Modeling and Prediction of the Wireless Vector Channel Encountered by Smart Antenna Systems

Transcription

1 Modeling and Predicion of he Wireless Vecor Channel Encounered by Smar Anenna Sysems Kapil R. Dandekar, Albero Arredondo, Hao Ling and Guanghan Xu A Kalman-filer based, vecor auoregressive (VAR) model is used o forecas mobile user uplink spaial signaures and improve downlink signal-o-inerference raio in imedivision duplex (TDD) sysems. Resuls are presened from compuaional elecromagneic (CEM) simulaions of a smar anenna sysem operaing a 1.8 GHz in an urban microcellular environmen. Keywords: Anenna Arrays, Array Signal Processing, Mobile Communicaion Inroducion: Mobile user displacemens of fracions of a single wavelengh can significanly degrade downlink beamforming performance as spaial signaures (SS) esimaed during uplink become oudaed. The reason for his performance degradaion is he changing mulipah fading environmen encounered as he mobile user moves along a given pah [1]. Thus, i is imporan for he base saion o have an accurae esimae of channel sae informaion (CSI). SS predicion uses uplink vecor channel knowledge o design downlink beamforming weighs for TDD smar anenna sysems o aim and adjus he phase of signal energy o where he mobile user will be in he fuure raher han use an unreliable las known posiion. Predicion of he fading channel encounered by convenional communicaions

2 sysems hrough auoregressive modeling has been sudied for scalar [2] and vecor [3] channels. These pas sudies sugges ha predicions are necessary on he order of ens of milliseconds ino he fuure, corresponding o several wavelenghs of mobile user displacemen. In his leer, a vecor auoregressive SS predicion mehod is developed. This mehod uses a Kalman-filer sae space formulaion o recursively build a model of vecor channel dynamics. This approach limis he number of large marix inversions and makes he mehod aracive for fuure real-ime implemenaion. The physical jusificaion for his model arises from he muual coupling sudy in [4]. Since he array elemens are locaed so close o one anoher, he correlaion among he elemen daa can be used beneficially in forecasing wihou soring many pas channel values. Each variable s forecas depends no only on he pas values of ha variable, bu also all on he pas values of he oher variables. Vecor Channel Model: A seering vecor characerizes he relaive phase response of he i h base saion anenna array elemen locaed a (x i, y i ), 1 i M, o an inciden signal wih direcion of arrival (DOA) θ. An expression for he i h componen of a seering vecor is given by Equaion (1): i ( θ) = exp( jk(x cosθ + y sin θ)) a (1) where k is he wavenumber of he inciden elecromagneic radiaion. The SS, v, considers uplink anenna array oupu, x (), due o a single user ransmiing s() o be a linear combinaion of he seering vecors of all he direc pah (θ 1 ) and mulipah (θ 2, i i

3 θ N ) componens. The α k conain he relaive ampliude and phase of he k h signal componen modeling aenuaion and delay relaive o he direc pah. x() a N ( θ ) s() + α a( θ ) s() = s() 1 k k v k= 2 (2) Mulivariae Predicion Mehod: The proposed SS predicion mehod is based upon he reamen in Harvey [5] of a linear regression model. y = ( B + e (3) c ) y is a 1 x M vecor corresponding o he ranspose SS vecor being prediced a ime. c is an h x 1 vecor ha conains he curren base saion CSI which are he pas SS used o generae he prediced SS. [ v ] v = g c (4) g is a consan ha specifies he number of lagged spaial signaures o use which is relaed o he dimension of c by h = Mg. The marix B is h x M and conains as is columns he vecor b, i for i = 1,, M., i b is an h x 1 column vecor ha specifies he coefficiens o apply o all componens of he lagged SS in c o develop he value of he i h componen of he forecas SS. e is a 1 x M vecor modeling he forecas error. h observaions are needed o develop an iniial esimae of B, (denoed ˆB h ): Bˆ h ( C hch ) ChYh = (5) where C is a x h marix ha conains as row j (j = 1,,), he vecor c j and Y is a x M marix ha conains as row j (j=1, ), he vecor y j. To develop a refined esimae of

4 ˆB, for > h+1, a Kalman filer represenaion of he model in Equaion (3) is used o build a recursive leas squares esimaor ha does no require any furher marix inversions. For each of he i componens (i=1, M) and > h+1: [5] ˆ b,i ˆ ˆ = b + ( C b -1, i 1C ) c (y,i c,i ) / f (6) ( C C ) C 1 = ( C C ) ( C C ) c c ( C ) / f (7) f = c (8) 1+ c ( C 1C ) Afer he given raining inerval is over, he esimae of ˆB is applied using he model form of Equaion (3) o forecas fuure SS based upon pas known SS values. As hese forecass go furher ino he inerval of ime when acual SS values are no known, c will only conain prediced SS and fuure forecass will be a funcion of pas forecass. Simulaion Seup: An urban microcell, shown in Figure 1, corresponding o a 4 x 4 square block area of Ausin, Texas was simulaed using CEM sofware [6]. This sofware models muual coupling and local scaering effecs wih he mehod of momens and models he mobile environmen using eleromagneic ray racing. The base saion anenna array was a uniform circular array wih half-wave dipole elemens operaing a 1.8 GHz. The base saion anenna array was locaed 20 meers off he ground a he cener of he microcell. A his heigh, he array was below he roofops of some of he buildings and he simulaed area had a combinaion of line of sigh (LOS) and non line of sigh (non-los) regions. Three separae user pahs were considered, corresponding o movemen down sixh (non- LOS), sevenh (LOS), and eighh (non-los) srees. Field simulaions were made every

5 λ/5 of mobile displacemen over approximaely 0.5 kilomeers of ciy sree. A TDD sysem was assumed, wih a oal raining inerval of 35 spaial signaures. This corresponds o he ype of sysem described in [3]. When regions of forecased SS are included in he mobile rajecory, corresponding o base saion predicions made during downlink, here were approximaely 200 uplink-downlink cycles considered per mobile rajecory. Resuls: The developmen of he model requires he number of lagged SS values, g. The linear regression form of Equaion (3) moivaes an analysis of variance based approach o deermine he minimum necessary lag o achieve an accepable level of explanaory power. Table 1 shows ha nearly all daa variaion (a leas 93%) in he one sep ahead SS forecass can be explained by using a lag of 2 spaial signaures. The predicive power of he model several seps ahead was evaluaed using he spaial signaure relaive angle change (RAC) meric [7]. Figure 1 illusraes he effeciveness of SS predicion over he firs 5 downlink cycles of he sixh sree mobile user rajecory. Convenional spaial signaures refer o he siuaion when he las known uplink SS are used during he enire downlink inerval. Forecas spaial signaures refer o predicions based upon known SS a firs and hen evenually based upon predicions alone. The ˆB from Equaion (3) is fixed a he ime of he las known SS when developing he forecass. The figure shows ha when convenional SS are used, he RAC wih respec o he acual spaial signaures quickly reaches 80 o 90%. Use of forecasing allows he base saion o have SS esimaes ha

6 are around 30% relaive o he acual values. This improvemen can lead o appreciable performance increases in downlink beamforming [7]. Resuls for all user rajecories are summarized in Table 2. I shows, on average, ha spaial signaure predicion provides an appreciable improvemen over he use of convenional spaial signaure esimaes during downlink. These improvemens, paricularly in he NonLOS scenarios will ranslae o improved performance during downlink beamforming [3,7]. Conclusions: A SS model was developed from a linear regression sysem using a Kalman filer o recursively updae he esimaed model coefficiens and avoid unnecessarily large marix inversions. This predicion mehod generaed forecased SS ha always ouperformed he las-known SS from uplink ha would oherwise be used during downlink. This increased performance is paricularly imporan in NonLOS scenarios where curren SS esimaes are more criical during downlink beamforming. Acknowledgemen: This work was suppored by he Texas Higher Educaion Coordinaing Board under he Texas Advanced Technology Program.

7 References [1] S. Jeng, G. Xu, H.-P. Lin, and W.J. Vogel, Experimenal sudies of spaial signaure variaion a 900 mhz for smar anenna sysems, IEEE Trans. on An. and Prop., vol. 46, pp , July [2] A. Duel-Hallen, S. Hu, and H. Hallen, Long-range predicion of fading signals, IEEE Signal Processing Magazine, vol. 17, pp , [3] A. Arredondo, K. R. Dandekar, and G. Xu, Vecor channel modeling and predicion for improvemen of downlink signal power, IEEE Trans. on Comm., Acceped for Publicaion. [4] K. R. Dandekar, H. Ling, and G. Xu, Effec of muual coupling on direcion finding in smar anenna applicaions, Elecronics Leers, vol. 36, Oc [5] A. Harvey, Time Series Models: second ediion, The MIT Press, Cambridge, Massachuses, [6] K. R. Dandekar, Space Division Muliple Access Sysems: Compuaional Elecromagneic Sudies of he Physical and Nework Layers, Ph.D. Disseraion - Universiy of Texas a Ausin. [7] A. Arredondo, K. R. Dandekar, G. Xu, The quaniaive effecs of inaccurae uplink spaial signaure observaions on downlink signal o inerference raio, 1999 IEEE 2 nd Workshop on Signal Processing Advances in Wireless Communicaions, pp , July Auhors affiliaions: K. R. Dandekar (Deparmen of Elecrical and Compuer Engineering, Drexel Universiy, 3141 Chesnu Sree Room 7-515, Philadelphia, PA 19104) Albero Arredondo, H. Ling and G. Xu (Deparmen of Elecrical and Compuer Engineering, Universiy of Texas a Ausin, Engineering Science Building 143, Ausin, TX 78712, USA) Corresponding Auhor Address: dandekar@ece.drexel.edu

8 Capions Figure 1 SS Predicion Performance for Non-LOS User Table 1 Coefficien of Deerminaion vs. Number of Lagged SS Table 2 Summary of Spaial Signaure Predicion Resuls

9 Table 1 Scenario Number of Lagged SS Coefficien of Deerminaion Sixh Sree (non-los) Sevenh Sree (LOS) Eighh Sree (non-los)

10 Table 2 Scenario Acual vs. Convenional RAC (%) Acual vs. Forecas RAC (%) Sixh Sree Sevenh Sree Eighh Sree

11 Figure 1