7/28/2019 01207772

1/4

An MIMO-OFDM Technique for High-speedMobile Channels*K yung Won Park, *Eun Sun Choi, **Kyung Hi Chang, and *Y ong So0 Cho*School of Electrical and Electronic Engineering, Chung-Ang Univ., Seoul 156-756, KOREA**Electronics and Telecommunications Research Institute, Taeon 305- 600,KOREAEmail: yscho@cau.ac.kr

Absrmcr-In this paper, U new orthogonal frequency-divisionmultiplexing (OFDM) technique for multiple-input multipleoutput (MIMO) channels is proposed to reduce interchannelinterference (ICI) caused by high-speed mobiles in cellularenvironments. After a closed-form of bit ermr nte (BER) isderived for MIMO-OFDM systems, the IC 1 caused by high-speed mobile channels is analyzed usi ng a simple m e iningtechnique. Then, a new MIMO-OFDM technique, based on theresult of the leakage pattern of IC1 in the frequency-domain,is proposed for reducing IC1 causedby time-varying channels.Performancesof the proposed technique s veri6ed by using theI.METRA channel, proposed for an MIMO channel to SGPP, andan MIMO-OFDM simulator designed for maaocelluar mobilecommunication. It is shown by computer simulation that thepmposed MIMO-OFDM technique is effective in reducing IC1and noiseas wel as in obtaining diversitv eain even underh i ehl v -._ ~correlated fast fading channels, compaml with the conventionaMIMO-OFDM schemes.

I. INTRODUCTION

In recent years, orthogonal frequency-division multiplexing(OFDM) for multiple-input multiple output channels (MIMO-OFDM) has been received a great deal of attention due toits potential of achieving high data rates. So far, most ofstudies concerning MIMO-OFDM have focused on slowlyfading channels. However, in order to support afull mobilityin macrocellular environments, the time variation of a fadingchannel over an OFDM block must be considered since itcauses alossof subchannel otthogonality, leading to interchan-ne1 interference (ICI). In the previous paper, the frequency-domain equalization technique for single-input single-output(SISO) OFDM systems was proposed to compensate for the ef-fect of channel variation in time-variant multipath channels[l].However, this technique requiresatime-domainpilot signal atthe end of every OFDM symbol to estimate channel variationduring an OFDM block period.

In this paper, after deriving a closed-form formula of biterror ratio (BFX) for MIMO-OFDM and analyzing the ICIcaused by high-speed mobiles, we propose a new MIMO-OFDM technique, requiring neither pilot signals nor a prioriinformationon mobile channels, in order to reduce the IC1aswell as to obtain diversity gain.

11. A SIMPLE ANALYSIS OF IC1 CAUSED BYTIME-VARYING CHANNELSAssuming that the multipath fading channel under consid-eration consists of P discrete paths, the received basebandOFDM signal after FFTcan be writtenas

~ ( k ) H,(0)e-jzrn.'IN x(L -)+I (~)+w(~)I )where N and n denote the number of subcarriers and thetime delay of the p-th path, respectively. Also, Hp(k) andI ( k ) represent the frequency response of a time-variant chan-nel, hp(n), nd the IC1 caused by the time-variant channel,respectively. Here, Hp(k)and I ( k ) are given by

(::: )N-1

Hp(k)=- hp(n)e-J 2=LnIN (2)"=OIf the channel is time-invariant during a symbol period,the term in the right-hand side of (1) contains only themultiplicative distortion, which can be easily compensated by

aone-tap frequency-domain equalizer. However, in fast fadingchannels, the time variation of a fading channel over an OFDMsymbol period causes a loss of suhchannel orthogonality,resulting in an error floor that increases with the speed ofthe vehicle[l].The time-variant channel within an OFDM block can beapproximated byaD-th order polynomial functionas follows:h,(n)=xap,dnd+bp, n=0,1, ..., - 1 (4)

Here, the parameters. ap,d and bp, can be found by solvingthe least-square equation. Then, the frequency responseAof heapproximated time-variant channel up to 2-nd order, hp(n),canbeobtained as

D

d=l

H~f O) +a, , zf N- I ) ( ZN- 1)/ 6. fm L=O$(,.)+a,,2 (N-2 )c- j ' " * I N- N1 , for l

7/28/2019 01207772

2/4

wheref I k ( k )represents the frequency responseof the approx-imated time-variant channel of I-st order, and is given by

The above equation (5)shows the approximate effectof IC1caused by a fast fading channel. If the channel is time-invariantduring an OFDM symbol period, i.e.,a,,> =ap,l =0, thereexists no IC1 sinceHp(k) =Oor k # 0. However, in the casewhere the channel is time-variant withinasymbol period, i.e.,ap,z# 0 or ap.l # 0, the leakage signals are distributed overall other subcarriers, resulting in ICI.From(1) and (5). onecan see that the frequency responseofa time-valying channel is equivalent to the Fourier transformof the averaged channel in the time domain as follows:

P-1-( k ) = H,,(0)eCj2"" pk/Np=O

In the process of verifiog the performances of variousMIMO techniques in time-varying channels, we'll use theabove equation (7) for a perfect channel.111. AN MIMO-OFDM TECHNIQUEOR HI GH- SPEEDMOBILE CHANNELSIn this section, after deriving a BER for MMO-OFDM,we propose a new MIMO-OFDM technique, requiring neitherpilot signals nor a priori informationon mobile channels, inorder to reduce the IC1as well as to obtain diversity gain.

A . A Bit-Ermr Pmbabiliry for M MIMO-OFDMIn this section, the closed-form formula of BER for MIMO-

OFDM is derived under the assumption that channel doesno1change during an OFDM symbol period. For an flat fadingM MO channel with L transmit antennas and M receiveantennas, the S NR distribution of t hc received signal afteimaximal ratio combining is given by

p(y)=ToLMyLM- le-7/m / W M ) (8)where ^o is given by Zo2G,(Et,/NO)/L.Here, yo and 6,denote the averageS NR of each branch and the coding gain,respectively, obtained by orthogonal design of SFBC or STBCscheme. r(.) epresents Gamma-function. By solving theintegral equation for Rayleigh fading channel, the conditionalbit-error probability of the MIMO-OFDM is derived as

where pb(y), given by a Q ( f i ) . represents the BER forstatic situation where a and p are variable parameters de-pending on the modulation scheme. Also, p is given by, / p y o / ( P yo+Z ) . Analytic BER for M branch MRRC-OFDM can be computed f" 9) by setting L = 1 and6, =1. In this paper, it is shown that the analytic result in(9)agrees well with Monte-Carlo simulation results for variousmodulation schemes.B . An MIMO-OFDM Techniquefor lime-Varying Channel

The IC1 reduction technique for MIMO-OFDM systems,derived in this paper, are based on the result of analysisregarding the leakage pattern of IC1 in the frequency-domain,given in (5). Since the IC1 term generated by the (IC)-thsubcarrier is similar to the one generated by the ( k+1)-th subcarrier with an opposite sign, the IC1 can be reducedsignificantly by appropriately assigning transmission data ontoG adjacent subcarriers as follows:

S(G .g+i )=a,-,,X (g), i =0, l , . . . , G - l (10)where S(G . g+ ) and G(=GL+GR+1) denote the i -th subcarrier of the g-th subcarrier group and the size of asubcarrier group, respectively. If the channel state informationis knownat the transmitter, the optimal value of the weightingfactor, a i - ~ r ran be easily found. If it is not the case,the weighting factor can be found by using the polynomialcoefficients as follows:

Fig. I shows a SFBC-OFDM scheme employing2 transmitantennas and a receive antenna. Also, in this f i gure, dataassignment schemeonto subcarrierss shown as follows:(12)This technique can be applied to anyMMO-OFDMsys-tems employing transmit diversity, receive diversity, and space-time coding.The& transmission data assigned onto two adjacent subcar-riers at the j-th transmit antenna is given by

Xz(2g)=-X;(29 +1);XZ(29+1)=X; ( Zg)

~~( 29 )Xj(g); Sj(2g+1) =aXj(g), for j =0,1 13)where a denotes the weighting factor. The value of a is setto - I for data subcarriers, whereas the absolute value of a isset to the one lessthan I for pilot subcarriers.In this scheme, the received OFDM signal isgiven by

N/2 -1Y(2g4 i ) = g~,~(m,(g -m)-t)X i (m)

m=ONIB-1+ E?2,p(m,2(9-m)+ )Xz(m)m-0+W(29+) ,g=O,.. . ,N/Z- l ; i =O, l (14)

981

7/28/2019 01207772

3/4

m

Tx ant.#

(a) A simpleblock diagram

T T I I T T ... T I ,, 2 , l" h.m,(b) Data assignment

Fig. 1. A simple block diagramof2TdIRr SFBC-OFDM sheme for reducingIC1caused by t i m e - v q i n g channel

where&j,p(m) s defined as

whereHj,,(m) represents the single-tone frequency responseof the pth time-variant channel between the j-th transmitantenna and receive antenna.Then, the received signals at the (29+1)-th subcarrier and(29)-thsubcarrier are added as follows:

the above equation (16) can be combined asxl(9)=(Ifll(s)I~+%b)12) xl(g) r i ; ( g ) I N ( g )

8&7+)=(I A l (s)l ~+l~~(S) I ~)X l (g+1)+fiz(g) IN *(g+1) (20)

-Ei1(g)IN'k? +1)+m; ( S ) I N ( g ) (21)where I N ( g ) denotes f1(g)+&(g ) +N(g) .In summary, the proposed SFBC-OFDM scheme compen-sates the IC1 effect caused by fast fading channels, as givenby (14) and (16). at the expense of transmission rate reductionby half, and obtains a diversity gain plus noise averagingeffect, as given by (20) and (21). The proposed scheme hasadvantages of not requiring any pilot signals or tracking ofchannel variation, unlike the one in [I]. However, since theproposed scheme was derived under the assumption that thechannel coefficients between adjacent suhcaniers are approx-imately identical. it is suitable for OFDM systems where thesubcarrier group spacing is narrowerthan the channel coherentbandwidth. Although the proposed technique is derived, here,only for the SFBC-OFDMcase, similar results areobtainedfor STBC-OFDM, SFTC-OFDM, and MRRC-OFDM cases.

IV. S IMUL AT IO N R E SUL TSIn this section, the performances of the proposed MIMO-OFDM scheme is compared with the conventionalM MO-OFDM schemes. The bandwidth used for downlink channelis 20 MHz at 2 GH z with a sampling frequency equal to25 MHz (oversampling ratio=1.25). Also, the guard intervaland OFDM symbol period are set to 18.08ps and 81.92 js.respectively, for macrocellular environments, implying that thetotal number of subcarriers is 2048 including virtual canien.Fig. 2(a) shows a sample function of the channel and theapproximated channel. given by ( 5 ) and (6). over an OFDMsymbol period when the termnal is moving a the speed of250k " . Also, Fig. 2(b) showsthecorresponding frequency-domain responses of the channels when 6(k) is applied forthe input of I FFT. Note that the approximated ICI, obtainedby (5). is almost identical with the actual ICI, even at veryhigh mobility. The performances of the proposed techniques

are verified by using the I-METRA channel, proposed foran MIMO channel to 3GPP. and an MIMO-OFDM simulatordesigned for macrocelluar mobile communication [ 5 ] .Two I -METRA MI MO channels are used for simulation: (1) CaseA corresponds to a flat Rayleigh fading channel with nocorrelations between antennas, (2) Case B corresponds toa typical urban macro cellular channel with 4 paths. Theparameters associated with Case B are as follows:22.5" angle-of-arrival (AOA), uniform power azimuth spectrum (PAS) over360" forUE,20" AOA and Laplacian PAS with 22.5" azimuthspread (AS) for BS. Fig. 3 shows downlink performancecomparison between the conventional SFBC-OFDM schemeand theproposed one when2 transmit and 1 receive antennasare used at BS and UE, respectively. From Fig. 3, one can

982

7/28/2019 01207772

4/4

(a) time-domain

I ...... :.. , . . . ; .....,.. ..: .... .,.. . . ..., ...... I

(b) frequency-domainFig. 2. Time- and frequency-domain charaeletisli csof a lime-variant channel

m aE w m

( b) CareBFig 3channelsBER performances of various SFBC-OFDM schemesfor fast fading

see that the conventional SFBC-OFDM scheme exhibitserrorfloor ohenomenon due to IC1 caused by the mobile at the REFERENCESspeedbf 250K " . Notice that the proposed scheme not onlyovercomes the error floor phenomenon but also gains about3dB, compared with the analytic result in(9).due to the effectsof noise averaging and IC1combining. Fig. 3(h) showsBERperformances of SFBC-OFDM schemes for Case B wherelransmit antennas are correlated and channel is frequency-selective. In this case, the envelop correlations of BS andUE are given by 0.976and 0.1023,respectively. From Fig. 3,one can conclude that the proposed scheme achieves robustperformance gain for the same data rate, even under highly-correlated fast fading channels.

ACKNOWLEDGMENTThe resultof ET projectI ST- 2000- 30148-METRA is usedfor simulation.

[I ] W.G. leon. K.H. Chang. and Y.S Cha. " An Equalization Technique forOFDM Systems in Time-Vadnt Multipath Channels:' IEEE Tmn. onConununicarionr.Vol. 47, No. 1. pp. 27-32. J am 1999.[2] S. M. Alamouti, "A simple transminer diversity scheme for wirelesscommunications," IEEE 3. Lkct. Areas C o n " , Vol. 16. No. 8. pp.1451-1458. on. 998.[31 V. Tamkh. N. Seshadri, and A.R. CalderbanL, "Space-tims ccdes forhigh data ratewirclcsscommuni cat i on: performanee criterionand codeconstruction." IEEE Tmn. om I n f om r i o n 7hheory. Vol. 44, No. 2, pp.744-765. M ar 1998.I41 A. F. Naguib. N. Seshadti, and A.R. C alderbmk, "Space-time codingand signal proeasing forhigh dam rate wireless communications:' IEEES i g w f Processing Mogozine. Vol. 17. No. 3, pp. 7692 , May 2wO.[SI EST1 Tech. R epon, "M ultiple-Input Multiple Outputan ten Processingfor HSDPA:' TR 25.876, v1.0.1, 2oM .

983