# Diversity Performance of Multiantenna Systems for UMTS Cellular Phones in Different Propagation Environments

Authors: A. Diallo; C. Luxey; P. Le Thuc; R. Staraj; G. Kossiavas
Journal: International Journal of Antennas and Propagation
 (2008)

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## Abstract

We present the evaluation of the diversity performance of several two-antenna systems for UMTS terminals. First, a two-antenna system with poor antenna-to-antenna isolation is described. Then, with the help of a neutralization technique, we introduced an optimized structure with high antenna-to-antenna isolation. The key parameters for an efficient diversity performance are then discussed,
some of them being actually dependent on the propagation environment (uniform, indoor, outdoor,  and outdoor-to-indoor chosen here). All these parameters, the total efficiency, the envelope correlation coefficient, the mean effective gain, the diversity
gain, and the effective diversity gain, are computed with the help of the simulated radiation patterns of
both antenna systems. Next, these key parameters are measured in a reverberation chamber to validate the simulations we achieved in the uniform environment. The comparison of the performance of the two prototypes is especially showing the usefulness of using a neutralization technique for enhanced diversity
antenna systems.


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## Body

## 1. Introduction

Today, wireless communications
are part of daily life. One of the major problems to solve in a communication between
a
portable unit and a base station is the deep fading caused by the multipath propagating
environment. To overcome this problem, one solution consists in using some diversity
technique at the terminal side of the wireless link by means of gathering several
antennas [1]. However, to design suitable multiantenna systems, the engineer
must take into account the working environment of all these radiators in the space-limited
mobile device. The main technical challenge is to keep high isolation between
the antennas; otherwise the diversity performance of the system can be
drastically reduced [2]. Moreover, the handset will definitively operate in various
multipath propagation environments, and the main parameters to take care of are
the total efficiency, the mean effective gain (MEG), the envelope correlation
coefficient ρe, the diversity gain (DG), and the effective diversity
gain (EDG). Recently, we designed several UMTS two-antenna systems operating on
a small ground plane whose size is representative of a typical mobile phone [3].
Some of these prototypes are using a neutralization technique to achieve high
antenna-to-antenna isolation and to enhance total efficiency [4]. These
prototypes have already been characterized in terms of S parameters, total
efficiency, and envelope correlation coefficient. This characterization shows
that these structures have a strong potential for an efficient implementation
of a diversity scheme at the terminal side of a wireless link.In this paper, we propose
to use the simulated 3D radiation patterns of these prototypes to further evaluate
their diversity performance. The goal is to compute their envelope correlation,
MEG, DG, and EDG in various and realistic propagation environments [2, 5–9]. To
validate these simulations, we also present some measurements in one of these
environments: the uniform multipath propagation case [10]. These measurements
have been done with the help of the COST 284 project, at Chalmers Institute of Technology,
Sweden, where the antenna group possesses a reverberation chamber and
the associated expertise needed through the Bluetest company [11–14]. The measured
envelope correlation coefficients, the total efficiency, the MEG, the DG, and
the EDG of all the prototypes are thus compared. The analysis of the results
demonstrates the overall improvement brought by the neutralization technique
and its usefulness for enhanced diversity antenna systems.


## 2. Presentation of the Two-Antenna Systems

The
two  structures of interest have been described in detail in [3]. The multiantenna systems were designed with the help of the electromagnetic
software tool IE3D [15]. The initial two-antenna system is presented in Figure 1.
It consists of two planar inverted-F antennas (PIFAs) positioned on the top
corner of a 40 × 100 mm2 printed circuit board
(PCB), spaced by 0.12 λ0 (18 mm at 2 GHz). They are fed by a metallic
strip soldered to an SMA connector and shorted to the PCB by an identical strip.
Each PIFA is optimized to cover the UMTS band (1920–2170 MHz) with a
return loss better than −6 dB. The final length is 26.5 mm and the final width
is 8 mm. A prototype was fabricated using a 0.3 mm thick nickel-silver material
(Cu, Ni, Zn, conductivity σ  = 4  ×  106 S/m). The simulated and measured
S-parameters of this initial structure are presented in Figure 2. Both antennas
are well matched and the S21  reaches a maximum of −5 dB in the
middle of the UMTS band which is considered as a poor isolation.Figure 1
3D view of the initial two-antenna system.Figure 2
Simulated and measuredS-parameters of the initial two-antenna system.In order to improve the  isolation between
the radiating elements of this initial structure, a suspended line as a neutralization
device was inserted between the feeding strips of the two PIFAs (Figure3). This
technique and the optimization of this line were already explained in [3, 4]. The
scattering parameters of this neutralized structure are now shown in Figure 4. In
addition to good matching, a strong improvement of antenna-to-antenna isolation
is observed in the bandwidth of interest. The S21 parameter has a
deep null in the middle of the UMTS band and always remains below −18 dB in
this whole band: a minimum enhancement of 15 dB is obtained in this band when
comparing this antenna-system with the initial structure. To show the benefit
of having a high antenna-to-antenna isolation on the performance of multiantenna
structures, the total efficiency of the two systems has been simulated with the
help of IE3D (the total efficiency is defined here as the radiation efficiency
+ the matching and the insertion losses [3, 4]). Both antennas of the initial
system have a maximum total efficiency of −1 dB at 2 GHz while the ones of the
neutralized structure have a total efficiency of −0.25 dB. Moreover, the neutralization
technique induces a total efficiency improvement on the whole UMTS band. All these
results seem very promising to implement some diversity in a UMTS mobile device.Figure 3
3D view of the neutralized
two-antenna system.Figure 4
Simulated and measuredS-parameters of the neutralized
two-antenna system.


## 3. Simulated Diversity Performance in Different Propagation Environments

It is well known that the overall performance of a
mobile phone antenna can be affected by the environment in which the device is
positioned [6]. Both the MEG values and the correlation of the signals arriving
at the system depend on the distribution of the incoming power and the
orientation of the antennas relative to this environment.


### 3.1. the Chosen Propagation Environments

To calculate the envelope correlation coefficientρe and the MEG, we need to take into consideration the statistical propagation
properties of both vertically and horizontally polarized incident radio waves.
The propagation effects are defined as the power spectrum of the polarized
incoming waves Pθ(Ω) and Pϕ(Ω)
expressed as statistical distribution functions [6, 7]:
(1)Pθ(Ω)=Pθ(θ,ϕ)=Pθ(θ)Pθ(ϕ),Pϕ(Ω)=Pϕ(θ,ϕ)=Pϕ(θ)Pϕ(ϕ).
In (1), Pθ(θ) and Pθ(ϕ) are the angular
density functions in elevation; Pϕ(θ) and Pϕ(ϕ) are the angular
density functions in azimuth. According to [2, 5–8], we choose some common distributions
like Gaussian, Laplacian, and elliptical (Table 1). These distributions can
describe some representative incoming polarized waves in elevation and/or
azimuth (more complicated measurement-based angular density functions can be
found in [9, 16]). In Table 1, mH and mV are the mean
elevation angles of respectively the horizontally and vertically polarized wave,
σH and σV are the horizontal and vertical standard
deviations and XPR is the cross-polar discrimination (ratio of time average vertical power (θ)
to the time average horizontal power (ϕ) of the incident
field). These parameters are fully
determined by a specific environment: indoor (In), outdoor (Out), and isotropic
(Iso). These three environments are shaped in elevation and uniformly
distributed in azimuth. The elliptical environment,
shaped in both elevation and azimuth, is the one that best fits some experimental
data acquired for outdoor-to-indoor communications [8]. Moreover, the
constants Aθ and Aϕ are determined
by the following
equation:
(2)∫02π∫0πPθ(θ,ϕ)sinθdθdϕ=∫02π∫0πPϕ(θ,ϕ)sinθdθdϕ=1.Table 1
Propagation models used to evaluate
the performance of the antenna systems.
ModelElevation/ azimutUniform  (isotropic)Gaussian/uniformLaplacian/uniformEllipticalStatistical
distributionsPθ(θ)=14πPθ(θ)=AθexpPθ(θ)=AθexpPθ(θ)×[−(θ−[(π/2)−mV])22σV2]×[−2|θ−[(π/2)−mV]|2σV]=Aθsθθ2sθθ2+(sinθ)2Pϕ(θ)=14πPϕ(θ)=AϕexpPϕ(θ)=AϕexpPϕ(θ)×[−(θ−[(π/2)−mH])22σH2]×[−2|θ−[(π/2)−mH]|2σH]=Aϕsϕθ2sϕθ2+(sinθ)2Pθ(ϕ)=1Pϕ(ϕ)=1Pθ(ϕ)=1High directivity (1/8 of the sphere)Pϕ(ϕ)=1Pϕ(ϕ)=1Pϕ(ϕ)=1Pθ(ϕ)=Aθaθ0Pϕ(ϕ)=Aϕ(aϕ0−bϕ|ϕ|)Low directivity (1/2 of the sphere)Pθ(ϕ)=Aθsθϕ2sθϕ2+(sinϕ)2Pϕ(ϕ)=Aϕsϕϕ2sϕϕ2+(sinϕ)2Scenario parametersXPR       =      5 dBXPR  =  5 dBmv=10∘mv=10∘IndoormH=10∘mH=10∘XPR =  5.5 dBσv=15∘σv=15∘sθθ  = 0.29σH=15∘σH=15∘sϕθ   = 1.06XPR = 1 dBXPR = 1 dBsθϕ   = 0.44mv=20∘mv=20∘sϕϕ  =  1.18OutdoormH=20∘mH=20∘aθ0 = 0.16σv=30∘σv=30∘aϕ0 = 0.70σH=30∘σH=30∘bϕ = 0.11XPR =  0 dBXPR =  0 dBmv=0∘mv=0∘Isotropic*mH=0∘mH=0∘σv=∞σv=∞σH=∞σH=∞*For
Gaussian/uniform and Laplacian/uniform, the isotropic environment is an
omnidirectionnal isotropic environment.


### 3.2. Envelope Correlation

The independence of the  fading signals incoming to the
receiver of the system can be computed using the general
expression ofρe when using the 3D radiation patterns
as in the following equation:
(3)ρe=ND1D2,
where N=|∫02π∫0π(XPREθ1(θ,ϕ)Eθ2*(θ,ϕ)Pθ(θ,ϕ)+Eϕ1(θ,ϕ)Eϕ2*(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ|2,D1=|∫02π∫0π(XPRGθ1(θ,ϕ)Pθ(θ,ϕ)+Gϕ1(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ|,D2=|∫02π∫0π(XPRGθ2(θ,ϕ)Pθ(θ,ϕ)+Gϕ2(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ|, with
(4)Gθn=Eθn(θ,ϕ)Eθn∗(θ,ϕ).
In (4), Eθn(θ,ϕ) is the θ
polarized complex electric field radiation pattern of the antenna number n (n=2
in our case).


### 3.3. Mean Effective Gain (MEG)

The MEG is a statistical
measure of the antenna gain in a mobile environment [6]. In a particular environment, the MEG defines the power
received by an antenna including the contribution of the radiation power
pattern, the antenna total efficiency, and the propagation effects as in the
following equation:
(5)MEG=∫02π∫0π(XPR1+XPRGθ(θ,ϕ)Pθ(θ,ϕ)+11+XPRGϕ(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ.
In(5), Pθ and Pϕ are the
angular density functions of the incident power  already defined in
Section 3.1
. XPR represents the cross-polarization discrimination
defined in the same paragraph. Gθ and Gϕ are,
respectively, the θ-  and  ϕ- polarized
components of the antenna power gain patterns defined in
(4)). The MEG is
normalized by a normalization of the gains as in the following equation:
(6)∫02π∫0π(Gθ(θ,ϕ)+Gϕ(θ,ϕ))sinθdθdϕ=4π.


### 3.4. Diversity Gain (DG) and Effective Diversity Gain (EDG)

The effectiveness of a diversity scheme is usually
presented in terms of DG. It can be defined as the difference between the
signal-to-noise ratio (SNR) of the combined signals of all the radiators of a
multiantenna system and the SNR of the best single antenna of the structure
as in the following equation:(7)DG=[γCΓC−γ1Γ1]P(γC<γS/Γ).
In (7), γC and ΓC are,
respectively, the instantaneous and the mean SNR of the combined signal, γ1 is the instantaneous SNR of the best branch, Γ1 is the mean value of
γ1, and γS/Γ is the threshold or reference level.  The
probability P depends on both the number M of the branches of the system and
the envelope correlation ρe. Equation (8) gives this probability for
two diversity branches when the probability of the combined signal be above the
given threshold x=γS/Γ [17]:
(8)P(γC<x)=1−exp(−xΓ1)⋅Q(2xΓ2(1−|ρe|),2ρexΓ1(1−|ρe|))−exp(−xΓ2)⋅[1−Q(2ρexΓ2(1−|ρe|),2xΓ1(1−|ρe|))].
In (8), Γ1 and Γ2 are the mean
SNR value for antennas 1 and 2 (these two values are not necessary the same
regarding the chosen environment and/or the orientation of the antennas in this
environment), and Q is the Marcum function [18]. The DG is usually given at the
probability value of 1% or 99% reliability level (Figure 5). However, the DG may
not strictly express a realistic gain. In practical applications, the total
efficiency of the best antenna of the system has to be taken into account. By
doing so, the effective diversity gain (EDG) represents the true benefit of the
diversity scheme toward a single-antenna system as in the following equation:
(9)EDG=DG∗ηtot.bestbranch.Figure 5
Simulated
DG of the neutralized antenna-system in a uniform
environment.


### 3.5. Computation of the Diversity Performance of the Two Structures

The computed diversity performance of the two antenna systems
in different propagation environments is given in Table2. The initial antenna system
with poor antenna-to-antenna isolation is denoted “Init” and the antenna system
with the neutralization line is called “Neutr.” The isotropic, indoor, and
outdoor cases are, respectively, called “Iso,” “In,” and “Out.” These values
have been computed at one frequency point: 2 GHz. It should be noted that the
PCB, in both cases, has been vertically positioned in the environment (parallel
to the xOy plane).Table 2
Diversity performance of the two
prototypes in different propagation environments at 2 GHz by using their simulated
3D radiation patterns.
Modelρe Init/NeutrMEG (dB) Init/NeutrDG (dB) at 99% reliability Init/NeutrEDG (dB) at 99% reliability Init/NeutrUniform0.015/0.002−4/−3.110.18/10.29.18/10.1Out0.15/0.12−12.3/−11.79.88/9.928.88/9.82Gaussian/uniformIn0.04/0.02−11.19/−10.710.11/10.169.11/10.06Iso0.02/0.004−11.7/−10.810.17/10.29.17/10.1Out0.16/0.14−12.4/−11.79.85/9.888.85/9.78Laplacian/uniformIn0.06/0.04−11.4/−10.610.09/10.129.09/10.02Iso0.02/0.004−11.7/−10.810.17/10.29.17/10.1EllipticalHigh0.067/0.012−17.44 & −17.65/−16.84 & −16.849.96/10.188.96/10.08Low0.0016/0.008−19.13 & −19.6/−17.5 & −17.59.97/10.198.97/10.09The
first comment goes on the envelope correlation coefficient: this parameter is
extremely low for both prototypes whatever the environment is. The
neutralization technique does not bring any obvious improvement; nevertheless, satisfactory
diversity performance is expected if this coefficient is less than 0.5 [19].The MEG
is then given for both structures, in a uniform environment. In this case and
with such an antenna system orientation, the maximum achievable MEG is −3 dB. The
MEG of the neutralized structure is always higher than the one of the initial
structure. This is a consequence of the better total efficiency of the antennas
of the neutralized structure. This is also the case for all the studied
environments. However, the MEG is always found to be lower than the uniform
case due to the spatial distribution of the incoming waves and therefore the
fact that less power is intercepted by the antennas of the system. The MEG
ratio has been computed for the elliptical case (two MEG values are given in
Table2 for each antenna of each prototype). This is due to the fact that in
all the other cases the PCB is set vertical and the azimuth distribution of the
incoming waves is kept uniform; consequently the MEG is equal for antenna 1 and
antenna 2 of a same prototype and the MEG ratio is then 1. For the elliptical
case, the MEG ratio remains always less than 1.12 or 0.5 dB which indicates
that both antennas of a same prototype are equally participating to the
diversity effort. There is not so much to say about the DG at the 99%
reliability level; this parameter is very similar for both the initial and the
neutralized structure. This comes not only
from
the fact that the envelope correlation coefficient is very low and almost the
same for both antenna systems but also from the fact that the 3D radiation
patterns of both structures are quite identical. Considering all the
propagation environments, the DG values are ranging from 9.85 dB to 10.2 dB.
These values are slightly better than the one encountered in [2, 5, 18]. The
combined signal was calculated considering the selection combining technique
which is not only the
simplest one regarding the RF chain requirements but also the one giving the
lowest DG [20]. When taking into account the total efficiency of each antenna
of a structure, the EDGs of the neutralized systems are always nearly 1 dB
better than the ones of the initial prototype. This comment is valid in every
propagation environment. These values are again approximately 1 dB better than
the ones encountered in [2, 5, 18] due to the implementation of the
neutralization technique and the high total efficiency of the antennas. What
is
also very interesting in Table 2 is to see that even if the MEG
is varying a
lot from the uniform case to other environments, the EDG
is not; the maximum
deviation of the EDGs is
less than 0.35 dB for both prototypes. This fact is very interesting for anyone
who has the adequate facility to measure and characterize a multiantenna system
in any of these environments; a relative extrapolation of the EDGs values in
the other environments could be “a posteriori” done. Finally, it should be
added that all these simulations were conducted at one frequency point, where
the neutralized system is the most efficient; however, for UMTS handheld
terminals, the diversity technique is not needed on the overall frequency band
but only in the receive mode that is 60 MHz from 2110 to 2170 MHz.


## 3.1. the Chosen Propagation Environments

To calculate the envelope correlation coefficientρe and the MEG, we need to take into consideration the statistical propagation
properties of both vertically and horizontally polarized incident radio waves.
The propagation effects are defined as the power spectrum of the polarized
incoming waves Pθ(Ω) and Pϕ(Ω)
expressed as statistical distribution functions [6, 7]:
(1)Pθ(Ω)=Pθ(θ,ϕ)=Pθ(θ)Pθ(ϕ),Pϕ(Ω)=Pϕ(θ,ϕ)=Pϕ(θ)Pϕ(ϕ).
In (1), Pθ(θ) and Pθ(ϕ) are the angular
density functions in elevation; Pϕ(θ) and Pϕ(ϕ) are the angular
density functions in azimuth. According to [2, 5–8], we choose some common distributions
like Gaussian, Laplacian, and elliptical (Table 1). These distributions can
describe some representative incoming polarized waves in elevation and/or
azimuth (more complicated measurement-based angular density functions can be
found in [9, 16]). In Table 1, mH and mV are the mean
elevation angles of respectively the horizontally and vertically polarized wave,
σH and σV are the horizontal and vertical standard
deviations and XPR is the cross-polar discrimination (ratio of time average vertical power (θ)
to the time average horizontal power (ϕ) of the incident
field). These parameters are fully
determined by a specific environment: indoor (In), outdoor (Out), and isotropic
(Iso). These three environments are shaped in elevation and uniformly
distributed in azimuth. The elliptical environment,
shaped in both elevation and azimuth, is the one that best fits some experimental
data acquired for outdoor-to-indoor communications [8]. Moreover, the
constants Aθ and Aϕ are determined
by the following
equation:
(2)∫02π∫0πPθ(θ,ϕ)sinθdθdϕ=∫02π∫0πPϕ(θ,ϕ)sinθdθdϕ=1.Table 1
Propagation models used to evaluate
the performance of the antenna systems.
ModelElevation/ azimutUniform  (isotropic)Gaussian/uniformLaplacian/uniformEllipticalStatistical
distributionsPθ(θ)=14πPθ(θ)=AθexpPθ(θ)=AθexpPθ(θ)×[−(θ−[(π/2)−mV])22σV2]×[−2|θ−[(π/2)−mV]|2σV]=Aθsθθ2sθθ2+(sinθ)2Pϕ(θ)=14πPϕ(θ)=AϕexpPϕ(θ)=AϕexpPϕ(θ)×[−(θ−[(π/2)−mH])22σH2]×[−2|θ−[(π/2)−mH]|2σH]=Aϕsϕθ2sϕθ2+(sinθ)2Pθ(ϕ)=1Pϕ(ϕ)=1Pθ(ϕ)=1High directivity (1/8 of the sphere)Pϕ(ϕ)=1Pϕ(ϕ)=1Pϕ(ϕ)=1Pθ(ϕ)=Aθaθ0Pϕ(ϕ)=Aϕ(aϕ0−bϕ|ϕ|)Low directivity (1/2 of the sphere)Pθ(ϕ)=Aθsθϕ2sθϕ2+(sinϕ)2Pϕ(ϕ)=Aϕsϕϕ2sϕϕ2+(sinϕ)2Scenario parametersXPR       =      5 dBXPR  =  5 dBmv=10∘mv=10∘IndoormH=10∘mH=10∘XPR =  5.5 dBσv=15∘σv=15∘sθθ  = 0.29σH=15∘σH=15∘sϕθ   = 1.06XPR = 1 dBXPR = 1 dBsθϕ   = 0.44mv=20∘mv=20∘sϕϕ  =  1.18OutdoormH=20∘mH=20∘aθ0 = 0.16σv=30∘σv=30∘aϕ0 = 0.70σH=30∘σH=30∘bϕ = 0.11XPR =  0 dBXPR =  0 dBmv=0∘mv=0∘Isotropic*mH=0∘mH=0∘σv=∞σv=∞σH=∞σH=∞*For
Gaussian/uniform and Laplacian/uniform, the isotropic environment is an
omnidirectionnal isotropic environment.


## 3.2. Envelope Correlation

The independence of the  fading signals incoming to the
receiver of the system can be computed using the general
expression ofρe when using the 3D radiation patterns
as in the following equation:
(3)ρe=ND1D2,
where N=|∫02π∫0π(XPREθ1(θ,ϕ)Eθ2*(θ,ϕ)Pθ(θ,ϕ)+Eϕ1(θ,ϕ)Eϕ2*(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ|2,D1=|∫02π∫0π(XPRGθ1(θ,ϕ)Pθ(θ,ϕ)+Gϕ1(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ|,D2=|∫02π∫0π(XPRGθ2(θ,ϕ)Pθ(θ,ϕ)+Gϕ2(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ|, with
(4)Gθn=Eθn(θ,ϕ)Eθn∗(θ,ϕ).
In (4), Eθn(θ,ϕ) is the θ
polarized complex electric field radiation pattern of the antenna number n (n=2
in our case).


## 3.3. Mean Effective Gain (MEG)

The MEG is a statistical
measure of the antenna gain in a mobile environment [6]. In a particular environment, the MEG defines the power
received by an antenna including the contribution of the radiation power
pattern, the antenna total efficiency, and the propagation effects as in the
following equation:
(5)MEG=∫02π∫0π(XPR1+XPRGθ(θ,ϕ)Pθ(θ,ϕ)+11+XPRGϕ(θ,ϕ)Pϕ(θ,ϕ))sinθdθdϕ.
In(5), Pθ and Pϕ are the
angular density functions of the incident power  already defined in
Section 3.1
. XPR represents the cross-polarization discrimination
defined in the same paragraph. Gθ and Gϕ are,
respectively, the θ-  and  ϕ- polarized
components of the antenna power gain patterns defined in
(4)). The MEG is
normalized by a normalization of the gains as in the following equation:
(6)∫02π∫0π(Gθ(θ,ϕ)+Gϕ(θ,ϕ))sinθdθdϕ=4π.


## 3.4. Diversity Gain (DG) and Effective Diversity Gain (EDG)

The effectiveness of a diversity scheme is usually
presented in terms of DG. It can be defined as the difference between the
signal-to-noise ratio (SNR) of the combined signals of all the radiators of a
multiantenna system and the SNR of the best single antenna of the structure
as in the following equation:(7)DG=[γCΓC−γ1Γ1]P(γC<γS/Γ).
In (7), γC and ΓC are,
respectively, the instantaneous and the mean SNR of the combined signal, γ1 is the instantaneous SNR of the best branch, Γ1 is the mean value of
γ1, and γS/Γ is the threshold or reference level.  The
probability P depends on both the number M of the branches of the system and
the envelope correlation ρe. Equation (8) gives this probability for
two diversity branches when the probability of the combined signal be above the
given threshold x=γS/Γ [17]:
(8)P(γC<x)=1−exp(−xΓ1)⋅Q(2xΓ2(1−|ρe|),2ρexΓ1(1−|ρe|))−exp(−xΓ2)⋅[1−Q(2ρexΓ2(1−|ρe|),2xΓ1(1−|ρe|))].
In (8), Γ1 and Γ2 are the mean
SNR value for antennas 1 and 2 (these two values are not necessary the same
regarding the chosen environment and/or the orientation of the antennas in this
environment), and Q is the Marcum function [18]. The DG is usually given at the
probability value of 1% or 99% reliability level (Figure 5). However, the DG may
not strictly express a realistic gain. In practical applications, the total
efficiency of the best antenna of the system has to be taken into account. By
doing so, the effective diversity gain (EDG) represents the true benefit of the
diversity scheme toward a single-antenna system as in the following equation:
(9)EDG=DG∗ηtot.bestbranch.Figure 5
Simulated
DG of the neutralized antenna-system in a uniform
environment.


## 3.5. Computation of the Diversity Performance of the Two Structures

The computed diversity performance of the two antenna systems
in different propagation environments is given in Table2. The initial antenna system
with poor antenna-to-antenna isolation is denoted “Init” and the antenna system
with the neutralization line is called “Neutr.” The isotropic, indoor, and
outdoor cases are, respectively, called “Iso,” “In,” and “Out.” These values
have been computed at one frequency point: 2 GHz. It should be noted that the
PCB, in both cases, has been vertically positioned in the environment (parallel
to the xOy plane).Table 2
Diversity performance of the two
prototypes in different propagation environments at 2 GHz by using their simulated
3D radiation patterns.
Modelρe Init/NeutrMEG (dB) Init/NeutrDG (dB) at 99% reliability Init/NeutrEDG (dB) at 99% reliability Init/NeutrUniform0.015/0.002−4/−3.110.18/10.29.18/10.1Out0.15/0.12−12.3/−11.79.88/9.928.88/9.82Gaussian/uniformIn0.04/0.02−11.19/−10.710.11/10.169.11/10.06Iso0.02/0.004−11.7/−10.810.17/10.29.17/10.1Out0.16/0.14−12.4/−11.79.85/9.888.85/9.78Laplacian/uniformIn0.06/0.04−11.4/−10.610.09/10.129.09/10.02Iso0.02/0.004−11.7/−10.810.17/10.29.17/10.1EllipticalHigh0.067/0.012−17.44 & −17.65/−16.84 & −16.849.96/10.188.96/10.08Low0.0016/0.008−19.13 & −19.6/−17.5 & −17.59.97/10.198.97/10.09The
first comment goes on the envelope correlation coefficient: this parameter is
extremely low for both prototypes whatever the environment is. The
neutralization technique does not bring any obvious improvement; nevertheless, satisfactory
diversity performance is expected if this coefficient is less than 0.5 [19].The MEG
is then given for both structures, in a uniform environment. In this case and
with such an antenna system orientation, the maximum achievable MEG is −3 dB. The
MEG of the neutralized structure is always higher than the one of the initial
structure. This is a consequence of the better total efficiency of the antennas
of the neutralized structure. This is also the case for all the studied
environments. However, the MEG is always found to be lower than the uniform
case due to the spatial distribution of the incoming waves and therefore the
fact that less power is intercepted by the antennas of the system. The MEG
ratio has been computed for the elliptical case (two MEG values are given in
Table2 for each antenna of each prototype). This is due to the fact that in
all the other cases the PCB is set vertical and the azimuth distribution of the
incoming waves is kept uniform; consequently the MEG is equal for antenna 1 and
antenna 2 of a same prototype and the MEG ratio is then 1. For the elliptical
case, the MEG ratio remains always less than 1.12 or 0.5 dB which indicates
that both antennas of a same prototype are equally participating to the
diversity effort. There is not so much to say about the DG at the 99%
reliability level; this parameter is very similar for both the initial and the
neutralized structure. This comes not only
from
the fact that the envelope correlation coefficient is very low and almost the
same for both antenna systems but also from the fact that the 3D radiation
patterns of both structures are quite identical. Considering all the
propagation environments, the DG values are ranging from 9.85 dB to 10.2 dB.
These values are slightly better than the one encountered in [2, 5, 18]. The
combined signal was calculated considering the selection combining technique
which is not only the
simplest one regarding the RF chain requirements but also the one giving the
lowest DG [20]. When taking into account the total efficiency of each antenna
of a structure, the EDGs of the neutralized systems are always nearly 1 dB
better than the ones of the initial prototype. This comment is valid in every
propagation environment. These values are again approximately 1 dB better than
the ones encountered in [2, 5, 18] due to the implementation of the
neutralization technique and the high total efficiency of the antennas. What
is
also very interesting in Table 2 is to see that even if the MEG
is varying a
lot from the uniform case to other environments, the EDG
is not; the maximum
deviation of the EDGs is
less than 0.35 dB for both prototypes. This fact is very interesting for anyone
who has the adequate facility to measure and characterize a multiantenna system
in any of these environments; a relative extrapolation of the EDGs values in
the other environments could be “a posteriori” done. Finally, it should be
added that all these simulations were conducted at one frequency point, where
the neutralized system is the most efficient; however, for UMTS handheld
terminals, the diversity technique is not needed on the overall frequency band
but only in the receive mode that is 60 MHz from 2110 to 2170 MHz.


## 4. Reverberation Chamber Measurements

The idea was to try to validate some of these simulations by measurements. Through
the COST284 project, we got the possibility to perform some measurements in the
Bluetest reverberation  chamber (RC) of Chalmers Institute in Gothenburg,
Sweden. An RC is known to reproduce an isotropic uniform multipath
environment. The total efficiency of an antenna
can be easily measured in the so-called RC. The procedure can be found in [11]. The measured total
efficiency in dB versus frequency of all the antenna systems is shown in Figure 6.
It can be seen two slightly different plain lines (one for each antenna) due to
the fact that the fabricated prototype suffers from small asymmetries. These
measurements are compared with the simulation curves obtained from IE3D (only
one dotted line in this case due to a perfectly symmetrical simulation model). We
can observe that all these curves are in a good agreement especially if we
compare their maximum values. The small frequency shift observed between
simulated and measured curves is due to the small frequency shift seen in Figures
2 and 4; it impacts directly the total efficiency. The improvement brought by
the neutralization technique is clearly shown on the overall UMTS band and
especially at 2 GHz; the maximum total efficiency of the neutralized antenna system
is around −0.25 dB, whereas the one of the initial structure is less than −0.9 dB. These values are also in good agreement with the ones obtained with the 3D pattern
integration, respectively, −0.1 dB and −1 dB (not shown in Table
2 but easily
extractible from the MEG).Simulated (IE3D) and measured (reverberation
chamber) total
efficiency of the antenna systems; (a) initial structure, (b) neutralized structure.
(a)(b)In
the case the antenna is located in a uniform environment, the MEG is equal to the total
efficiency minus 3 dB [9]. The measured MEG can be deduced
from the previous measured total efficiency values by subtracting 3 dB. A good
agreement is then observed with the simulated values from Table 2 (uniform
environment line). Moreover, to achieve a good DG, the average received
power from each antenna element must be nearly equal; it corresponds to get the
ratio of the MEG of the two antennas close to unity [19]. As a summary, the
total efficiency and the MEG of the two structures are given in Table 3. The “Sim
IE3D” values have been obtained directly from IE3D. The “Sim 3D” values have
been computed using the simulated IE3D radiation patterns of the structures. The
RC values are taken from the previous measurements. We can notice that using the neutralization line enhances the total
efficiency and the MEG as expected from the previous results. The MEG
ratios of the two antennas of the different prototypes have been also computed
from the RC measurements. It is seen that the antennas have a comparable
average received power; all the ratios are very close to unity: 1.12 for the
initial structure and 1.07 for the neutralized one.Table 3
Simulated (3D pattern integration or IE3D values) and measured total efficiency
of each antenna of the different antenna systems.
Total efficiency (dB) antenna1Total efficiency (dB) antenna2SimulatedRCSimulatedRCInitial structure−1−0.85−1−1.25Neutralized structure−0.1−0.2−0.1−0.5To measure the
correlation between the antennas of our systems in the RC, each branch is
connected to a separate receiver, and the outputs of the receivers are combined
in such a way that the signal-to-noise ratioS/N of the combined signal is
larger than S1/N1 and S2/N2 of the
signals in each branch. This is possible if the fading characteristics of the signal
S1 and S2 are uncorrelated in the two branches. The measured
envelope correlation coefficients of all the antenna systems are presented in
Figure 7. They are compared with those obtained using (3) with the IE3D simulated
complex 3D radiation patterns. All  these curves are in a moderate agreement. We
especially notice that the measured values are always higher than the simulated
ones but the same trend shapes are observed in both cases. Moreover, the
envelope correlation coefficient of all the prototypes is always largely lower
than 0.15 on the whole UMTS band; significant performances in terms of
diversity are thus expected.Simulated (3D patterns) and measured (reverberation
chamber) envelope correlation coefficient
of the two antenna systems; (a) initial structure, (b) neutralized structure.
(a)(b)We also extracted the DG
of our two structures from the RC measurements. We can see in Figure8 the power
samples of each antenna system. Due to the measurement procedure, these
measurements have been extracted over a 10 MHz frequency band around 2 GHz, and
therefore they cannot be directly compared with the results from Table 3,
computed at one frequency point. In any graph, we can observe that the curve of
the combined signal with the selection combining scheme (solid line) is steeper
than the two curves of each antenna element of one system taken alone (dotted
lines). This is the benefit of combining the two signals received by each
antenna of the structure. The diversity gain is then determined by the power level improvement at a certain
probability level. In Figures 8(a), 8(b), we have chosen 1% outage probability or 99%
reliability level. The difference between the
strongest antenna element curve and the combined signal curve is then the DG.
The power improvement is 7.6 dB for the initial
system, whereas it is 9.1 dB for the neutralized
system. When taking into account the total efficiency of the antennas, we can
compute the EDG: 6.85 dB for the initial
system, 8.8 dB for the neutralized prototype. However, by just looking
at the curves in Figure 8 for low probability levels, the uncertainty on the DG
values might not be neglected. The curves are in fact slightly shaky for low probability
levels because of a lack of the number of the samples due to the old
measurement procedure (this problem has been now solved in the new Bluestest
chamber). The data from Figure 8 were then processed with the “smooth function”
of Matlab [21] in order to evaluate the validity of our measurements. Several
“smooth steps” were tried out in this operation and the new curves are
presented in Figure 9. It appears that the two DGs were formerly underestimated.
The new EDGs are now 7.74 dB and 9.55 dB for, respectively, the initial and the
neutralized antenna systems. A summary of all these values is given in Table 4.
These results are  consistent with the ones of Table 2 (resp., 9.18 dB and 10.1 dB) even if they are not directly comparable; measurements are just mean values
over a 20 MHz bandwidth while the values of Table 2 are only given at a single
frequency point. This fact explains why the measured values are lower than the
simulated ones, computed at the optimum performance of both prototypes.
Nevertheless, all these results confirm
the benefit of using a neutralization technique between the radiators to
enhance the diversity performance.Table 4
Summary of the measured and processed DGs and EDGs of all the antenna systems.
PrototypesTotal efficiency Best branchDiversity gain RC data/smoothed dataEffective diversity gain RC data/smoothed dataInitial structure−0.85 dB7.6 dB/8.39 dB6.85 dB/7.74 dBNeutralized structure−0.2 dB9.1 dB/9.75 dB8.8 dB/9.55 dBMeasured cumulative probability of the two-antenna systems
over a 20 MHz bandwidth at 2 GHz; (a) initial structure, (b) neutralized structure.
(a)(b)Processed cumulative probability of the two-antenna systems
with the smooth function of Matlab; (a) initial structure, (b) neutralized structure.
(a)(b)


## 5. Conclusion

In this paper, we
presented two multiantenna systems with poor and high antenna-to-antenna
isolation for diversity purpose in UMTS mobile phones. First, we computed their
key parameters for diversity performance in several realistic propagation
environments from their simulated 3D radiation patterns at a single frequency
point: total efficiency, envelope correlation coefficient, MEG, diversity gain,
and effective diversity gain. A low envelope correlation was obtained in both cases; however, the EDG of
the neutralized structure is always found to be better than the one of the
initial structure whatever the environment is. In addition, the maximum deviation of the EDGs considered in all
the propagation environments is
less than 0.35 dB for both prototypes. To validate
some simulated results in a uniform multipath environment, we performed some
measurements in the reverberation chamber of the antenna group at Chalmers
Institute, Sweden.
Those measurements have validated our simulations and shown that even if the
envelope correlation coefficient of these systems is very low, having a multiantenna
system with high antenna-to-antenna isolation will improve their total
efficiency and the EDG. It also points out the usefulness of our simple neutralization
solution to achieve efficient multiantenna systems at the terminal side of a
wireless link for diversity applications. The fact that the RC is able to accurately characterize the EDG of a multiantenna
system in a uniform environment is very interesting because with only one
measurement in a specific environment, an extrapolation of the value in other
environments can be “a posteriori” done if previous simulations are achieved. In
this way, the RC could be accepted as a measurement standard for DG, as the
anechoic chamber is for “ideal” free space line-of-sight environments.



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*Source: 836050-2008-03-23.xml*