PILOT SYMBOL DESIGN FOR CHANNEL ESTIMATION IN MIMO-OFDM SYSTEMS WITH NULL SUBCARRIERS

h European Signal Processing Conference (EUSIPCO- Aalborg, Denmark, Augus -7, PILOT SYMBOL DESIGN FOR CHANNEL ESTIMATION IN MIMO-OFDM SYSTEMS WITH NULL SUBCARRIERS Emmanuel Manasseh, Shuichi Ohno, Masayoshi Nakamoo Dep. of Arificial Complex Sysems Engineering, Hiroshima Universiy -- Kagamiyama Higashi-Hiroshima, 79-57, JAPAN E-mail: {manassehjc,ohno,msy}@hiroshima-u.ac.jp ABSTRACT In his paper, pilo design for channel esimaion in muliple inpu muliple oupu orhogonal frequency division muliplexing (MIMO-OFDM sysems wih null subcarriers is considered, where he mean square error (MSE is chosen as our opimizaion crierion. We design he placemen of pilo symbols and heir powers for muliple ransmi anennas o minimize he MSE of he leas square (LS channel esimaes. To reduce he inerference of pilo symbols from oher ransmi anennas, an algorihm ha ensures ha he pilo symbols are disjoin from he ones of any oher anenna is proposed. Simulaion resuls based on IEEE.e are presened o illusrae he superior performance of our proposed mehod over he exising sandard and he parially equi-spaced pilo symbols.. INTRODUCTION Robusness of OFDM sysems in mulipah environmens ogeher wih he significan informaion capaciy gain as well as improved BER performance of MIMO sysems, highligh he subsanial poenial of MIMO-OFDM sysems. However, in comparison o a single anenna sysem wih only one channel o be esimaed, a MIMO sysem wih ransmi and N r receive anennas necessiaes N r channels o be esimaed. This increased number of channels o be esimaed may reduce he higher daa rae of a MIMO sysem if pilo subcarriers are no well opimized []. Therefore, he placemen and power disribuion o pilo symbols o efficienly rack he channel variaion boh in ime and/or frequency domains is crucial as he designed pilo symbols has impac on he channel esimaion performance and he BER performance of he sysem. In he lieraure, raining signal design for channel esimaion have been predominanly developed for single inpu single oupu (SISO-OFDM sysems [ ], and he reference herein. Opimal pilo symbols for OFDM sysems in he absence of null edges subcarriers are considered in [ 5] where equi-disan and equi-powered pilo symbols were found o be opimal wih respec o several performance measures. In [7], a novel mehod for opimal preamble and pilo symbols design for SISO-OFDM sysems wih null subcarriers is considered in a frequency-selecive block-fading channel esimaion. Boh pilo power and placemen were obained by minimizing he MSE of channel esimae wih convex opimizaion mehods. The same problem is addressed in [] where he placemen of raining signals is obained by parameric opimizaion, while he pilo power is obained by minimizing he infinie norm of he channel MSE wih convex opimizaion. However, in [7] i has been repored ha, formulaion of he convex opimizaion problem in [] uses some approximaion in he objecive funcion which may no accuraely represen he infiniy norm of he channel MSE. Furhermore, he accuracy of cubic funcion based opimizaions in [] depends on many parameers o be seleced for every channel/subcarriers configuraion, which complicae he design especially when he mehod is o be adoped in MIMO-OFDM sysem ha requires pilo se of every ransmi anenna o be disjoin from he ones of any oher anenna. A number of pilo design mehods for MIMO-OFDM sysems have been sudied, e.g. in [ ]. In [9], equipowered pilo symbols are sudied for channel esimaion in muliple anenna OFDM sysem wih null subcarriers. Bu hey are no always opimal even for poin-o-poin OFDM sysem. Pilo sequences designed o reduce he channel MSE in muliple anenna OFDM sysem are also repored in [] bu hey are no necessarily opimal. In [], parially equispaced pilo symbols ( for MIMO-OFDM wih null edge subcarriers is proposed, however he pilo placemens are no unique and may no resul ino good pilo se for some channel/subcarriers configuraions. In his paper, we uilize he mehod proposed in [7] for SISO sysems where pilo symbols are obained from he opimal preamble by ieraive removal of pilo symbols wih minimum power. We exend his echnique o MIMO sysems wih some modificaions o ensure ha he pilo symbols of one anenna are disjoin from he pilo symbols of any oher anenna. A modified algorihm is proposed o ensure ha he composie pilo sequence from all anennas are posiioned in he acive subcarriers and are placed symmerically abou he cener of he acive subcarrier zone. Our novel mehod can be used o easily design pilo symbols for MIMO-OFDM sysems wih differen channel/subcarriers configuraions. Furhermore, our approach inroduces a new pilo design paradigm ha suppors a prominen number of ransmi anennas wih more racabiliy in erms of complexiy as well as applicabiliy o OFDM sysems wih differen frame srucures. Several design examples based on IEEE.e are provided in Secion 5 o demonsrae he efficacy of our impressive design. The res of his paper is organized as follows: The MIMO-OFDM sysem model is briefly described in Secion. Channel esimaion in MIMO-OFDM is concisely presened in Secion, while he proposed muliple anennas pilo design is addressed in. In Secion 5, simulaion resuls demonsraing he performance of our proposed algorihm as compared o he sandard and he scheme in [] are presened and finally, Secion concludes our paper. EURASIP, ISSN 7-5

. MIMO-OFDM SYSTEM MODEL We consider a frequency selecive MIMO-OFDM wireless sysem wih ransmi and N r receive anennas. We assume ha he discree-ime baseband equivalen channel beween each ransmi-receive anenna has FIR of maximum lengh L, and remains consan in a leas one OFDM block, i.e., is quasi-saic. Le us denoe he channel from he ih ransmi anenna o he mh receive anenna as h im =[h im [],h im [],...,h im [L ]] T. ( Our OFDM symbol is assumed o have N subcarriers. We consider one OFDM symbol duraion and denoe he ransmied OFDM symbol from he ih ransmi anenna as s i = [s i [],s i [],...,s i [N ]] T ( = d i +p i, ( where d i consiss of daa symbols, while p i pilo symbols. We assume had i andp i are in disjoin subcarrier posiions. A he ransmier, each s i undergoes serial-o-parallel (S/P followed by an N-poins inverse discree Fourier ransform (IDFT o produce an OFDM symbols. Each OFDM symbol is parallel-o-serial (P/S convered and a cyclic prefix (CP of lengh N p is appended o miigae he mulipah effecs. Then, our discree-ime baseband equivalen ransmied signals can be expressed as s i [n]= N s i [k]e j πkn N, n [,N ]. ( N k= Assume ha N p L so ha here is no iner-symbol inerference (ISI beween consecuive OFDM symbols. A he receiver, we assume perfec iming synchronizaion. Afer removing CP, he received ime-domain signal a he mh receive anenna is given by Ỹ m = i= D( s i h im + W m, (5 where D( s i represens he diagonal marix whose diagonal enries are s i =[ s i [], s i [],..., s i [N ]] T and W m is assumed o be i.i.d. circular Gaussian vecor wih zero mean and variance σ wi. Applying discree Fourier ransform (DFT o he received ime-domain signal Ỹ m = [ỹ m [],ỹ m [],...,ỹ m [N ]] T we obain Y m [k]= i= H im [k]s i [k]+w m [k], ( where H im [k] is he channel frequency response of he(i,mh channel a frequency πk/n given by. CHANNEL ESTIMATION IN MIMO-OFDM For a discree se I, we denoe I as he number of elemens of I. Le K s be he se of acive subcarriers. We assume ha he number of pilo symbols in each OFDM symbol o be N p. For OFDM symbol ransmied from he ih ransmi anenna, we pu pilo and daa symbols a subcarrier ses denoed as K pi and K di, respecively. To simplify he LS esimaion, we se K pi for i =,,..., o be disjoin such ha K pi K pn = / for i n. ( We also assume ha here are no pilo symbols a K di, i.e., K di K s \ ( K p K p K pn where\denoes se difference. Since he same channel esimaion process is performed a each receive anenna, we only need o consider ransmi anennas and one receive anenna in designing pilo symbols, ha is, he channel is modeled as a superposiion of mulipleinpu single-oupu (MISO channels, as in [, ]. Thus, wihou loss of generaliy, we can describe he firs receive anenna and omi he receive anenna index. Suppose ha we esimae he channels for coheren deecion wih pilo ses K p,k p,...,k pn, hen, o ransmi daa symbols, i is necessary o mee K s N p > Le us define he frequency-domain channel gain a (9 H i =[H i [k ],...,H i [k Ks ]] T, ( where k n < k n if n<n. We define F as an N N DFT marix whose (m+,n+ h enry is e jπmn/n, and F L =[f,...,f N ] H ( as an N L marix consising of N rows and firs L columns of a DFT marix F, where ( H is he complex conjugae ranspose operaor. We also define an N p L marixf pi havingfk H n for k n K pi as is nh row. Then, he received signals in ( having pilo symbols from he ih ransmi anenna is expressed as Ỹ i =D pi F pi h i + W i, ( where D pi is a diagonal marix consruced from pilo symbols from he ih ransmi anenna and W i is he corresponding sub-vecor of W m. Similar of pi, we define a K s L marixf s havingf H k for k K s as is kh row, where k n < k n if n<n. Then, we obain H i =F s h i. ( From ( and (, he LS esimaeĥ i ofh i is given by L H im [k]= l= and he noise{w k } is he DFT of W m. h im [l]e j πkl N, (7 where Ĥ i =F s (F H p i Λ pi F pi (D pi F pi H Ỹ i, ( Λ pi =D H p i D pi = diag ( λ i,,...,λ i,np. (5

Le us define he sum of he mean-square error (MSE of he channel gain a K s as Preamble Pilo η i = E{ Ĥ i H i }, ( where is he Euclidean norm. i.e. l norm. Then, he channel MSE η i can be expressed as [, 7] [ η i =F s (F ] H σw pi Λ pi F pi F H s (7 For a given pilo se, he opimal pilo power λ i,,...,λ i,np ha minimizes he channel MSE η i can be found numerically by resoring o convex opimizaion echnique [7]. Since we have N r receive anennas, he average of he LS channel MSE of each receive anenna is given by ξ = σ w i= ] F r [F s (F Hpi Λ pi F pi Hs ( In he following, based on (, we deermine he ses K p,k p,...,k pn and power disribuions o pilo subcarriers by using convex opimizaion echnique.. PILOT DESIGN FOR MIMO-OFDM To deermine pilo ses and power disribuions o pilo subcarriers, we modify he algorihm in [7] o accommodae muliple anennas while guaraneeing ha he designed pilo ses are disjoin from each ransmi anenna. The main objecive of disjoin pilo sequences in each ransmi anenna is o ensure appropriae separaion of pilo sequences in he receiver. The pilo se for he firs ransmi anenna is obained from he designed opimal preamble wih semidefinie programming (SDP by ieraive removal of N m minimum subcarriers symmerically, followed by opimizaion of he remaining subcarriers as in [7]. Once he pilo se for he firs ransmi anenna is found, he se is excluded from he acive subcarrier se and he pilo se for he second ransmi anenna is obained from he remaining acive subcarriers using he ieraive algorihm unil he second pilo se is obained. The algorihm is execued unil pilo ses for all ransmi anennas are obained. The modified pilo placemen and power design procedure for ransmi anennas is summarized as follows:. Iniialize K r = K s, where K r sands for he se of available subcarriers.. while i=,..., (a Define he emporary se K = K r and opimize K subcarriers using convex opimizaion (b Save he obained posiion and power of he subcarriers (c If N p < K, remove N m minimum subcarriers symmerically o he zeroh subcarrier, else go o sep f (d Updae K ( K = K N m. (e Opimize he power of he remaining subcarriers using SDP and go o sep b (f Save pilo posiion as K pi and is power disribuion (g Updae K r = K r \K pi, i i+ and reurn sep a unil i λ 5 5 Subcarrier Figure : Pilo posiion and power disribuion for four ransmi anennas In he algorihm, once he se K pi is obained, i is excluded from he he remaining acive subcarriers K r \ K pi. This assures ha he opimized pilo symbols from all ransmi anennas are locaed in disjoin pilo se in any non null subcarriers, while he symmerical removal of N m subcarriers afer every opimizaion, check for he disjoin pilo ses o be placed symmerically abou he cener of he signal band. When he algorihm exi, we will obain he pilo posiions and he normalized pilo powers for each anenna. To opimally disribue power beween pilo symbols and daa subcarriers, we can also modify he mehod in [7] depending on he daa ransmission scheme. If one adops OFDMA for daa ransmission, he mehod in [7] can be direcly applied, while if one prefers space ime block coding for daa ransmission, he mehod in [7] should be modified accordingly o he daa ransmission scheme. 5. SIMULATION RESULTS In his secion, we demonsrae he effeciveness of our proposed pilo design hrough compuer simulaions, where we se σw =. The parameers of he ransmied OFDM signal sudied in our design examples are as in he IEEE.e sandard in [, p.9], where an OFDM frame wih N= 5 is considered. Ou of 5 subcarriers, are used as daa subcarriers. Of he remaining 5 subcarriers, are null in he lower frequency guard band while 7 are nulled in he upper frequency guard band and one is he cenral DC null subcarrier. Of he used subcarriers, are allocaed as pilo subcarriers, while he remaining 9 are used for daa ransmission or null for pilo symbols of oher anennas. To design disjoin pilo ones o muliple ransmi anennas, we consruc a composie pilo sequence wih index ses {K p } having N p subcarriers wih significan pilo power and reasonable posiion. The pilo se for he firs anenna is obained as in [7], hen by uilizing our algorihm in Secion, which exclude he designed pilo se from he preamble and repea he same procedure for he remaining subcarriers, we can obain he pilo ses for all ransmi anennas. Through our modified algorihm, we obain he normalized opimal pilo symbols for he ransmi anennas, hen we uilize he mehod proposed in [7] o disribue power o pilo and daa subcarriers for a given OFDM power per

NMSE(dB Propsed IEEE. Proposed λ 5 Subcarrier Number 5 5 5 Subcarrier Figure : Comparison of channel esimae MSE beween he proposed and he sandard Figure : Comparison of pilo design for hree ransmi anennas frame. The proposed mehod in [7] plos he BER as a funcion of he power allocaion raio α. Then opimal value of power allocaion raio α which minimizes he BER and make pracical significance is obained direcly from he plo. Fig. shows he designed disjoin opimal pilo se for ransmi anennas when N p = L=, and he oal ransmied power per OFDM frame is E =. We use he opimal value of α =. obained in [7] for all ransmi anennas. This implies ha, he oal pilo power for each anenna is he same for all ransmi anennas. For all anennas he pilo power and locaion are well disribued wihin he in-band region which promises beer esimaion of he channel even a he edge of he band. For he opimal preamble where all acive subcarriers are considered as pilo symbols hereby α = and he oal power dedicaed o one OFDM frame is disribued o he pilo symbols according o heir normalized opimal power. In he following we compare each of he designed pilo se wih he exising IEEE.e sandard pilo symbols separaely i.e SISO-OFDM mode. The aim is o observe he performance of he designed pilo symbols in each anenna wih respec o he sandard one o ensure ha each designed pilo se have beer performance. A noeworhy fac is ha, when some SISO-OFDM mehods are adoped in MIMO- OFDM pilo designs he performance of some designed pilo ses deerioraes wih increased number of ransmi anennas. Tha is only few pilo ses yields a significan performance. In Fig., he normalized channel esimae MSE of he designed disjoin pilo symbols in Fig. is compared wih he exising sandard which places he eigh subcarriers a {±, ±, ±, ±}. The oal pilo power for each anenna is aken o be N p, for boh he sandard (equally spaced, equi-powered pilo symbols and our proposed mehod. From he plo i is clear ha he performance of each anenna ouperforms he sandard. The sandard pilo design does a poor job of esimaing channel a he subcarriers near he guard band, his is due o lack of he pilo subcarriers a he edge of OFDM symbols in he IEEE.e sandard, and here by he esimaion via he exrapolaion for he edge subcarriers resuls in a higher error []. The possible soluion would be o increase he number of pilo subcarriers a he edge subcarriers as proposed in [5], how- ever his would decrease he specral efficiency of he sysem. Our proposed design illuminaes he improvemen obained by rearranging he pilo symbols wihou any addiion of pilo subcarriers a he edge as suggesed in [5]. This clarify ha he uniform-spaced and equal power pilo symbols are subopimal for an OFDM sysem wih null subcarriers. In [], i is saed ha, he power of pilo symbols decreases when he pilo symbols are close o he null/virual carriers zone due o he fac ha here are less daa carriers, his migh be rue, however he power allocaed o hese subcarriers need o be significan, oherwise he problem of channel esimaion via he exrapolaion for he edge subcarriers will sill persis. Fig. compares our proposed pilo symbols and he parially equi-spaced pilo ( symbols proposed in [] for L = N p =. In he wo designs, he oal pilo power from he differen ransmi anennas are equal. For our proposed design power allocaed o he edge pilo symbols is slighly lower han ha of he mid pilo symbols, however he difference is no as large as in he design. In [], pilo placemen does no consider any performance crierion, however he power allocaion is based on minimizing he channel MSE o he designaed pilo subcarriers. This reduces he compuaion complexiy of he design bu does no guaranee opimal pilo se. In our proposed design boh pilo posiion and power are aken ino consideraion and hereby ensuring beer performance under differen performance crieria. In Fig., we made a comparison of he channel esimae MSE o each acive subcarrier symbol for he designed disjoin pilo symbols in Fig.. From he plo, i is clear ha he performance of our proposed design ouperforms he for some anennas. The design does a poor job of esimaing channel a he subcarriers near he guard band, his is no due o lack of he pilo subcarriers a he edge of OFDM symbols bu insignifican power allocaed o he pilo symbols close o he null subcarrier zone. This furher sugges ha boh pilo powers and placemens need o be carefully considered in he design. To furher demonsrae he poenial of our proposed design, we made a comparison of he average channel esimae MSE vs channel lengh L. To obain he channel MSE of our proposed design as well as he scheme, we varied 5

NMSE(dB 5 5 Propsed Subcarrier Number Figure : Comparison of channel MSE beween he proposed and he MSE(dB Proposed L Figure 5: Channel MSE of pilo symbols for hree ransmi anennas he channel lengh L, from o. Fig. 5 presens he average channel MSE. The proposed opimized pilo symbols exhibi lesser channel MSE han he symbols. This furher demonsrae he efficiency of our proposed design.. CONCLUSION In his paper we addressed he problem of channel esimaion for MIMO-OFDM sysems wih null subcarriers. Specifically, we exended he opimizaion mehod for designing pilo symbols in a SISO-OFDM sysem in [7] o MIMO sysems. Through numerical simulaions, we have verified ha he designed pilo subcarrier se for each ransmi anenna has a beer channel esimae performance han he exising equally spaced and equi-powered IEEE.e sandard and he parially equi-spaced pilo symbols. The resuls verify ha he proposed algorihm is a prominen candidae for he design of disjoin pilo sequences in each ransmi anenna ha ensures appropriae separaion of sequences a he receiver, while aaining a superior channel esimaion over he equally spaced equal powered pilo symbols. We have also verified ha he proposed mehod can be used o design pilo symbols in MIMO-OFDM sysems wih differen channel/subcarriers configuraions. REFERENCES [] M. K. Ozdemir and H. Arslan, Channel esimaion for wireless OFDM sysems, IEEE Communicaions Surveys & Tuorials, vol. 9, no., pp., 7. [] L. Tong, B. M. Sadler, and M. Dong, Pilo-assised wireless ransmissions: general model, design crieria, and signal processing, IEEE Sig. Proc. Mag., vol., no., pp. 5,. [] R. Negi and J. Cioffi, Pilo one selecion for channel esimaion in a mobile OFDM sysem, IEEE Trans.on Consumer Elec., vol., no., pp., 99. [] S. Ohno and G. B. Giannakis, Opimal raining and redundan precoding for block ransmissions wih applicaion o wireless OFDM, IEEE Trans.on Com., vol. 5, no., pp.,. [5] S. Adireddy, L. Tong, and H. Viswanahan, Opimal placemen of raining for frequency-selecive blockfading channels, IEEE Trans. on Info. Tech., vol., no., pp. 5, Aug. [] R. J. Baxley, J. E. Kleider, and G. T. Zhou, Pilo design for OFDM wih null edge subcarriers, IEEE Trans on Wireless Com., vol., pp. 9 5, Jan. 9. [7] S. Ohno, E. Manasseh, and M. Nakamoo, Pilo symbol design for channel esimaion in OFDM wih null subcarriers, Asia Pacific Signal and Informaion Processing Associaion (APSIPA, pp. 9 99, Oc. 9. [] M. Shin, H. Lee, and C. Lee, Enhanced channelesimaion echnique for MIMO-OFDM sysems, IEEE rans. on Veh. Tech., vol. 5, no., pp. 5, Jan.. [9] E. G. Larsson and J. Li, Preamble design for mulipleanenna OFDM-based WLANs wih null subcarriers, IEEE Sig. Proc. Le., vol., no., pp. 5 7, Nov.. [] D. Hu, L. Yang, Y. Shi, and L. He, Opimal pilo sequence design for channel esimaion in MIMO OFDM sysems, IEEE Com. Le., vol., no., pp., Jan.. [] Q. Huang, M. Ghogho, and S. Freear, Pilo design for MIMO OFDM sysems wih virual carriers, IEEE Trans. on Sig. Proc., vol. 57, no. 5, pp. -9, May 9 [] Z. Li, Y. Cai, and Y. Xu, Opimal raining signals design for MIMO OFDM sysems wih guard subcarriers, Proc. VTC -Spring Vehicular Technology Conference IEEE rd, vol., pp. 5 5,. [] M. Sandell, J. Coon, Near-opimal raining sequences for MIMO-OFDM sysems wih nulled subcarriers, IEEE GLOBECOM 5, vol., pp. 9, Dec. 5 [] IEEE Sandard for Local and Meropolian Area Neworks Par : Air Inerface for Fixed Broadband Wireless Access Sysems, IEEE Sd.,. [5] M. Morelli and U. Mengali, A comparison of piloaided channel esimaion mehods for OFDM sysems, IEEE rans. on Sig. Proc., vol. 9, no., pp. 5 7, Dec..