Exact representation of antenna system diversity performance from input parameter description

f . . . . . . -5 OI B -10 ; a -15 -20 -25 -150 -75 0 75 150 mm Fig. 3 Predicted ond mensrrredpower distribution/or. 126 nmfhcol length orrq ui 10 GHz -predicted - -0- -measured t I I I I* -75 0 75 150 mm Fig. 4 Predicied and meosur.edpo,~,erdi.~iriburionfi,r 300 rnnr,focal Ien,qi/t urroy ai IO GHz -predicted ~ -0- -measured The ncw antenna has a significant size advantage over the previous focused beam solutions. For example. the same beam waist size was obtained with the 150 x 150 mm antenna array described here as that obtained with a spherical lens with 200 mm diameter illuminated by a standard X band hom antenna. In addition, the antenna array with a focused beam has a patentidl to provide advanced sensing options for microwave inspection applications. Acknodedgmenrs: This work was funded by the New Zealand Foundation for Research, Science and Technology. The authors thank K. J. Crcsswell and W. S. Holmes for their help and support. 14 Fehrubv 2003 0 IEE 2003 Electronic.< Letters Online No: 20030479 DO/: 10.1049/e1:20U30479 M. Bagosanovich (Indrrsirid Reseurch Lid, PO Bm 2225 Paraell, Auckland, New Zealrind) E-mail: [email protected] 4.G. Williamson (Departmenr of Electrical and Electronic Engineering. The Universit). of Auckland, Privote Bag 92019, Auckland. New Zealand) References 1 BOGOSANOVIC, M., WILLIAMSON, A.C., .rHAKUR. K.P, HOLMES. WS., and CRESSWELL. K.J.: 'A comparison ofthe systems for non-contact and nondestmctive namral product inspection'. 5th BEMA Conf., Rotorua, New ZealanJ March 2003 (accepted for publication) BOGOSANOVtC. M.: New Zealand Patent Application No. 52 1823, October 2002 GOODMAN. J.w: 'Introduction to Fourier optics' (Academic, New York, 19821 Exact representation of antenna system diversity performance from input parameter description S. Blanch, J. Romeu and I. Corbella A simplc formulation Io compute thc envelope correlation of an antenna divemiry system is dcrired. 11 is shown how to compute the envelope correlation hom the S-parameter descnplian of the antenna system. This approach has the advantage that it does not require the computation nor the measurement of the radiation panem of the antenna system. It also offers the advantage of providing a clca understanding ofthe effects ofmutual coupling and input match on the diversity performance of the antcnnii system. Introduction: Antenna diversity is acknowledgcd as onc of the techniques to increase spectrum efficiency in mobile communication systems. It is also recognised that mutual coupling of tho antenna degrades the performance of a diversity antenna system. Therefore antenna designers try to design antenna systems that minimise coupling between pons while mceting the input matching requirements. Following [I] the envelope correlation for a two-antenna system is computed as: ISS[FI(B.d)*~*(8.dj]dR12 JJIPl(0. In d)/*dflJJl~~VL I" 4jI2dn (1) 4n Pr = where E.(U, 4) is the field radiation panern of the antenna system when pan i is excited, and denotes the Hermitian product. To compute (I) it is necessary to know the mdiatian pattern of the antenna system and perform the numerical integrations. This is a cumbersomc process, whether it is done numerically OT experimentally Nevertheless this is the approach that is followed by most antenna designcrs [Z, 31. In [4] it is experimentally shown that the diversity antenna system performance can be determined from (I), mutual coupling measurements or direct envelope correlation measurement. In the following Section an exact expression to compute (I) from the S-parameter characterisation of the antenna system will bc derived. This approach has the advantage that it is not necessary to know the radiation panem of the antenna system, and that the explicit influencc of muhlal coupling and input match is revealed. =1 w bl f-- Fig. 1 General gevmetrpfor fwo-onfenno diverrity sy.~ienz ELECTRONICS LE77ERS Ist May 2003 Vol. 39 No. 9 705 Mathematical derivation: Consider the situation shown in Fig. 1 in which two antennas are driven by two generators at the same frequency. The antennas are not necessarily well matched and have nonzero mutual coupling. For a given point at co-ordinates (I, 0, 4) in the far-field region, the total radiated electric field is the sum of the contributions from each antenna: where '1 is the free-space wave impedance, k the wave number, D, the maximum directivity of antenna i and 610, 4) its normalised complex voltage pattern, which includes the effect of the other antenna termnated by the reference impedance Z,. Note that both pattems are referred to a common co-ordinate system and are defined in terms of the incident wave (ai and oz, respectively). The total powr radiated by both antennas is the integral of the power density over the whole space far i, j=l or 2. In these equations, the differential solid angle dn = dS/s is uscd. From the definition of the scalar product, it follows that C,= q. Equation (4) can be written in a more compact form as: P=a+Ca (7) where a is the column vector of a, and u2 and C is a 2 x 2 correlation matrix having (5) and (6) as elements. However, the radiated power should be equal lo the total power entering the two antennas. From S-parameter theory, this is: 2 2 i=l ,=I P = Ea, - b, = 8+8 - b+b = a+iI - S+S)a (8) being I the identity matrix and S the S-parameters defined in the input ports of the antennas. The symbol ' + ' indicates Hermitian transpose operation. Identifying this with (7), it follows that C = I ~ S+S which is equivalent to the two following conditions: antenna system input parameters and radiation pattems have been computed using MOM. It is clearly seen that both inethods provide exactly the same result. It is also interesting to note that mutual coupling alone does not provide a good estimate for the envelope correlation. Another simple application of (I I) is to evaluate the envelope correlation against operating frequency. In Fig. 3 the envelope correlation and the S-parameters for an orthogonal-fed square microstrip patch antenna is shown against frequency. Note that by using (11) the envelope correlation computation is straightforward from numerical simulation or laboratory measurement. On the contrary, the evaluation using (I) implies the computation or the measurement of the radiation patterns at each frequency. 0 -1 0 -20 m * -30 -40 -50 0 0.5 1 .o 1.5 2.0 2.5 separation between antennas. dlh Fig. 2 Envelope correlation and S-parumetrrsjor two collinear holf-wwr dipoles againsi their separation O1 -1 0 . . - - St1 parameter 0- - - St1 parameter . . --- -IO - . . -20 _.C' m 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 -50 ' 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 frequency. GHz Fig. 3 Envelope correlation and S-parameirrsfor ortltob.onol-fed square microsnip patch ontenna ugainrt Jkquency Therefore by considering (9) and (IO) the envelope correlation given by (I) can be exDressed in terms of the S-~arameters of the antenna system as: Applicution: As an example application, the envelope correlation for a two-antenna system formed by two collinear half-have dipoles has been computed following (I) and (I I). In Fig. 2 the results obtained by both methods are shown against the spacing between antennas. The Conclusion: The expression that has been derived can be applied to compute the envelope correlation of any two-port antenna diversity system. It provides a simple functional to he minimised in an optimisation procedure dcsign. It also shows that a certain set of simultaneous specifications such as muhlal coupling, input match and cross-polar radiation may be redundant and in certain cases incompatible. Finally, this expression providcs clear criteria in antenna design for minimising the envelope correlation. The expression can be easily cxtended to a multiple port antenna system, and can be applied in designing and assessing the diversity performancc of antennas in mobile communications and remote sensing. Acknowledgmenfs: This work has been partially supported by the Spanish Govemment through grant TIC 2001-26364-CO3-01, the EC 706 ELECTRONICS LETTERS 1st May 2003 Vol. 39 No. 9 through the project IST 2001-33055 and the Department d'Universitats, Recerca i Societat de la lnformacidn (DURSI) de la Generalitat de Catalunva. 0 IEE 2003 Elecrronics Letlers Online No: 20030495 Dol: IO. 1049/e1:200304Y5 S. Blanch, J. Romeu and I. Corbella (Electromugnetics & Photonics Engineering Group, Deportment qf Signol Themy and Comniuwicution.s. Universitot Politecnico de Catnlcmnya. c/Jordi Gimna, 1-3, MAdrrl D3, Campus Nord UPC, 08034 Barcelona, Spain) E-mail: [email protected] S. Blanch, J. Romeu and I. Corbella: Also with the Centre de Tecnalogia de Telecamunicacions de Catalunya (CTTC) 19 Fehruav 2003 References VAUGHAN. R.G., and ANDERSEX. J.B.: 'Antenna diversity in mobile communications', IEEE Trons. Eh. Techno/., 1987. 36. pp. 149-172 DIETRICH, c.B.. DIETZC. K., NEALS, R.J.. and STLIIZMAN. w.~: 'Spatial, polanration and panem diversity for widess handheld terminals', IEEE %om Antennas Pmpug, 2001.49, pp. 1?71-12UI JENSEN, M.A., and RAHMAT~SAMII. Y: 'Performance analysis Of antennils for hand-held IranscciveB using FDTD', IEEE Tmuns. Antennns Pmpag., 1YY4,42, pp. I 106-1 1 I3 KO. S.C.K., and MURCII. RD.: 'Compact integrated divenity antenna for wireless communications', IEEE Trons. Anfennos Pmpog., 2001, 49, pp. 954-960 Uniplanar PBG screens for forming antenna patterns C.R. Simovski and B. Sauviac The possibility of farming the widehand U-shaped panem of an antenna in thc Il-plane with rhe usc of a uniplanar phoionic bvndgap screen (UPPBGS) is studied. TW vmants of UPPBGS arc compared. The first is the known structure developed by the group ofT. Itoh, the second is ifs suggested modification (presenred hy the authors). It is shown that the modified stmc~re operates at IOWT frequencies than does the known S~NCIU~C (for the same cell rizc). htrodrrcrion: In modem microwwc tcchniques, printed circuit antennas are widely uscd. Generally thcsc antennas are positioned on the interface of a diclcctric layer with a metal ground plane. Often, one needs to make its thickness h very small compared fa the wavelength I. in free space. To obtain canstmctive interaction of the antenna with the substrate and not to spend the greater part ofenergy in exciting the lateral waves in the dielectric, it is possible to use high-impedance surfaces (HIS). The HIS is usually thought afas a resonant magnetic wall (MW) with h<<i/4 [I]. A uniplanar photonic bandgap screen (UPPBGS) representing a complementing screen with respect to the grid of metal Jerusalem crosscs (JC), which was suggested and studied by T. Iroh's group, found many applications. Of thcse, we consider the use of a UPPBG for shaping the antenna panern. It is easy to prow that B planar perfectly conducting structure cannot behave as a HIS on its own. To have the propenies of a HIS (MW) a UPPBGS must be associated with a metal ground plane. However. there are some cases when the sINc~re should not be impenetrable. Far example, the practical requirement can be to suppress the Iatcral radiation of the antenna, whereas the radiation is required in both upper and lower half-spaces (to form the %shaped pattem in the H-plane). In this case the UPPBGS can be applied alone since it suppresser the surface waves within rather wide frequency bands. It was shown in [2] that the moderate inductive surface impedance Z.? =jX, (where X, > 0 is the surface reactance) is preferable to divert the radiation of the horizontal antenna from the impedance planc over which the antenna is positioned. It concerns both the far-zone and nearzone of the antenna. When the surface reactancc is high compared to the free-space impedance X,>>il (the regime of MW). the total radiation of the given antenna current is maximal, but lateral radiation is significant and the pattern in the H-plane is close to the semi-circle. When X\->r, the total radiation is smaller but the latcral one is suppressed and both near-field and far-field panems are diverted from the plane 121. In this Letter we show that the suppression of the lateral radiation holds also for a complex surface impedance (the real pan of Z, describer the transmission of the electromagnetic waves through the impedance surface). The main difference with the case of -the purely inductive Z, (the case of HIS) is that the panem is 8-shaped. To obtain this kind of panem it is possible to use the known UPPBGS [3] as the impedance surface with complex surface impedance. In practice, suppressing the lateral waves is not sufficient for proper operatian of the radiating system. It must be efficient, of COUTSC. Therefore, we need to obtain constwctive interaction between the horizontal SOUKC and the UPPBGS. It is possible if X, is positive and high enough with rcspect to the surface resistance R,. Thus, there is a certain frequency band in which the UPPBGS 131 operates as required. Note, that the same consideration can be made for the source of TMwaves (vertical or horizontal magnetic antenna) when the required X, is, in this case, negative (the case of a capacitive UPPBGS). b Fig. I Unit cells o Unit cell ofknown smichlre (conventional JC) h Unit cell of suggertcd shLIcNre (modified JC) conventional JC normal reflection % a 0.2 -0.6 -1.0 -0.8 ~onvent~onal JC 2. 0.6 0.4 '... d 4.2 b -0.4 LR -0.6 -1.0 -o.au io 15 20 25 30 35 40 frequency, GHr b Fig. 2 Reflection coeflcient, and nonnalired surfice impedunce, for known UPPBGS [;I U Reflection coefficient 6 Nomali>cd surface impedance - Re(R) - Im(b) - ~ ~ Im(R) - ~ ~ Re(&) Band in which laferal radiation is efficiently suppressed is shown When the working frequencies are low, and the horizontal dimensions ofthe whole SINCture are restricted by a few centimetres, thc use of UPPBGSs becomes difficult. In this situation, the required grid period turns out to be rathcr high and can be comparable with the ELECTRONlCS LEmERS 1st May 2003 Vol. 39 No. 9 707