Compact Multi-user Wideband MIMO System using Multiple-Mode Microstrip Antennas

Transcription

1 Copact Multi-user Widebad MIMO Syste usig Multiple-Mode Microstrip Ateas Aitav Mukherjee ad Hyuck M. Kwo Departet of Electrical ad Coputer Egieerig, Wichita State Uiversity 84. Fairout, Wichita, KS 6726 USA Eail: {axukherjee, Abstract A coplete ultiple-iput ultiple-output (MIMO) couicatio syste with orthogoal frequecy-divisio ultiplexig (OFDM) based o ultiple excitatio odes for a sigle circular icrostrip atea is itroduced. Traditioal diversity techiques such as spatial diversity by eas of a liear atea array or polarizatio diversity by eas of a crosspolarized atea array ay prove to be usuitable i the case of severe restrictios o atea size ad spacig. A icrostrip atea eployig ultiple odes is foud to be coparable to traditioal atea arrays i a urba icro-cell settig as defied by the Third-Geeratio Partership Project (3GPP) at a uch lower cost i ters of size ad spacig. The throughput perforace ad sigal detectio of ultiode ateas i flat ad frequecy-selective fadig eviroets is exaied subsequetly. Idex Ters Atea radiatio patters, MIMO, ultiple-ode atea, receptio diversity. I. ITRODUCTIO THE usage of ultiple-iput ultiple-output (MIMO) systes at both the base statio (BS) ad the obile statio (MS) has received widespread attetio i the past decade for the purposes of vastly iproved chael capacity []. However, the traditioal MIMO approach of usig a liear atea array with ultiple eleets separated by halfwavelegth or ore poses various ipleetatio probles. Fittig several atea eleets oto a sall MS hadset with the correspodig feed requireets is a challege due to the severe restrictios o space ad aesthetics. Furtherore, it is expesive to calibrate ad aitai atea arrays with ay atea eleets. Alterative diversity solutios such as polarizatio diversity [2]-[3] also suffer fro siilar ipediets, though to a lesser degree. A diversity echais based upo the differet far-field radiatio patters of higher-order atea odes is a alterative that should be cosidered to resolve the probles stated above. Deerle ad Wiesbeck ipleeted this for of patter diversity usig a sigle bicoical atea eleet i [4] ad showed that Spatial Divisio Multiple Access (SDMA) was achievable. Svatesso [] exteded ultiode ateas (bicoical ad icrostrip patch) to iclude MIMO applicatios ad deostrated that ultiode ateas offer characteristics siilar to those of a uifor liear array (ULA) by usig oly a sigle atea eleet. However, [] used a rough approxiatio of the far-field patters of a circular icrostrip atea give i [4] by eglectig the aziuthal copoet. The case of a two-eleet array of collocated ultiode circular patch ateas was exaied i [6], but cosidered oly oe higher-order ode geeratio at a tie o each eleet. The odeled eviroet was the idoor clustered 82. odel where due to collocatio, spatial diversity was also ot a factor. Additioally, possible MIMO applicatios are cosidered i [4], [] ad [6] fro the perspective of achievable receive diversity gai without ay ephasis o the proble of detectio ad separatio of user data streas at the receiver. The chael odel used i [] ad ay other articles o MIMO systes is a siplistic oe-rig or two-rig odel which provides overly optiistic chael capacity results whe copared with experietal results [8], [9]. I additio, [6] uses the Kroecker chael odel which has bee show to have iaccurate utual iforatio ad expected error perforace [9]. This paper is the first to exaie a sigle icrostrip circular atea eployig ultiple higher-order odes i a frequecy-selective fadig sceario as see i widebad MIMO chaels. This sceario is aalyzed to deterie the suitability of ultiode ateas for the 3GPP urba icrocell spatial chael odel defied i []. The reaider of this work is orgaized as follows- Sectio II reviews the electroagetic aspects of ultiode icrostrip ateas. Sectio III itroduces the urba icrocell syste odel. Sectio IV the exaies the proble of user differetiatio at the receiver ed whe usig ultiode diversity. Sectio V presets siulatio results coparig ultiode throughout perforace to covetioal liear arrays ad we coclude i Sectio VI. II. MULTIMODE MICROSTRIP ATEA The pheoeo of higher order atea odes has bee well docueted i atea-specific literature. The key idea that allows such odes to be used as idividual atea ports for MIMO is that differet odes have differig far-field radiatio patters that are also depedet upo the aziuthal orietatio. The th -order ode far-field radiatio patter at a -22/$. 27 IEEE 84

2 radial distace r for a icrostrip atea of radius a ad thickess h is [7] jk f r e E = ( E, + φe, φ), () r where jvka f E, = ( J+ ( z) J ( z) ) cos[ ( φ φ)] 2 jvka f E, φ = ( J+ ( z) J ( z) ) cos( )si[( ( φ φ)] 2 z = kf asi( ). (2) J (x) represets the secod Bessel fuctio of order ad arguet x, ad ad φ represet the elevatio ad aziuthal agles respectively. I additio, φ is the referece agle correspodig to the iput feed poit with peak iput voltage V for the th ode, ad k f is the free-space propagatio costat (wave uber). Fig. depicts the farfield radiatio patters for odes, 2, ad 6. The th or fudaetal ode has a isotropic radiatio patter which ay be iferred fro (2), thereby rederig it usuitable for the purpose of creatig directioal patters. curret sheets. I order to excite higher-order odes we have off-ceter ultiple feeds with coordiates (ρ, φ ) where < ρ < a, ad assue a sigle ode is excited by a sigle feed. The icrostrip atea is cofigured such that ultiple higherorder odes exist siultaeously as see i [4]. All odes are assued to have the sae polarizatio; therefore polarizatio diversity is ot icluded i the aalysis. At ay give tie, the trasitted radiatio patter is deteried by the uber of active iput feeds to the atea. If each iput feed represets a idepedet data strea, the axiu uber of data streas that ca be trasitted is obviously govered by the uber of odes the atea ca support. Therefore, each ode is aalogous to a eleet of a covetioal liear atea array. Fig. 2 shows the et radiatio patters obtaied by the siultaeous geeratio of ultiple odes. The advatage of usig ultiple odes at the sae tie is obvious: a sigle-ode trasissio schee as i [] ad [6] ca carry oly oe data strea at a tie, copared to ultiple data streas (up to ) for our proposed syste (a) (b) Fig. 2. Far-field radiatio patters obtaied by superipositio of ultiple odes. (a) et patter for = 2, 3 ad. (b) et patter for =, 3, 4, ad (c) (d) Fig.. Idividual far-field atea radiatio patters for a icrostrip circular atea excited with ultiple odes. (a) =. (b) = 2. (c) =. (d) = 6. The radius of the ultiode atea is proportioal to the uber of odes that ca be supported, as show here []: ' a = χ λ 2π ε (3) r where λ is the wavelegth correspodig to the syste carrier frequecy, ε r is the dielectric costat of the patch substrate, ' ad χ is the first zero of the derivative of Bessel fuctio J. For a carrier frequecy of 2 GHz ad ε r = 2., 6 atea odes ay be supported by a patch radius of 2 c. The feed geoetry for excitig ultiple odes o a circular icrostrip atea is give i detail i [] ad [7]. We assue coaxial feeds that are odeled as ifiitesially thi plae III. SYSTEM MODEL The broadbad spatial chael odel (SCM) for MIMO [] is chose for aalysis as it is be cosidered to be ore realistic tha the i.i.d Rayleigh fadig or the oe/two-rig outdoor chael odels [9]. I brief, the SCM is a 2-D paraeter chael odel, which cosiders clusters of scatterers. Each cluster correspods to a There are M uresolvable sub-paths withi a path (M = 2 for SCM). BS array Ω BS Cluster Subpath,, BS δ,,,,, δ, BS array broadside,, MS array broadside MS Ω MS v MS directio of travel Fig. 3. 3GPP SCM for atea-arrays o the syste dowlik []. v MS array For a S eleet liear base statio (BS) array ad a U eleet liear obile statio (MS) array, the chael coefficiets for oe of ulti-path copoets are give by a U S atrix of coplex aplitudes. If we deote the chael 8

3 atrix for the th ulti-path copoet ( =,, ) as A () t, the the (u,s)th copoet (s =,,S; u =,,U) of A () t is deoted by h(t) ad writte as (,, ) exp si ( ) G BS ( j k fds,, +Φ, ) M Pσ SF h[ t, u, s] = GMS (,, ) exp (4) M = ( jk fdu si (,, ) ) exp( jk f v cos(,, v) t) where P σ SF M,, is the power of the th The power delay profile is expoetially decayig i ature. is the logoral shadow fadig, applied as a bulk paraeter to the paths for a give drop. is the uber of sub-paths per is the for the th subpath of the th,, is the for the th subpath of the th G ) is the BS atea gai of each array BS (,, GMS (,, ) eleet. is the MS atea gai of each array eleet. j is the square root of -. d is the distace i eters fro BS atea s d u Φ, v v eleet s fro the referece (s = ) atea. For the referece atea s =, d =. is the distace i eters fro MS atea eleet u fro the referece (u = ) atea. For the referece atea u =, d =. is the phase of the th subpath of the th is the agitude of the MS velocity vector. is the agle of the MS velocity vector. The (U S) overall path atrix betwee the sth trasit ode (or array eleet for the trasit ULA) with gai gs( φ ) ad the uth receive ode (or array eleet for the receive ULA) with gai gu ( φ) ay be represeted as f H( us, ) = h( tuse,, ) g( φ) g( φ). () = jk r s u The istataeous chael capacity of a MIMO chael is represeted as [] SR C = log 2 + I HH, (6) where. deotes the atrix deteriat, ad idetity atrix. I is the A. Flat Fadig Here, the flat fadig sigifies the odulated sigal badwidth is uch arrower tha the chael coherece badwidth. Hece, o OFDM odulatio is used because the copoet chael frequecy respose is relatively costat over a sigal badwidth. Usig the above paraeters for the geeratio of ( ), i.e., (U S) chael coefficiet atrix H, the received sigal vector of our ultiode MIMO syste with odes ay be odeled as SR rk = Hsk +, (7) k where SR is the sigal-to-oise ratio, k is the sybol idex, r is the received sigal vector, s is the trasitted sigal vector, ad is the coplex zeroea additive white Gaussia oise vector with covariace atrix E [ ] = I, where sigifies the cojugate traspose operatio. B. Frequecy-selective Fadig For the widebad trasissio sceario, each ode coprises a orthogoal frequecy divisio ultiplexig (OFDM) trasitter eployig c subcarriers (toes). The coherece badwidth is costat over a subcarrier but varyig over the etire badwidth which geerates a frequecyselective fadig chael. I this case, the received vector r c o the c th subcarrier ca be represeted as SR rc = Hsc + c, (8) where s c is the trasitted vector, c is additive oise with zero ea ad uit variace, ad H is the diesioal frequecy-selective chael atrix for the cuulative ultipaths. TABLE : OFDM Paraeters Data subcarriers 64 Subcarrier spacig OFDM Sybol Tie Guard Iterval khz 64 sybol periods 6 sybol periods Modulatio Order, 2, 4, 6 or 8 We cosider a axiu of = 6 ultipaths geerated usig the power delay profile specified by the 3GPP urba 86

4 icro-cell SCM []. Adaptive bit-loadig [3] ad variablerate variable-power M-ary Quadrature Aplitude Modulatio (MQAM) up to 6-QAM is adopted for perforace optiizatio. IV. SIGAL DEMODULATIO AD DETECTIO A. Matched Filter/Detector Give the above represetatio for the received sigal at the MS, we ay apply techiques such as atched filter/detector or MMSE [4] for sigal detectio ad separatio. This is siplified by the assuptio that the radiatio patters of all the odes used for couicatio are kow both to the trasitter as well as receiver. Let the iforatio bit-strea for user i at tie t be deoted i by d () t ad is selected for trasissio usig ode. Assuig biary phase-shift keyig (BPSK), the trasitted sigal for the th data strea is s () d i t = () t g( φ)cos(2 π fct). (9) Therefore, the et trasitted sigal vector s is a cobiatio of all the user sigals active over ay give sybol period. This suggests that a siple detectio ethodology would be to perfor a sigal correlatio (usig ier product) betwee the received sybol r k ad each of the kow ode patters i parallel. As etioed earlier, the ier product of dissiilar odes is egligible. Sybol detectio ay the be perfored by a hard decisio o the sig of the ier product with a threshold of zero. The reaiig paraeters are the default values specified for the urba icro-cell eviroet i []. Capacity (b/s/hz) 2 2 paths 3 paths 6 paths i.i.d 2 SR (db) Fig. 4. Multiode capacity versus SR i flat-fadig 3GPP urba icro-cell eviroet for = 6 odes at both BS ad MS, ad =2, 3 ad 6 ultipaths. Fig. 4 is a copilatio of 6-ode icrostrip capacity perforace versus SR i flat Rayleigh fadig with 2, 3 ad 6 ultipaths i the SCM eviroet. As expected, syste capacity icreases with the richess of the ultipath eviroet, for exaple the SCM with 6 scatterers ehaces ultiode throughput by 37. % copared to 2 scatterers at 2 db SR. B. Successive Patter Cacellatio (SPC) Higher order odes preset i a super-iposed trasissio sigal will exhibit a higher correlatio with the et sigal copared to lower order odes. Therefore, for ehaced odal detectio, successive iterferece cacellatio (SIC) with regard to the ultiode patters ay be applied as a additioal stage after the iitial atched filter baks. The atched filter values for all odes are arraged i ascedig order to deterie the doiat ode preset. The radiatio patter correspodig to this ode is the subtracted fro the received sigal r ad the ode detectio stage is repeated to esure that all the trasitted odes have bee detected. Capacity (b/s/hz) paths 3 paths 6 paths i.i.d C. Zero-Forcig ad MMSE detectio Zero-forcig equalizatio (ZFE) is a well-kow cadidate for ode detectio with the iheret disadvatage of oise power ehaceet. Miiu ea-square error (MMSE) estiatio is aother cadidate for liear ultiode detectio i both the flat-fadig as well as OFDM (frequecy-selective fadig) scearios. V. SIMULATIO RESULTS The followig SCM paraeters were chose: TABLE 2: Siulatio Paraeters uber of paths 2, 3 ad 6 Subpaths per path M 2 MS velocity v /s 2 SR (db) Fig.. Throughput versus SR i flat-fadig 3GPP urba icro-cell eviroet for ULA with 6 dipoles at both BS ad MS, ad = 2, 3 ad 6 ultipaths. For copariso purposes, the capacity results are also obtaied for a uifor liear array (ULA) of 6 dipoles at BS ad MS operatig i a idetical 3GPP flat-fadig SCM sceario as see i Fig.. The 6 dipole ULA outperfors the ultiode atea with 6 odes by o ore tha 2% at ay SR value. The results for the ultiode ad ULA throughput i the 3GPP SCM show siilar treds to the oerig odel capacity evaluatio i []. 87

5 Throughput (bits/s/hz) 2 6 x 6 ULA, = 6 6 ode patch, = 6 x ULA, = 6 2 Eb/ (db) Fig. 6. Throughput versus SR i 3GPP urba icro-cell eviroet for ULA with 6 dipoles at both BS ad MS, ultiode patch with 6 odes, ad ULA with dipoles with frequecy-selective fadig. Fig. 6 is a copariso of the throughput of a 6-ode icrostrip ad ULA with ad 6 dipoles versus SR i a frequecy-selective Rayleigh fadig SCM eviroet with = 6 ultipaths. Oce agai the 6-dipole ULA outperfors the 6-ode icrostrip e.g. by % at db SR. However, the 6- ode patch is see to offer cosistetly higher throughput tha the -dipole ULA at all SR values. Syste BER) x 6 ULA, = 6 6 ode patch, = Eb/ (db) Fig. 7. Syste BER versus SR (db) for frequecy doai ZF detectio for ad 6-dipole ULA ad 6-ode ultiode atea, adaptive MQAM odulatio, frequecy-selective fadig chael. Fig.7 displays the error perforace of the 6-dipole ULA ad 6-ode icrostrip patch atea respectively for ZF OFDM sybol equalizatio. It is observed that the 6-ode icrostrip BER is withi.9 db of the 6-dipole ULA for all SR values. TABLE 3: Iitial Spatial Matched Filter Stage Output, SR = db Mode Mode 3 Mode 4 Mode Mode TABLE 4: Secod Matched Filter Stage Output after SPC (Reoval of doiat ode), SR = db Mode Mode 3 Mode 4 Mode Mode Tables 3 ad 4 illustrate the iproveet i ultiode atched-filter detectio by applicatio of SPC. The detectio of weaker odes is ehaced by 4% for ode =, for exaple. V. COCLUSIOS This paper deostrates the feasibility of ultiple-ode diversity usig a sigle atea i a realistic urba icro-cell eviroet for both flat ad frequecy-selective fadig scearios. A icrostrip patch atea eployig up to 6 higher-order odes is foud to be coparable to a covetioal liear atea array with a sigificatly lower cost i ters of size ad spacig. The 3GPP SCM is odeled as the propagatio eviroet to obtai pragatic theoretical perforace results that should be ore copatible with experietal evaluatios. Future research i this area ay focus o cobiig spatial ad ultiode diversity by eas of a ultiode atea array, as well as a ore thorough ivestigatio o the optial sigal processig desig for ultiode ateas. REFERECES [] E. Telatar, "Capacity of ulti-atea gaussia chaels," Europea Tras. o Telecou., vol., pp. 8--9, ov. /Dec. 999 [2] C. Dege ad W. Keusge, Perforace evaluatio of MIMO systes usig dual-polarized ateas, i Proc. IEEE Global Telecou. Cof., Feb. 23, vol. 2, pp [3] T. Svatesso, O capacity ad correlatio of ulti-atea systes eployig ultiple polarizatios, i Proc. IEEE Ateas Propagat. Syp., Ju. 22, vol. 3, pp [4] F. Deerle ad W. Wiesbeck, "A bicoical ultibea atea for space-divisio ultiple access," IEEE Trasactios o Ateas ad Propagatio, vol. 46, o. 6, pp , 998. [] T. Svatesso, Correlatio ad chael capacity of MIMO systes eployig ultiode ateas, IEEE Trasactios o Vehicular Techology, vol., pp. 4-3, ov 22. [6] A. Foreza ad R. Heath, Beefit of Patter Diversity via Two-Eleet Array of Circular Patch Ateas i Idoor Clustered MIMO Chaels, IEEE Trasactios o Couicatios, vol. 4, pp , May 26. [7] R. G. Vaugha, Two-port higher ode circular icrostrip ateas, IEEE Tras. Ateas Propagat., vol. 36, pp. 9 32, Mar [8] A. F. Molisch, M. Steibauer, M. Toeltsch, E. Boek, ad R. S. Thoa, "Capacity of MIMO systes based o easured wireless chaels," IEEE Joural o Selected Areas i Couicatios, vol. 2, pp. 6-69, April 22. [9] M. Herdi, M. Gritsch, G. Badic, E. B. Boek, The ifluece of chael odels o siulated MIMO perforace, i Proc. IEEE VTC Mila, Sprig,24. [] 3rd Geeratio Partership Project (3GPP), Spatial chael odel for ultiple iput ultiple output (MIMO) siulatios (3gpp tr.996 versio 6.. release 6), ETSI, Tech. Rep., 23. [] R. Garg, P. Bhartia, I. Bahl, ad A. Ittipiboo, Microstrip Atea Desig Hadbook: Artech House, 2. [2] C. Balais, Atea Theory: Aalysis ad Desig, Joh Wiley & Sos, Ic., 982. [3] C. Wog et al, Multiuser OFDM with Adaptive Subcarrier, Bit, ad Power Allocatio", IEEE Joural o Selected Areas i Couicatios, Vol. 7, o., pp , October 999. [4] S. M. Kay, Fudaetals of Statistical Sigal Processig: Estiatio Theory, Pretice Hall, 993. [] J. Proakis, Digital Couicatios, McGraw-Hill, 4 ed., 2. 88