# A Multiband Diversity Antenna System for  Compact Mobile/Wireless Devices: Modeling and  Performance Evaluation

Authors: M. Karaboikis; V. Papamichael; C. Soras; V. Makios
Journal: International Journal of Antennas and Propagation
 (2008)

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## Abstract

A novel compact multiband diversity antenna system appropriate for integration onto space-limited devices is
presented. It comprises three pairs of printed fractal Minkowski and Koch monopole antennas which resonate in the
1.67–2, 2.3–2.56 and 4.55–5.55 GHz bands, respectively, supporting thus a large variety of wireless technologies for mobile
and wireless local area networks (WLANs) applications. The operational characteristics of the antenna system were
extracted by simulation using a method-of-moment- (MoM-) based electromagnetic field solver. The diversity performance
in a uniform multipath environment under the maximal-ratio combining (MRC) scheme is also evaluated for the two extreme
modes of operation, that is, when all three antenna pairs operate simultaneously (worst case) and when only one pair is active while the others being open-circuited (best case). The calculated effective diversity gain (EDG) for the worst/best case
is 5.8/6.4, 5.8/7.2 and 7.1/7.5 dB for the 1.8, 2.4 and 5.2 GHz frequencies, respectively.


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## Body

## 1. Introduction

Multiradio antenna systems which support multiple wireless standards are the trend for future communication systems. The performance of these systems can be significantly enhanced using antenna diversity, which combats efficiently the
multipath fading. Dual-band diversity antennas which operate in 2.4 and 5.2 GHz
industrial, scientific, and medical (ISM) frequency bands have been extensively
reported in literature (e.g., [1–4]). The
attention to multiband diversity antenna systems, on the other hand, is currently
very limited [5, 6].In
[5], two planar inverted-F antenna (IFA) arrays, which cover the 2.4 and
5.25/5.8 GHz ISM bands, are proposed for WLAN applications. In [6], the
proposed multiband diversity antenna is very compact and covers in addition the
1.8 GHz band, which supports digital wireless protocols and thus can be used
for mobile applications as well. However, in both [5, 6] the performance
evaluation of the investigated multiband diversity antenna systems, when
operating in multipath fading environments, is not presented.In
this study, a novel compact multiband diversity antenna system suitable for
integration on space-limited mobile/wireless devices is presented along with
its diversity performance evaluation. The antenna system is formulated using printed
Koch and Minkowski fractal monopoles which were selected due to their extremely
compact dimensions [7–9] and can be integrated
onto a device almost at no cost. The modeling of the proposed antenna structure
was performed using a method-of-moment- (MoM-) based commercial electromagnetic
software [10]. This multielement antenna (MEA) system covers a wide range of
frequencies (1.67–2, 2.3–2.56, and 4.55–5.55 GHz) which can support the following wireless technologies: GSM and DCS (1.67–2 GHz), 802.11 b/g/n, Wi-Fi and Bluetooth (2.3–2.55 GHz), and 802.11a/j and HIPERLAN/2 (4.55–5.55 GHz) [11, Chapter 2]. During its operation in these bands, two extreme modes are investigated in
detail: in the first mode, the antennas operate simultaneously in the three
bands (worst case); while in the second mode only one band is active (best
case).The
paper is organized as follows. In Section2, the methodology for evaluating the
diversity performance under the maximal-ratio combining (MRC) scheme is
described. Specifically, the effective diversity gain (EDG) [12] is evaluated through the signals covariance matrix, which is formulated by means of the complex
correlation coefficient (ρc) of the received signals [13] and the mean
effective gain (MEG) [14] of the antenna elements. Section 3 presents the design
of the proposed antenna system along with its operational characteristics. Section
4 presents the simulated diversity performance in a uniform propagation
environment for the two extreme modes of operation. The study is summarized in
Section 5.


## 2. Two-Branch Maximal-Ratio Combining Diversity Performance Evaluation Methodology

In this section, the metrics for the
diversity performance evaluation are presented. These metrics are the envelope
correlation coefficient (ρe) of the received signals, the mean effective gain(MEG) of the antenna elements,  and the achieved effective diversity gain
(EDG) under the MRC scheme, which as well known provides the upper bound on
diversity performance.The envelope correlation coefficient
between the two antenna branches can be calculated through the complex
correlation coefficient by [13].
(1)ρe12≈|ρc12|2,ρc12=∯Z(Ω)dΩ∯Q1(Ω)dΩ∯Q2(Ω)dΩ,Z(Ω)=Γ⋅Eθ1(Ω)⋅Eθ2*(Ω)⋅Pθ(Ω)+Eφ1(Ω)⋅Eφ2*(Ω)⋅Pφ(Ω),Q1(Ω)=Γ⋅Gθ1(Ω)⋅Pθ(Ω)+Gφ1(Ω)⋅Pφ(Ω),Q2(Ω)=Γ⋅Gθ2(Ω)⋅Pθ(Ω)+Gφ2(Ω)⋅Pφ(Ω),where Eθ and Eφ are the θ and φ polarized, realized (i.e., mismatch included),
active [15] (i.e., mutual coupling included) electric field patterns of the
antennas; Γ is the cross-polarization power ratio (XPR) ofthe incident waves; Pθ and Pφ are the θ and φ components of the angular density functions of
the incoming plane waves; Gθ and Gφ are the θ and φ polarized components of the antennas realized active
power gain patterns; and Ω is the solid angle. The asterisk denotes the
complex conjugate.The MEG of an antenna element, which
is defined as the ratio of the mean received (Prec) to the mean incident power at element
(Pinc), can be calculated from [14]
(2)MEG1,2=Prec1,2Pinc=∮[Γ1+ΓPθ(Ω)Gθ1,2(Ω)+11+ΓPφ(Ω)Gφ1,2(Ω)]dΩ.In the
case of a uniform propagation environment where Γ=1 and Pθ=Pφ=1/4π, (2) simplifies to
(3)MEG1,2=etot1,22,
with etot1,2 being the total efficiency of the respective
antenna element. In turn, etot1,2 is defined as the product of the antenna
mismatch efficiency; emis1,2 times the radiation efficiency erad1,2 (which incorporates the conduction and
dielectric losses):(4)etot1,2=emis1,2⋅erad1,2.Diversity performance, which is the
ability of a multielement antenna system to mitigate fading, can be achieved
when the following two criteria are met [16]:
(5)ρe12<0.5,MEG1MEG2≅1.
A widely used measure of the diversity performance of different antenna systems is the effective diversity gain (EDG) which is defined
mathematically as [12].
(6)EDG =PdivPideal|p%,
where Pdiv is the received power of the combined signal,
and Pideal is the power received by an ideal antenna
operating in the same environment. In this paper, the ideal antenna is a
dual-polarized isotropic radiator with unit radiation efficiency [14]. Pdiv and Pideal are calculated at the same probability level (p%)
in a cumulative probability density versus relative power-level plot. The
cumulative density function (CDF) of Pideal follows the Rayleigh distribution while the
CDF of Pdiv follows the distribution of MRC signals which is given by [17, pages 364–366], [18] as
follows:
(7)P(γ≤x)=1λ1−λ2[λ1{1−e−x/λ1}−λ2{1−e−x/λ2}].
In (7), λ1,2 are the eigenvalues of the signals covariance matrix Λ which is formulated using the calculated
values ρcof and MEGs,
(8)Λ=Pinc[MEG1ρc12MEG1MEG2ρc12*MEG1MEG2MEG2].
For the M-branch MRC case, the covariance
matrix-based methodology for evaluating EDG can be found in [19, 20].


## 3. Compact Printed Multielement Antenna System Design

The geometry and dimensions of the
investigated configuration are depicted in Figure1. It has the typical
dimensions of a PC card, whereas the dimensions of the ground plane are 46 mm × 89 mm. The system
consists of two 35 μm thick copper layers with the antennas placed at the upper
one and the ground plane at the bottom.  The antennas are printed at the edge of
the device’s ground plane on an 8-mil-thick substrate with
εr=3.38 and tan δ=0.0027.Geometry and dimensions of the multiband antenna diversity system.
(a)(b)The antennas used are the folded Koch
monopole [7] and the modified Minkowski monopole of the second iteration [8, 9]. Both monopoles were chosen primarily due to their extremely compact size (Minkowski:
(λ0/10)×(λ0/18);
and Koch: (λ0/10)×(λ0/12)), given the restricted space available on the
mobile/wireless terminal devices. These fractal antennas provide in addition
wide bandwidth, omnidirectional radiation patterns, and ease of fabrication
with no additional cost.The configuration depicted in Figure1 was simulated using IE3D, a commercial method-of-moment-based electromagnetic
field solver [10]. The pairs A, B, and C are well tuned at the 1.67–2 GHz, 2.3–2.56 GHz, and
4.55–5.55 GHz
frequency bands, respectively, as derived from the computed Sii parameters of Figure 2. Apart from the Sii parameters, the mutual coupling (Sij parameters) between the elements
comprising each antenna pair (interpair coupling) is also depicted in Figure 2.  It can be observed that
despite the fact that the physical distance between the antenna elements from
pair A to C decreases, the interpair coupling also decreases. This is
attributed to the increase of the electrical distance between the elements of
the antenna pairs as the frequency increases. Table 1 depicts the radiation
efficiency of the antenna elements proving that these antennas are excellent
radiators despite their miniature size. Due to the symmetrical placement of the
antennas, the presented results are valid for both elements that comprise each
antenna pair.Table 1
Radiation efficiency of the multiband diversity system’s antennas.
Frequency (GHz)Pairerad(%)1.8A91.72.4B91.45.2C91.5SimulatedSii and Sij (interpair coupling) parameters of the three antenna pairs.
(a)(b)(c)Aside
from theinterpair coupling, the mutual
coupling between neighboring elements which resonate in different frequency
bands, hereafter called interband coupling, is also present and affects the antennas operation. As depicted in Figure 3, in the frequencies where neither of any two antenna pairs resonate, the interband coupling among them is negligible3.  Pairs A and C exhibit
also negligible interband coupling at both 1.8 and 5.2 GHz frequencies due to
the fact that their “frequency distance” is the largest (3.4 GHz). The
increased interband coupling between pairs A and C for frequencies below 5 GHz
is attributed to a higher-order resonance of pair A that occurs at 4.5 GHz. From
Figures  3(a) and 3(b), it can be concluded that pairs A and B exhibit the
highest values (~−8dB) of interband coupling at 1.8 and 2.4 GHz which is caused by their relatively small “frequency
distance” (~600 MHz). The interband coupling between pairs C and B is also negligible at both 2.4 and 5.2 GHz due to their large “frequency distance” (2.8 GHz).SimulatedSij parameters (interband coupling) between any two antenna pairs in the three frequency bands.
(a)(b)(c)


## 4. Diversity Performance in a Uniform Environment

In this section, the performance of
the configuration presented in Figure1 when operating in a receive diversity
system is evaluated for two extreme operation modes. In the first mode, the
device is assumed to operate simultaneously in three representative frequencies
(1.8, 2.4, and 5.2 GHz), and thus all antenna elements are terminated to 50 Ω loads. In the second mode
of operation, on the other hand, only one pair is active whiles the remaining two
antenna pairs are open-circuited. The first mode is characterized
as the worst case of operation, since a
great amount of power is lost on the termination loads of the antenna pairs
that operate at the other frequencies, whereas the second one as the best case via
the reverse reasoning. The
MRC performance is investigated using the metrics presented in Section 2 in a
uniform propagation environment, which has been proved to be a fair
approximation for many indoor and outdoor propagation scenarios [20].


### 4.1. Worst Case of Operation

In this mode of operation, the three antenna pairs operate simultaneously being all terminated to
50 Ω loads. The simulated realized active
power gain patterns of the antenna elements on the azimuth (x-y) plane are shown
in Figure4. The
complementary performance of the antenna pairs due to symmetry of the
configuration is obvious, proving that it is a hybrid space-pattern diversity
system with omnidirectional antennas. The total efficiencies of the elements,
the envelope correlation coefficients, as well as the mean effective gains of
the antennas are shown in Table 2. The MEG ratio in every case is unity indicating
that the mean power received by each antenna branch is the same. This is
attributed to the fact that the elements of the antenna pairs have symmetrical
radiation patterns and operate in a uniform propagation environment. The
calculated values of ρe indicate that all antenna branches receive
uncorrelated signals since ρe is far below 0.5, which is attributed to the
inherent space-pattern diversity
(see Figure 4).Table 2
Total efficiency, correlation coefficient, mean effective gains, and effective diversity gain of the multiband diversity system for the worst case.
PairFrequency (GHz)etot(%)ρeMEGEDG (dB)A1.8520.042−5.65.8B2.4522.2×10−3−5.65.8C5.2730.012−4.47.1Simulated azimuth plane (x-y) realized active power gain patterns for the three antenna pairs under the worst case of operation.
(a)(b)(c)Regarding the effective diversity
gain, the antenna pair C exhibits the best performance with 7.1 dB of effective
diversity gain at 5.2 GHz, whereas pairs A and B provide 5.8 dB gains at 1.8 and
2.4 GHz, respectively, (see Table2). This gain reduction is attributed solely to
the additive impact of the interpair and interband mutual couplings, which lowers the
total efficiencies of these pairs and thus their MEG values as in (3). For pair C,
however, both interpair and interband
couplings have less impact as presented in Section
3 which is reflected to the higher EDG value.


### 4.2. Best Case of Operation

In this mode of operation, only one antenna pair operates with its elements being terminated to 50 Ω loads whiles the rest are
retained, open-circuited. The realized active power gain patterns for the best case of operation differ
from those of the worst case due to the fact that different termination has been used. These antenna patterns on the azimuth (x-y) plane are shown in Figure5, where the complementary performance due to symmetry is again obvious.Simulated azimuth plane (x-y) realized active power
gain patterns for the three antenna pairs under the best case of
operation.
(a)(b)(c)For this
operation mode, the mean value of the gain patterns is higher than before, which is caused by the absence of theinterband coupling. Table 3 lists the total efficiencies, the envelope correlation
coefficients, and the mean effective gains of the antennas for the best case. The
total efficiencies and thus MEGs, according to (3), are also improved since no extra power is consumed in the elements of the nonactive antenna pairs. In every case, the calculated values of ρe are far below 0.5 as in the previous mode.Table 3
Total efficiency, correlation coefficient,
mean effective gains, and effective diversity gain of the multiband diversity system for the best case.
PairFrequency (GHz)etot(%)ρeMEGEDG (dB)A1.8610.011−5.26.4B2.4759.6×10−3−4.37.2C5.2782.9×10−3−4.17.5Regarding the effective diversity
gain, the antenna pair C exhibits again the best performance with 7.5 dB of
effective diversity gain at 5.2 GHz, whereas pairs A and B provide 6.4 and 7.2 dB gains at 1.8 and
2.4 GHz, respectively, (see Table3). The undesired impact of the interband mutual coupling has been removed, causing an improved diversity performance for the three investigated frequencies.


## 4.1. Worst Case of Operation

In this mode of operation, the three antenna pairs operate simultaneously being all terminated to
50 Ω loads. The simulated realized active
power gain patterns of the antenna elements on the azimuth (x-y) plane are shown
in Figure4. The
complementary performance of the antenna pairs due to symmetry of the
configuration is obvious, proving that it is a hybrid space-pattern diversity
system with omnidirectional antennas. The total efficiencies of the elements,
the envelope correlation coefficients, as well as the mean effective gains of
the antennas are shown in Table 2. The MEG ratio in every case is unity indicating
that the mean power received by each antenna branch is the same. This is
attributed to the fact that the elements of the antenna pairs have symmetrical
radiation patterns and operate in a uniform propagation environment. The
calculated values of ρe indicate that all antenna branches receive
uncorrelated signals since ρe is far below 0.5, which is attributed to the
inherent space-pattern diversity
(see Figure 4).Table 2
Total efficiency, correlation coefficient, mean effective gains, and effective diversity gain of the multiband diversity system for the worst case.
PairFrequency (GHz)etot(%)ρeMEGEDG (dB)A1.8520.042−5.65.8B2.4522.2×10−3−5.65.8C5.2730.012−4.47.1Simulated azimuth plane (x-y) realized active power gain patterns for the three antenna pairs under the worst case of operation.
(a)(b)(c)Regarding the effective diversity
gain, the antenna pair C exhibits the best performance with 7.1 dB of effective
diversity gain at 5.2 GHz, whereas pairs A and B provide 5.8 dB gains at 1.8 and
2.4 GHz, respectively, (see Table2). This gain reduction is attributed solely to
the additive impact of the interpair and interband mutual couplings, which lowers the
total efficiencies of these pairs and thus their MEG values as in (3). For pair C,
however, both interpair and interband
couplings have less impact as presented in Section
3 which is reflected to the higher EDG value.


## 4.2. Best Case of Operation

In this mode of operation, only one antenna pair operates with its elements being terminated to 50 Ω loads whiles the rest are
retained, open-circuited. The realized active power gain patterns for the best case of operation differ
from those of the worst case due to the fact that different termination has been used. These antenna patterns on the azimuth (x-y) plane are shown in Figure5, where the complementary performance due to symmetry is again obvious.Simulated azimuth plane (x-y) realized active power
gain patterns for the three antenna pairs under the best case of
operation.
(a)(b)(c)For this
operation mode, the mean value of the gain patterns is higher than before, which is caused by the absence of theinterband coupling. Table 3 lists the total efficiencies, the envelope correlation
coefficients, and the mean effective gains of the antennas for the best case. The
total efficiencies and thus MEGs, according to (3), are also improved since no extra power is consumed in the elements of the nonactive antenna pairs. In every case, the calculated values of ρe are far below 0.5 as in the previous mode.Table 3
Total efficiency, correlation coefficient,
mean effective gains, and effective diversity gain of the multiband diversity system for the best case.
PairFrequency (GHz)etot(%)ρeMEGEDG (dB)A1.8610.011−5.26.4B2.4759.6×10−3−4.37.2C5.2782.9×10−3−4.17.5Regarding the effective diversity
gain, the antenna pair C exhibits again the best performance with 7.5 dB of
effective diversity gain at 5.2 GHz, whereas pairs A and B provide 6.4 and 7.2 dB gains at 1.8 and
2.4 GHz, respectively, (see Table3). The undesired impact of the interband mutual coupling has been removed, causing an improved diversity performance for the three investigated frequencies.


## 5. Conclusions

In this study, a novel compact multiband diversity antenna system for mobile and WLAN applications has been proposed.
The simulated results indicate that the antenna structure is suitable for a variety of wireless technologies in the 1.8/2.4/5.2 GHz frequency bands. The
diversity performance in a uniform multipath environment was quantified through
the effective diversity gain calculated using the signals covariance matrix for two extreme modes of operation. In any case, the diversity criteria are fulfilled,
and the calculated diversity gain offered by the proposed system for the
worst/best case of operation is 5.8/6.4, 5.8/7.2, and 7.1/7.5 dB for the 1.8,
2.4, and 5.2 GHz frequencies, respectively.



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*Source: 782153-2008-03-23.xml*