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Int. J. Communications, Network and System Sciences, 2010, 3, 350-354
doi:10.4236/ijcns.2010.34044 blished Online April 2010 (http://www.SciRP.org/journal/ijcns/)
Copyright © 2010 SciRes. IJCNS
Envelope Correlation Parameter Measurements in a
MIMO Antenna Array Configuration
Constantinos Votis, George Tatsis, Panos Kostarakis
Physics Department, University of Ioannina, Ioannina, Greece
Email: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Received January 11, 2010; revised February 12, 2010; accepted March 15, 2010
In a 2 × 2 MIMO antenna array system envelope correlation coefficient “ρ” shows the influence of different
propagation paths of the RF signals that reach the antenna elements. The approximated value of this coeffi-
cient is based on a simple closed-form equation and also varies from 0 to 1. Quite perfect performance for
MIMO applications is achieved when this parameter approximates to zero. In this paper, we evaluate an an-
tenna diversity MIMO system by measuring the envelope correlation coefficient. The corresponding results
in our antenna array configurations show that the measured “ρ” has very small values and approximates to
zero. This observation indicates quite perfect behavior and performance of our MIMO antenna array system.
Keywords: Scattering Parameters, Envelope Correlation, Printed Dipole Antenna
Multiple Input Multiple Output (MIMO) systems have
received a great attention, recently. This architecture uses
more than one antenna elements in transmitter and re-
ceiver ends and is able to overcome the limit of channel
capacity in a rich multipath environment . The theo-
retical capacity of the system increases linearly with the
number of elements in MIMO antenna arrays. However,
practical considerations indicate that the corresponding
capacity of the system may be reduced if the received
signals in any of the different antenna elements are cor-
related . This effect proposes that diversity gain is
obtained in the antenna system when the value of “ρ” is
less than 0.5 . It is obvious that correlation affects
MIMO performance and represents a crucial parameter
for modern wireless applications .
Moreover, MIMO design considerations include these
antenna diversity techniques that also increase spectrum
efficiency. It is also recognized that mutual coupling of
the antenna degrades the performance of these systems.
These observations and an amount of corresponding
research activities indicate that MIMO system performa-
nce is a crucial topic and for this investigation some par-
ameters need to be considered. The envelope correlation
between antenna elements is one of most important beca-
use it is related with the spectral efficiency and may pro-
vide degradation on performance of these applications.
Antenna correlation calculation procedure is provided
by appropriate methods of analysis. Basically, three met-
hods are used for these envelope correlation coefficient
calculations. One of them is based on the far-filed radia-
tion pattern. However, it is a time-consuming process [5,6].
This requires the corresponding numerical or experimental
analysis and therefore is a cumbersome process. The sec-
ond method is based on Clarke’s formula  and has re-
cently been used [8,9]. The third method is suitable for
experimental measurements and requires the knowledge of
scattering parameters obtained on the antenna elements.
This last method is the one we adopted throughout this
paper. The procedure of calculating the correlation be-
tween antennas in a two - antenna system using the scat-
tering parameters is proposed in . In our study, enve-
lope correlation of eight antenna array types are presented
and investigated for two indoor environments.
The present paper is structured as follows: in Section 2,
the basic theoretical background is presented; the pro-
posed antenna array implementation aspects are intro-
duced in Section 3. Antenna array configurations are inv-
estigated in terms of envelope correlation and the corre-
sponding results are discussed in Section 4. The experi-
mental observations are summarized in Section 5.
The method of calculating envelope correlation of ele-
C. VOTIS ET AL. 351
ments in each antenna array configuration is based on a
fundamental Equation (1) that requires 3-dimensional
radiation pattern considerations.
The parameter 1
(,)F is the field radiation pattern
of the antenna system when only the port i is excited and
all other ports are terminated to 50 Ω load. The symbol
also denotes the Hermitian product [4,10].
Recent research activities have shown that the enve-
lope correlation can be well defined by a simple closed-
form equation that relates the scattering parameters of
the elements in an antenna array configuration. Especia-
lly, in case of a multipath indoor environment with a
uniform distribution of Equation (2) is proved to be a
good approximation . For two antenna elements this
equation using the scattering parameters becomes:
11 2122 12
It is obvious that radiation pattern in Equation (1)
makes the calculation more complicated than the enve-
lope correlation calculations based on in Equation (2).
The practical advantage of the third method that is based
on second equation is that not only is quite simple to use
it experimentally, but also provides sufficiently accurate
results in many experimental environments such as in-
door environments with rich multipath propagation per-
3. Antenna Array Aspects
The mathematical consideration given by in Equation (2)
is related to the corresponding antenna array structure
that is comprised by two identical printed dipole anten-
nas with integrated balun and a plane reflector of alumi-
num. Figure 1 presents the layout of antenna dipole.
Geometry parameters of the printed dipole have been
further studied and investigated [11-13]. Its characteris-
tics are summarized in Table 1. Each of the two identical
printed dipoles has a resonance point close to the fre-
quency range of 2.4 GHz and the corresponding reso-
nance bandwidth is quite 500 MHz. In addition, the re-
flector backplane (Figure 2) is designed and imple-
mented to allow the positioning of the antenna elements
in various configurations. From these considerations it is
obvious that this antenna array structure supports wire-
less applications in frequency range of 2.4 GHz. A typi-
cal antenna array configuration is shown in Figure 3.
(a) Bottom Layer
(b) Top Layer
Figure 1. Printed dipole antenna.
Table 1. Results for printed dipole (simulated/measured).
Definition Symbol Simulated Measured
Frequency f0 (GHz) 2.3 2.4
Resonance Bandwidth BW (GHz) 0.5 0.5
Return Loss RL (dB) -58 -42
Figure 2. Top site of plane reflector.
Figure 3. Typical antenna array configuration.
opyright © 2010 SciRes. IJCNS
C. VOTIS ET AL.
4. Analysis and Discussion
The antenna system that has been introduced is studied
and investigated in terms of envelope coefficient meas-
urements. The corresponding results have been obtained
in each case of eight antenna array configurations. The
first four of them corresponds to side by side placement
of identical printed dipoles and are grouped to the first
part of the present investigation. The last four represent
collinear form and provides the second part. Figure 4
and Figure 5 show the corresponding groups of antenna
array configurations for each part of the proposed inves-
The corresponding S-parameters that are provided by
experimental procedure have been concentrated and used
to the mathematical formula proposed by in Equation (2).
These experimental measurements of scattering parame-
ters have been provided by a Network Analyzer and have
taken place in two Laboratory’s Environments A and B.
In each of the two indoor environments and for Group A
and Group B antenna array configurations these parame-
ters have been obtained. With these measured results we
calculate the envelope correlation coefficient. As mention-
ed above, this procedure is based on in Equation (2).
The corresponding calculations provide envelope cor-
relation values in a frequency range of 1 GHz with center
frequency of 2.4 GHz. The experimental results for
Group A antenna array configurations are shown in Fig-
ure 6 and Figure 7 for two different Laboratory Envi-
ronments A and B, respectively.
In each case of Group A configurations the corre-
sponding envelope correlation curve has been plotted.
From Figure 6 and Figure 7, it seems that the “ρ” pa-
rameter has almost small values in this frequency range.
In particular, at frequency range of 1.5 to 2.1 GHz the
(a) (b) (c) (d)
Figure 4. Relating antenna elements positions in the reflec-
tor backplane (Group A).
(e) (f) (g) (h)
Figure 5. Relating antenna elements positions in the reflec-
tor backplane (Group B).
Figure 6. Measured results of envelope correlation for Group
A in Laboratory A environment.
Figure 7. Measured results of envelope correlation for Group
A in Laboratory B environment.
envelope correlation coefficient has a value close to
0.015 for all antenna array configurations in Group A.
This observation indicates that the parameter “ρ” remains
stable as the distance between the dipoles increases in
side by side antenna array configuration of Group A.
Instead, at frequency range from 2.1 to 3.5 GHz the
value of envelope correlation coefficient has variations in
a range of 0 to 0.05 for the smallest distance between the
dipoles in Group A antenna array configuration. In other
cases these variations are neglected.
For Group B the corresponding results for parameter
“ρ” are depicted in Figure 8 and Figure 9 for Labora-
tory’s environment A and B, respectively.
From these experimental results, it seems that the pa-
rameter of envelope correlation has also quite small val-
Copyright © 2010 SciRes. IJCNS
C. VOTIS ET AL. 353
ues in the frequency range of 1.5 to 3.5 GHz. Small
variations of this parameter is introduced at the frequ-
ency range from 1.5 to 2 GHz only for the smallest dis-
tance between the dipoles in antenna array configuration
of Group B. These variations are not provided by other
values of distance between the elements bigger than one
wavelength for collinear antenna array configuration.
Moreover, in the frequency range from 2 to 3.5 GHz the
parameter of envelope correlation coefficient remains
stable and close to zero for each of the collinear antenna
array configuration in Group B.
It is also important that these considerations for group
A and B antenna array configurations are valid for labo-
ratory’s environments A and B. The corresponding de-
clines between the two different propagation envi-
Figure 8. Measured results of envelope correlation for Group
B in Laboratory A environment.
Figure 9. Measured results of envelope correlation for Group
B in Laboratory B environment.
ronments are neglected. In each of these indoor envi-
ronments it is the rich multipath propagation procedure
that provides this important agreement in the corre-
sponding measured results. It is convenient that the in-
door environments offer propagation processes with a
big number of independent signal paths. This observation
indicates that in rich multipath environments the corre-
sponding signal paths are uncorrelated and are impossi-
ble to be in deep fade, simultaneously. This feature im-
proves the performance of MIMO communication appli-
cations and systems.
Another important consideration is that in Group B
antenna array configurations the envelope correlation is
quite low relative to Group A. Different antenna array
geometry may be an important issue for this effect. In
any case of them, the value of envelope correlation is
quite small and less of value 0.5.
To sum up, these antenna array configurations provide
low envelope correlation between the signals that have
received or transmitted from the corresponding elements.
In particular, Group B configurations have quite better
correlation performance and offer more efficiently in
MIMO applications’ performance.
Antenna array configurations have been studied and inves-
tigated in terms of envelope correlation coefficient from
the scattering parameters of two dipole antenna ele-
ments. The corresponding closed-form expression has
been introduced and used to calculate this crucial pa-
rameter. This mathematical formula requires less labori-
ous calculations and provides knowledge on antenna di-
versity optimization. Measured results indicate that rich
multipath environment yields to low correlation coeffi-
cients for the proposed antenna array configurations.
Several distances between antenna elements do not affect
this parameter, dramatically. The corresponding consid-
erations are very crucial for MIMO system’s perform-
ance and are supported by an accurate method for inves-
tigation on modern wireless applications’ design.
This research project (PENED) is co-financed by E.U.
-European Social Fund (80%) and the Greek Ministry of
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