Integration of inverted F-antennas in small mobiledevices with respect to diversity and MIMO systems

S. Schulteis1, C. Kuhnert1, J. Pontes1, and W. Wiesbeck1

1 Institut fur Hochstfrequenztechnik und Elektronik (IHE)Universitat Karlsruhe (TH), Germany

Tel: +49-721-608-7676, Fax: +49-721-691-865E-mail: Stephan.Schulteis@ihe.uka.de

Abstract— For multimedia applications three antennas areplaced inside the housing of a personal digital assistant (PDA)with respect to MIMO and diversity. One planar and two newlydesigned buckled inverted F antennas are used. As diversity per-formance indicator the correlation coefficient is applied. MIMOcapacity is calculated with a MIMO system model includingaccurate antenna modeling and a double-directional multipathindoor channel model. Both analysis are carried out underconsideration of the influence of a user. It will be shown, that fornew, efficient diversity and MIMO systems, antenna design andplacement must take into account the complete system includingthe user.

I. I NTRODUCTION

New upcoming data and multimedia devices require highand reliable data rates. The need of efficient communicationsystems with high reliability of connectivity can be fulfilledwith the use of diversity and multiple input multiple output(MIMO) techniques.

Development of small antennas for the integration into smallmobile devices plays a significant role for implementation ofdiversity and MIMO systems. In [1] and [2] the inverted Fantenna is miniaturized for the application in MIMO systems.Compact and efficient arrays can be designed by the use ofpolarization diversity [3].

For coverage of both wireless local area network (WLAN)spectrums at 2.45 GHz and at 5.2 GHz dual band antennasare required. Additionally, placement and design of antennasshould consider not only housing but also the adjacent bodyparts of the user. In this paper a housing of a personal digitalassistant (PDA) is taken to integrate three dual band W-LANantennas. For this, the antennas are miniaturized with respectto bandwidth and impedance. It is commonly known thatsize reduction decreases the antenna bandwidth whereas theimpedance also diminishes, see [4] and [5].

In section II the design and the integration of balanced dualband, miniaturized IFA antennas into the housing of a PDAis shown. Simulations concerning antenna parameters likeinput impedance, pattern and gain are carried out. For MIMOpurposes coupling of antennas is analyzed. Measurement re-sults regarding the integration of three antennas into a PDAhousing are presented in section III. Constitutive to previoussections a model for the investigation of user’s influence ispresented in section IV. The diversity performance parametersare explained and analyzed for the PDA model equipped withthree antennas under consideration of users influence, section

V. MIMO capacity is investigated in section VI. Finally aconclusion is drawn.

II. I NTEGRATION OF ANTENNAS INTO APDA

The integration of three miniaturized antennas into a smallhousing of a PDA is very challenging. For integration threebalanced inverted F antennas are used. The shape of a balancedinverted F-antenna is shown in figure 1.

L

H D

Fig. 1. Parameter of a balanced, non-miniaturized inverted F antenna.

The lengthL and the heightH determine the resonantfrequency according to equation (1).

T = L + H ≈ λres/4 (1)

The input impedance can be adjusted with the stub lengthD. A detailed description of the influence of all parameters canbe found in [2]. The benefits of balanced antennas comparedto unbalanced antennas are a reduced sensitivity to objects inthe near surrounding of the antenna [6] and a doubled inputimpedance. Additionally the antenna design is independent ofgroundplane size thus the antenna design does not depend onthe design of the PCB.

For integration of three antennas into a small housing likea PDA housing the antennas have to be as small as possible.Therefore inverted F antennas are miniaturized by capacitiveand inductive loading, see figures 2 and 3.

For inductive loading the parameters are the width of themeander structurebm, the gap between the meander linesxm

and the width of the meander line itselfdm. As can be seenin figure 3 for capacitive loading a capacitance is integratedwith width uc of and heightvc. A detailed description ofthe influence of these parameters can be found in [?]. Eachantenna is connected to a 50Ω coaxial cable by a feedingnetwork. The dual band operation can be achieved by aparasitic element in addition to the inverted F antenna shape,

Fig. 2. Simulation model for inductively loaded inverted F antenna.

Fig. 3. Simulation model for capacitively loaded inverted F antenna.

see [?]. For an increase of bandwidth the parasitic elementand the antenna structure are placed on different sides ofthe substrate. In addition the antenna structure is shifted byq = 0.0082 λ2.45 and p = 0.0525 ·λ2.45 for a resonantwavelengthλres at 2.45 GHz as can be seen in figure 4.

For decoupling the antennas must be spaced as far awayfrom each other as possible and polarization diversity shouldbe exploited.

pq

Fig. 4. Asymmetric positioning of parasitic element for an increasedbandwidth.

Space in PDA’s housing is limited thus a decoupling ofantennas due to spacing is not possible. Further on, an antennaas shown in figure 4 cannot be integrated vertically in thehousing, because the height is too small. As solution to theselimitations the antenna is buckled in the middle of the heightof the antenna, see figure 5.

According to the buckled shape of one antenna type, thepolarization and pattern is different for the two types ofinverted F antennas.

For the placement of antennas in a PDA housing someconsiderations concerning user’s influence should be made. Itis expected that the user covers the lower part of the housingin most cases. In fewer cases the user’s hand covers the upperpart of the housing. Hence it is beneficial to place the antennasin that way that in most cases only one antenna is covered.

Figure 6(a) shows the simulation model of the PDA, whichis developed under previous considerations, with three anten-nas integrated.

One possibility is shown here, the two buckled inverted F

Fig. 5. Simulation models for buckled miniaturized dual band inverted Fantennas.

(a) (b)

Fig. 6. Simulation model and model for measurements of three inverted Fantennas integrated into a PDA’s housing.

antennas are placed at the top in the right and left corner.The third antenna, a planar inverted F antenna is placed at thebottom.

The model of the PDA (8 cm x 12 cm x 1.5 cm) consistsof a metallic block, representing the battery and the displayof the device, and a PVC housing with a wall thickness of4 mm. The permittivity of the PVC material equalsεr = 3,the loss factortan δ = 1 · 10−4. For simulations the housingis closed by a top cover.

All simulations were carried out with FEKO, see [7], astandard EM code based on method of moments. FEKO wasapplied for calculating the pattern of the coupled antennasystem as well as mutual coupling and self impedances ofthe antennas.

III. A NTENNA MEASUREMENTS

In order to verify the simulations measurements have beenare carried out at both frequencies 2.45 GHz and 5.2 GHz.Gain and pattern measurements were carried out in an ane-choic chamber. The patterns can be found in figure 7. The gainfor the inverted F antennas integrated into the PDA housingcan be found in table I.

The antenna patterns differ clearly in horizontal and verticalpolarization, which is a good premise for pattern diversity. Ifantenna patterns are too similar, correlation would degradediversity performance.

Coupling and S-parameters were measured with a networkanalyzer. The reflection coefficient of theith antenna isdenoted asSii. As an example the reflection coefficient ofthe first antenna is shown in figure 8. The antenna is suitablefor both frequencies.

TABLE I

MEASURED GAIN FOR INTEGRATED ANTENNA STRUCTURES IN THE

PDA’S HOUSING WITHOUT USER’ S INFLUENCE, SEE FIGURE6(B) AT

2.45 GHZ AND 5.2 GHZ.

@2.45 GHz @5.2 GHzIFA1 0.8 dBi 1.2 dBiIFA2 0.8 dBi 1.2 dBiIFA3 5.5 dBi 1.2 dBi

(a)

−15dB

−10dB

−5dB

60°

−120°

30°

−150°

0°

180°

−30°

150°

−60°

120°

−90° 90°

simulation 5.2 GHzmeasurement 5.2 GHzsimulation 2.45 GHzmeasurement 2.45 GHz

(b)

−15dB

−10dB

−5dB

60°

−120°

30°

−150°

0°

180°

−30°

150°

−60°

120°

−90° 90°

simulation 5.2 GHzmeasurement 5.2 GHzsimulation 2.45 GHzmeasurement 2.45 GHz

(c)

−20dB

−10dB 60°

−120°

30°

−150°

0°

180°

−30°

150°

−60°

120°

−90° 90°

simulation 5.2 GHzmeasurement 5.2 GHzsimulation 2.45 GHzmeasurement 2.45 GHz

Fig. 7. Simulated and measured azimuth pattern for horizontal polarizationof the (a) IFA 1, (b) IFA 2, and (c) IFA3.

Figure 9 shows the measurement and simulation results forcoupling coefficients of different pairs of antennas integratedin the PDA. It can be seen, that simulations and measurementspredict a coupling of less than−18 dB in the frequency bandbetween 2 GHz and 6 GHz.

The gain and pattern simulations and measurements demon-strate that the antennas are suitable for MIMO and diversitysystems at both WLAN frequency bands.

2 3 4 5 6−25

−20

−15

−10

−5

0

frequency in GHz

S11

in d

B

simulation

measurement

Fig. 8. Simulation and measurement results for the reflection coefficient ofthe integrated antenna, denoted with number one, see figure 6(b).

2 3 4 5 6−90

−80

−70

−60

−50

−40

−30

−20

frequency in GHzS

in d

B

S12 simulationS12 measurementS13 simulationS13 measurementS23 simulationS23 measurement

Fig. 9. Simulated and measured coupling coefficient between the ports ofintegrated dualband inverted F antennas.

IV. I NVESTIGATION OF USER’ S INFLUENCE

For investigation of diversity systems and MIMO capacitythe influence of user’s hand is not negligible. Therefore a handmodel is included. Two different hand positions are analyzed.One where the user holds the PDA at the top and the secondand most significant one, where the user places his hand atthe bottom of the PDA, see figure 10.

(a) (b)

Fig. 10. Simulation model of PDA and the investigated hand position onbottom 10(a), covering one antenna, and with hand on top 10(b), coveringtwo antennas.

The shape of the hand is like a U profile. The hand modelhas an extension of 10 cm by 10 cm on bottom. The heightbelow the PDA is 1.5 cm and the height of the side platesequals 4.9 cm. The width of side plates is 1 cm and the gapbetween the hand an the PDA housing on bottom is 0.9 cmand between the side plates and the PDA it is 0.5 cm. Forbottom position, the part of the PDA which is not covered

by the hand has a length of 4.4 cm. For top position it has alength is 3.5 cm.

Power is absorbed in the hand, hence power transfer in thecommunication system is possibly affected.

V. D IVERSITY PERFORMANCE

The received signal level correlation coefficient can be usedto investigate antenna array’s quality for diversity applications[8], [9]. However, correlation of signals is only given for twosignals. In the case of more than two antennas, a figure ofmerit must be found, which should not only concentrate oncorrelation properties but also on received signal strength fromthe antennas.

For investigation of correlation properties of antenna arraysthe power correlation coefficientρe,v

iv

jfor all possible pairs

of antennas has to be computed according to [8].vi,ξiαdenotes

the received voltage of antennai, if the antenna is not loaded.α denotes the polarization, for exampleα = h for horizontalandα = v for vertical polarization.

ρe,vivj≈ |ρv,vi,ξih

vj,ξih+ ρv,vi,ξiv

vj,ξiv|2

≤ |ρv,vi,ξihvj,ξih

|2 + |ρv,vi,ξivvj,ξiv

|2 (2)

For this equation the cross polarized power correlation forthe antennas is neglected. The power correlation coefficientsof all antennas are placed in a power correlation matrixρNN .

ρNN =

ρe,v1v1(∆~x) . . . ρe,v1vN

(∆~x)...

. .....

ρe,vN v1

(∆~x) . . . ρe,vN vN

(∆~x)

(3)

N denotes the maximum number of antennas used in thearray. The main diagonal elementsρe,v1v1

(∆~x) are equalto one. The matrix elements are all less than 1 and dueto equation (2) larger than or equal to zero. Due to thefact that the matrix is symmetric the eigenvaluesλn, withn ∈ 1 . . . N, are real numbers. The maximum eigenvaluecan be used as a basic parameter for investigation of antennaarray power correlation. It is referred to as correlation factor.

Figure 11 shows the correlation factor for the previouslydescribed positions of user’s hand. Impinging power is uni-formly distributed in azimuth and Gaussian distributed, withexpectation value of90 and standard deviation of60, inelevation.

Correlation properties are influenced by the user’s hand.However, the correlation factor is less than 0.1, which isremarkable. Sophisticated antenna placement exploits spatial,pattern and polarization diversity, leading to decorrelated sig-nals.

VI. MIMO PERFORMANCE

For determination of MIMO performance simulations arecarried out with a MIMO system model, see section VI-A. Asfigure of merit the transmission gain and the spectral efficiencyare applied.

2.4 2.42 2.44 2.46 2.480.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

frequency in GHz

corr

elat

ion

fact

or

verticalhorizontal

Fig. 11. Power correlation factor for typical indoor channel distributedimpinging power with users hand on top (+) and users hand on bottom ().

A. MIMO System Model

For evaluation of MIMO performance of this antenna de-sign, a system model of a complete transmission link isapplied [10].

The model of the whole MIMO transmission link allows fora very accurate antenna modeling, including all mutual cou-pling effects, and a precise analysis of the power transmissiongain and therewith the efficiency of the arrays. The basic ideais to model the whole MIMO transmission link to be composedof single network units, which are the transmitter, the transmitarray STxA, the propagation channelSC , the receive arraySRxA and the receiver. It is essential to take the transmitterand receiver as load networks, connected to the antenna arraysinto account to model the matching of the antennas and themutual coupling effects correctly. The antenna arraysSTxA

and SRxA are modeled by scattering parameters, too. Thebasic idea of the scattering parameter representation of anantenna array is that each single antenna is a two port devicewith an excitation port and a directional far field port. Forthe following investigations the base station consists of threedipoles arranged as triangle. As channel model an indoorstochastic double-directional multipath indoor channel modelgiven in [11] is used. 2000 realizations of the channel havebeen generated for random positions of the transmitterTx andthe receiverRx.

B. Power transmission gain

Since PDAs are battery-driven, the efficiency of the antennasis an important topic. Mutual coupling among closely spacedantennas does not only influence the signal flow and thecorrelation properties, it can also strongly reduce the efficiencyof an array in terms of power. The system model, given in[10], allows for considering the power transmission gain ofthe whole MIMO link, including the antennas. The powertransmission gain is the ratio of the power received at thesignal drain to the power fed into the transmit antennas. Thelatter is not equal to the power which is radiated from thetransmit antennas, if the efficiency of the transmit array is not100%.

By comparing the power transmission gain of MIMO sys-tems with different arrays in the same channel, conclusions onthe performance of the arrays in terms of power can be drawn.

Figure 12 shows the cumulative distribution function of thepower transmission gain for different hand positions at thePDA. For comparison, a single input single output (SISO)system with a single dipole element at transmit and receiveis show.

−180 −160 −140 −120 −1000

0.2

0.4

0.6

0.8

1

transmission gain in dB

P(t

rans

mis

sion

gai

n <

abs

ciss

a)

with hand on bottomwith hand on topSISO

Fig. 12. Simulation result of MIMO power transmission gain for the indoorchannel and different hand positions compared to SISO case at 2.45 GHz

It seems to be surprising, that if the hand is on top the powertransmission gain is lower than if the hand is on bottom. Thisphenomenon can be explained by the gain of the antennas.The planar inverted F antenna on bottom has a gain of 5.5 dBi@2.45 GHz in comparison to the buckled antennas, 0.8 dBi@ 2.45 GHz, which are covered if the user’s hand is on top.

C. Spectral efficiency

Spectral efficiency calculations are carried out taking allcoupling effects and the user’s hand into account. In order toassess a MIMO transmission system by the spectral efficiencyusually a fixed SNR and a channel matrix, which is normalizedby the Frobenius norm, is used. With this normalization, theinfluence of the correlation properties of the channel matrix onthe spectral efficiency becomes visible, but any interrelationbetween the SNR and the correlation properties ofH isneglected. IfH is not normalized, that means the path lossand the gain of the single antenna elements are included inH, the spectral efficiency is

C = log2(det(I +PT

σ2mHH†)) (4)

PT is the transmit power, which is equally distributedamong them transmit antennas if no channel state informationis available at the transmitter.σ2 is the noise power. Thisformula allows for a comparison of different MIMO systems,including the influence of the transmission gain and therewithof the SNR.

The transmit power remains fixed, i.e. no normalizationin terms of power is performed. As a result the cumulativedistribution function (cdf) for the MIMO spectral efficiencyat 2.45 GHz is shown in figure 13. The spectral efficiencyis relatively large with respect to the limited space availablefor the antennas in a PDA and with respect to the dual-bandoperation.

Hold in mind, that if the hand is on top, the two buckledinverted F antennas are covered. In this case the powertransmission gain is lower than if only the planar inverted F

antenna is covered. Despite degradation of power transmissiongain if one antenna is covered the spectral efficiency for user’shand on bottom is enlarged in comparison to user’s hand ontop. This is because if only one antenna is covered the residualtwo antennas on top can be used for MIMO. However, even ifthe user’s hand is placed on top and both buckled antennas arecovered, the spectral efficiency is higher than for SISO case.

0 5 10 150

0.2

0.4

0.6

0.8

1

spectral efficiency in bit/(s*Hz)

P(s

pect

ral e

ffici

ency

< a

bsci

ssa)

with hand on bottom

with hand on top

SISO

Fig. 13. Simulation result of MIMO spectral efficiency for different handpositioning on PDA at 2.45 GHz

VII. C ONCLUSION

A sophisticated dual-band antenna design and its integrationinto a PDA has been presented. The antenna design and place-ment has been carried out taking MIMO and diversity aspectsinto account. The results show that this antenna configurationis appropriate for MIMO in both WLAN frequency bands.The influence of user’s hand is not negligible, especially theabsorption of power in the human tissue, if some antennaelements are covered by the hand.

REFERENCES

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Parts of the work are outcome of the ACE network of excellence.