2013 COST 28-31 May 2013, Illemenau, Germany

A concept study on MIMO antenna system forsmall size CPE operating in the TV White Spaces

Montaha Bouezzeddine 1,Werner L. Schroeder 2

RheinMain University of Applied Sciences, Am Brueckweg 26, D-65428 Ruesselsheim, Germany1montaha.bouezzeddine@hs-rm.de, 2werner.schroeder@hs-rm.de

Abstract—A concept study on multi-port MIMO antennasystems for relatively small size Customer Premises Equipmentis presented. The antenna system is meant to operate in theTV White Spaces from 470 MHz to 790 MHz and to supportCognitive Radio applications. The design concept is derived froma characteristic modes’study of the shielding enclosure of thedevice. Advantages and difficulties incurred by this approachare discussed. Preliminary results of attainable instantaneousbandwidth are shown.

I. Introduction

The switchover from analog to digital TV, known underthe name of ’digital dividend’, accompanied by the bandssaturation of mobile communication have urged to definea new strategy in assigning the spectrum resources. TheCognitive Radio (CR) or what is called DSA! (DSA!) permitsto re-allocate the unused resources of the primary users andreconfigure the wireless system to adapt to the secondaryusers’s needs in order to exploit more efficiently the spectrumradio, especially where some bands are frequently unused. Themain functionalities of a CR system reside in scanning thespectrum to detect the spectrum holes, and tuning itself towork in the unused bands [1].

In parallel, Multiple-Input Multiple-Output (MIMO) tech-nologies constitute another trend in communication systemsthat allow to improve the link reliability of the wirelesschannel taking advantage from the diversity and the spatialmultiplexing. These technologies aim at facing the increasein data traffic, and the need for reliability, by increasing thefrequency Bandwidth (BW) and the Signal to Noise Ratio(SNR).

Equipping CR systems with MIMO antennas lead to newpossibilities such as reducing the interferences caused toprimary users, and performing a more accurate spectrumscanning.

Nevertheless, building a multi-ports antenna system posesseveral challenges, in particularly for small devices wherewe lack enough space. Many concerns raise regarding thelocations of the antennas, the kind of antennas to use, andhow to reduce the effects of the surrounding objects.

In this paper, we employ the Theory of Characteristic Modes(TCM) to design our antenna system. In the first section, wepresent a theoretical review of the TCM. Before demonstratingthe pros and cons of applying the mentioned theory for MIMO

system, we state the requirements of this latter. Lastly, adesign concept for a 4-ports antenna system is described andevaluated.

II. Characteristic modes: Theoretical review

Introduced by Garbacz [2], and developed by Harringtonand Mautz [3] , the TCM is a frequency-domain analysis. Themain idea of considering the TCM, here, resides in using thedevice’s chassis as a main radiator, after exciting it with somecouplers placed around. To determine suitable dimensions ofthe chassis and the locations of couplers, we proceed to thecalculation of the eigencurrents on a metallic surface. Let usfirst draw the main lines of this theory, but readers can referto [3] and [4] for details.

We consider an incident wave Einc on a conductor surface,in which is induced a current surface density Js. This cur-rent gives rise to a secondary field. The boundary conditionassociated to the vanishing of the tangential component of theelectric field on a perfect conductor is given by[

Z[Js] + Einc]tan

= 0 (1)

We can write Z = R + jX, where the operators R and X aresymmetric and real. Furthermore R is positive.

The eigenvalue problem is formulated as

X[Js,n] = λnR[Js,n]. (2)

The vectors solutions of the eigenvalue problem are orthog-onal functions and real; in this particular case, we call themeigencurrents with corresponding eigenvalues λn.

The orthogonality relations between different eigenmodescan be written in the form

〈Js,m|RJs,n〉S = 2Pnδmn, (3)

〈Js,m|XJs,n〉S = 2Pnλnδmn, (4)

〈Js,m|ZJs,n〉S = 2Pn(1 + jλn)δmn (5)

where m and n refer respectively to the m-th and n-thcharacteristic modes, δmn is the Kronecker symbol and theterm Pn designates the power radiated by the n-th mode. Thefactor 2 is due to the consideration of peak values instead ofeffective ones. The eigenfields are expressed as

En = Z[Js,n] = (1 + jλn)R[Js,n] (6)

Any total surface current density Js can be written as asuperposition of the eigencurrents

Js =∑

n

αnJs,n, (7)

with the coefficient of expansion given by

αn = 〈Js,n|RJs〉S =1

(1 + jλn)〈Js,n|ZJs〉S (8)

By applying the Poynting theorem and equating with (5), itcan proved that

1η

SEn

∗EmdS = 2Pnδmn (9)

We conclude that the characteristic fields are equally orthog-onal.

The eigenvalues are related to the time average of the storedelectric and magnetic energy, and consequently to the radiationquality factors.

λn = 2ω〈Wmag,n〉 − 〈Wele,n〉

Pn(10)

The eigenvalues bring important information about the modesthat could be efficiently excited. In fact, the smaller is theλn, the more efficiently the n-th characteristic mode couldbe excited. When the electric stored energy is equal to themagnetic one, the mode is at resonance and λn = 0.

III. Characteristic modes andMIMO

A. MIMO requirements

To design an efficient N-ports MIMO antenna system, wehave to fill, from the antenna point of view, some requirements,among which we can cite:• Well matched antennas to reduce losses and increase the

efficiency of each single antenna.• Well decoupled antennas to guarantee that the applied

power to port i is not reinjected in port j due to coupling.({i, j} ∈ {1,N}; i , j).The first condition is meaningless if not accompaniedby this condition. For an optimal case, the S-parametersmatrix is equal to the null matrix, i.e,

S = 0 (11)

The S matrix is associated to a reciprocal 2N-portsnetwork where the inputs are the incident waves comingfrom the RF Front-End and the outputs correspond to theantenna ports(receive case).

• Orthogonal patterns measured by the pattern correlationcoefficient.

B. TCM procedure

In many references [5]–[7], MIMO antenna systems arebuilt using the TCM approach. We will give an insight onthe main steps of this approach. After setting the chassisdimensions, a Method of Moments (MoM) code is appliedto calculate the eigencurrents and the eigenvalues.

Meet the requirements

Theory of Characteristic

Modes

of the modes

Smallest Eigenvalues

Frequency, Isolation

Bandwith, pattern,

(BW)?

Yes

Feeding Structure Design Modify the exciters

(Geometry, position, dimensions)

Modelling Antenna with MoM

Selecting most efficient modes

Calculating Q factor

No

Antenna Design Requirements

Fig. 1: Diagram of antenna design procedure when exploitingthe TCM.

1) Find the most efficient modes that could be exciteddepending on λ values in the frequency range of interest.

2) Select the needed number of modes that corresponds tothat of the antennas to be used. If the modes available arenot sufficient, designer could think about adding someextensions to decrease the modes’s resonant frequencies.

3) Determine the type of coupling to be chosen: capacitiveor inductive.

4) Optimize the exciters’s parameters: location with respectto the chassis depending on the charge distributions ofthe selected modes, and the distance from the chassis.In our case, the optimization’s criterion is based on themodal BW increase, to be defined later. If many modesshare the same exciters, compromise might be made tooptimize the BW of some modes at detrimental of others.

5) In case multiple modes share the same exciters, afeeding network or what we call a Mode DecompositionNetwork (MDN) is required to distinguish the excitedmodes.

6) For optimal performances, the signals applied to theMDN should be relatively matched to avoid high losses.Hence, a matching network is required before reachingthe MDN.

Now that we have illustrated MIMO requirements and theprocedure to build a MIMO antenna system by exploitingthe TCM, we will present the advantages and inconveniencesinduced by this approach.

C. TCM pros and cons

The application of the TCM for a MIMO antenna systemhas been frequently adopted. Still, some authors prefer ratherto use a classic design (patches, meander line antenna, etc).What are the advantages and the drawbacks related to each ofboth approaches?

When using the chassis as a main radiator, we are exploitingthe whole available volume to design the antenna systemthus it is more advantageous in terms of BW and antenna’sefficiency. In fact, both electrical parameters are stronglydependent on to the physical parameters, i.e antenna’s size.

The other major interest of using the TCM resides in thefact of obtaining orthogonal patterns, as proven in a previousparagraph.This feature is primordial when dealing with MIMOantenna. Besides a low coupling between the modes could beachieved.

From the other side, the application of this approach demon-strates some weakness points. Sharing the same exciters andchassis could have an effect on the coupling between themodes. At the same time, the antennas could be dramaticallyaffected by the electronics surrounding.

Secondly, we cannot control the radiation patterns, whichare imposed by the selected modes. Besides, a geometricaltuning is hard to be implemented when using the chassisas a main radiator (some solutions still could be found). Ifworking over a large frequency range, difficulties connectedto the chassis dimensions emerge. Let us take our case as anexample; we are working in the range [470; 790]MHz so theratio between the upper frequency and the lowest is almost 2.The modes behave completely different at the lower and upperband, and we still have to cope with the fixed dimensions ofthe chassis.

Two other major problems will appear in advanced levels. AMDN should be built if many modes share the same exciters.We have equally to design a simultaneous Matching Network(MN). A large difference between the modal reflection co-efficients makes it quasi-impossible to match all the modessimultaneously. Besides, with a simultaneous MN, we riskto sacrifice the large BW obtained for some modes. Finally,attention must be given for the couplers to avoid excitingunwanted signals that can increase the correlation between theantennas.

When opting for a classic solution, design does not demandany MDN. Furthermore, the radiation patterns are more flex-ible depending on the chosen types of antennas.

The MDN is not required but we still need to design adecoupling network to guarantee a high isolation between thedifferent antennas, especially that their patterns won’t be notnecessarily orthogonal. But it should kept in mind that evenwhen applying a classic approach, the coupling due to thechassis, or the ground plane plays a major role on the antenna’sperformances, that could be harmful, if not well understood.

The parameters BW and efficiency of each single antennacould not be optimal for the studied application especiallywhen dealing with Electrically Small Antenna (ESA).

To achieve high performances with both concepts, we needto realize a Characteristic Modes (CM) analysis to evaluatethe eigenmodes that could be possibly excited on the chassisthat contributes dominantly to the radiation.

Fig. 2: Eigenvalues magnitude versus frequency for the first 8modes.

+

+ + +

−+

Mode 1

Mode 3

Mode 2

Mode 4

−

− −

−

−

−

− +

+

+ +

+

Fig. 3: Current and charge patterns of the four selected modes.

IV. Multi-antenna system design

A. Antenna design

We consider a 220 · 180 · 56 mm3 box to be used as a CPE.The analysis of CM allowed us to select the modes that can beefficiently excited and build a 4-ports MIMO antenna system.The results are obtained by applying a MoM code based onRao-Wilton-Glisson (RWG) basis functions.

We plotted the λ values versus the frequency as shown inFig.2. As we have seen in a previous paragraph, generally, thesmaller the λ, the more efficiently the modes could be excited.

Fig. 4: Box structure with four exciters placed at the corners.

Fig. 5: Modal reflection coefficients for the 4 selected modesafter introducing the exciters.

We have selected 4 capacitive modes to excite. In Fig.2, theycorrespond to the modes {1, 2, 3, 8}. As a next step, we drewthe current distribution and charge distribution (see appendix)to determine the most suitable locations of the exciters. Bothdistributions are summarized in Fig.3, where the (+) and(−) signs characterize a positive and negative dense chargedistribution and will refer later to the phases that should beapplied to the exciters.

To excite the modes efficiently, the couplers should belocated at the maximum of the electric field and the chargedistribution.

Fig.4 show the box used as a main radiator with non-resonant exciters placed at the corners.

In this paper, we content ourselves to present the resultsobtained for the 4 modes using WIPL-D [9]. Due to thesymmetry properties of the couplers, we simulated the quarterstructure of the box by defining electric and magnetic walls,Perfect Electric Conductor (PEC) and Perfect Magnetic Con-ductor (PMC) at the center. For each configuration, we selectthe convenient symmetry planes.

We illustrate the modal reflection coefficients in Fig.5. Tomention that the 4th was not efficiently excited with the excitersplaced at the corners, for two reasons: Firstly, the eigenvaluesof this mode (mode 8 in Fig.2) are not small comparing tothe others. Secondly, the maximum distribution of the chargeis located at the middle of the edges. We do not show, in thispaper, the complete structure.

During the simulation, we modified the exciters parametersin order to maximize the BW, calculated using the formula

Q =f0

2RdXd f

(12)

Then we calculate the 7-dB return loss BW, by applying

BW7dB =fQ, (13)

In the table 1, we present the results in terms of the maximalBW that could be obtained for each mode at some frequencies.Those results do not include any matching option, they onlyillustrate the coupling between the exciters and the chassis.

TABLE I: Modal Instantaneous BW in MHz of the 4 consid-ered modes.

F(MHz) mode1 mode2 mode3 mode4500 110 150 40 10600 68 120 180 25700 54 95 �200 52800 56 85 �200 100

To verify the estimated BW values obtained via the formu-las, we added a pi-circuit as shown in fig.6. An optimizationalgorithm, consisting of minimizing the mean of the modalreflection coefficients, was used in order to determine thecomponents values of the circuit.

The 7dB return loss BW for each mode after adding a MNare tabulated.

TABLE II: Instantaneous BW in MHz of the 4 modes obtainedwith a MN.

F(MHz) mode1 mode2 mode3 mode4500 80 90 26 ∅

600 57 84 180 10700 49 68 ≈300 50800 52 76 �300 80

We observe that the BW obtained with the proposed MNcircuit are comparable to the modal coefficients. The fact that

Fig. 6: Repetitive motif of the pre-matching circuit.

the estimated BW are due whether to the fact that the formulashown above is approximate and mainly used at resonancewith the hypothesis about R being constant.

Employing another algorithm or modifying the MN’s struc-ture could lead to similar results.

V. Conclusions

A MIMO antenna system for CR applications was discussedin this paper. We have tackled the TCM approach to build amultiple ports antenna system. First, we gave a theoreticalinsight about the theory that helped us conclude about thepros and cons of employing such approach. A MIMO systemdesign using the TCM was illustrated briefly.

Glossary

BW BandwidthCM Characteristic ModesCR Cognitive RadioDSA Dynamic Spectrum AccessESA Electrically Small AntennaF-FDD Full-Frequency Division DuplexMDN Mode Decomposition NetworkMIMO Multiple-Input Multiple-OutputMN Matching NetworkMoM Method of MomentsPEC Perfect Electric ConductorPMC Perfect Magnetic ConductorRWG Rao-Wilton-GlissonSNR Signal to Noise RatioTCM Theory of Characteristic Modes

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