mode-based beamforming arrays for miniaturized platforms

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 1, JANUARY 2009 45

Mode-Based Beamforming Arraysfor Miniaturized Platforms

Lap K. Yeung, Member, IEEE, and Yuanxun E. Wang, Member, IEEE

Abstract—In this paper, a new and practical mode-based arrayconcept is proposed. The key principle of this mode-based ap-proach is the use of orthogonal radiation modes existing in highlycoupled arrays as individual information channels so as to avoidmutual coupling and correlation. Consequently, mode-based ar-rays can be very compact in size but without suffering undesiredeffects such as impedance mismatch or pattern distortion. Whileproviding a general theoretical discussion for this mode-basedapproach, a practical application example, namely, a compactelectronically scanning array module is developed. With a suitablesignal combining algorithm, the module is capable of formingand full 360 scanning of a high-gain radiation pattern in theazimuth plane. An experimental prototype has been fabricated ona traditional printed circuit board to validate the practicabilityof the proposed concept. Measurement results obtained are ingood agreement with theoretical simulations, showing promisingpotential of mode-based array modules for modern miniaturizedwireless devices.

Index Terms—Antenna arrays, array signal processing, beam-forming systems, mutual coupling.

I. INTRODUCTION

I N RECENT years, miniaturization techniques for antennaarrays have drawn a great amount of attention owing to the

ever-increasing interest in the multiple-input–multiple-output(MIMO) wireless communication architecture [1], whichpromises significant improvements on both communicationcapacity and diversity, for compact mobile platforms. In ad-dition, traditional smart antenna and phased array systems[2] are continuing in demand of array modules with betterperformance and lower cost in smaller and lighter formats.However, a major limitation of the conventional approach forthese multiantenna systems is that the array element spacing isusually around to avoid mutual coupling. Hence, there is aserious size concern which prevents these systems from beingimplemented in today’s small-size handheld electronics withwireless communication capability.

Traditionally, the design of compact antenna arrays is com-plicated due to the fact that array elements are not independentof each other. Instead, they interact electromagnetically through

Manuscript received May 29, 2008; revised August 29, 2008. First publishedDecember 12, 2008; current version published January 08, 2009. This workwas supported in part by the National Science Foundation under Grant ECCS-0725929.

The authors are with the Electrical Engineering Department, Univer-sity of California at Los Angeles, Los Angeles, CA 90095 USA (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2008.2008944

what is called mutual coupling. In fact, in a strong coupling en-vironment, the elements in an array can sometimes be dramat-ically different from their isolated counterparts in terms of op-erating frequency, bandwidth, and radiation pattern. A consid-erable amount of research has been devoted in the past to studythe impact of mutual coupling on multiantenna systems, espe-cially for MIMO-based systems [3]–[6]. In general, it is foundthat the resulting impact is often undesirable, including reduc-tion in capacity due to channel correlation and reduction in gaindue to impedance mismatch.

To overcome this problem, researchers have proposed tech-niques [7]–[12] to decouple closely spaced antennas using amultiport passive network. Furthermore, it has been proven the-oretically [8] that the capacity of a multiantenna system withcoupling and correlation effects can be fully exploited by usingan optimum lossless matching network. Recently, a mode-basedapproach [13]–[17] for closely spaced arrays has been proposedfor both beamforming and MIMO applications. It makes use ofa mode decomposition network (MDN) to perform the decou-pling and offers several major advantages. First, the MDN is an-tenna element independent as long as the array symmetric con-dition is satisfied. Second, in contrast to the intrinsic narrow-band isolation of the transmission-line and capacitive decou-plers, the isolation between different decoupling ports is broad-band. Third, this mode-based approach can readily be extendedonto many other array configurations with great numbers or dif-ferent orientations of antenna elements.

This paper focuses on the mode-based technique for thebeamforming and scanning operation. A compact four-antennaarray module is designed. It consists of a passive MDN, threematching networks and four monopoles of spacing. Asuitable signal combining formulation is also developed sothat the module is capable of forming and full 360 scanningof a high-directivity radiation pattern. While providing thebasic theoretical background for the mode-based technique,an electronically scanning experiment has been carried outon a prototype module, which is fabricated on a finite-sizeprinted circuit board (PCB), to demonstrate the feasibility ofthe technique.

II. THEORY

A. Orthogonal Radiation Modes

Consider a circular array of four identical quarter-wavelengthmonopoles that are parallel to each other along the -axis, as de-picted in Fig. 1. The spacing between two adjacent monopolesis assumed to be small ( in this example) to allow strongcoupling among all monopoles. It is further assumed that each

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46 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 1, JANUARY 2009

Fig. 1. Circular array of four monopoles with independent sources.

monopole is connected to an independent source so as its excita-tion can be controlled separately. For the proposed mode-basedtechnique, instead of treating each antenna element as a separateentity, the whole array is treated as one single multiport net-work. Hence, mutual coupling effects are automatically takeninto consideration

To simply our analysis, a conventional multiport circuitmodel is used to characterize the array. Here, a four-port scat-tering matrix taking advantage of the array symmetry is usedand has the form of (see the Appendix)

with (1)

where and are vectors of power waves going into andcoming out from the antenna ports. By performing the eigen-value decomposition on the matrix, it can be written as

(2)

where is a diagonal matrix containing all eigenvalues ofis an orthonormal matrix consisting of the corre-

sponding eigenvectors, and is the matrix inverse of .Due to the unique symmetric feature of the matrix, the or-thonormal matrix is real and is given by

(3)

Now, if we define a new incoming power wave vector as, and a new outgoing power wave vector as ,

we can rewrite (1) as

(4)

According to (4), it is seen that the array is decoupledin the sense that the four newly defined excitation modesor eigenmodes (given by

Fig. 2. Directivity patterns of the four eigenmodes. (a) Mode 1, (b) Mode 2,(c) Mode 3, and (d) Mode 4 (and their corresponding excitations).

and ), donot interfere with each other because of the diagonal feature of

. This is also true for their corresponding radiation patterns.In other words, given the th and th eigenmode patterns as

and , we have the following orthogonal prop-erty:

for (5)

which leads to no mutual coupling and zero spatial correla-tion at the full angular spread scenario (signals coming fromall directions). Therefore, if we can independently control theseeigenmodes, a total of four radiation information channels canbe utilized for transmission and reception. To excite these fourorthogonal radiation modes, power waves fed to the four an-tenna ports should be equal to the four column vectors of .For example, the first eigenmode can beobtained by having , whichstands for an equal amplitude and phase excitation of all antennaports. These excitations and their corresponding full-wave sim-ulated directivity patterns are shown in Fig. 2. In order to havean intuitive and simplified understanding of these eigenmodes,a somewhat simplified analysis is carried out by approximatingthe monopoles with infinitely long current wires.

Given that the cylindrical coordinates of the four currentwires as and , theelectric field with the condition of can be expressed as

(6)

where and are the th-order Bessel function of thefirst kind and Hankel function of the second kind, respectively,and the “ ” signs represent the excitation phases for the fourantennas.

YEUNG AND WANG: MODE-BASED BEAMFORMING ARRAYS FOR MINIATURIZED PLATFORMS 47

Fig. 3. Wave impedances of the four eigenmodes.

By retaining only the dominant term, the field expression foreach of the eigenmodes can be approximated by

(7a)

(7b)

(7c)

(7d)

Clearly, these functions satisfy the inner product relationshipdefined in (5) and are, thus, orthogonal to each other. They canthus be used as individual information channels so as to reducemutual coupling and correlation. However, there is a major lim-itation, which should be pointed out clearly. It is shown that(see the Appendix) the reduction in element spacing results insignificantly increased radiation quality factors of the higherorder modes. This is also verified from Fig. 3 that the wave im-pedances of the higher order modes have their realparts much smaller than their imaginary parts for small elementspacing. This will lead to higher order modes that may not beusable if the element spacing is too small. For our current anal-ysis, the third eigenmode has little practical use at less thanspacing and will not be considered further.

B. MDN

In order to transmit/receive signals using those radiationeigenmodes, the antenna ports should be excited/combinedaccording to the eigenvectors listed in (3). In this research, apassive MDN for circular arrays of four identical antennas isproposed for such purpose. Fig. 4 shows the schematic diagramof the proposed MDN. The network consists of four 180hybrids connected in a specific way. It decomposes the foureigenmodes by means of separating them to four individualsignal ports that are used for both transmission and reception.For example, signals going into or coming out from the firstport (Port- ) will be radiated or captured by the array throughMode 1. Mathematically, this decomposition characteristic of

Fig. 4. MDN for four-antenna circular arrays. The four ports are theoreticallyisolated from each other.

the network can be understood from its scattering parameterformulation.

By considering power waves going into one side of the MDNand coming out from the other, we have

(8a)

and

(8b)

Notice that the orthonormal matrix appears in the aboveexpressions. When the multiport array scattering model is cas-caded to the MDN, the overall matrix equation is

(9)

which has exactly the same form as (2) and, thus, offers inde-pendent access of the eigenmodes through the four signal ports:Port- , Port- , Port- , and Port- . This, in turn, makesthe use of eigenmodes for MIMO or beamforming applicationspractical. It is important to point out that the MDN must givea real matrix so that (9) is indeed the process of eigenvaluedecomposition.

C. Beamforming Operation

As the signal ports are isolated from each other, indepen-dent matching and access of the modes become possible. Con-sequently, a maximum directivity (or gain because the ports arematched) pattern with 360 scanning capability can be achieved


Fig. 5. Mode-based beamforming system.

by simply combining Modes 1, 2, and 4 according to the fol-lowing mathematical relationship:

with (10)

where and are the power ratios for signals feeding intoPort- , Port- , and Port- , respectively, and and

are, respectively, the directivities associated with these threeports at the azimuth angle where the resulting radiation beamwill be pointing to. To see why this is the case, we first let thetotal input power to the array module be constant . Now, as-suming the power going into or coming out from Port- is

, for Port- is , and for Port- is, where should be equal to 1. The total com-

bined directivity (after proper phase adjustments) should then be

(11)

Using the Cauchy–Schwarz inequality, we have

(12)

which attains its maximum when (10) holds. From (7), we seethat there is a sine–cosine relationship between the fields ofModes 2 and 4. Since is proportional to the field strength,we can conclude that the maximum combined directivity is con-stant over the azimuth angle and, therefore, the 360 scanningis possible.

Fig. 5 depicts the schematic diagram for a mode-basedbeamforming system during transmission. The input signal isproperly gain and phase adjusted before feeding into each arraymodule’s port. After an initial calibration, a 90 wide scanningis possible by only adjusting the gain parameters according to(10). Switching to a different 90 quadrant can be achieved byadding extra 180 to one or more phase shifters.

III. EXPERIMENTAL ARRAY MODULE

An experimental prototype array module with elementspacing consists of four monopole antennas, an MDN,and three matching networks has been fabricated and tested toverify our proposed concept. For convenience, the MDN and

Fig. 6. (a) PCB layout and (b) actual prototype with an extended ground planeof the compact antenna array module.

matching networks are fabricated together on microstrip on asingle piece of PCB with the monopole antennas soldered on itseparately. Fig. 6 depicts the PCB layout and actual prototypeof the prototype module operating at 2.45 GHz. The matchingnetworks, MDN and monopole antennas are clearly indicatedon the layout. Several key features about this module are worthbeing mentioned. Firstly, the MDN is implemented by four 90hybrids rather than four 180 hybrids, as described in Section II.This particular configuration of the MDN does not need anycrossover connections and thus leads to a simple single-layerPCB implementation. However, in order to provide the missing90 phase shift, each hybrid requires a 90 transmission lineconnected at one of its ports. This inevitably limits the networkbandwidth. Secondly, matching networks are used only atPort- , Port- , and Port- , but not Port- of the module.As mentioned earlier, Mode 3 excited from Port- has a veryhigh radiation quality factor and is not considered in this work.Finally, a finite-size ground plane of 128 mm 128 mm isused. In this circumstance, the actual eigenmode patterns willbe different from those obtained by using ideal monopoles,especially in the elevation plane ( -plane).

Measured return losses of the signal ports and isolationsamong them are shown in Fig. 7. A 13-dB return loss at the


Fig. 7. Measured scattering parameters of the module. More than 10-dB returnloss has been achieved for each transmitting/receiving port. In addition, isolationbetween any two ports is less than �15 dB.

operating frequency of 2.45 GHz has been achieved for each ofthe signal ports. In addition, isolation between any two ports isin average less than 16 dB. These numbers indicate that mostof the incident energy is dissipated in terms of radiation andohmic losses. It is thus expected that the measured eigenmodegain patterns should be close to their corresponding directivitypatterns. The operating bandwidths in this case are limitedby the MDN and matching networks rather than the intrinsicradiation quality factors.

The measured - and -plane radiation gain patterns forMode 1, Mode 2, and Mode 4 are depicted in Fig. 8. The gaincurves are obtained through power measurements with refer-ence to the standard gain horn. Here, the maximum gain foreach mode in the -plane occurs at around 40 in elevation

because of the finite-size ground plane effect. Ac-cording to these plots, the measured -plane gain patterns havesimilar characteristics to the simulated directivities shown inFig. 2. In comparison to the directivities of 2.8 dBi for the firstmode and 4.1 dBi for the second and fourth modes, the measuredmaximum gains for them are, respectively, 1.8 and 3.8 dBi. It isinteresting to see that the measured gain at has a valuegreater than 4.1 dBi because of the shielding effects from theSMA connectors. In addition, their measured radiation efficien-cies are approximately 75%, 77% and 81%, respectively. Thesevalues are obtained by integrating the measured 3-D gain pat-terns as

(13)

IV. BEAMFORMING AND SCANNING EXPERIMENT

The setup shown in Fig. 9 is used to demonstrate themode-based pattern scanning operation by using the prototypearray module. In this experiment, a single 2.45-GHz tone iscontinuously generated and sent out from the RF source. Thetransmitted signal is received by the module under test, whichis connected to three individual and identical RF processing

Fig. 8. Measured eigenmode gain patterns. The top and bottom graphs de-pict the�- and �-plane patterns, respectively, for various orthogonal radiationmodes.

Fig. 9. Experimental setup for demonstration of the mode-based pattern scan-ning operation.

chains at Port- , Port- , and Port- . The output signalsfrom these ports are then amplified and shifted down to ap-proximately 10 MHz before being sampled and captured by adigital oscilloscope. As the three RF chains are not identicalin practice, signals going through them may undergo differentlosses and delays. To calibrate the system, a standard antennaof known gain is used as a reference. Data captured from thechains based on the reference antenna are then compared toobtain the loss and delay for each channel so that adjustmentscan be made accordingly.

During the measurement process, the module under test isundergoing a complete 360 revolution in the azimuth planewhile data is being captured at every 10 interval. Consequently,


Fig. 10. Measured patterns steered towards various angles in the azimuth plane.

there are in total 36 sets of measured data. Forming a high-gainpattern oriented towards a particular direction can be done bycombining signals from the three chains according to the max-imum gain combining technique. The first step is to calculate thepower for each received signal at a particular direction whichwe would like the resulting pattern oriented to. Assuming theseresults are and . Signals at all 36 different azimuthangles are then combined in the following way:

(14)

Finally, the power of the combined total signal at each of the 36azimuth angles is calculated. The calculated results can be usedto obtain the radiation pattern. Fig. 10 shows the radiation gainpatterns with pointing directions of 90 , 120 , 150 , and 180in the azimuth plane. It is expected that the combined gain at 90or 180 should be around 4.8 dBi based on the full-wave simula-tion. According to the patterns shown in Fig. 10, the gain valuesat these two directions are around 4.4 dBi, which is 0.4 dB lessthen the expected value. In addition, the maximum combinedgain of around 6.9 dBi is achieved at the elevation plane, asshown in Fig. 11.

V. CONCLUSION

A practical mode-based array approach for smart antennasystems has been demonstrated. In this approach, orthogonal

Fig. 11. Measured maximum achievable combined gain in the elevation plane.

radiation modes that are eigenmodes of highly coupled arraysare utilized as independent information channels to avoid mu-tual coupling and correlation, resulting in much more compactarrays, but without suffering impedance mismatch and patterndistortion. Comparing with the traditional array approach,mode-based array modules can be much smaller in size and bemore readily integrated into miniaturized handheld devices. Ithas also shown that the ultimate limit of the miniaturization isthe high radiation quality factors associated with higher ordereigenmodes at small array spacing that limits their usefulness.

A compact four-monopole array module with one-tenth ofthe operating wavelength element spacing, including matching


Fig. 12. Equivalent circuit models for the four radiation eigenmodes.

networks and the MDN, has been fabricated. The eigenmodesfor this particular module have been clearly seen in the exper-imental measurements. Software-based beam forming experi-ments have been carried out. A full 360 mode-based scanningoperation has been demonstrated, which provides a strong sup-port for the feasibility of the proposed approach for many clas-sical as well as new smart antenna applications.

APPENDIX

Equation (1) can be obtained by realizing that the array hasidentical and circularly arranged antenna elements (see Fig. 1).Under this circumstance, each element port has the same valueof power reflection . In addition,couplings between two adjacent elements are the same

. Therefore, if we use these conditions on thegeneral scattering matrix of

(15)

we then have the scattering matrix of the form as (1).We can define the normalized wave impedance for the eigen-

modes in the usual way and which has a general expression as

(16)

Using the recurrence property of the Hankel function, (16)can be viewed as an input impedance of an equivalent ladderLC network. The equivalent circuits representing the four eigen-modes are shown in Fig. 12.

For the first mode , the equivalent circuit componentvalues and fundamental radiation quality factor ( ) limit can bederived in a way similar to [18], [19], which are given by

(17)

(18)

(19)

where is the smallest possible radius of a cylinder whichcan completely enclose the wire array. On the other hand, thearray operating in the second and fourth modes hascircuit component values of and . In addition,the fundamental limit is calculated as

(20)

When comparing with Mode 1, these two modes have a muchhigher limit so that they are inherently narrowband. At

, they differ approximately by a factor of 5.6. Obviously, it isclear that the third mode has an even higher limitsuch that it has little practical use.

REFERENCES

[1] M. A. Jensen and J. W. Wallace, “A review of antennas and propagationfor MIMO wireless communications,” IEEE Trans. Antennas Propag.,vol. 52, no. 11, pp. 2810–2824, Nov. 2004.

[2] B. D. Van Veen and K. M. Buckley, “Beamforming: A versatile ap-proach to spatial filtering,” IEEE ASSP Mag., vol. 5, no. 2, pp. 4–24,Apr. 1988.

[3] J. W. Wallace and M. A. Jensen, “Mutual coupling in MIMO wirelesssystems: A rigorous network theory analysis,” IEEE Trans. WirelessCommun., vol. 3, no. 4, pp. 1317–1325, Jul. 2004.

[4] C. Waldschmidt, S. Schulteis, and W. Wiesbeck, “Complete RFsystem model for analysis of compact MIMO arrays,” IEEE Trans.Veh. Technol., vol. 53, no. 3, pp. 579–586, May 2004.

[5] T. Svantesson and A. Ranheim, “Mutual coupling effects on the ca-pacity of multielement antenna systems,” in IEEE ICASSP, May 2001,pp. 2485–2488.

[6] H. J. Chaloupka and X. Wang, “On the properties of small arrays withclosely spaced antenna elements,” in IEEE AP-S Symp., Jun. 2004, pp.2699–2702.

[7] J. B. Andersen and H. H. Rasmussen, “Decoupling and descatteringnetworks for antennas,” IEEE Trans. Antennas Propag., vol. AP-24,no. 6, pp. 841–846, Nov. 1976.

[8] J. W. Wallace and M. A. Jensen, “Termination-dependent diversity per-formance of coupled antennas: Network theory analysis,” IEEE Trans.Antennas Propag., vol. 52, no. 1, pp. 98–105, Jan. 2004.

[9] H. Steyskal and J. S. Herd, “Mutual coupling compensation in smallarray antennas,” IEEE Trans. Antennas Propag., vol. 38, no. 12, pp.1971–1975, Dec. 1990.

[10] J. P. Daniel, “Reduction of mutual coupling between active monopoles:Application to superdirective receiving arrays,” IEEE Trans. AntennasPropag., vol. AP-25, no. 6, pp. 737–741, Nov. 1977.

[11] S. Dossche, S. Blanch, and J. Romeu, “Optimum antenna matching tominimize signal correlation on a two port antenna diversity system,”Electron. Lett., vol. 40, no. 19, pp. 1164–1165, Sep. 2004.

[12] H. J. Chaloupka, X. Wang, and J. C. Coetzee, “A superdirective 3-el-ement array for adaptive beamforming,” IEEE Microw. Opt. Technol.Lett., vol. 36, no. 6, pp. 425–430, Mar. 2003.

[13] S. Dossche, S. Blanch, and J. Romeu, “Three different ways to decor-relate two closely spaced monopoles for MIMO applications,” in IEEEInt. Wireless Commun. Appl. Comput. Electromagn. Conf., Apr. 2005,pp. 849–852.

[14] X. Wang and Y. E. Wang, “A ‘zoom-in’ scanning array for wirelesscommunications,” in IEEE Radio Wireless Symp., Jan. 2007, pp.491–494.

[15] T. I. Lee and Y. E. Wang, “A planar multipolar antenna for MIMOapplications,” in IEEE AP-S Symp., Jun. 2007, pp. 2429–2432.


[16] T. I. Lee and Y. E. Wang, “A mode-based supergain approach withclosely coupled monopole pair,” in IEEE AP-S Symp., Jun. 2007, pp.5901–5904.

[17] T. I. Lee and Y. E. Wang, “Mode-based beamforming with closely-spaced antennas,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007,pp. 1723–1726.

[18] L. J. Chu, “Physical limitations of omni-directional antenna,” J. Appl.Phys., vol. 19, pp. 1163–1175, 1948.

[19] J. S. McLean, “A re-examination of the fundamental limits on the radi-ation� of electrically small antennas,” IEEE Trans. Antennas Propag.,vol. 44, no. 5, pp. 672–676, May 1996.

Lap K. Yeung (S’00–M’02) received the B.Eng. de-gree in electrical and information engineering fromthe University of Sydney, Sydney, Australia, in 1998,the M.Eng. degree in electronic engineering fromthe Chinese University of Hong Kong, Shatin, HongKong, in 2002, and is currently working toward thePh.D. degree at the University of California at LosAngeles (UCLA).

During 1999, he was with the CommonwealthScientific and Industrial Research Organization(CSIRO), Sydney, Australia, where he was a Re-

search Engineer involved in the numerical modeling of different antenna

structures. From 2003 to 2006, he was with the Chinese University of HongKong, where he is involved in various LTCC multichip-module (MCM)designs and the development of numerical algorithms for analyzing multilayerembedded RF modules.

Yuanxun E. Wang (S’96–M’99) received the B.S.degree in electrical engineering from the Universityof Science and Technology of China (USTC), Hefei,China, in 1993, and the M.S. and Ph.D. degrees inelectrical engineering from the University of Texasat Austin, in 1996 and 1999, respectively.

From 1999 to 2002, he was a Research Engineerand Lecturer with the Department of ElectricalEngineering, University of California at Los Angeles(UCLA), prior to joining the faculty. In November2002, he became an Assistant Professor with the

Electrical Engineering Department, UCLA. He is a technical consultant inradar and microwave systems for several companies. He has authored orcoauthored over 100 refereed journal and conference papers. His research isin the general area of microwave systems with an emphasis on antennas andpower amplifiers. His research interests feature the fusion of signal-processingand circuit techniques into microwave system design for novel architecturesand circuit configurations.

mode-based beamforming arrays for miniaturized platforms

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