I. J. Communications, Network and System Sciences, 2008, 2, 105-206
Published Online May 2008 in SciRes (http://www.SRPublishing.org/journal/ijcns/).
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
Impact of Depolarization Phenomena on Polarized MIMO
Channel Performances
Nuttapol PRAYONGPUN, Kosai RAOOF
Laboratoire Grenoble Images Paroles Signal Automatique (GIPSA-LAB), UMR CNRS 5216
961, Rue de la Houille Blanche - BP 46 - 38402 Saint Martin d'Hères, France
E-mail: {nuttapol.prayongpun, kosai.raoof}@gipsa-lab.inpg.fr
Abstract
The performance and capacity of multiple-input multiple-output (MIMO) wireless channels are limited by
the spatial fading correlation between antenna elements. This limitation is due to the use of mono polarized
antennas at receiver and transmitter sides. In this paper, in order to reduce the antenna correlation, the
polarization diversity technique is employed. Although the spatial antenna correlation is attenuated for multi-
polarization configurations, the cross-polar components appear. This paper highlights the impact of
depolarization effect on the MIMO channel capacity for a 4×4 uniform linear antenna array. We assume that
the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is
distributed to each of the transmit antennas. The numerical results illustrate that for low depolarization and
spatial correlation, the capacity of single-polarization configuration behaves better than that of multi-
polarization configuration.
Keywords: Multiple-input Multiple-output (MIMO), Channel Capacity, Spatial Fading Correlation, Multi-
polarized Antenna Arrays, Depolarization Effects.
1. Introduction
For the next-generation of wireless communication
systems, multiple antennas at both transmitter and
receiver could be engaged to achieve higher capacity
and reliability of wireless communication channels,
under rich scattering environments, in comparisons with
traditional single antennas. Due to the potential use of
MIMO systems on a limited bandwidth and transmission
power, the initial researches demonstrate that the
uncorrelated channel capacity can be proportionally
increased according to the number of antennas [4,5].
Unfortunately, in practice, the performances of
MIMO communication channel are affected by spatial
correlation and channel environments [6]. The spatial
correlation depends on the array configuration such as
radiation pattern, antenna spacing and array geometry.
The channel environments are dependent on the
environment characteristics such as number of channel
paths, distribution and properties of scatterers, angle
spread and cross-polarization discrimination [8–10].
Thus, the antenna arrays at transmitter and receiver
should be properly designed to reduce the spatial
correlation effects and to improve the communication
performances [11].
However, it is possible to reduce this effect
traditionally by increasing antenna array spacing, but it
is not often suitable to apply in some wireless
applications where the array size is limitted. Therefore,
to eliminate spatial correlation effects with high
transmission performances, there are essentially two
diversity techniques; pattern and polarization diversity
techniques [12,16]. For pattern diversity technique, the
radiation of antennas should be generated in a manner to
isolate the radiation pattern. For polarization diversity
technique, the antennas are designed to radiate with
orthogonal radiation polarizations to create uncorrelated
channels. In general, there are more than two diversity
techniques employed in MIMO wireless systems.
However, there are also other techniques such as
multimode diversity that exploits the difference of
higher order modes to obtain low correlated channel [14].
Polarization diversity technique can be used with pattern
IMPACT OF DEPOLARIZATION PHENOMENA ON POLARIZED MIMO 125
CHANNEL PERFORMANCES
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
diversity technique in order to boost channel capacity.
Numerous MIMO channel models have already been
proposed in literature. In this paper we focus on
geometry-based stochastic channel models (GSCM)
[15,16]. This calculates the channel response by taking
into account the characteristics of wave propagation, Tx-
Rx environments, and the scattering mechanisms. All
parameters are statistically set to closely match the
measured channel observation.
In this paper, we define a geometric scattering model
based on a three-dimensional double bouncing model
that takes into account the antenna configuration [17–19].
All antennas are provided as a uniform linear array with
isotropic or dipole antennas at transmitter and receiver
sides. However, all scatterers are uniformly distributed
on scattering areas and take into account the cross-polar
discrimination (XPD). This parameter indicates the ratio
of the co-polarized average power to the cross-polarized
average power. Therefore, scattering matrix is used to
describe the depolarization of incident wave for each
scatterer. Afterward, to simplify the simulated
environment configuration, we assume that the angle of
arrival and that of departure are uniformly distributed.
Figure 1. Geometries of MIMO channel
We present a simulation study of the spatial
correlation and moreover the channel capacity of single-
and dual-polarized antenna arrays applied to 4×4 MIMO
system. All antenna elements are separated by a half
wavelength even in the case of the dual polarization
configuration. In addition, we examine the cross-polar
discrimination effects on MIMO polarized channel
capacity for different antenna configurations.
In Section 2, we provide electromagnetic patterns
regarding different electric dipoles. These patterns are
then used in Section 3 to create a channel model
combining the effect of space separation, polarization
antenna gains and depolarization mechanisms. In
Section 4, we apply the information theory in order to
examine the MIMO channel capacity. Finally, in Section
5, we analyze the numerical results of single- and dual-
polarization configurations.
2. Antennas
In practice, not only the propagation environment has an
important role but the proper implementation of the
antennas plays also another dominant role for
determining the multiple antenna transmission
performances. The receiving signals on one element
antenna can be correlated to that of another element
antenna. Therefore, the systems, which can achieve the
best performances, should properly reconfigure the
transmitting or/and receiving antenna element arrays
with the channel state information derived from the
propagation channels.
Table 1. Patterns for different electric dipoles
x
G
y
G
z
G
(
)
,G
θ
θ
φ
cos cos
θ
φ
cos sin
θ
φ
sin
θ
(
)
,G
φ
φ
sin
φ
cos
φ
0
Here we are interested in one array configuration.
Orthogonally oriented antennas can offer orthogonal
polarization, which corresponds to a complete separation
between individual channels, although the antennas are
co-located. Thus, using multiple polarization technique
helps to guarantee an effective antenna deployment
space. However, the receiving energy can be reduced
due to the imbalance of depolarization mechanisms.
Three dipole antennas are concerned in this paper; x-,
y- and z-oriented dipole antennas. Their patterns of
electromagnetic radiations can be simplified by
neglecting path loss and distance phase because the
electromagnetic radiations are homogenously and
identically diffused in the far field case. Their simple
expressions of radiation patterns are given by [1]
(
)()
,,GG G
θφ
θ
φθ θφφ
=+
r
r
(1)
where
(
)
,G
θ
θ
φ
and
(
)
,G
φ
θ
φ
are the antenna gains at
elevation and azimuth directions. These gains also
depend on the propagation direction. The radiation
patterns of differently oriented dipoles are shown in
Table 1.
In this paper, the propagation patterns of these
antennas are normalized with the isotropic antenna
which is specified as the reference antenna.
3. Geometric Scattering Modelling
We focus on a useful model called “geometric scattering
model” which is based on the assumption that scatterers
around the transmitter and receiver organize the AOD
and AOA respectively within transmit and receive
scattering areas [15,16,18]. The scatterers are randomly
located with according to a certain probability
distribution. In particular, the scatterers are additionally
used to represent the depolarization and attenuation
mechanism of incident waves. To reduce the
computational time, we consider that only one
126 N. PRAYONGPUN ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
propagation path channel occurs when one of transmit
and one of receive scatterers are randomly linked. Then
the actual channel impulse response is established by a
simplified ray-tracing route.
By using our simulated double bounce geometric
scattering model as seen in Figure 1, we employ a
uniform linear array at both transmitter and receiver. The
height of transmitter and receiver has the same level.
Moreover, transmit and receive scatterers are uniformly
distributed within an angular region characterized by
22
φ
πφ
+≤∆
in elevation area and 22
θ
πθ
+≤∆
in azimuth area at transmitter and 22
φ
πφ
−≤∆ in
elevation area and 22
θ
πθ
−≤∆ in azimuth area at
receiver.
Subsequently transmit and receive scatterers are
randomly paired as previously mentioned. From one
transmit scatterer to one receive scatterer, there is a
double depolarization mechanism which is replaced by
one scattering matrix. We also assume that the channel
coherence bandwidth is larger than the transmitted
bandwidth of the signal. This channel is usually called
frequency non-selective or flat fading channel.
In the case of far field transmission without line-of-
sight channel, the narrowband (flat fading) transmission
channel between the antenna p at the transmitter and the
antenna m at the receiver can be expressed as [20]
(2)
where Ns is the number of scatterers at the receiver and
the transmitter; Tx
v
rand Rx
v
rare the velocity vector of the
transmitter and the receiver; ()i
k
r
and ()i
k
r
are the vectors
of wave number in the direction of the ith transmit
scatterer and the ith receive scatterer where
()() 2
ii
kk
π
λ
==
vv
;
()
,
p
ii
G
θ
θ
φ
and
()
,
p
ii
G
φ
θφ
are the
gain in the direction of
θ
r
and
φ
r
of the pth transmit
antenna in the direction of the ith transmit scatterer.
()
,
m
ii
G
θ
θ
φ
and
()
,
m
ii
G
φ
θ
φ
are the gain in the direction
θ
r
and
φ
r
of the mth receive antenna in the direction of
the ith receive scatterer; t is time; ()i
m
a is the mth element
of the local vector of the receive antenna, so that the
local receive vector can be expressed as
() ()
11
()
Rx 1
ii
M
ijk rjk r
ee
−⋅ −⋅
⎡⎤
=⎢⎥
⎣⎦
a
rr
rr
L, ()i
p
a is the pth
element of the local vector of the transmit antenna,
where a local transmit vector is expressed as
()
()
1
1
()
Tx 1 i
i
N
jk rijk r
ee
′′
′′ −⋅
−⋅
⎡⎤
=⎢⎥
⎣⎦
a
r
rr
r
L; ()i
mp
S are the
scattering matrix for the pth transmit scatterer and the
mth receive scatterer and is also defined as
() ()
()
() ()
ii
i
mp ii
SS
SS
θ
θφθ
θ
φφφ
=
S (3)
The cross polarization discrimination (XPD) is
defined as the average power ratio of the co-polarization
component and the cross-polarization component.
{
}
{
}
{}{}
22
22
XPD ESES
XPD ESES
θθθ θφ
φφφ φθ
=
=
(4)
In some conditions such as the imbalance of
depolarization and the use of different antenna patterns,
X
PD XPD
θ
φ
. We assume that the sum of the co-
polarized power and the cross-polarized power is
constant. Therefore the scattering matrix can be written
as
(5)
where ()i
θ
φ
ϕ
denotes phase offset of ith incident wave
which changes from
θ
r
direction to
φ
r
direction and
superposing on mp channel.
4. MIMO Capacity
In this section, we assume that the noise has a Gaussian
distribution. Therefore, the optimal distribution of input
signal is Gaussian for maximizing the mutual
information (MI). The mutual information is given by
[4,5]
()
(
)
1
2
log detR
N
=+Φ
n
IHHKI (6)
where
(
)
EΦ= xx is the spatial covariance matrix of the
input vector x under the total transmitting power
constraint
(
)
t
tr P
=
Φ and Kn is the covariance matrix of
the noise vector n.
()
denotes the conjugate transpose
operator,
(
)
E
is the expected value and
(
)
tr
is the
trace operator.
When the MIMO channel state information (CSI) is
known at the receiver but unknown to the transmitter
and n is complex additive white Gaussian noise (AWGN)
vector with zero mean, the covariance is equal to
2
R
N
σ
=
nn
KI. When CSI is not available at the
transmitter, the transmitter splits equally the total power
to each transmitting antenna. Then the input covariance
matrix is a diagonal matrix T
tTN
PNΦ= ⋅I.
IMPACT OF DEPOLARIZATION PHENOMENA ON POLARIZED MIMO 127
CHANNEL PERFORMANCES
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
(a)
(b)
Figure 2. 4×4 MIMO channel capacity of isotropic
antennas: (a) single-polarization system and (b) dual-
polarization system
Therefore, the average MI, E(I), called the ergodic
channel capacity, with equal-power allocation at
transmitter can be written as
()
22
log detR
H
t
noCSI N
T
P
CEE N
σ
⎡⎤
⎛⎞
== +
⎢⎥
⎜⎟
⎝⎠
⎣⎦
H
n
IHHI (7)
By applying an eigenvalue decomposition, (7) can be
rewritten as
2
2,
2
1
log 1
M
t
noCSI i
iT
P
CE N
λ
σ
=
⎡⎤
⎛⎞
=+
⎢⎥
⎜⎟
⎝⎠
⎣⎦
HH
(8)
where M = min(NT,NR) that corresponds to the rank of
channel matrix and 2
,i
λ
H is the ith eigenvalue of H.
5. Simulation Results Based on Geometric
Scattering Modelling
5.1. Capacity Versus Angle Spread
The antenna correlation effect is an important indicator
for transmission performance since lower correlation
will tend to produce higher mean channel capacity for
single polarization system as seen in Figure 2. Thus
employing polarization and angular diversity techniques
is an attractive way to improve MIMO systems. The 4×4
MIMO systems employ isotropic antennas for λ/2
antenna spacing as shown in Figure 1. In order to
estimate the channel capacity of different antenna
configuration, the simulated environments must be
identical. Hence the channel capacities are studied in
terms of different antenna configurations. The radiation
patterns of each antenna are normalized by the radiation
pattern of an isotropic antenna.
As mentioned in previous section, the distribution of
angles of departure is assumed to have a uniform
elevation distribution 22
φ
πφ
+≤∆
and a uniform
arrival azimuth distribution 22
θ
πθ
+≤∆ and the
distribution of angles of arrival is assumed to have a
uniform elevation distribution 22
φ
πφ
−≤∆ and a
uniform arrival azimuth distribution 22
θ
πθ
−≤∆
where AS
φ
θ
=∆ = and XPDθ=XPDØ=XPD=0dB with
20 scatterers at both transmitter and receiver and 15 dB
of SNR. The aim of this section is to study the effects of
angle spreads and antenna radiation patterns in terms of
ergodic capacity.
Figure 2 demonstrates 4×4 MIMO channel capacity
of single and dual polarized configuration. For single-
polarization case, only azimuth isotropic antennas are
employed and for dual-polarization case, we put
successively azimuth and elevation isotropic antennas in
order with λ/2 antenna spacing. From Figure 2a, the
MIMO channel capacity increases as the angle spread
increases at transmitter and receiver for the same
polarization antennas. In contrast, the dual polarization
achieves better channel capacity due to the lower
antenna correlation. It founds that the MIMO channel
capacity is significantly dependent on the antenna
correlation. The polarization diversity technique can
diminish the spatial correlation effect and improve the
system performances as shown in Figure 2b.
Figure 3. Difference between dual-polarized and single-
polarized channel capacity of 4×4 MIMO systems in
functions of XPD and AS
128 N. PRAYONGPUN ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
(a)
(b)
Figure 4. A 4×4 MIMO configuration of 20° transmit and
180° receive angle spreading: (a) Channel capacity and (b)
Subchannel power
5.2. Capacity Versus Depolarization Effects
If multi-polarized antenna array is employed, the spatial
correlation effect can be reduced or eliminated due to
low radiation pattern interference. Nevertheless, the
cross-polarization discrimination (XPD) becomes the
most important parameter because XPD represents the
ratio of the co-polarized average received power to the
cross-polarized average received power. Then, with high
XPD value, less energy is coupled between the cross-
polarized channels. Even if the capacity of multi-
polarized antenna arrays can remain high particularly at
lower XPD and the higher K-factor values [17], single-
polarized antenna array performance can effectively
provide better than that of multi-polarized antenna array
at higher XPD and lower spatial correlation value.
Figure 3 explains the difference between dual-
polarized and single-polarized channel capacity of 4×4
MIMO systems
()
single-polar dual-polar
CC C∆= − in
functions of XPD and AS. We also consider that they
have the same angle spreads (AS) at both transmitter and
receiver sides. For a high XPD and a sufficiently wide
angle spread, we note that the MIMO channel capacity
of the single-polarized antenna is superior to that of the
dual-polarized antenna because a product of the
subchannel power is higher.
Figure 4 demonstrates the capacity variation in
function of polarization decoupling and also subchannel
power of channel matrix for isotropic and dipole
antennas. We setup a 4×4 MIMO system with 20°
transmit and 180° receive angle spreading to achieve
high transmit and low receive spatial correlation.
The channel capacity of the isotropic and dipole
antenna configurations in Figure 4a is slightly different,
because the transmission power is normalized with
respect to the transmission power of the isotropic
antennas. That is the reason why we have the same
subchannel power for the isotropic and dipole antennas
in Figure 4b. Although MIMO subchannel power of
single polarization system is superior to that of dual
polarization at high XPD, the single-polarized MIMO
configuration cannot benefit of this high channel power
due to the significant transmit correlation as shown in
Figure 4a.
The subchannel power of channel matrix can be
calculated by employing the Frobenius norm. The
numerical results confirm that for high XPD case, the
co-polarized channel components still have a significant
value compared to the cross-polarized channels. The
average transmission power of single-polarized isotropic
antenna arrays is given by
4416
xx
RT
FNN
=
=×=H (9)
where ()
x
represents the dipole orientation. In the case
of low XPD, the average transmission power of single-
polarized antenna arrays tends to zero,0
FH,
because of the loss of co-polarized channel power as
shown in Figure 4b. The channel power is directly
proportional to the channel capacity as shown in Figure
4a and Figure 4b. In contrast, the average transmission
power of dual-polarized antenna arrays is independent of
the XPD value, and it approaches to
2222 8
+=×+×=Hxx zz
RT RT
FNN NN (10)
as illustrated in Figure 4b where ()
x
and ()
z
denote the
dipole type shown in Table 1.
6. Conclusions
The performance of MIMO communication systems is
essentially affected by the spatial correlation and
channel environments. The spatial correlation depends
on the array configurations and the channel
characteristics. Therefore to achieve the optimum
IMPACT OF DEPOLARIZATION PHENOMENA ON POLARIZED MIMO 129
CHANNEL PERFORMANCES
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
performances with MIMO systems, the proper selection
of array configuration is required. In this paper, we
studied the MIMO wireless channel capacity of single-
and multi-polarized antenna arrays applied to a uniform
linear array with two isotropic antenna configurations.
The simulation results demonstrate that for the non-
line-of-sight (NLOS) case, the use of multi-polarization
antennas can provide capacity improvement over
conventional single-polarization antennas for narrow
angle spread. However, when the cross-polarization
discrimination is superior than 0dB corresponding to
high co-polarized channel power and low cross-
polarized channel power, the subchannel power of
single-polarization system can be higher by employing
the same polarization as that of the co-polarized channel.
Thus, with high XPD and low spatial correlation values,
single-polarized antenna array performance can
effectively provide better capacity than that of multi-
polarized antenna array. Finally, the cross-polarization
discrimination should be also investigated before
employing the polarization diversity technique.
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