Smart Antenna Array Calibration Procedure Including Amplitude and Phase Mismatch and Mutual Coupling Effects

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1 Smat Antenna Aay alibation Pocedue Including Amplitude and Phase Mismatch and Mutual oupling Effects Kapil R. Dandeka, Hao Ling, and Guanghan Xu Univesity of Texas at Austin, Dept. of Elec. And omp. Eng. Engineeing Science Building 43 Austin, TX Phone: ABSTRAT This pape pesents a pocedue used to calibate a smat antenna aay to compensate fo channel amplitude and phase mismatch as well as mutual coupling effects between antenna aay elements. A theoetical basis fo this calibation pocedue in tems of the smat antenna mathematical model is given. Diection of Aival (DOA) analysis of data collected using the Smat Antenna Testbed at the Univesity of Texas at Austin is pesented to illustate the effectiveness of this calibation pocedue and quantify the impovement in system pefomance. It is shown that amplitude and phase mismatch effects have a much stonge impact on oveall system pefomance compaed to mutual coupling between aay elements. I. INTRODUTION Smat antenna technology will be an integal component of thid geneation cellula communications systems. Fully ealizing the potential of these systems equies effective aay calibation. Aay calibation is necessay to compensate fo vaious non-ideal aay effects including: Amplitude and phase mismatch between physical antenna element hadwae Amplitude and phase mismatch between element cabling Mutual coupling effects Towe effects Impefect knowledge of element locations In the liteatue thee ae geneally two kinds of calibation techniques. The fist type of method uses signals fom known diections tansmitted on-site to the antenna aay being calibated and then analyzes the aay output [-3]. onceptually, these techniques addess each of the above issues. Howeve, in an actual mobile envionment, it is vey difficult to appopiately place the calibation tansmitte because of unpedictable multipath effects. The second type of method [4,5] injects an equal phase signal to all of the channels of the antenna aay. While this does addess the cabling mismatch issues, it does not addess mutual coupling effects, antenna diffeences, towe effects, o uncetain senso locations. This pape motivates a pocedue that is used to calibate a smat antenna testbed and demonstates the effectiveness of this method in field measuements. This pocedue is an extension of the types of methods pesented in [4,5] with additional consideation added fo mutual coupling compensation and involves netwok analyze measuements and computational electomagnetic (EM) simulations. Futhe development of this method could also be used to conside antenna diffeences and towe effects, depending on the complexity of aay model used. The pape is oganized as follows. Section II contains the mathematical model fo antenna aay output with and without calibation. Section III descibes the method used to solve fo the model paametes given in Section II. Section IV contains a desciption of the envionment in which field measuements wee taken. Section V contains expeimental esults illustating the pefomance of the descibed calibation method and Section VI concludes the pape. II. ARRAY MODEL We fist develop the theoetical M-antenna aay model and descibe how non-ideal effects can be modeled. The antenna aay elements ae theoetically located at (x i, y i ), i M. A steeing vecto chaacteizes the elative phase esponse of each antenna aay element to an incident signal with DOA

2 θ fom a single mobile use. Equation () epesents the basic fom of an ideal steeing vecto. exp( jk(x cosθ + y sin θ)) exp( jk(x 2 cosθ + y 2 sin θ)) () a U ( θ) = exp( jk(x cosθ + y sin θ)) 3 3 exp( jk (x cosθ + y sin θ)) M M In the above equation, k is the wavenumbe of the incident electomagnetic adiation that can be expessed as 2π/λ. Note the implicit assumptions of this model do not take into account any of the nonideal aay effects given in Section I. Specifically, the equal gain of each of the channels shows that amplitude and phase mismatch between channels is not consideed. Also, the model of the steeing vecto in Equation () does not include any tems indicating the etansmission of signal components fom one aay element to anothe (i.e. mutual coupling). Finally, the model assumes that the element locations (x i, y i ) ae known exactly. If the actual antenna element locations ae petubed by a significant electical length, the steeing vecto can be advesely affected. A distotion matix, (θ), is geneally used to encapsulate all of these non-ideal effects. In the liteatue, this matix is estimated fom collected measuement data [3,6] and is applied to the equation of the ideal steeing vecto fom of () to develop a compensated steeing vecto. a ( θ) = ( θ a ( θ) ) The distotion matix is geneally consideed to be independent of angle. Thus, methods using this compensation technique do not coect fo towe effects and geneally assume the aay elements to be vey simila, if not identical. Methods using a distotion matix geneally conside sepaately the issue of amplitude and phase mismatch between aay element cabling. To take this into account, we apply the M-vecto g that contains the complex values equied to compensate fo this mismatch and solve fo the eal steeing vecto a ( θ) R (whee the subscipt i indicates the i th vecto component) which can be used in DOA analysis: R,i U ( θ) = g a ( θ) i, i (2) a (3) In Section III, we descibe the pocedues used to solve fo g and ( θ) a and thus detemine an estimate fo the actual aay steeing vecto. III. ALIBRATION PROESS A. able Measuements Figue shows a diagam illustating how the vecto g is detemined. Thee ae two sets of elative amplitude and phase infomation that make up this detemination. The fist set coesponds to the long cabling leading to the antenna aay itself on the cellula towe (efeed to as aay cables in Figue ). The second set coesponds to the combined effect of the cables used to connect the basestation to the aay cables (efeed to as basestation cables in Figue ) and the vaying impedance seen looking into the pots of the basestation hadwae. Aay ables alibation Splitte RF Signal Geneato Basestation ables Basestation Figue Oveview of able alibation Pocess It is elatively staightfowad to detemine the elative amplitude and phase esponse of the aay cables using a netwok analyze. We efe to this vecto as l and it only needs to be detemined once fo each set of aay cables. This vecto contains the elative amplitude and phase esponse of each of the cables with espect to a given efeence cable (that has a 0 as its coesponding enty in the l vecto). It is slightly moe difficult to detemine the elative amplitude and phase esponse of the basestation cables and RF impedance looking into the vecto) since this measuement must be made evey time the basestation is poweed up. Again, this measuement is made with espect to a efeence channel. Using a powe splitte basestation (efeed to as the s with a known elative amplitude and phase esponse, p, (detemined via netwok analyze) an RF signal

3 fom a signal geneato is injected into the basestation cables. The esulting data etuned by the basestation nomalized by the efeence channel value ae the elements of the s vecto. g is then detemined by: l s i i g i = (4) pi The ight hand side of Equation (4) contains the elative amplitude and phase mismatch of the aay cables and basestation cables/hadwae. The effect of the powe splitte must be emoved since the splitte was included in the measuement of the s vecto but is absent fom nomal system opeation. The EM package used in this study is NE (Numeical Electomagnetics ode), which was oiginally developed at the Lawence Livemoe Laboatoy [9] to pefom moment method analysis to model the inteaction between electomagnetic fields and wie segments. A wie segment model of an abitay geomety antenna aay can be specified in an input file to NE. Figue 2 shows the model of a single antenna aay element used in simulations. An aay of these elements ae placed accoding to aay geomety, and incident signals ae launched, one at a time, fom all diections. The aay output vecto fo each of these incident signals is ( θ) a. IV. EXPERIMENT SETUP The aay consideed in this study is a unifom cicula antenna aay (UA) opeating at.8 GHz. Field measuements wee made at the Pickle Reseach ampus at the Univesity of Texas at Austin. To educe multipath signal components, measuements wee made in a field with buildings fa off in the distance. An RF signal geneato attached to a dipole antenna was used to epesent a mobile use. Measuements wee made with this mobile use at seveal diffeent locations elative to the basestation. DOA analysis of the eceived data is made with the Multiple Signal lassification (MUSI) algoithm [0]. V. RESULTS A. Pe-alibation Spatial Spectum Figue 2 Antenna Aay Element Model 3 B. EM Simulations Thee ae two diffeent ways to solve fo ( θ) a. The fist is to estimate the matix algoithmically in Equation (2) as is done in [3] and then use this estimate to detemine ( θ) EM simulations [8] to detemine a ( θ) a. An altenative method [7] uses diectly. Figue 3 MUSI Spatial Spectum No alibation Figue 3 shows the MUSI spatial spectum due to a mobile use located at 80 elative to the basestation. As seen by the above plot, the lobes in the nomalized spatial spectum do not coespond at all to the signal of the desied mobile use. In fact, the lobes 0

4 in this spatial spectum do not coespond to any known signal o multipath component, which is not supising due to the lack of any kind of aay calibation. B. Amplitude and Phase Mismatch ompensation Figue 4 shows the MUSI spatial spectum of Figue 3, with compensation added fo aay cables and basestation cables/hadwae, as discussed in Section III.A. As this figue shows, the mobile use at 80 can now be esolved easily. Howeve, again thee is a lobe at 280 that does not coespond to any known signal component o multipath Figue 4 MUSI Spatial Spectum able alibation and phase mismatch due to aay cables and basestation cables/hadwae, as well as calibation including mutual coupling effects. While thee is still an extaneous lobe in this Figue, it is not as lage as the lobes in Figues 3 o 4, which could easily be counted as multipath signal components fom diffeent DOAs. In addition, compaison of Figue 4 and 5 shows a naowe peak in Figue 5 that coesponds to the DOA of the desied mobile use. This geneal esult was obseved in all tested cases. VI. ONLUSIONS The esults of this pape quantify the effects of a multi-step smat antenna calibation pocess. As shown by noting the elative impovement fom Figues 3 and 4 and the impovement fom Figues 4 and 5, it is clea that amplitude and phase mismatch effects in aay cables and basestation cables/hadwae ae much moe significant than mutual coupling effects. This is not to imply that mutual coupling calibation is not necessay since Figue 5 clealy shows that lobes that could have been mistaken fo multipath signal enegy wee effectively educed. In addition, mutual coupling calibation makes the peak in the spatial spectum coesponding to the desied mobile use naowe. The pocedue pesented in this pape is impotant because it does not equie expensive and involved site-specific calibation. The netwok analyze measuements can all be made elatively easily and the EM simulations can be pefomed off-line using the fee and well-accepted package NE. The combination of these two steps allow fo vey effective aay calibation. AKNOWLEDGEMENTS This wok is suppoted by the Texas Highe Education oodinating Boad unde the Texas Advanced Technology Pogam and by the Office of Naval Reseach unde contact no. N Figue 5 MUSI Spatial Spectum Full Aay alibation Applied. Mutual oupling ompensation Figue 5 displays the esult of adding the mutual coupling compensation discussed in Section III.B. to the spectum shown in Figue 4. Specifically, the esults in this figue includes calibation fo amplitude 0 REFERENES [] Y. hen, A. hang, and H. Lee, Aay alibation Methods fo Senso Position and Pointing Eos, Micowave and Optical Technology Lettes, vol. 26, pp , [2] B. Kang, H. Subbaam, and B. Steinbeg, Impoved Adaptive-Beamfoming Taget fo Self-alibating a Distoted Phased Aay, IEEE Tansactions on Antennas and Popagation, vol. 38, pp , 9.

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