectively. Ω is the solid angle over (θ, φ). In
general, A
i
and A
j
contain both amplitude and phase. Suppose
antennas i and j are collocated with no spatial diversity, it
follows that the phases of A
i
and A
j
are the same with respect
to angle Ω. As in (2), the entries of Ψ
r
are the weighted
correlations between receive antennas, where the weights are
the angular spectrum of the incident field E. In order to achieve
large channel capacity, Ψ
r
needs to be close to an identity
matrix. The correlation coefficient Ψ
(i,j)
r
,fori = j, can be
diminished by reducing the similarity in antenna polarizations
and/or patterns over the angular space.
III. S
YSTEM ASSUMPTIONS AND HANDSET MODEL
In the simulation, we consider a MIMO system that employs
three transmit antennas at the BTS and three receive antennas
at the MS. The antennas at the BTS can be placed sufficiently
apart to provide decorrelation. Therefore, the channel matrix
G has the same statistics as Ψ
1/2
r
G
w
[17]. The orientations
of the BTS antennas are different, e.g., 90
◦
slanted to each
other, in order to provide multipolarized transmission. Based
on the results on dual-polarized systems [5], [6], it is unlikely
that the scatterers, especially in a suburban environment, would
depolarize signals significantly. However, incident waves with
different polarizations are important for the receiver to exploit
the antenna polarization diversity. With this special transmit
geometry coupled with the random orientation of the receive
handset, we may assume that the incident waves arriving at the
MS have equal average power in all polarizations.
The MS has a compact array structure consisting of three
quarter-wavelength monopoles mounted on a conducting box
of dimensions 3 × 5 × 10 cm
3
(to simulate the handheld unit).
With a carrier frequency of 2 GHz, the length of each monopole
antenna is about 3.75 cm. The feed points of the monopoles are
collocated. Each antenna is symmetrically slanted with an angle
ω with respect to the zenith, thus creating polarization dissim-
ilarity. The NEC is used to simulate the antenna radiation pat-
terns and polarizations. We used the standard “active element”
approach to fully take into account the electromagnetic cou-
pling between the elements and casing effects. This approach
determines the gain pattern with one element excited and all
the other elements terminated in their source impedances [18].
Fig. 1(a) shows the wire mesh used in the NEC simulation.
Fig. 1(b) shows an experimental MS antenna prototype. The
antenna radiation patterns from simulation and measurement
DONG et al.: SIMULATION OF MIMO CHANNEL CAPACITY WITH ANTENNA POLARIZATION DIVERSITY 1871
Fig. 2. Channel capacity of a 3 × 3 MIMO system with antenna polarization
diversity in various environments. Average receiver SNR = 10 dB. (a) Capac-
ity of 3 × 3 Rayleigh channel. (b) Capacity of 3 × 1 Rayleigh channel.
are compared in Fig. 1(c). It shows the patterns in the X–Z plane
at ω =45
◦
, with the excitation at one antenna port and 50-Ω
terminations at the other two ports. The antenna pattern from
the NEC model agrees well with that from the measurement.
The NEC results are used throughout our simulations.
The propagation environments for the MS are simulated
in three scenarios: indoor, outdoor dense urban, and outdoor
suburban. For indoor, the angular spectrum of incident waves
is assumed to have a uniform elevation spectrum θ ∈ [0, 180
◦
)
and a uniform azimuth spectrum φ ∈ [0, 360
◦
). For outdoor
dense urban, the angular spectrum of incident waves is limited
to a uniform elevation spread of 30
◦
about the horizontal plane,
with a uniform azimuth spectrum. For outdoor suburban, the
incident waves are also assumed to have a uniform elevation
spread of 30
◦
about the horizontal plane, but with a Laplacian
azimuth spectrum of σ
φ
=5
◦
[19] and the main azimuth direc-
tion randomly selected in [0, 360
◦
).
IV. R
ESULTS
Fig. 2 illustrates the dependence of channel capacities on the
slanting angle ω of the MS monopoles in different propagation
environments. We assume perfect transmit power control, hence
a normalized channel. Suppose ρ =(P/n
T
N)=10dB, where
P , n
T
, and N are defined in (1). Note that the difference
of receive branches is considered in the transfer matrix G.
With a normalized G, ρ is the average SNR over all receive
antennas. We observe that in rich scattering environments such
as indoor or outdoor dense urban, the decorrelation of signals
at local antennas can be achieved with moderate slanting angle
(ω>20
◦
), and the channel capacity approaches the capacity of
an uncorrelated 3 × 3 Rayleigh channel. In the suburban envi-
ronment with small azimuth spread, the capacity performance
is degraded modestly.
In addition to the polarization difference among the receive
antennas, the angular patterns in the principal polarization are
also different. Since antenna pattern diversity and polarization
Fig. 3. Channel capacity of a 3 × 3 MIMO system with different diversity
schemes. Average receiver SNR = 10 dB. (a) Capacity of 3 × 3 Rayleigh
channel. (b) Capacity of 3 × 1 Rayleigh channel.
diversity are always coupled in practice, the simulation devel-
oped here offers a tool to examine which one is more essential
in contributing to the capacity gain. We carry out the simulation
by deviating from the NEC antenna radiation model to two
ideal models.
1) Polarization-diverse only: We use the antenna polariza-
tions from the NEC model, but set the angular patterns to
be isotropic in radiation intensity. That is, we substitute
(A
i
(Ω)/|A
i
(Ω)|) and (A
j
(Ω)/|A
j
(Ω)|) for A
i
(Ω) and
A
j
(Ω) in (2), respectively.
2) Pattern-diverse only: We use the pattern differences in
radiation intensity, but no polarization diversity. That is,
we substitute |A
i
(Ω)| and |A
j
(Ω)| for A
i
(Ω) and A
j
(Ω)
in (2), respectively.
Fig. 3 compares the MIMO channel capacity of the trimono-
pole antennas with those from the polarization-diverse-only and
the pattern-diverse-only models. Indoor environment is simu-
lated to maximize the effects of different diversity factors. We
observe that the channel capacity of the polarization-diverse-
only model is very close to that of the actual trimonopole
system. The capacity of the pattern-diverse-only model, on
the other hand, is much lower. Thus, it is indeed polarization
diversity that accounts for most of the capacity increase in
antenna-diverse MIMO systems. This confirms the assumption
by Andrews et al. [7].
Finally, we compare the capacity of the trimonopole system
to that of the idealized tridipole model used in previous works.
Three electrically short dipoles are orthogonally collocated in
the ideal tridipole model, where the antenna radiation pattern
of a vertical dipole (ω =0)is A(Ω) = sin(θ)
ˆ
a
θ
. The mutual
coupling between local antennas and the casing effect are
not considered. In the outdoor dense urban environment, the
slanting angle of antennas that maximizes the channel capac-
ity can be calculated as ω
∗
≈ (1/2) cos
−1
[−(π + 15)/(7π +
9)] = 62.9
◦
. This agrees with the simulation result in Fig. 4.
In the outdoor suburban environment with Laplacian azimuth
spectrum, Ψ
r
cannot be exactly an identity matrix due to
1872 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY 2005
Fig. 4. Channel capacity of a 3 × 3 MIMO system with antenna polarization
diversity (ideal model). Average receiver SNR = 10 dB. (a) Capacity of 3 ×
3 Rayleigh channel. (b) Capacity of 3 × 1 Rayleigh channel.
the asymmetry of the weighted correlations. Therefore, the
channel capacity cannot reach the capacity of the uncorrelated
3 × 3 Rayleigh channel, as shown in Fig. 4. One observation
comparing Fig. 4 with Fig. 2 is that practical antennas with
mutual coupling and casing effects can provide large capacity
increase with less constraint on antenna configurations than the
idealized tridipole system.
V. C
ONCLUSION
We presented a simulation study of MIMO channel capacity
as a function of antenna configurations and propagation envi-
ronments. For a size-constrained receiver, antenna polarization
diversity provides local decorrelation, hence increased channel
capacity. We focused on a simple yet realistic trimonopole
antenna structure, and we took into account all the mutual
coupling and casing effects using full-wave electromagnetic
simulation. We arrived at the following conclusions.
1) The trimonopole antennas can provide a large channel
capacity that approaches the capacity of the uncorrelated
Rayleigh channel; the increase is especially pronounced
when the mobile is in a rich-scattering environment.
2) Although the decorrelation of received signals is due to a
combination of antenna polarization and pattern diversity,
the capacity gain is mainly attributed to the polarization
diversity.
3) The trimonopole antennas with mutual coupling and cas-
ing effects can provide large capacity increase with less
constraint on antenna configurations than the idealized
tridipole system.
Further research will be conducted on polarization-diverse
MIMO systems using improved propagation models and re-
laxing the channel normalization assumption. This will involve
more sophisticated models of the channel matrix.
R
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DONG et al.: SIMULATION OF MIMO CHANNEL CAPACITY WITH ANTENNA POLARIZATION DIVERSITY 1873
Liang Dong (S’96–M’02) was born in Shanghai,
China, on February 15, 1974. He received the B.S.
degree in applied physics and computer engineer-
ing from Shanghai Jiao Tong University, Shanghai,
China, in 1996, and the M.S. and Ph.D. degrees in
electrical and computer engineering from the Univer-
sity of Texas, Austin, in 1998 and 2002, respectively.
From 1996 to 2002, he was a Research Assistant
with the Department of Electrical and Computer En-
gineering, University of Texas at Austin. From 1998
to 1999, he was an Engineer at CWiLL Telecom-
munications Inc., Austin, TX, where he participated in the design and imple-
mentation of a smart antenna communications system. During the summer of
2000, he was a Consultant for Navini Networks Inc., Richardson, TX. From
2002 to 2004, he was a Research Associate with the Department of Electrical
Engineering, University of Notre Dame, Notre Dame, IN. He joined the faculty
of Western Michigan University, Kalamazoo, MI, in August 2004, where he is
currently an Assistant Professor of Electrical and Computer Engineering. His
research interests include array signal processing for communications, channel
estimation and modeling, space–time coding, and wireless networking.
Dr. Dong is a member of Sigma Xi, Phi Kappa Phi, and Tau Beta Pi.
Hosung Choo (S’00–M’04) was born in Seoul, Ko-
rea, in 1972. He received the B.S. degree in radio
science and engineering from Hanyang University,
Seoul, Korea, in 1998, and the M.S. and Ph.D. de-
grees in electrical and computer engineering from
the University of Texas at Austin, in 2000 and 2003,
respectively.
From 1999 to 2003, he was a Research Assistant
with the Department of Electrical and Computer
Engineering, University of Texas at Austin. In Sep-
tember 2003, he joined the School of Electronic
and Electrical Engineering, Hongik University, Seoul, Korea, where he is
currently a Full-Time Instructor. His principal area of research is the use of the
genetic algorithm in developing microstrip and wire antennas and microwave
absorbers. His studies include broadband and multiband antennas for wireless
communications and miniaturized antennas for HF frequency bands.
Robert W. Heath, Jr. (S’96–M’01) received the
B.S. and M.S. degrees from the University of Vir-
ginia, Charlottesville, in 1996 and 1997, respectively,
and the Ph.D. degree from Stanford University, Stan-
ford, CA, in 2002, all in electrical engineering.
From 1998 to 1999, he was a Senior Member of
the Technical Staff at Iospan Wireless Inc., San Jose,
CA, where he played a key role in the design and
implementation of the physical and link layers of
the first commercial MIMO–OFDM communication
system. From 1999 to 2001, he served as a Senior
Consultant for Iospan Wireless Inc. In 2003, he founded MIMO Wireless
Inc. Since January 2002, he has been with the Department of Electrical and
Computer Engineering, University of Texas at Austin, where he serves as an
Assistant Professor as part of the Wireless Networking and Communications
Group. His research interests include interference management in wireless
networks, sequence design, and all aspects of MIMO communication including
antenna design, practical receiver architectures, limited feedback techniques,
and scheduling algorithms.
Dr. Heath serves as an Associate Editor for the IEEE T
RANSACTIONS
ON
COMMUNICATIONS and the IEEE TRANSACTIONS ON VEHICULAR
TECHNOLOGY.
Hao Ling (S’83–M’86–SM’92–F’99) was born in
Taichung, Taiwan, R.O.C., on September 26, 1959.
He received the B.S. degree in electrical engineer-
ing and physics from the Massachusetts Institute
of Technology, Cambridge, in 1982, and the M.S.
and Ph.D. degrees in electrical engineering from the
University of Illinois at Urbana-Champaign, in 1983
and 1986, respectively.
He joined the faculty of the University of Texas
at Austin, in September 1986, and is currently a
Professor of Electrical and Computer Engineering
and holds the L. B. Meaders Professorship in Engineering. During 1982,
he was associated with the IBM Thomas J. Watson Research Center, York-
town Heights, NY, where he conducted low-temperature experiments with the
Josephson Department. He participated in the Summer Visiting Faculty Pro-
gram in 1987 at the Lawrence Livermore National Laboratory. In 1990, he was
an Air Force Summer Fellow at Rome Air Development Center, Hanscom Air
Force Base. His principal area of research is in computational electromagnetics.
His recent research interests also include radar signal processing, automatic
target identification, antenna design, and physical layer modeling for wireless
communications.
Dr. Ling was a recipient of the National Science Foundation Presidential
Young Investigator Award in 1987, the NASA Certificate of Appreciation in
1991, as well as several teaching awards from the University of Texas at Austin.
... Sinking mutual coupling in compact UWB devices is stimulating and techniques such as neutralization line [21], electromagnetic band-gap (EBG) structures [22], meta-materials [23], decoupling and identical networks become less reasonable as these are additional auspicious for narrowband and wideband MIMO antennas [24]. Some designs addressing broadband applications such as satellite, mobile, radiolocation, etc. as well as their parametric study have been distributed [25]- [26]. ...
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  • Mar 2022
In this paper, a compact (22×22×1.6 mm3) dual-port UWB (Ultra-wide-band) MIMO (Multiple-input-multiple-output) microstrip antenna are perceived with gain, bandwidth and isolation enhancement for downlink of the X-band satellite communications. The proposed MIMO antenna system consists of two identical glue gun-shaped radiating element associated with ground plane as well as co-axial feeds. Four antenna designs (A1-A4) are systematically inspected of proposed antenna (A4) have been elevated for desired antenna parameters and operations. The proposed and measured dual-band behavior at (7.99-8.38) GHz and (9.10-12.97) GHz with impedance bandwidth of 5.13% and 35.07% respectively for port-1 and (7.96-8.39) GHz and (9.10-13.03) GHz with impedance bandwidth of 5.13% and 35.51% respectively at port-2 is observed and moreover achieved the pent-resonances has 8.10 GHz, 9.65 GHz, 10.92 GHz, 11.97 GHz and 12.61 GHz with peak gain of 2.67 dBi, 6.78 dBi, 5.90 dBi, 5.03 dBi and 3.79 dBi respectively at port-1 and 8.10 GHz, 9.65 GHz, 10.92 GHz, 11.97 GHz and 12.61 GHz with peak gain of 2.67 dBi, 6.78 dBi, 5.90 dBi, 5.03 dBi and 3.79 dBi respectively at port-2. The proposed antenna has minimum isolation less than-15 dB (a major portion <-20 dB), envelope correlation coefficient (ECC) less than 0.0451, diversity gain (DG) between 9.954-9.996, total active reflection coefficient (TARC) less than-10 dB, antenna gain varies in the range of (2.67-6.78) dBi and radiation efficiency up to 75% is obtained during the entire operating frequency bands. The simulated and measured results of the proposed antenna have been validated and minor deviation between simulated and measured results has been observed. The proposed design is simulated on FR-4 epoxy substrate (εr= 4.4, tan δ = 0.02 and h = 1.6 mm) with carried out by ANSOFT HFSS 13 electromagnetic solver.
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... Recently, dual-polarized antennas are being employed as useful option for implementation of polarization diversity or MIMO schemes and thus, increasing the channel capacity of modern body centric wireless communication systems (Lindmark and Nilsson 2001). The microstrip patch or slot antenna is considered as an attractive candidate for dual polarization radiation owing to its low profile, low cost, and easy integration (Dong et al. 2005). ...
Compact Dual Band and Dual Polarized CPW-Fed Triangular Shaped Wearable Antenna for ISM band Applications
Article
  • Jan 2022
A coexisting compact dual coplanar waveguide (CPW)-fed dual-band and dual-polarized triangular-shaped wearable antenna (TSWA) is proposed for 2.45 GHz and 5.8 GHz ISM (Industrial, Scientific and Medical) frequency bands. The proposed antenna of area 722 mm² is fabricated on polyimide substrate (thickness of 1.6 mm and relative permittivity of 3.5). The two identical inverted-L-shaped feed stubs are employed orthogonally in wide triangular slot to provide both horizontally and vertically polarized radiations in both ISM bands. An additional Y-shaped copper strip is introduced to isolate the two inverted-L-shaped feed stubs in order to achieve higher isolation in both 2.45 and 5.8 GHz operational frequency bands. The proposed TSWA achieves similar −10 dB impedance bandwidths of 21.7% (2.30 ̶ 2.86 GHz) and 14.26% (5.60 ̶ 6.46 GHz) respectively for dual-polarized radiations along with more than 20 dB isolation in both 2.45 and 5.8 GHz ISM bands. The effect of human loading on performance of proposed TSWA is also studied. The proposed antenna is designed, fabricated, and tested. The simulated results are verified and validated with measured ones and thus, makes it suitable for wearable ISM bands applications.
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... It has been shown that the polarization diversity can provide a considerable gain to the MIMO system [1]. Channel capacity is also increased due to the polarization diversity [2]. Pattern diversity can be used to improve radiation coverage. ...
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High-Capacity Compact Massive MIMO Array with Hybrid Decoupling Scheme
Article
  • Oct 2022
The staggered placement of array antenna is a neoteric configuration to improve antenna isolation. On this basis, how to further effectively reduce the mutual couplings of different adjacent positions is a challenging subject. This article presents a novel decoupling strategy that integrated surrounding resonance net, array-antenna decoupling surface (ADS), and composite decoupling surface (CDS) that are introduced for $\pm 45^{\mathrm {^{\circ }}}$ dual-polarized, high-density, wideband base station applications. The proposed decoupling method is robust in reducing concurrently multicouplings occurring between various co-polarized antenna elements with the minimum spacing of only $0.3\lambda $ under staggered configuration. The results show that good co- polarized isolation of both the E- and H-plane orientations >25 dB over the 6–8 GHz can be attained. The good agreement between simulation and measurement proved that such a decoupling method can be suitable for base stations that have a stringent space constraint. Finally, the modified envelope correlation coefficient (ECC) and channel capacity of the proposed MIMO array are also studied, and the improvement of the communication quality by the proposed decoupling method is verified again.
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A Polarization Diversity Merging Technique for Low Elevation Frequency Hopping Signals
Chapter
  • Jun 2021
In the process of wireless signal transmission at low elevation angle, multipath effect is easy to be formed due to the reflection signal of the ground, which can cause signal distortion and interruption. Polarization diversity merging technique is an effective way to combat signal fading, which can improve the quality of wireless communication without increasing transmission power and bandwidth. However, the diversity signals merged with different frequency and phase will cause mutual interference. In the frequency hopping mode, residence time of each frequency hopping point is short and the closed-loop control method is unsuitable to rectify the deviations of each hop. To solve this problem, an open-loop control method is proposed in this paper, which can correct and merge the frequency deviation of polarization diversity signals in real time. It has the advantages of simple structure and fast processing speed, and is very suitable for the reception of low elevation frequency hopping signals.
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A circular polarized reflectarray antenna with electronically steerable beam and interchangeable polarizations
Article
  • Aug 2020
The purpose of this paper is the design of a novel single layer reflectarray antenna in X-band, which can electronically steer the antenna beam and change its polarization. Each antenna element includes a circular patch and rings around it, equipped with two varactor diodes, which are positioned perpendicular together to create a circular polarization. First, using these elements, a circular polarized active electromagnetic band-gap (EBG) reflector is implemented. Then, a special feed is placed in a proper distance with respect to EBG reflector and a circular polarized reflectarray antenna is designed, which has capability of switching electronically between right- and left-handed circular polarizations. An electronic active board is designed and fabricated to provide the biasing voltages, control signals, and indicators. The elements of the reflectarray are designed and arranged in such a way that the varactor diodes can be biased independently. Consequently, a 3D beam is created, which can steer up to ±40 o . For evaluating the antenna performance, the radiation patterns and the axial ratio of the antenna are determined at the operational frequency of 11.4 GHz. It is illustrated that, increasing the steering angle in θ direction decreases the directivity and the gain of the reflectarray antenna.
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Simulation of mutual coupling effect in circular arrays for direction-finding application
Article
Full-text available
  • Sep 2000
  • MICROW OPT TECHN LET
The effect of mutual coupling on direction finding in circular arrays is simulated using rigorous electromagnetic computation and the MUSIC superresolution algorithm. The various scenarios studied include element spacing, noise level, antenna gain and delay, and platform effects. Our results show quantitatively the effect of mutual coupling on the direction-of-arrival estimates. The compensation of the coupling effect using the coupling matrix approach is also examined. This approach is found to be quite satisfactory in most cases, except when the array calibration data contain a high noise level or when strong platform effects are present. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 331–336, 2000.
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A model for insulated wires in the method of moments code NEC (Numerical Electromagnetics Code)
Article
  • Jan 1988
The numerical electromagnetics code (NEC) is a general purpose computer program for modeling antennas by the numerical solution of an integral equation. NEC solves an electric field integral equation for wire structures and a magnetic field integral equation for surfaces, and can evaluate the effect of an interface between air and a lossy half space by means of a reflection coefficient approximation or the rigorous solution involving Sommerfeld integrals. This report describes an extension of NEC to model an insulating sheath on wires in air or buried in a lossy half space including, if desired, the effect of the air-ground interface.
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Numerical/Electromagnetics Code (NEC)
Article
  • Nov 1984
A hybrid numerical electrodynamics code (NEC) code which uses an Electric Field Integral Equation (EFIE) to model wire-like objects and a Magnet Field Integral Equation (EFIE) to model wire-like objects and a Magnetic Field Integral Equation (MFIE) to model surface-like objects with time harmonic excitation is discussed. A three-term sinusoidal spline basis is employed for the wire current while a pulse basis is used for the surface current, with delta-function weights employed everywhere. Provision is made for connection of wires to surfaces via an attachment, or interpolation, basis. NEC includes a number of features for efficient modeling of antennas and scatterers in their environments. The most recent addition, in the version NEC-3, was the capability of modeling wires that are buried or penetrate the ground-air interface. The current status of NEC-3 and plans for Future NEC are discussed. Some typical results are included.
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In: Microwave Mobile Communcations
Article
  • Jan 1974
From the Publisher: IEEE Press is pleased to bring back into print this definitive text and reference covering all aspects of microwave mobile systems design. Encompassing ten years of advanced research in the field, this invaluable resource reviews basic microwave theory, explains how cellular systems work, and presents useful techniques for effective systems development. The return of this classic volume should be welcomed by all those seeking the original authoritative and complete source of information on this emerging technology. An in-depth and practical guide, Microwave Mobile Communications will provide you with a solid understanding of the microwave propagation techniques essential to the design of effective cellular systems.
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Capacity of Multi-antenna Gaussian Channels
Article
  • Nov 1999
  • EUR T TELECOMMUN
We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas. We show that the potential gains of such multi-antenna systems over single-antenna systems is rather large under independenceassumptions for the fades and noises at different receiving antennas.
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On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas
Article
  • Jan 1998
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%
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Modeling the indoor MIMO wireless channel
Article
This paper demonstrates the ability of a physically based statistical multipath propagation model to match capacity statistics and pairwise magnitude and phase distributions of measured 4 x 4 and 10 x 10 narrow-band multiple-input multiple-output data (MIMO) at 2.4 GHz. The model is compared to simpler statistical models based on the multivariate complex normal distribution with either complex envelope or power correlation. The comparison is facilitated by computing channel element covariance matrices for fixed sets of multipath statistics. Multipolarization data is used to demonstrate a simple method for modeling dual-polarization arrays. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 5, MAY 2002 591 Modeling the Indoor MIMO Wireless Channel Jon W. Wallace, Student Member, IEEE, and Michael A. Jensen, Senior Member, IEEE Abstract—This paper demonstrates the ability of a physically based statistical multipath propagation model to match capacity statistics and pairwise magnitude and phase distributions of measured 4 4 and 10 10 narrow-band multiple-input multiple- output data (MIMO) at 2.4 GHz. The model is compared to simpler statistical models based on the multivariate complex normal distribution with either complex envelope or power correlation. The comparison is facilitated by computing channel element covariance matrices for fixed sets of multipath statistics. Multipolarization data is used to demonstrate a simple method for modeling dual-polarization arrays. Index Terms—Channel models, indoor channels, measured channel data, multiple-input multiple-output (MIMO) channels, polarization. I. INTRODUCTION RECENT STUDIES have demonstrated the impressive theoretical capacity of wireless systems operating in a multipath environment and employing multiple antennas on both transmit and receive [1]–[4]. These multiple-input multiple-output (MIMO) systems must cleverly exploit the structure of the channel transfer matrix (denoted as ) to maximize data throughput. Accurate models that capture the complex spatial behavior of the propagation channel facilitate the development of these MIMO systems. Many avenues exist for modeling the MIMO channel. For example, simple analytical models have initially been employed to understand possible gains from the MIMO channel [1]–[3]. Although advantageous for closed-form derivation of various channel parameters, these simple models often fail to capture the behavior of real channels. Alternately, direct measurement provides an exact characterization of for the specific measurement scenario [5]–[9], and empirical statistical models may be developed based on an ensemble of measurements. However, applicability of such models may be limited to the specific array configuration or propagation environment under test. Deterministic physical models such as ray tracing [10], [11] simulate specific propagation scenarios and may be combined with Monte Carlo analysis to provide statistical channel information. Such methods promise an accurate characterization of the channel at the expense of computational resources. Finally, physically based statistical models [12]–[14] derive channel behavior from basic principles of radio propagation. The necessary channel parameters are then obtained by fitting the models to measured data. Such models are attractive since they are applicable to Manuscript received June 7, 2001; revised December 21, 2001. Thisworkwas supported in part by the National Science Foundation under Wireless Initiative Grant CCR 99-79452 and in part by the Information Technology Research Grant CCR-0081476. The authors are with the Wireless Research Group, Brigham Young University, Provo, UT 84602-4099 USA (e-mail: wall@ieee.org; jensen@ee.byu.edu). Publisher Item Identifier S 0018-926X(02)05452-2. TABLE I PARAMETERS DESCRIBING THE MEASURED DATA SETS COLLECTED FOR THIS WORK many different array geometries and propagation environments and require modest computational resources. In this paper, we employ a physical model that statistically describes the time of arrival (TOA), angle of arrival (AOA), and angle of departure (AOD) of each multipath component [12], [13]. We show that this model can match capacity, joint magnitude, and phase probability density functions (pdfs) of measured data for realistic model parameters. We also assess the applicability of simpler multivariate complex normal models based on power correlation and complex envelope correlation. Finally,we present a simple polarization model based on indoor dual-polarized measurements. II. MEASURED CHANNEL DATA For this study, MIMO channel data was collected on the fourth floor of the engineering building on the Brigham Young University campus [5], [6]. This measurement platform is able to measure the MIMO channel transfer matrix for up to 16 transmit and 16 receive antenna channels. The center frequency for measurements is tunable within the lower microwave bands, although all measurements presented here have been performed near 2.45 GHz. The system modulates (binary phase shift keyed or BPSK) the signals for each transmit antenna using a unique binary code sequence and the channel matrix is then estimated at the receiver using a maximum-likelihood algorithm. Table I lists the measurement parameters for the data sets under consideration. Set 1 contains 4 4 data from five different scenarios. In each scenario, the transmitter was fixed in one room, while the receiver was moved to several different locations in another room. Since the rooms shared a wall only in one scenario, the data set exhibited fairly rich multipath interference. In Set 2, the receive array assumed six possible positions in one room, and the transmit array assumed four possible positions in another nonadjacent room. Every combination of transmit and receive position was measured. Due to wide separation of transmit and receive, this set also exhibited rich multipath interference. 0018-926X/02$17.00 © 2002 IEEE Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 12:06 from IEEE Xplore. Restrictions apply. 592 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 5, MAY 2002 In Set 3, the effect of polarization was explored using arrays with two dual-polarization patches separated by . The transmitter was placed in a hallway at six different locations. The receiver was placed in a room off of this hallway in six other locations. Each possible combination of locations for transmit and receive was probed. The transmit and receive patch arrays faced each other in each case, and therefore a strong line-of-sight (LOS) path was present. III. CHANNEL MODEL PRELIMINARIES There are several important issues relevant to modeling the MIMO wireless channel. For this discussion, the receive by transmit narrowband-channel matrix relates the transmit and receive complex baseband vectors as (1) where is the independent and identically distributed (i.i.d.) complex white Gaussian receiver noise vector. A. Channel Normalization Obtaining a good statistical sample of the indoor channel requires collecting data in a variety of scenarios. Large movement in transmit and receive location leads to substantial change in the bulk path loss of propagating signals. Effects of path loss can easily overshadow interesting channel behavior such as spatial correlation of transmit and receive signals. One way to remove this effect from collected data is to normalize the channel matrices. Unless otherwise specified, channel matrices were normalized to force unit average single-input single-output (SISO) gain. The individual receiver noise is then given as , where is the total transmit power and SNR represents the desired signal-to-noise ratio at the receiver. This normalization is equivalent to specifying the average receiver SNR when transmit streams are uncorrelated. The normalization constant may be computed for each individual matrix or over all matrices at a single location. In this paper, the normalization was computed on each matrix for capacity and over all matrices at a location for other quantities. Removal of channel path loss is justified for modeling the subtle effects of multipath propagation. Realistic models should include path loss as a bulk signal attenuation which varies with separation of transmit and receive. When comparing various transmission schemes (e.g., dual polarization, directional antennas), care also must be taken that normalization does not force unwarranted conclusions. B. Capacity In this paper, capacity is computed by normalizing channel matrices to obtain an average SISO SNR of 20 dB. Capacity is computed using thewater-filling solution on the channel orthogonalized with the singular value decomposition (see [2], [15]). C. Joint pdfs The complete joint probability density function (pdf) for all elements of the matrix provides a complete statistical description of the narrowband MIMO channel. If sufficient data were collected, one could compare measured and modeled channels by appropriately sampling this multidimensional pdf. However, as the number of antennas on transmit and receive increases, the dimensionality of the pdf becomes prohibitive and marginal pdfs or statistical moments must be used instead. As a first step toward comparison of measured and modeled channels, we use pairwise joint pdfs on magnitude and phase. We concentrate specifically on the statistics of adjacent elements at transmit and receive, since these will be the most correlated. The measured bivariate pdf for adjacent transmit/receive element magnitude is (2) where for transmit or receive and HIST2 is a two-dimensional (2-D) normalized histogram operation. The measured univariate pdf for adjacent transmit/receive element phase difference is given as (3) where HIST is a one-dimensional (1-D) normalized histogram operation. D. Multivariate Complex Normal Distribution The multivariate complex normal distribution is fundamental to the study of the various models. Aspects relevant to this study are presented here for convenience. 1) Joint pdf: The joint multivariate complex normal distribution [16] is given as (4) where is the covariance matrix, is the dimensionality of , and is the mean vector. The pairwise joint pdf is given as (4) with replaced by the covariance submatrix , or (5) where has been assumed. 2) Pairwise pdfs: When , the pairwise joint magnitude pdf is (6) Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 12:06 from IEEE Xplore. Restrictions apply. WALLACE AND JENSEN: MODELING THE INDOOR MIMO WIRELESS CHANNEL 593 where , and . The pdf for pairwise phase difference is (7) where and in this case we express as . Averaging the pdfs associated with all element pairs for a given transmit and receive spacing results in an average pairwise pdf, which is analogous to those given in Section III-C. 3) Covariance Matrices and Simplifying Assumptions: The zero mean multivariate complex normal distribution is completely characterized by the covariance matrix . For the purpose of modeling , the covariance matrix is defined as (8) where and combine to form a row index of and and combine to form a column index of . A number of assumptions are convenient when working with the covariance matrix. Separability assumes that the full covariance matrix may be written as a product of transmit covariance and receive covariance or (9) For such channels, the transmit and receive covariance matrices can be computed from the full covariance matrix as (10) (11) where and are chosen such that (12) In the case where is a correlation coefficient matrix, we may choose and . Separability makes implications about the statistical independence of multipath fading due to transmit location and receive location. Shift-invariance assumes that the covariance matrix is only a function of antenna spacing and not absolute antenna location. The relationship between the full covariance and shift-invariant covariance is (13) Fig. 1. Transmit and receive parameters for a single cluster in the SVA model. The combination of separability and shift-invariance allows full covariance matrices to be generated from existing correlation functions, which relate correlation to receive element displacement. For example, we may use Jakes’ model to obtain (14) where is the vectorial location of the th transmit or receive antenna in wavelengths, and is the vector norm. 4) Computer Generation: Computer generation of zero mean complex normal vectors for a specified covariance matrix is performed by generating vectors of i.i.d. complex normal elements with unit variance . The transformation (where and are the matrix of eigenvectors and the diagonal matrix of eigenvalues of , respectively) yields a complex normal vector with the proper correlation structure. IV. SALEH–VALENZUELA MODEL WITH AOA/AOD This section demonstrates that an extension of the Saleh–Valenzuela model [12] that includes AOA statistics [13] is able to match capacity pdfs and pairwise element pdfs of the measured channel. Here, AOD statistics are assumed to follow the same distribution as AOA, which is reasonable for the indoor channel with the same basic configuration on transmit and receive. We refer to the Saleh–Valenzuela model with AOA/AOD as the SVA model for brevity. The SVA model characterizes the channel by representing each multipath component in terms of its amplitude, arrival time, and AOA/AOD. Based upon experimental observations, these arrivals or rays arrive in clusters in both space and time. Fig. 1 shows the model parameters for a single cluster in the SVA model. The directional channel impulse response arising from clusters and rays per cluster is (15) where and are transmit and receive angles, is the complex ray gain, and are the mean transmit and receive angles within the th cluster, and and are the transmit and receive angles of the th ray in the th cluster, relative to the respective mean angles in each cluster. Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 12:06 from IEEE Xplore. Restrictions apply. 594 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 5, MAY 2002 To simplify the model, average-ray power in each cluster is constant so that , where denotes the complex normal distribution with mean and variance . The cluster amplitude is Rayleigh distributed with the expected cluster power (or variance) satisfying , where is the arrival time of the th cluster, and is the cluster decay time constant. The arrival time distribution is a conditional exponential with a normalized unit arrival rate. Details concerning the model implementation can be found in [12], [13], [17]. The notation is used in this paper to denote the SVA model with constant average ray power and unit cluster arrival rate, where is the cluster decay constant and is the standard deviation of ray AOA/AOD. The narrow-band channel matrix is computed from the directional impulse response as (16) where is the antenna gain pattern, , and . Based upon measured data taken in [13], a twosided Laplacian distribution is assumed for the ray AOA/AOD distribution whose pdf is (17) where is the standard deviation of angle in radians. A. Complex Normal Approximation matrices may be generated directly by computing (16) for each realization of the SVA model. An alternate method computes channel matrices according to a complex normal distribution for each fixed set of cluster statistics. This method reduces computational time and links the model to simpler complex normal models. For a fixed set of cluster statistics and ray arrival angles is a weighted sum of zero mean complex normal random variables, resulting in a correlated complex normal distribution. If the angular spread on is small, the will look closely complex normal even if the are allowed to vary. In this case, we find the average covariance matrix as (18) Fig. 2. Radiated power (dB) for vertical/horizontal polarized patch antenna relative to a uniform radiator, as a function of azimuth angle. where statistical independence of complex ray gain, AOA, and AOD has been assumed. If the gains of distinct rays are independent and ray AOA/AOD are i.i.d., the expression simplifies to (19) where (20) is the ray angle of arrival/departure pdf and For certain special cases, closed-form expressions for (20) exist. For arbitrary antenna gain and angular ray distributions, however, (20) is computed numerically. The result is a relatively simple expression for the mean channel covariance matrix for a fixed set of cluster statistics. We note that although the covariance matrix given by (19) is not strictly separable (Section III-D3) for a single cluster realization, it approaches separability when averaged over many random cluster realizations where transmit and receive statistics are independent. Also, assuming a uniform linear array with one gain pattern for all transmit elements and another for all receive elements results in a shift-invariant covariance matrix. B. Comparison of Model and Data In [13], high-resolution AOA measurements were performed on the same floor of the BYU engineering building as in this study. Although the measurements were at a much higher frequency ( 7 GHz), the extracted parameters serve as a logical starting point. The key parameters are (see [13]) . For simulation, transmit and receive cluster arrival angles are assumed to be uniform on . Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 12:06 from IEEE Xplore. Restrictions apply. WALLACE AND JENSEN: MODELING THE INDOOR MIMO WIRELESS CHANNEL 595 Fig. 3. Comparison of capacity pdfs and joint magnitude and phase pdfs for 4
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Experimental characterization of the MIMO wireless channel: data acquisition, analysis, and modeling
Article
  • Jan 2003
Detailed performance assessment of space-time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the narrowband channel transfer matrix for wireless communications scenarios. The system is used to directly measure key multiple-input-multiple-output parameters in an indoor environment at 2.45 GHz. Linear antenna arrays of different sizes and construction with up to ten elements at transmit and receive are utilized in the measurement campaign. This data is analyzed to reveal channel properties such as transfer matrix element statistical distributions and temporal and spatial correlation. Additionally, the impact of parameters such as antenna element polarization, directivity, and array size on channel capacity are highlighted. The paper concludes with a discussion of the relationship between multipath richness and path loss, as well as their joint role in determining channel capacity. IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 2, NO. 2, MARCH 2003 335 Experimental Characterization of the MIMOWireless Channel: Data Acquisition and Analysis JonW.Wallace, Member, IEEE, Michael A. Jensen, Senior Member, IEEE, A. Lee Swindlehurst, Senior Member, IEEE, and Brian D. Jeffs, Member, IEEE Abstract—Detailed performance assessment of space–time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the narrowband channel transfer matrix for wireless communications scenarios. The system is used to directly measure key multiple-input–multiple-output parameters in an indoor environment at 2.45 GHz. Linear antenna arrays of different sizes and construction with up to ten elements at transmit and receive are utilized in the measurement campaign. This data is analyzed to reveal channel properties such as transfer matrix element statistical distributions and temporal and spatial correlation. Additionally, the impact of parameters such as antenna element polarization, directivity, and array size on channel capacity are highlighted. The paper concludes with a discussion of the relationship between multipath richness and path loss, as well as their joint role in determining channel capacity. Index Terms—Indoor channels, measured channel data, multiple- input–multiple-output (MIMO) channels. I. INTRODUCTION THE increasing demand for capacity in wireless systems has motivated considerable research aimed at achieving higher throughput on a given bandwidth. One important finding of this activity is the recent demonstration that for an environment sufficiently rich in multipath components, the wireless channel capacity can be increased using multiple antennas on both transmit and receive sides of the link [1]–[5]. For example, recent research results have demonstrated data rates as high as 40 b/s/Hz in an indoor environment [6]. Algorithms that achieve this increased capacity actually exploit the multipath structure by cleverly coding the data in both time and space. Therefore, in order to assess the performance of systems that implement these algorithms, we must gain an improved understanding of the complex spatial behavior of wireless multiple-input–multiple-output (MIMO) channels [7]. Past methods for characterizing multipath MIMO channels include approximate statistical analyses [1] and ray tracing procedures [8]. These solutions offer information concerning the general channel behavior but suffer from their inability Manuscript received March 24, 2001; revised February 27, 2002; accepted June 12, 2002. The editor coordinating the review of this paper and approving it for publication is J. V. Krogmeier. This work was supported in part by the National Science Foundation under Wireless Initiative Grant CCR 99-79452 and in part by the Information Technology Research Grant CCR-0081476. The authors are with the Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602 USA (e-mail: wall@ieee.org; jensen@ee.byu.edu; swindle@ee.byu.edu; bjeffs@ee.byu.edu). Digital Object Identifier 10.1109/TWC.2003.808975 to accommodate an adequately detailed representation of the propagation environment. More recently, experimental measurement campaigns have been initiated in order to statistically characterize both indoor and outdoor wireless MIMO channels [9]–[11]. Results from these experiments have provided considerable insight concerning the capacity increases possible using MIMO systems. In this work, we report the development of and results from an experimental platform designed to probe the transfer matrix for indoor MIMO channels. This system is used to obtain narrowband channel transfer matrix data at 2.45 GHz using two different linear arrays: one with four dual-polarization elements and one with ten single polarization elements. The key aspects of the hardware system are presented, including a discussion of measurement issues and data processing methodologies. Representative data obtained with the instrument in several indoor environments are also provided, with emphasis placed on key parameters such as channel stationarity, transfer matrix element statistics, and channel spatial correlation. Additionally, the paper highlights the effect of such factors as antenna element polarization and directivity on the capacity, and illustrates the decrease in capacity per antenna that occurs as the array size increases. Finally, a discussion is provided concerning the relationship between multipath richness and path loss, as well as their joint role in determining channel capacity. II. MEASUREMENT SYSTEM Experimental probing of the MIMO wireless channel involves measuring the transfer matrix , where the element represents the frequency dependent transfer function between the th transmitter and th receiver antennas. The experimental platform, depicted in Fig. 1, uses a custom narrowband MIMO communications system operating with a center frequency between 0.8 and 6 GHz [12]. For this work, a center frequency of 2.45 GHz has been chosen. The system operates by transmitting uniquely coded and co-channel binary phase-shift keyed (BPSK) signals from distinct antennas. The receiver downconverts the signal from each of the antennas and stores the resulting sequences on a PC for post-processing. The system can accommodate up to transmit and receive antenna elements although only ten channels are used in this study. A calibration procedure is applied before data collection to remove the effects of unequal channel gains and phases in the transmitter and receiver hardware. The calibration coefficients obtained are applied during the data post-processing. 1536-1276/03$17.00 © 2003 IEEE Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 11:59 from IEEE Xplore. Restrictions apply. 336 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 2, NO. 2, MARCH 2003 Fig. 1. High-level system diagram of the narrowband wireless MIMO measurement system. Fig. 2. Algorithm for recovering the carrier phase. A. Transmitter The transmit system consists of a custom radio frequency (RF) subsystem that accepts binary sequences from an external digital pattern generator and a local oscillator (LO) signal from a tunable microwave source. The subsystem distributes these signals to 16 individual cards, each of which amplifies the LO signal and multiplies it with one of the binary sequences to produce BPSK modulation. The resulting signal is amplified to 0.5 W and fed to one of the transmit antennas. The pseudorandom binary sequences used in the system are constructed using a shift-generator initialized with a maximum-length sequence polynomial. The resulting codes have good correlation properties but are not perfectly orthogonal, necessitating the channel inversion technique discussed in Section III-C. B. Receiver The receive system consists of a second RF subsystem that accepts a LO signal from a microwave source. Each of 16 receive cards amplifies, downconverts, and filters the signal from one of the receive antennas. The resulting intermediate frequency (IF) signals are sampled on a 16-channel 1.25 Msample/s analog-to-digital (A/D) conversion card for storage on the PC. This data is then post processed according to the procedures outlined below. III. DATA PROCESSING The raw data collected using the measurement platform is processed to obtain estimates of the time-variant channel matrix. The technique consists of 3 basic steps: 1) code synchronization; 2) carrier recovery; and 3) channel estimation. A. Code Synchronization Locating the start of the modulating codes begins by correlating the signal from one of the receive antennas with a baseband representation of one of the transmit codes. A fast Fourier transform (FFT) of this result produces a peak at the IF when the known code and the code in the receive signal are aligned. The algorithm expedites the process by using shortened correlating codes and coarse steps at the beginning of the search process, and adaptively reducing the step size and switching to full-length codes as the search converges. Additionally, if the signal carrying the specified code is weak, the maximum correlation may not occur at code alignment. To overcome this, our procedure searches over every combination of receive channel and code to ensure accurate code synchronization. B. Carrier Recovery The FFT peak obtained during code synchronization provides an estimate of the IF. This result is refined using a subplex optimization loop that maximizes the magnitude of the discrete time Fourier transform (DTFT) of the despread signal (known aligned code multiplied by the receive signal). Following frequency estimation, the phase variation is recovered by moving a window along the despread signal and correlating this waveform against a complex sinusoid at the IF, as shown in Fig. 2. The phase of this result represents the phase at the center of the recovery window. An averaging window is then used to smooth this phase estimate. Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 11:59 from IEEE Xplore. Restrictions apply. WALLACE et al.: EXPERIMENTAL CHARACTERIZATION OF THE MIMO WIRELESS CHANNEL 337 C. Channel Estimation Because the pseudorandom codes used in the probing system are not strictly orthogonal, it is necessary to perform an inversion to extract the complex channel transfer matrix from the measured data. This inversion is formulated by first recognizing that the IF signal on the th receive channel is composed of BPSK codes, with each code represented by an amplitude and phase . If represents the th sample of the th code, the discrete received signal is given as (1) where is the discrete (recovered) carrier frequency, is the randomly varying carrier phase, and represents the discrete noise sample that is assumed to be spectrally white with a zero-mean Gaussian amplitude distribution. To construct channel matrices, we must infer channel parameters and from the sequence . To this end, consider forming an estimate of these parameters based upon samples of the sequence (corresponding to the code length). Also assume that is the observed signal. Using the zero-mean Gaussian distribution of the noise, the maximumlikelihood estimation (MLE) of the channel parameters results from finding the values of that minimize the expression (2) where (3) In order to determine the MLE values of , we take the derivative of with respect to both and , , and set the result to zero. Performing this operation produces (4) (5) where , , and . These equations can now be formed into the block matrix (6) The channel matrix elements are given by . TABLE I MEASUREMENT SYSTEM LOCATIONS WITHIN THE ENGINEERING BUILDING ALONG WITH ANTENNA CONFIGURATIONS IV. CHANNEL MATRIX CHARACTERISTICS The measurement system was deployed on the fourth-floor of the five-story engineering building on the Brigham Young University campus. This building, constructed with cinder-block partition walls and steel-reinforced concrete structural walls contains classrooms, laboratories, and several small offices. Data were collected at a center frequency of 2.45 GHz using 1000-bit binary codes at a chip rate of 12.5 kb/s, yielding a nominal bandwidth of 25 kHz. This narrow bandwidth is clearly not representative of most modern communications systems and, therefore, additional work is required to fully characterize the frequency behavior of the MIMO channel matrix. However, the results obtained can be used to assess the channel spatial behavior and temporal variation, as well as the effect of antenna characteristics on the achievable channel capacity. The 12.5-kb/s chip rate produces one channel matrix estimate every 80 ms, where the estimate represents the average channel response over the code length. Because channel changes occur on the time scales of relatively slow physical motion (people moving, doors closing, etc.), this sample interval is adequate for the indoor environment under investigation (see Section IV-B for a discussion of channel temporal variation). Shorter codes could be used to reduce this time if necessary. Alternatively, a higher speed data acquisition system could be employed in conjunction with a higher chip rate to decrease the time between channel estimates. Table I lists the five different locations for the transmit and receive subsystems used in this study. Rooms 400 and 484 are central labs in the building separated by a hallway (designated as “Hall”), “5 Rooms” and “Many Rooms” in the table indicate that the receiver was placed at several locations in different rooms. The specific linear antenna arrays employed were four-element single polarization patches with spacing (4SP), two-element dual polarization (V/H) patches with spacing (2DP), and ten-element monopole antennas with spacing (10SP). Data records were each 10 s long. Since the actual received power varies as a function of the transmit and receive locations, some type of channel normalization is required to facilitate comparison of the results. One reasonable normalization is to scale the channel matrices such that on average, the power transfer between a single transmit and single receive antenna is unity. To see this, let and represent the observed and normalized matrices, respectively, where the superscript denotes the index of the matrix sample in time. Using to represent a normalization constant such that Authorized licensed use limited to: Brigham Young University. Downloaded on February 6, 2009 at 11:59 from IEEE Xplore. Restrictions apply. 338 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 2, NO. 2, MARCH 2003 Fig. 3. Plot illustrating the power dynamic range of the receiver system and histogram of the received power level for all measurements used in this analysis. , the unity average power gain constraint may be expressed as (7) where is the total number of matrix samples. Solving this equation for leads to (8) If the matrix samples include the entire data set under consideration, this scaling allows assessment of the effects of path loss on the channel characteristics. If, on the other hand, is used, each individual matrix will produce the same signal-tonoise ratio (SNR). This is useful when assessing the impact of antenna parameters such as polarization, directivity, or array size on capacity. In this paper, therefore, data is normalized using unless specifically stated in the discussion. Finally, it is important to assess the dynamic range of the receiver system. To accomplish this, the carrier modulated with a single code was directly injected into each receive channel and the channel estimation procedure was applied. The carrier power was varied linearly until saturation occurred at high power and until the carrier estimation procedure failed at low power. Fig. 3 shows the response from one of the channels (all channels were within 1 dB of each other). This plot also contains a histogram of the received power level for all measurements used in this work. These results imply that the effective SNR for most measurements is above 40 dB and never falls below 20 dB. It is important to point out that error in the carrier recovery introduces about 1% error, producing an upper bound of 40 dB on the effective channel SNR. This high SNR level implies that the statistical channel properties will be minimally influenced by the noise. A. Channel Matrix Element Statistics We begin this study by presenting the marginal probability density functions (PDF) for the magnitude and phase of the elements of . These empirical PDFs are computed according to HIST (9) Fig. 4. Empirical PDFs for the magnitude and phase of the 4
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Tripling the capacity of wireless communications using electromagnetic polarization
Article
  • Feb 2001
Wireless communications are a fundamental part of modern information infrastructure. But wireless bandwidth is costly, prompting a close examination of the data channels available using electromagnetic waves. Classically, radio communications have relied on one channel per frequency, although it is well understood that the two polarization states of planar waves allow two distinct information channels; techniques such as 'polarization diversity' already take advantage of this. Recent work has shown that environments with scattering, such as urban areas or indoors, also possess independent spatial channels that can be used to enhance capacity greatly. In either case, the relevant signal processing techniques come under the heading of 'multiple-input/multiple-output' communications, because multiple antennae are required to access the polarization or spatial channels. Here we show that, in a scattering environment, an extra factor of three in channel capacity can be obtained, relative to the conventional limit using dual-polarized radio signals. The extra capacity arises because there are six distinguishable electric and magnetic states of polarization at a given point, rather than two as is usually assumed.
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