A New Multimode Antenna for MIMO Systems Using a Mode Frequency Convergence Concept

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A new multimode antenna for MIMO systems using a mode frequency convergence concept J. Sarrazin, Y. Mahé, Member, IEEE, S. Avrillon, Member, IEEE, and S. Toutain

Abstract—A new multimode antenna is proposed in this paper. The structure is based on a mode frequency convergence concept. A microstrip square patch antenna is modified in order to force different modes to resonate at the same frequency. Then, with a common/differential excitation, these modes can be fed independently. Thus, three radiation patterns are available simultaneously, thereby producing diversity. With dimensions less than a guided wavelength (≈0.88λg), the proposed structure is well suited to reduce the size of multiple antennas used in diversity applications such as MIMO systems. The antenna has been designed in the 2.45 GHz band for Wi-Fi applications. Index Terms— Multimode antennas, Multiple Input Multiple Output (MIMO) systems, microstrip antennas, radiation pattern diversity, envelope correlation

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I. INTRODUCTION

ULTIPLE Input Multiple Output (MIMO) systems can drastically improve wireless communication capacity and robustness by exploiting multipath effects [1]. Performances of these multiple antenna systems largely depend on the correlation between received signals. To maximize the capacity, this correlation must be as low as possible. Spatial diversity is commonly used to reduce it. However, this requires a space between antennas of less than 0.5λ up to several λ (depending on which kind of environment is considered). This is not always compatible with the limited volume available on a wireless terminal. That is why other kinds of diversity such as radiation pattern diversity are also investigated. By using antennas with different radiation patterns, it is possible to reduce the size of the multiple antenna system while keeping a low correlation between received signals. To achieve this pattern diversity, the concept of co-located antennas has been introduced [2]. The idea is to co-localize several antennas radiating different polarizations [3-5]. This concept, mainly based on polarization diversity, has been extended to amplitude pattern diversity in order to provide a compact system integrating a larger number of antennas [6]. More recently, promising solutions based on multimode antennas have been proposed [7-13]. These structures have different modes of resonance depending on how the excitation is performed. Since the generated modes produce uncorrelated radiation patterns, diversity is achieved. J. Sarrazin is with the LTCI research institute, Telecom ParisTech, Paris, France (e-mail: [email protected]). Y. Mahé and S. Toutain are with the IREENA research institute, University of Nantes, France (e-mail: [email protected]). S. Avrillon is with the IETR research institute, University of Rennes I, France (e-mail: [email protected]).

Thus, this kind of structure appears to be well suited for MIMO systems. However, most of these multimode antennas are based on spiral shapes and do not contain any ground plane. This can be problematic when the antenna has to be integrated with a front-end. In this paper, this problem is overcome by introducing a multimode antenna based on a new mode frequency convergence concept. The original structure is a microstrip dual-polarized square patch antenna. Hence, it has the advantages of having a low profile and a ground plane, thereby making it suitable for any integration in a multilayer front-end. However, the number of uncorrelated radiation patterns available on such kind of antenna is only two (one per polarization). So the idea is to modify the square patch structure in order to obtain different modes resonating at the same frequency. Then, by an appropriate excitation, the different modes are fed independently. Thus, radiation pattern diversity is achieved between the fields radiated by the different modes. The mode frequency convergence concept is explained in section II. Using this approach, a dual-mode antenna is designed and is presented in section III. Then, in section IV, the concept is extended to both polarizations of the square patch in order to obtain a dual-mode dual-polarization antenna. S-parameter and radiation pattern measurements have been conducted and the results are shown in section V. Diversity performances of the structure are discussed in section VI by calculating envelope correlations. II. ANTENNA THEORY AND ANALYSIS A. The mode frequency convergence concept The main idea of the antenna system presented in this paper is to take advantage of multiple resonant modes of a microstrip patch antenna in order to produce radiation pattern diversity. Indeed, a structure such as a patch antenna contains some resonant modes and so it has the potential to radiate with different electromagnetic field distributions. These multiple field distributions lead to different radiation patterns which can be used to produce radiation pattern diversity. However, two major problems must be taken into account. The first one is to find a way to independently feed every mode. The second one is to force these modes to resonate at the same frequency. Thus, the patch antenna will act as different antennas performing pattern diversity. B. The dual-mode aspect In this study, we focus on two modes of the patch antenna: the TM20 and the TM21. The reasons of this choice are the

AP1005-0461 following. Firstly, resonance frequencies of these modes are quite close together and with some design modifications, can converge. Secondly, as we will see, their electromagnetic field distributions are suitable to feed them independently. Let consider a square patch antenna of length L = 58 mm and thickness h = 1.58 mm. The substrate permittivity is εr = 4.4. According to the cavity model [14], resonance frequencies are f20 = 2.46 GHz for the TM20 mode and f21 = 2.75 GHz for the TM21 mode. Fig. 1a and Fig. 1b show the current distribution of TM20 and TM21 modes respectively. One possible location for the feeding accesses on the square patch antenna is also indicated. The short-circuit axis are also shown (s.c.). In Fig. 1a, the + sign indicates the location of the two input accesses, here feeding the patch in phase. In Fig. 1b, + and – signs indicate the inputs out of phase and consequently, feeding a differential mode. According to TM20 and TM21 field distributions, the electric field phase at probe locations are identical in the TM20 mode (Fig. 1a) and are opposite in the TM21 mode (Fig. 1b). Thus, the common excitation feeds only the TM20 mode and the differential one, only the TM21 mode. Therefore, this technique requires a dualfeeding for each MIMO branch which can be a disadvantage compare to usual MIMO systems involving a single-feeding per branch. However, this limitation can be overcome with the use of a Rat-Race coupler such as the one used in section III. By observing current distributions in Fig. 1a and Fig. 1b (the warmer the colour, the higher the current density), one can notice that the TM21 one is spatially more concentrated than the TM20 one. So by changing the patch design in the high density current areas indicated in Fig. 1b, both resonance modes will be disturbed but the TM21 will be more affected than the TM20. As it will be shown in the next section, inductive slots have been etched in these areas to slow down the current in order to decrease resonance frequencies of both modes. However, since the effect is stronger on the TM21 mode than on the TM20 one, both resonance frequencies converge down to a single one. So TM20 and TM21 modes are able to produce two different radiation patterns at the same frequency.

(a)

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high density current areas of both polarizations, the four different modes resonate at the same frequency. Consequently, four radiation patterns are available to produce diversity. The feeding system principle is presented in Fig. 2. The shared short-circuit axis of TM20 and TM21 modes are drawn as well as those of TM02 and TM12 modes. It appears that four short-circuit points are identical for the four modes. Labels 1 and 2 represent the location of TM20 and TM21 inputs and labels 3 and 4, the location of TM02 and TM12 inputs. Inputs 1 and 2 are located on TM02 and TM12 short-circuit axis and inputs 3 and 4 on TM20 and TM21 short-circuit axis. This has been done in order to avoid mutual coupling between the two orthogonal polarizations.

Fig. 2 - Feeding of the dual-mode dual-polarization square patch antenna III. DUAL MODE ANTENNA A. Antenna overview The design of the proposed structure is given in Fig. 3 and its dimensions in TABLE 1. Two coaxial probes, F1 and F2, are used to feed the antenna with a common and a differential mode. Consequently, the structure is able to resonate respectively in the TM02 mode or in the TM12 mode. Four metallic via holes are located on the shared short-circuits in order to make easier finding out 50Ω locations for the probes (it has also the effect to bring resonance frequencies down). We firstly consider only one polarization of the square patch antenna. Height clusters of eleven inductive slots have been etched on the patch. Their locations are in the TM12 mode’s high density current areas (as indicated in Fig. 1b) but also of the TM21 mode, since both polarizations will be used later.

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Fig. 1 - Current distributions of (a) TM20 mode with a common feeding and (b) TM21 mode with a differential feeding C. Dual-polarization aspect On a square patch, TM20 and TM02 modes resonate naturally at the same frequency, as well as TM21 and TM12 ones. So, using four input accesses and etching inductive slots in the

Fig. 3 - Design of the proposed dual-mode antenna

AP1005-0461 TABLE 1 PARAMETERS VALUES OF THE ANTENNA STRUCTURE

Parameter εr h W1 W2

Values 4.4 1.58 mm 51 mm 25.5 mm

Parameter offset lm wm gm

Values 2.6 mm 6.04 mm 0.5 mm 0.5 mm

B. Simulated S-parameters The structure has been simulated with CST Microwave Studio. Common and differential feedings have been achieved directly with the software. Firstly, a parametric study on the slot length lm has been conducted. The resonance frequency of both the TM02 and TM12 modes has been recorded and plotted in Fig. 4. As expected from the earlier discussion, the resonance frequency of the TM02 mode is less affected by the slots than the TM12 one. Consequently, a value of lm exists for which both the resonance frequencies converge. This value is found to be lm = 6.04 mm. One can also notice that the slots lead to a miniaturization of the structure.

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function. Furthermore, the simulation has been conducted with Ansoft HFSS. Since the meshing process in HFSS and in Microwave Studio are different and since the bandwidths involved are very narrow, a comparison of the results obtained with both software seems to be appropriate. The dual-mode antenna and its hybrid coupler are presented in Fig. 6. It is a two dielectric layers structure. The upper dielectric layer has the same characteristics as the previous simulation. The patch antenna is etched on the upper side and the ground plane takes place on the lower side (so between the two substrate layers). On the lower dielectric layer, a Rat-Race coupler has been designed following the procedure described in [15] with a substrate of permittivity εr = 4.4 and of thickness h = 0.762mm. The two inputs of the coupler are located on the edge of the substrates whereas the outputs are connected to the patch with metallic via-holes through the ground plane. Thus, depending on which coupler input is fed, the coupler outputs produce an in-phase or an out-of-phase excitation.

Fig. 6 - Dual-mode antenna with its Rat-Race coupler Fig. 4 - Variation of the resonance frequency according to the slot length Simulated S-parameters are given in Fig. 5. Reflection coefficients show that common and differential modes resonate at the same frequency, f0 = 2.468 GHz, with a bandwidth of 0.25% and 0.13%, respectively. The frequency bandwidth is narrow as expected. In fact, inductive slots as well as metallic via holes disturb the resonating modes thereby acting as miniaturization techniques. For such techniques, narrow bandwidths are common. The coupling is very low (about -80 dB at the operating frequency), which is typical from idealistic simulations.

The S-parameters obtained by the simulation are given in Fig. 7. S11 corresponds to the common excitation (TM02 mode), and S22 to the differential excitation (TM12 mode). Obtained results are in good agreement with the previous ones even though slight differences are there. This is naturally expected when the bandwidths involved are narrow. S21 is the coupling between the two modes. Results are much more realistic than those of previous simulation since the maximum coupling is now about -20 dB. The increase of the coupling level in this simulation may be due to the fact that the inphase/out-of-phase excitation comes from a simulated RatRace coupler and not directly from the software. The common/differential excitation generated by the software is perfectly accurate over the whole bandwidth of interest but this is not the case with the simulated Rat-Race.

Fig. 5 - Simulated S-parameters Another simulation has been performed to validate the dualmode antenna concept. Instead of implementing the common and differential feeding mode directly with the software, an hybrid coupler (Rat-Race) has been designed to perform this

Fig. 7 - Simulated S-parameters obtained with the RatRace coupler

AP1005-0461 C. Simulated field distribution The electric field distributions obtained from the simulation with HFSS are given in Fig. 8a and Fig. 8b respectively for the common mode and the differential mode. The boxes which can be observed under the slots are only there to help for the meshing. The substrate is completely homogeneous and these boxes are a part of it. In Fig. 8a, the electric field distribution of the TM02 mode can be observed. The variation of the field is in agreement with the one of a classical patch [14]. Of course the distribution itself is not homogeneous anymore because of the slot and metallic via hole effect but the mode can still be recognized. The Fig. 8b presents the electric field obtained by the differential feeding. This mode can be identified as the TM12 one, even if the distribution has been greatly altered by the slots. By observing carefully, it can be observed that the electric field phase shifts twice along y-axis while it shifts only once along x-axis. So by feeding the antenna either with common or differential mode, it is possible to excite two different resonating modes, respectively the TM02 and the TM12, even though they are altered from those of an original square patch antenna.

z x

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one, a maximum in this same direction (as the TM12 mode). Both radiation patterns being different, radiation diversity is so achieved between common and differential modes.

Fig. 9 - Gain of common mode and differential mode IV. DUAL-MODE DUAL-POLARIZATION ANTENNA A. Antenna overview We now propose to extend the dual-mode concept to the two polarizations available on the square patch antenna. The structure remains the same as the previous one except that two additional feeding inputs are added to the ones already present. Thus, a dual-mode dual-polarization antenna is obtained as it is shown in Fig. 10. Inputs F1 and F2 allow to feed common and differential modes of the first polarization, say TM20 and TM21 and F3 and F4 the common and differential modes of the second polarization, say TM02 and TM12.

(a)

y z x

y (b) Fig. 8 - Electric field distribution of (a) TM02 mode and (b) TM12 mode D. Simulated radiation pattern Gains of the common and differential modes are given in Fig. 9. Patterns are drawn in the +/-45° planes in respect to the x-axis presented in Fig. 8. Antenna’s broadside direction is at θ=90°. The maximum gain of the common mode is 3dB whereas the maximum gain of the differential mode is about 5.7dB. The patterns obtained are not exactly similar to those expected from a rectangular patch resonating in the TM02 and TM12 mode. The difference is mainly due to the inductive slots which modify the field distribution and so the radiation. However, the radiation shape can be identified since the common mode’s pattern presents a null in the patch’s broadside direction (as the TM02 mode) and the differential’s

Fig. 10 - Design of the dual-mode dual-polarization antenna B. Simulated S-parameters The simulation has been performed with CST Microwave Studio by using the direct common and differential excitation proposed by the software. The S-parameters results are presented in Fig. 11. The reflection coefficients (Fig. 11a) are given for both polarizations: S11 and S22. For each polarization, common and differential mode results are distinguished. Hence, S11common corresponds to the reflection coefficient of the first polarization when inputs F1 and F2 are in-phase (TM20 mode) and S11differential when F1 and F2 are outof-phase (TM21 mode). Also, S22common is the reflection coefficient of the second polarization when inputs F3 and F4 are in-phase (TM02 mode) and S22differential when F3 and F4 are out-of-phase (TM12 mode). The obtained results are in good agreement with the previous single-polarization antenna. The slight differences are probably due to the addition of the two inputs F3 and F4. Theoretically, these inputs should be located

AP1005-0461 on the short-circuit axis of the modes excited by inputs F1 and F2 (and F1 and F2, on the short-circuit axis of the modes excited by F3 and F4). However, due to the slots, inputs are not located anymore exactly on these short-circuit axis. So their impact may explain the differences in reflection coefficient results. The Fig. 11b shows the transmission parameters between the four modes available on the antenna. The coupling between all the modes can be neglected except S2common1common which reaches -2.8 dB at the maximum. This parameter represents the coupling between common modes along both the polarizations (TM20 and TM02). This happens when all the inputs are fed in phase. In order to understand this strong coupling, the electric field distribution of these common modes is now discussed.

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Thus, rather than two different modes, TM20 and TM02 modes can also be seen as a single hybrid mode.

(a)

(b) (a)

(b) Fig. 11 - Simulated S-parameters: (a) reflection coefficients and (b) transmission coefficients C. Simulated field distribution The electric field distribution of common modes along both polarizations is shown in Fig. 12. The field pattern in Fig. 12a occurs when F1 and F2 are fed in-phase and corresponds to the TM20 mode. The pattern of Fig. 12b is obtained by feeding F3 and F4 in phase and corresponds to the TM02 mode. Distributions of the modes are, except the phase, similar. However, by observing carefully in the low intensity field region, one can notice that these modes are not exactly identical, thereby making them identifiable from each other. The fact that TM20 and TM02 modes are quite similar is obviously due to the presence of the slots which largely modify their field distribution. To illustrate the mechanism, we refer to the electric potential shown in Fig. 12. The Fig. 12a presents the electric potential of the TM20 mode and the Fig. 12b, the TM02 one. According to the field distribution presented in Fig. 12, we notice that the field is mainly concentrated in four regions. These four regions are indicated by four circles in Fig. 12. Now, if we consider the field pattern only in these four regions, it is similar for both modes. To summarize, the TM20 and TM02 modes are so modified by the slots that their respective field distribution became similar.

Fig. 12 - Electric field distribution (left) and potential (right) of (a) TM20 mode and (b) TM02 mode D. Simulated radiation pattern Radiation patterns have been obtained by simulation and are drawn along the two polarizations θ and Φ. The pattern along θ is defined using the electric field projection on the vector uθ and the pattern along Φ using the projection on the vector uΦ of a spherical coordinate system. Fig. 13 presents the radiation patterns of the common modes in the same planes than in Fig. 9. Patterns of Fig. 13a is obtained when inputs F1 and F2 are fed in phase and patterns of Fig. 13b is obtained when inputs F3 and F4 are fed in phase. As expected regarding the field distribution of these two modes, their radiation patterns are similar. The radiation patterns of the differential modes are shown in Fig. 14. Patterns of Fig. 14a is obtained when inputs F1 and F2 are fed out of phase and patterns of Fig. 14b, when F3 and F4 are out of phase. Patterns of Fig. 14a and Fig. 14b are similar except that they are completely orthogonal. So it means that the differential modes excited by the couple F1 and F2 and the couple F3 and F4 have orthogonal polarizations, which is highly suitable to achieve pattern diversity.

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(b)

Fig. 13 – Radiation pattern (a) TM20 mode and (b) TM02 mode

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Differences may be due to the fabrication tolerances. In fact, by considering the narrow bandwidth of the antenna and the fact that it is a miniaturized structure, it is not surprising that the design is very sensitive to the tolerance of fabrication. It has been observed in simulation that a 10 µm variation of the slot length leads to notable changes in the S-parameter results, and the tolerance of the used chemical etching is precisely about 10 µm.

(a)

(b)

Fig. 14 - Radiation pattern of (a) TM21 mode and (b) TM12 V. FABRICATION AND MEASUREMENTS A. Prototypes Two prototypes have been fabricated, one with two inputs (dual-mode single-polarization antenna) and one with four inputs (dual-mode dual-polarization antenna). Since both are identical apart from the number of coaxial inputs, only the picture of the dual-mode dual-polarization antenna is presented in Fig. 15. The patch design has been etched on a FR4 epoxy substrate of permittivity εr = 4.4 and thickness h = 1.58 mm. The four metallic via holes have been manually welded and can be observed in Fig. 15a. With the four coaxial accesses (Fig. 15b), it is possible to feed common and differential modes of both polarizations.

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(b) Fig. 16 - Reflection coefficients of the (a) singlepolarization antenna and (b) dual-polarization antenna C. Radiation pattern measurements

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(b)

Fig. 15 - Dual-mode dual-polarization antenna prototype (a) upper view (b) lower view B. S-parameters measurements The S-parameters have been measured for both the prototypes: the single-polarization antenna and the dualpolarization antenna. From a classical S-parameter measurement, the reflection coefficients of the common and differential modes of the antennas have been determined by using the method described in [16, 17]. Reflection coefficients of the single-polarization antenna are shown in Fig. 16a and those of the dual-polarization one in Fig. 16b. With both antennas and for all the common and differential modes, a resonance can be observed around 2.45 GHz. However, impedance matching levels are not as good as in simulation. Minima obtained with the single-polarization antenna are about -9.5 dB for the common mode and -6.2 dB for the differential mode. For the dual-polarization prototype, minima are between -3.6 dB and -4.6 dB. Measured and simulated results are in good agreement regarding the frequency resonance but not regarding the reflection coefficient levels.

Radiation pattern measurements have been conducted in a near-field anechoic chamber. Then a near-field/far-field transformation has provided the radiation pattern along Φ and θ in a 4π steradian range. Measured results are given for the dual-polarization antenna only and are plotted in the same +/45° planes than previously (4π steradian range results are used in section VI for envelope correlation calculations). Common and differential excitation modes have been obtained by using a Rat-Race coupler to feed the coaxial inputs of the antenna. Fig. 17 shows the radiation patterns of the common modes. Ripples on the curves are probably due to the metallic stand located below the antenna during the measurement process. As expected from the simulation, both modes (TM20 and TM02) produce the same radiation pattern and consequently no diversity is achieved. Only one of these two modes should be used at the same time in a multiple antenna communication scheme. Differential mode results are presented in Fig. 18. Patterns of both modes (TM21 and TM12) being different, polarization diversity is achieved between them. If one common mode is considered in addition, three different modes on this single compact antenna structure can be used to perform radiation pattern diversity (in amplitude as well as in polarization), thereby acting as three different antennas. To quantify the achieved diversity, envelope correlation calculations are conducted in the next section.

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Fig. 17 - Radiation pattern of (a) TM20 mode and (b) TM02 mode

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Fig. 18 - Radiation pattern of (a) TM12 mode and (b) TM21 mode VI. RADIATION PATTERN DIVERSITY ANALYSIS

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levels between patterns of the different modes available on the antenna are below 0.18 except for ρe12. This indicates that radiation pattern diversity is achieved between the differential modes as well as between the differential and the common modes. Consequently, this structure can act as three different antennas in a diversity communication scheme. The correlation between the common modes ρe12 is quite high as expected. In fact, the pattern of the common modes being very similar, it is logical that the envelope correlation is high. Hence, these two modes should not be used simultaneously in a diversity communication scenario. Fig. 20 shows the correlation with a Laplacian AoA distribution in the elevation plane as suggested in [19]. The angular deviation is σθ=20° about θi (with θi=90° being the antenna’s broadside direction). Even by taking into account an AoA distribution, correlation levels remain quite low. So pattern diversity is still efficient. It is well known that power imbalance in MIMO system branches leads to degradation of performances [20, 21]. For that purpose, Fig. 21 shows the self-correlation of each mode using the same previous Laplacian AoA distribution. Selfcorrelations are expressed in dB and show the differences between modes’ average power. Power imbalance between common modes (ρe11 and ρe22) and between differential modes (ρe33 and ρe44) never exceeds 2.5 dB. However, power imbalance up to 10 dB exists between common and differential modes for certain values of θi. So adequate processing should be considered. However, as it has already been mentioned, only three modes have to be used simultaneously in a MIMO context. So only one branch will undergo power imbalance. This suggests that the processing may be less complex than in the case where power imbalance would occur with all the three branches.

The envelope correlation ρe provides a measure of the radiation pattern diversity performances. The lower the correlation, the better the antenna diversity performances. This coefficient is defined as [18]: 2

∫ (XE

)

* * 1θ E 2θ pθ + E1ϕ E 2ϕ pϕ dΩ

ρe =

Ω

∫ (XE

1θ

Ω

)

(

)

E1*θ pθ + E1ϕ E1*ϕ pϕ dΩ ∫ XE 2θ E 2*θ pθ + E 2ϕ E 2*ϕ pϕ dΩ Ω

where E1θ, E1Φ, E2θ, E2Φ are complex electric fields along Φ and θ radiated by two different antennas. The parameter X is the cross-polarization discrimination (XPD) of the incident field and is defined as XPD = Sθ/SΦ (where Sθ and SΦ represent the average power along the spherical coordinates θ and Φ). The angle Ω is defined by θ [0:π] in elevation and Φ [0:2π] in azimuth. pθ and pφ are the Angle-of-Arrival (AoA) distributions of incoming waves. Fig. 19 presents the envelope correlation between the measured patterns of the dual-mode dual-polarization antenna with a uniform AoA distribution. The mode 1 is the common mode of the polarization 1 (TM02), the mode 2 the common mode of the polarization 2 (TM20), the mode 3 the differential mode of the polarization 1 (TM12) and the mode 4 the differential mode of the polarization 2 (TM21). Thus, as an example, ρe13 represents the correlation between the patterns of TM02 and TM12 modes. It can be observed that correlation

Fig. 19 - Envelope correlation between modes with a uniform AoA

Fig. 20 - Envelope correlation between modes with an AoA distribution

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Fig. 21 - Self-correlations (power imbalance) VII. CONCLUSION A new multimode antenna has been introduced. Our approach had led to modifications of the design of a microstrip square patch in order to obtain different modes resonating at the same frequency. Then, with an appropriate excitation, these modes can be fed independently. Through a common/differential excitation, the proposed structure is thus able to produce three different radiation patterns, thereby acting as three independent antennas suitable for MIMO systems or any systems based on antenna diversity. This concept has been validated in simulation as well as in measurement in the 2.45 GHz frequency band. In conclusion, the observation of the electromagnetic field of square patch modes has made possible the development of a new concept which may be applicable not only to the square patch antenna but also to other structures. VIII. REFERENCES [1] A. Paulraj, D. Gore, R. Nabar and H. Bölcskei, “An overview of MIMO communications – a key to gigabit wireless”, Proc. of the IEEE, vol. 92, no. 2, pp. 198-218, Feb. 2004 [2] A.S. Konanur et Al., “Increasing wireless channel capacity through MIMO systems employing co-located antennas”, IEEE Trans. on Microwave Theory and Tech., vol. 53, no. 6, pp. 1837-1844, June 2005 [3] H.-R. Chuang and L.-C. Kuo, “3-D FDTD design analysis of a 2.4 GHz polarization diversity printed dipole antenna with integrated balun and polarizationswitching circuit for WLAN and wireless communication applications IEEE Trans. on Microwave Theory and Tech, vol. 51, no. 2, pp. 374-381, Feb. 2003. [4] C.-Y. Chiu, J.-B. Yan, and R. Murch, “Compact threeport orthogonally polarized MIMO antennas”, IEEE Antennas and Wireless Propagation Letters, vol. 6, pp. 619-622, 2007. [5] J. Sarrazin, Y. Mahé, S. Avrillon, and S. Toutain, “Investigation on cavity/slot antennas for diversity and MIMO systems: the example of a three-port antenna," IEEE Antennas and Wireless Propagation Letters, vol. 7, pp. 414-417, Nov. 2008 [6] J. Sarrazin, Y. Mahé, S. Avrillon, and S. Toutain, “Collocated microstrip antennas for MIMO systems with a low mutual coupling using mode confinement”, ”, IEEE Trans. on Antennas and Propag., vol. 58, no. 2, pp. 589-592, Feb. 2010

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[7] O. Klemp, M. Schultz and H. Eul, “Novel logarithmically periodic planar antennas for broadband polarization diversity reception”, Inter. Journal of Electro. and Comm., vol. 59, pp. 268-277, April 2005 [8] C. Waldschmidt and W. Wiesbeck, “Compact wide-band multimode antennas for MIMO and diversity”, IEEE Trans. on Antennas and Propag., vol. 52, no. 8, pp. 1963-1969, Aug. 2004 [9] D. Chew, I. Morfis and S. Stavrou, “Quadrifilar helix antenna for MIMO system”, IEEE Antennas and Wireless Propag. Letters, vol. 3, pp. 197-199, 2004 [10] S. Ko and R. Murch, “Compact integrated diversity antenna for wireless communications”, IEEE Trans. on Antennas and Propag., vol. 49, no. 6, pp. 954-960, June 2001 [11] A. Khaleghi, A. Azoulay, J. Bolomey and N. RibièreTharaud, “Design and development of a compact WLAN diversity antenna for wireless communications”, Conf. JINA, Nov. 2004 [12] E. Rajo-Iglesias, O. Quevado-Teruel and M. PabloGonzales, “A compact dual mode microstrip patch antenna for MIMO applications”, IEEE Antennas and Propag. Inter. Symp., July 2006 [13] T. Svantesson, “An antenna solution for MIMO channels: the multimode antenna”, 34th Asilomar Conf., vol. 2, pp. 1617-1621, 2000 [14] J.R. James, P.S. Hall and C. Wood, “Microstrip antenna theory and design”, Institution of Electrical Engineers, 1981 [15] M. Mandal and S. Sanyal, “Reduced-length Rat-Race couplers”, IEEE Trans. on Microwave Theory and Tech., vol. 55, no. 12, pp. 2593-2598, Dec. 2007 [16] R. Meys and F. Janssens, “Measuring the impedance of balanced antennas by an S-parameter method”, IEEE Antennas and Propag. Magazine, vol. 40, no. 6, pp. 6265, Dec. 1998 [17] T. Milligan, “Parameters of a multiple-arm spiral antenna from a single-arm measurement”, IEEE Antennas and Propag. Mag., vol. 40, no. 6, pp. 65-69, Dec. 1998 [18] R. Vaughan and J. Andersen, “Antenna diversity in mobile communication”, IEEE Trans. on Vehicular Tech., vol. VT-36, no. 4, pp. 149-172, Nov. 1976 [19] K. Kalliola, K. Sulonen, H. Laitinen, O. Kivekäs, J. Krogerus, and P. Vainikainen, “Angular power distribution and mean effective gain of mobile antenna in different propagation environments”, IEEE Trans. on Vehicular Technology, vol. 51, no. 5, pp. 823-838, Sept. 2002. [20] K. Ogawa, S. Amari, H. Iwai and A. Yamamoto, “Effect of received power imbalance on the channel capacity of a handset MIMO”, IEEE Inter. Symp.PIMRC, pp. 1-5 Sept. 2007 [21] O. Klemp and H. Eul, “Diversity efficiency of multimode antennas impacted by finite pattern correlation and branch power imbalances”, Inter. Symp. ISWCS, pp. 322-326, Oct. 2007