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

Integration of inverted F-antennas in small mobile devices with respect to diversity and MIMO systems S. Schulteis 1, C. Kuhnert 1, J. Pontes 1, and W. Wiesbeck 1 1 Institut für Höchstfrequenztechnik und Elektronik (IHE) Universität Karlsruhe (TH), Germany Tel: +49-721-68-7676, Fax: +49-721-691-865 E-mail: Stephan.Schulteis@ihe.uka.de Abstract For multimedia applications three antennas are placed inside the housing of a personal digital assistant (PDA) with respect to MIMO and diversity. One planar and two newly designed buckled inverted F antennas are used. As diversity performance indicator the correlation coefficient is applied. MIMO capacity is calculated with a MIMO system model including accurate antenna modeling and a double-directional multipath indoor channel model. Both analysis are carried out under consideration of the influence of a user. It will be shown, that for new, efficient diversity and MIMO systems, antenna design and placement must take into account the complete system including the user. V. MIMO capacity is investigated in section VI. Finally a conclusion is drawn. II. INTEGRATION OF ANTENNAS INTO A PDA The integration of three miniaturized antennas into a small housing of a PDA is very challenging. For integration three balanced inverted F antennas are used. The shape of a balanced inverted F-antenna is shown in figure 1. L I. INTRODUCTION New upcoming data and multimedia devices require high and reliable data rates. The need of efficient communication systems with high reliability of connectivity can be fulfilled with the use of diversity and multiple input multiple output (MIMO) techniques. Development of small antennas for the integration into small mobile devices plays a significant role for implementation of diversity and MIMO systems. In [1] and [2] the inverted F antenna is miniaturized for the application in MIMO systems. Compact and efficient arrays can be designed by the use of polarization diversity [3]. For coverage of both wireless local area network (WLAN) spectrums at 2.45 GHz and at 5.2 GHz dual band antennas are required. Additionally, placement and design of antennas should consider not only housing but also the adjacent body parts of the user. In this paper a housing of a personal digital assistant (PDA) is taken to integrate three dual band W-LAN antennas. For this, the antennas are miniaturized with respect to bandwidth and impedance. It is commonly known that size reduction decreases the antenna bandwidth whereas the impedance also diminishes, see [4] and [5]. In section II the design and the integration of balanced dual band, miniaturized IFA antennas into the housing of a PDA is shown. Simulations concerning antenna parameters like input impedance, pattern and gain are carried out. For MIMO purposes coupling of antennas is analyzed. Measurement results regarding the integration of three antennas into a PDA housing are presented in section III. Constitutive to previous sections a model for the investigation of user s influence is presented in section IV. The diversity performance parameters are explained and analyzed for the PDA model equipped with three antennas under consideration of users influence, section Fig. 1. H D Parameter of a balanced, non-miniaturized inverted F antenna. The length L and the height H determine the resonant frequency according to equation (1). T = L + H λ res /4 (1) The input impedance can be adjusted with the stub length D. A detailed description of the influence of all parameters can be found in [2]. The benefits of balanced antennas compared to unbalanced antennas are a reduced sensitivity to objects in the near surrounding of the antenna [6] and a doubled input impedance. Additionally the antenna design is independent of groundplane size thus the antenna design does not depend on the design of the PCB. For integration of three antennas into a small housing like a PDA housing the antennas have to be as small as possible. Therefore inverted F antennas are miniaturized by capacitive and inductive loading, see figures 2 and 3. For inductive loading the parameters are the width of the meander structure b m, the gap between the meander lines x m and the width of the meander line itself d m. As can be seen in figure 3 for capacitive loading a capacitance is integrated with width u c of and height v c. A detailed description of the influence of these parameters can be found in [?]. Each antenna is connected to a 5 Ω coaxial cable by a feeding network. The dual band operation can be achieved by a parasitic element in addition to the inverted F antenna shape,

Fig. 2. Simulation model for inductively loaded inverted F antenna. Fig. 5. Simulation models for buckled miniaturized dual band inverted F antennas. Fig. 3. Simulation model for capacitively loaded inverted F antenna. see [?]. For an increase of bandwidth the parasitic element and the antenna structure are placed on different sides of the substrate. In addition the antenna structure is shifted by q =.82 λ2.45 and p =.525 λ2.45 for a resonant wavelength λres at 2.45 GHz as can be seen in figure 4. For decoupling the antennas must be spaced as far away from each other as possible and polarization diversity should be exploited. q p Fig. 4. Asymmetric positioning of parasitic element for an increased bandwidth. Space in PDA s housing is limited thus a decoupling of antennas due to spacing is not possible. Further on, an antenna as shown in figure 4 cannot be integrated vertically in the housing, because the height is too small. As solution to these limitations the antenna is buckled in the middle of the height of the antenna, see figure 5. According to the buckled shape of one antenna type, the polarization and pattern is different for the two types of inverted F antennas. For the placement of antennas in a PDA housing some considerations concerning user s influence should be made. It is expected that the user covers the lower part of the housing in most cases. In fewer cases the user s hand covers the upper part of the housing. Hence it is beneficial to place the antennas in that way that in most cases only one antenna is covered. Figure 6 shows the simulation model of the PDA, which is developed under previous considerations, with three antennas integrated. One possibility is shown here, the two buckled inverted F Fig. 6. Simulation model and model for measurements of three inverted F antennas 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 the bottom. The model of the PDA (8 cm x 12 cm x 1.5 cm) consists of a metallic block, representing the battery and the display of the device, and a PVC housing with a wall thickness of 4 mm. The permittivity of the PVC material equals εr = 3, the loss factor tan δ = 1 1 4. For simulations the housing is closed by a top cover. All simulations were carried out with FEKO, see [7], a standard EM code based on method of moments. FEKO was applied for calculating the pattern of the coupled antenna system as well as mutual coupling and self impedances of the antennas. III. A NTENNA MEASUREMENTS In order to verify the simulations measurements have been are carried out at both frequencies 2.45 GHz and 5.2 GHz. Gain and pattern measurements were carried out in an anechoic chamber. The patterns can be found in figure 7. The gain for the inverted F antennas integrated into the PDA housing can be found in table I. The antenna patterns differ clearly in horizontal and vertical polarization, which is a good premise for pattern diversity. If antenna patterns are too similar, correlation would degrade diversity performance. Coupling and S-parameters were measured with a network analyzer. The reflection coefficient of the ith antenna is denoted as Sii. As an example the reflection coefficient of the first antenna is shown in figure 8. The antenna is suitable for both frequencies.

TABLE I MEASURED GAIN FOR INTEGRATED ANTENNA STRUCTURES IN THE PDA S HOUSING WITHOUT USER S INFLUENCE, SEE FIGURE 6(B) AT 2.45 GHZ AND 5.2 GHZ. @2.45 GHz @5.2 GHz IFA1.8 dbi 1.2 dbi IFA2.8 dbi 1.2 dbi IFA3 5.5 dbi 1.2 dbi 3 5dB 1dB 15dB 3 S 11 in db 5 1 15 2 simulation measurement 25 2 3 4 5 6 Fig. 8. Simulation and measurement results for the reflection coefficient of the integrated antenna, denoted with number one, see figure 6. 9 9 12 12 2 3 15 3 18 5dB 1dB 15dB measurement 15 5.2 GHz simulation 2.45 GHz 3 9 9 S in db 4 5 6 S12 simulation S12 measurement 7 S13 simulation S13 measurement 8 S23 simulation S23 measurement 9 2 3 4 5 6 Fig. 9. Simulated and measured coupling coefficient between the ports of integrated dualband inverted F antennas. 12 12 3 15 18 3 1dB 2dB measurement 15 5.2 GHz simulation 2.45 GHz IV. INVESTIGATION OF USER S INFLUENCE For investigation of diversity systems and MIMO capacity the influence of user s hand is not negligible. Therefore a hand model is included. Two different hand positions are analyzed. One where the user holds the PDA at the top and the second and most significant one, where the user places his hand at the bottom of the PDA, see figure 1. 9 9 (c) 12 15 18 12 measurement 5.2 GHz 15 simulation 2.45 GHz Fig. 7. Simulated and measured azimuth pattern for horizontal polarization of the IFA 1, IFA 2, and (c) IFA3. Figure 9 shows the measurement and simulation results for coupling coefficients of different pairs of antennas integrated in the PDA. It can be seen, that simulations and measurements predict a coupling of less than 18 db in the frequency band between 2 GHz and 6 GHz. The gain and pattern simulations and measurements demonstrate that the antennas are suitable for MIMO and diversity systems at both WLAN frequency bands. Fig. 1. Simulation model of PDA and the investigated hand position on bottom 1, covering one antenna, and with hand on top 1, covering two antennas. The shape of the hand is like a U profile. The hand model has an extension of 1 cm by 1 cm on bottom. The height below the PDA is 1.5 cm and the height of the side plates equals 4.9 cm. The width of side plates is 1 cm and the gap between the hand an the PDA housing on bottom is.9 cm and between the side plates and the PDA it is.5 cm. For bottom 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 a length is 3.5 cm. Power is absorbed in the hand, hence power transfer in the communication system is possibly affected. V. DIVERSITY PERFORMANCE The received signal level correlation coefficient can be used to investigate antenna array s quality for diversity applications [8], [9]. However, correlation of signals is only given for two signals. In the case of more than two antennas, a figure of merit must be found, which should not only concentrate on correlation properties but also on received signal strength from the antennas. For investigation of correlation properties of antenna arrays the power correlation coefficient ρ e,vi v j for all possible pairs of antennas has to be computed according to [8]. v i,ξiα denotes the received voltage of antenna i, if the antenna is not loaded. α denotes the polarization, for example α = h for horizontal and α = v for vertical polarization. ρ e,vi v j ρ v,vi,ξih v j,ξih + ρ v,vi,ξiv v j,ξiv 2 ρ v,vi,ξih v j,ξih 2 + ρ v,vi,ξiv v j,ξiv 2 (2) For this equation the cross polarized power correlation for the antennas is neglected. The power correlation coefficients of all antennas are placed in a power correlation matrix ρ NN. ρ NN = ρ e,v1 v 1 ( x)... ρ e,v1 v N ( x)....... ρ e,vn v 1 ( x)... ρ e,vn v N ( x) (3) N denotes the maximum number of antennas used in the array. The main diagonal elements ρ e,v1 v 1 ( x) are equal to one. The matrix elements are all less than 1 and due to equation (2) larger than or equal to zero. Due to the fact that the matrix is symmetric the eigenvalues λ n, with n {1... N}, are real numbers. The maximum eigenvalue can be used as a basic parameter for investigation of antenna array power correlation. It is referred to as correlation factor. Figure 11 shows the correlation factor for the previously described positions of user s hand. Impinging power is uniformly distributed in azimuth and Gaussian distributed, with expectation value of 9 and standard deviation of 6, in elevation. Correlation properties are influenced by the user s hand. However, the correlation factor is less than.1, which is remarkable. Sophisticated antenna placement exploits spatial, pattern and polarization diversity, leading to decorrelated signals. VI. MIMO PERFORMANCE For determination of MIMO performance simulations are carried out with a MIMO system model, see section VI-A. As figure of merit the transmission gain and the spectral efficiency are applied. correlation factor.1.9.8.7.6.5.4 vertical horizontal.3 2.4 2.42 2.44 2.46 2.48 Fig. 11. Power correlation factor for typical indoor channel distributed impinging power with users hand on top (+) and users hand on bottom ( ). A. MIMO System Model For evaluation of MIMO performance of this antenna design, a system model of a complete transmission link is applied [1]. The model of the whole MIMO transmission link allows for a very accurate antenna modeling, including all mutual coupling effects, and a precise analysis of the power transmission gain and therewith the efficiency of the arrays. The basic idea is to model the whole MIMO transmission link to be composed of single network units, which are the transmitter, the transmit array S T xa, the propagation channel S C, the receive array S RxA and the receiver. It is essential to take the transmitter and receiver as load networks, connected to the antenna arrays into account to model the matching of the antennas and the mutual coupling effects correctly. The antenna arrays S T xa and S RxA are modeled by scattering parameters, too. The basic idea of the scattering parameter representation of an antenna array is that each single antenna is a two port device with an excitation port and a directional far field port. For the following investigations the base station consists of three dipoles arranged as triangle. As channel model an indoor stochastic double-directional multipath indoor channel model given in [11] is used. 2 realizations of the channel have been generated for random positions of the transmitter T x and the receiver Rx. B. Power transmission gain Since PDAs are battery-driven, the efficiency of the antennas is an important topic. Mutual coupling among closely spaced antennas does not only influence the signal flow and the correlation properties, it can also strongly reduce the efficiency of an array in terms of power. The system model, given in [1], allows for considering the power transmission gain of the whole MIMO link, including the antennas. The power transmission gain is the ratio of the power received at the signal drain to the power fed into the transmit antennas. The latter is not equal to the power which is radiated from the transmit antennas, if the efficiency of the transmit array is not 1%. By comparing the power transmission gain of MIMO systems with different arrays in the same channel, conclusions on the performance of the arrays in terms of power can be drawn.

Figure 12 shows the cumulative distribution function of the power transmission gain for different hand positions at the PDA. For comparison, a single input single output (SISO) system with a single dipole element at transmit and receive is show. P(transmission gain < abscissa) 1.8.6.4.2 with hand on bottom with hand on top SISO 18 16 14 12 1 transmission gain in db Fig. 12. Simulation result of MIMO power transmission gain for the indoor channel 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 power transmission gain is lower than if the hand is on bottom. This phenomenon 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,.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 all coupling effects and the user s hand into account. In order to assess a MIMO transmission system by the spectral efficiency usually a fixed SNR and a channel matrix, which is normalized by the Frobenius norm, is used. With this normalization, the influence of the correlation properties of the channel matrix on the spectral efficiency becomes visible, but any interrelation between the SNR and the correlation properties of H is neglected. If H is not normalized, that means the path loss and the gain of the single antenna elements are included in H, the spectral efficiency is C = log 2 (det(i + P T σ 2 m HH )) (4) P T is the transmit power, which is equally distributed among the m transmit antennas if no channel state information is available at the transmitter. σ 2 is the noise power. This formula allows for a comparison of different MIMO systems, including the influence of the transmission gain and therewith of the SNR. The transmit power remains fixed, i.e. no normalization in terms of power is performed. As a result the cumulative distribution function (cdf) for the MIMO spectral efficiency at 2.45 GHz is shown in figure 13. The spectral efficiency is relatively large with respect to the limited space available for the antennas in a PDA and with respect to the dual-band operation. Hold in mind, that if the hand is on top, the two buckled inverted F antennas are covered. In this case the power transmission gain is lower than if only the planar inverted F antenna is covered. Despite degradation of power transmission gain if one antenna is covered the spectral efficiency for user s hand on bottom is enlarged in comparison to user s hand on top. This is because if only one antenna is covered the residual two antennas on top can be used for MIMO. However, even if the user s hand is placed on top and both buckled antennas are covered, the spectral efficiency is higher than for SISO case. P(spectral efficiency < abscissa) 1.8.6.4.2 with hand on bottom with hand on top SISO 5 1 15 spectral efficiency in bit/(s*hz) Fig. 13. Simulation result of MIMO spectral efficiency for different hand positioning on PDA at 2.45 GHz VII. CONCLUSION A sophisticated dual-band antenna design and its integration into a PDA has been presented. The antenna design and placement has been carried out taking MIMO and diversity aspects into account. The results show that this antenna configuration is appropriate for MIMO in both WLAN frequency bands. The influence of user s hand is not negligible, especially the absorption of power in the human tissue, if some antenna elements are covered by the hand. REFERENCES [1] S. Schulteis, C. Waldschmidt, C. Kuhnert, and W. Wiesbeck. Design of a miniaturized dual band inverted f antenna. IEEE Antennas and Propagation Society International Symposium, 3:3123 3126, June 24. [2] S. Schulteis, C. Waldschmidt, W. Soergel, and W. Wiesbeck. A small planar inverted f antenna with capacitive and inductive loading. IEEE Antennas and Propagation Society International Symposium, 4:4148 4151, June 24. [3] C. Waldschmidt, C. Kuhnert, S. Schulteis, and W. Wiesbeck. Compact mimo-arrays based on polarization diversity. IEEE Antennas and Propagation Society International Symposium, 2:499 52, June 23. [4] R. C. Hansen. Fundamental Limitations in Antennas. Proceedings of the IEEE, 69(2):17 182, February 1981. [5] J. S. McLean. The Radiative Properties of Electrically-Small Antennas. IEEE International Symposium on Electromagnetic Compatibility, pages 32 324, August 1994. [6] A.T. Arkko. Effect of Ground Plane Size on the Free-Space Performance of a Mobile Handset PIFA Antenna. Proceedings International IEE Conference on Antennas and Propagation, pages 316 319, April 23. Conf. Publ. No. 491. [7] http://www.feko.info. [8] K. Fujimoto, A. Henderson, K. Hirasawa, and J.R. James. Small Antennas. Research Studies Press LTD., 1993. [9] William C. Jakes, editor. Microwave Mobile Communications. Wiley, New York, 1974. [1] C. Waldschmidt, S. Schulteis, and W. Wiesbeck. Complete RF system model for the analysis of compact MIMO arrays. IEEE Trans. on Veh. Techn., 53(3):579 586, May 24. [11] T. Zwick, C.Fischer, and W. Wiesbeck. A stochastic multipath channel model including path directions for indoor environments. IEEE Journal on Sel. Areas in Comm., 2:1178 1192, 22. Parts of the work are outcome of the ACE network of excellence.