Single-Carrier Frequency-Domain Equalization for Orthogonal STBC over Frequency-Selective MIMO-PLC Channels

Transcription

1 Journal of Communcaton Engneerng, Vol., o., Autumn 0 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC over Frequency-Selectve MIMO-PLC Channels Mohsen Shekh-Hossen, Mohammad Molav-Kakhk and Ghosheh Abed Hodtan Department of Electrcal Engneerng, Ferdows Unversty of Mashhad, Mashhad, Iran mo_sh40@stu.um.ac.r, molav@um.ac.r, hodtan@um.ac.r correspondng auor: Mohsen Shekh-Hossen Abstract In s paper we propose a new space dversty scheme for broadband PLC systems usng orogonal space-tme block codng (OSTBC) transmsson combned w sngle-carrer frequency-doman equalzaton (SC-FDE). To apply s dversty technque to PLC channels, we frst propose a new technque for combnng SC-FDE w OSTBCs applcable to all dspersve multpa channels mpared by mpulsve nose. The proposed technque s en appled to ndoor and outdoor PLC channels under dfferent channel scenaros n e presence of background and mpulsve noses. We perform e smulatons for SISO, MISO and MIMO confguratons and show at a sgnfcant SR gan s acheved when SC-FDE s combned w dversty technques. We also compare our proposed technque w OFDM usng Alamout code for broadband PLC and show e superorty of our technque. Inde Terms broadband power lne communcaton, frequency-selectve fadng channel, mpulsve nose, orogonal space tme block codng, sngle-carrer frequency-doman equalzaton. I. ITRODUCTIO Usng power grd for communcaton purposes s not a new dea. In fact e use of narrowband power lne communcaton (PLC) technology for management and montorng of power networks started from early 900s by usng conventonal sngle-carrer (SC) modulaton n low frequency band (below 500kHz) supportng bt rates up to a few kbps. Durng e last decade, broadband low voltage PLC has receved an ncreasng nterest as an attractve soluton for last mle access of communcaton networks, n-buldng networkng and fast nternet access. Recently w e emergng of smart grd concept, PLC technology has receved great attenton as a promsng canddate for e smart grd where bo narrowband and broadband PLC systems are proposed for smart grd applcatons lke automatc meter readng, vehcle-togrd communcaton and networkng of consumer home applances []-[]. Manuscrpt Receved 7-September-0 and revsed 4- ovember-0 ISS: -96 Accepted on -December-0

2 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. However, broadband communcaton over power lnes requres a hgh bandwd to support data rates n ecess of 00Mbps and power lnes are very harsh medums for hgh speed transmsson and mpose serous lmtatons due to er tme and frequency dependent attenuaton and also due to mpulsve nose and multpa effects []. The multpa nature of PLC channels s due to mpedance msmatchng of electrcal networks where transmtted sgnal propagates along several pas w dfferent attenuatons and delays. Echo superposton of transmtted sgnal w dfferent delays lead to nter-symbol nterference (ISI) destroyng transmtted data. Hgh speed transmsson n such tme dspersve channels can span ISI over a remarkable number of data symbols. For eample, n 00Mbps bnary communcaton over typcal PLC channel w µs delay spread, ISI span over symbols [4]. Orogonal frequency dvson multpleng (OFDM) for ts robustness to multpa echoes and selectve fadng s an attractve canddate for PLC systems and s adapted to some standards such as Homeplug.0 and HomeplugAV. Despte ts great attracton n academc and ndustral communtes, OFDM effcency s lmted by some drawbacks lke hgh peak to average power rato and carrer frequency offset senstvty. Sngle-carrer frequency-doman equalzaton (SC-FDE) s anoer technque for broadband communcaton over hghly dspersve channels. Smlar to OFDM, SC-FDE s a block transmsson technque w cyclc pref (CP) nserton at e transmtter, and usng fast Fourer transform (FFT) and nverse FFT (IFFT) algorms. The mplementaton complety and achevable performance of SC-FDE s comparable to at of OFDM whle avodng e OFDM drawbacks [4]-[6]. Recent research actvtes n s area have focused on usng STBCs combned w SC-FDE. For s combnaton e orgnal symbol-level STBCs desgned for flat channels have to be etended to block-level for frequency-selectve channels. Ths was frst proposed by Al-Dhahr for Alamout code over a mult-nput sngle-output (MISO) wreless channel [7]. However, s technque s only applcable to specal structures of orogonal STBC (OSTBC) where e elements of each tme-slot are eer from e set 0,,..., or e set,,..., K 0 K, where s e comple conjugate of symbol. An eample of ese codes s gven n (A.) n Append. Ths technque s not applcable to e OSTBCs n whch e elements of tme-slots are members of e set0,,,...,,. To overcome s lmtaton, we propose a new desgn meod n secton III. K K For e frst tme, we addressed e applcaton of SC-FDE technque n sngle-nput sngle-output (SISO) PLC systems n [8]. In s paper, we appled SC-FDE w decson feedback equalzer (DFE) to ndoor PLC systems and compared e results w conventonal tme-doman DFE and OFDM for dfferent mpulsve nose levels. Ecept s work, SC-FDE w lnear equalzer s also employed n SISO-PLC channels n [9]-[0]. To e best of our knowledge, no prevous work has been reported for employng SC-FDE technque n mult-nput mult-output (MIMO) PLC channels, n order to eplot

3 Journal of Communcaton Engneerng, Vol., o., Autumn 0 bo dversty and FDE advantages. In s paper, to employ SC-FDE combned w orogonal STBCs n PLC channels, we frst generalze e Al-Dhahr work to all OSTBCS n whch e elements of tme-slots are members of e set0,,,...,, and propose a new technque applcable to all dspersve multpa K K channels mpared by mpulsve nose. We en apply e proposed technque to PLC channels and smulate e BER performance for bo ndoor and outdoor PLC channel under dfferent nose condtons. We show at a sgnfcant mprovement n BER performances s acheved when dversty technques are combned w SC-FDE. We also compare e BER performance of Alamout code n bo SC-FDE and OFDM and show e superorty of SC-FDE scheme. The remander of s paper s organzed as follows: A bref revew of e SC-FDE and STBC technques and PLC channel confguraton are presented n secton II. Secton III presents our proposed technque for combnng SC-FDE w OSTBCs over dspersve multpa channels. Applyng s technque to PLC channels and smulaton results for bo ndoor and outdoor PLC channels are presented n secton IV. Secton V ncludes e concluson. otaton: Bold upper case and bold lower case letters denote matrces and column vectors respectvely; unbold lower case letter stand for scalar quantty;.,. T and. * denote comple conjugate, transpose, and comple conjugate transpose, respectvely; 0 s a zero matr; and dag,,..., stands for dagonal matr w,,..., on ts dagonal entres. II. PRELIMIARY In s secton, we frst brefly eplane e prncpal of SC-FDE and STBC technques and en present e PLC channel and nose models. A. SC-FDE System Model Fg. shows a smplfed block dagram of a SC-FDE system w lnear equalzer. In e transmtter sde, e uncorrelated zero-mean symbols w varance s are dvded nto blocks of symbols and each block s prepended w a L-leng CP, where L s e mamum leng of e channel mpulse response. Fnally, e +L leng blocks are transmtted rough multpa channel. ote at, transmttng CP w each block turn out e lnear convoluton between transmtted block and channel vector to crculant convoluton, and elmnate nterblock nterference (IBI) by dscardng e CP at e recever sde [6]-[7]. At e recever, e CP s removed and e receved block after dscardng CP s epressed as: y H + n ()

4 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. 4 Input Data Modulator CP Inserton Multpa Channel ose Demodulator IFFT Channel Equalzaton FFT CP Removng Receved Data Fg.. SC-FDE system w lnear equalzer where y, and n are receved, nput and nose blocks respectvely. H s e channel crculant matr and can be decomposed as * H F F. Where F and * F are e FFT and IFFT matres respectvely. s an dagonal matr and ts nn, element s e coeffcent of channel mpulsve response h,..., h L T h. Therefore, e frequency doman output of FFT block s as: n DFT r = z +v () where r = F y, z = F and v = F n. The frequency doman lnear equalzers based mnmum mean square error (MMSE) crtera can be epressed by a vector w, whose elements w MMSE n, are equal to: * nn, w MMSE n, n,..., nn, SR () where SR s n, s and n are e average power of e transmtted symbols and nose samples respectvely. Fnally, e equalzer output s converted to tme doman by IFFT operaton and detecton s made based on hard decson by a slcer. B. A Bref Revew of STBC STBC technque was orgnally desgned for transmttng multple copes of a data stream across multple antennas n frequency-flat fadng channels. In general, a STBC s presented by a matr,,..., P n C K transmttng K comple symbols,,..., K durng P tme-slot ntervals (STBC delay) from n t antennas w a spatal rate defned as R K P. ote at each row of STBC matr s a tme-slot. t

5 Journal of Communcaton Engneerng, Vol., o., Autumn 0 5 OSTBC s one of e most attractve STBC schemes snce due to ts orogonalty, a full dversty gan and mamum-lkelhood decodng by searchng sngle symbols can be acheved. Orogonal STBC desgn was frst proposed by Alamout [] for transmt antennas and en generalzed to more by Tarokh, Jafarkhan and Calderbank []. They showed at for comple constellatons, when e number of transmt antennas eceeds, e code rate s less an unty. For hgher number of antennas, ey proposed a desgn meod w a code rate equal to /. However, s meod s not rate and delay optmal. For eample, er proposed code for and 4 transmt antennas results n delay P 8. As an alternatve, Trkkonrn and Hottnen [] proposed a /4 rate code for ree transmt antennas w delay P 4. C. PLC Channel Confguraton Remarkable attempts have been devoted by researchers to characterze e power lne channel and several modelng approaches have been presented for PLC channel. These approaches can be categorzed nto two general classes: e frst s based on e multpa model, proposed by Zmmermann and Destort [4] and e second s based on e two and mult conductors transmsson lne eores [5]-[6]. Whle e former presents e transfer functon of e channel w a small set of parameters, e letter needs e whole parameters of e network components. In s paper, we use e multpa approach for channel modelng. Multpa approach s based on e fact at n a wrng network, PLC sgnals do not propagate along a sngle pa, but suffer from reflectons caused by mpedance msmatches. In tme doman, s model can be descrbed by channel mpulsve response as follows: L. t h t l l l (4) where and are e ampltude and arrval tme of e l l l multpa component. L s e number of e propagaton pas. However, snce e network topology, cable types and connected loads to power networks are not fed and vary w tme and place, s model s not general. To overcome s lmtaton, open PLC European research allance (OPERA) presented several reference models for ndoor and outdoor PLC channels based on e multpa model [7]. Power-lne noses are categorzed nto two general classes; background and mpulsve [8]. Two attractve and popular models for PLC nose are Bernoull-Gaussan [9] and Mddleton class A [0]-[]. The nose samples for ese models are presented by (5) and (6) respectvely: n m w m b mg m (5) n m w m P mg m (6)

6 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. 6 where nm s PLC nose sample. w m s e background nose and s modeled w a comple AWG w zero-mean and varance G. Impulsve nose n Bernoull-Gaussan approach s modeled by e product of two ndependent random sequences bm and g m : where real Bernoull sequence w e probablty of success p, and g m zero-mean and varance b m s a s a comple AWG w I. ote at e parameter p can be consdered as e probablty of mpulse occurrence. P m n (6) s a statcally ndependent Posson dstrbuted random sequence whose power densty functon s characterzed by e mpulsve nde A (mean value of Posson dstrbuton) and g m s a comple AWG w zero-mean and varance I A. In bo cases e random sequences are ndependent and e mpulsve to background power rato s defned as PR. I G The estng PLC modems use only one transmttng port and one recevng port between phase and neutral wres. To ncrease e roughput of PLC channels, t s possble to apply MIMO concept to PLC systems by consderng emttng/recevng ports n mult-conductor power lnes as transmttng and recevng antennas []-[]. In ree wres ndoor nstallatons, only two dfferent nput ports are avalable at e transmtter sde. For outdoor communcatons four wres usually est and hence up to ree dfferent transmttng ports are avalable. We now combne SC-FDE w OSTBCs for multpa channels n net secton. ote at whle STBC elements for flat fadng channels are symbols, for frequency-selectve fadng channels ese elements are blocks of symbols. III. A EW TECHIQUE FOR COMBIATIO OF SC-FDE AD OSTBC As mentoned n secton I, e technque proposed by Al-Dhahr s not applcable to every OSTB code. For eample, Al-Dhahr technque s not applcable to e code gven n (A.) n Append. Therefore, to combne SC-FDE and e OSTBCs n whch e elements of tme-slots are members of e set0,,,...,,, a new desgn meod s needed. We wll present s meod n s secton. Let e t K K P n matr C,..., K denotes a comple OSTBC for a flat fadng channel. To combne SC-FDE w s code, we need to etend s symbol-level code to a block-level applcable to frequency-selectve fadng channels. Consder a MISO confguraton w nt transmt antennas and assume at e output symbols of modulator are dvded nto blocks (column vectors) of symbols and K blocks form a group,..., STBC. The transcever structure s presented below. K. The generated groups are used for formng e block-level

7 Journal of Communcaton Engneerng, Vol., o., Autumn 0 7 A. Transmtter Desgn Smlar to e dversty technque proposed by Al-Dhahr for Alamout code, we propose e followng procedure for etenson of symbol-level STBC,..., Each zero s replaced by a zero vector denote by 0. Each comple symbol Each comple conjugate symbol conjugate of ), where symbol n e block. The n element of s [7]: s replaced by e block. C K to block-level: s replaced by a -leng vector (e comple s 0,,..., T and n s e n n mod, n 0,..., (7) Hence, e dscrete Fourer transforms of e blocks and are e same. Havng generated e block-level OSTBC C,..., make e MISO subchannels crculant. B. Recever Desgn The receved block after dscardng CP, n t j j j K, ts elements are prepended w a L-leng CP to remove IBI and y, s epressed as: y H c n,,..., P (8) where H j s e channel crculant matr correspondng to e transmtted block and e transmtted block from e j j transmt antenna n e c s e element of block-level OSTBC matr C,..., j antenna. n s e nose vector n e n K correspondng to receved block where ts samples are assumed to be ndependent and dentcally dstrbuted (..d) and generated accordng to e presented modeles n () and (4). The MISO subchannels mpulse responses are assumed to be constant over P consecutve blocks and vary ndependently. Therefore we have: H... H H, j,..., n (9) P j j j t The channel matr H s crculant matr correspondng to j j MISO subchannels T h j h,..., h L j j and s decomposed lke prevous secton. To desgn a MMSE equalzer, e receved tme-doman blocks T T T T y are converted to frequency- P P doman usng FFT block and en rearranged as a r r,..., r, r,..., r T, where

8 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. 8 r F y s a vector. Ths rearrangement overcomes e lmtaton n Al-Dhahr technque and allows us to combne SC-FDE w any OSTBC. Usng s rearrangement r a can be rewrtten as: r z v (0) a where a T s a P K comple orogonal matr, z z,..., z a P P,...,,,..., T T T T v v v v v z can be calculated as follows: T, where v T T z F, where K F n. The nose samples of e nose vector j l l l z n.ep j j l l n j,,..., () where z j s e j element of e frequency-doman nose vector z. n l s e l entry of e tmedoman nose vector n and n n j j.ep l l l. As we mentoned before, e tmedoman nose entres n l are ndependent non-gaussan random varables and have been generated usng (5) and (6). Therefore, n l samples are also ndependent. As can be seen from (), e frequency-doman nose sample z j s sum of e ndependent non-gaussan random varables n l. For suffcently large, from central lmt eorem, e nose sample z j can be consdered as a zero-mean Gaussan random varable [4]. Gaussan appromaton for nose samples at e output of e FFT block s also used n [5]-[6]. In addton, e FFT operaton wll mantan e..d. property of e nose samples and does not change e varances of e nose samples. Hence n s work, e frequency-doman nose samples varables w varance n, where z j have been consdered as..d. zero-mean Gaussan random n s e varance of e tme-doman samples n l. * Multplyng bo sdes of (0) by e orogonal matr a yelds: r r = z v () * a a c where r and v * a v are K vectors. It s wor sayng at e orogonal transformaton a wll mantan e..d. and Gaussan propertes of e nose samples. Hence, e elemets of e vector v are..d. zero-mean Gaussan random varables w auto-corelaton matr equal to C., where * s a K K dagonal matr equal to c,..., K c element s a dagonal matr gven by k a a dag. The dagonal n t d for,,..., K, n whch d s a kj k kj j j v n c *

9 Journal of Communcaton Engneerng, Vol., o., Autumn 0 9 postve nteger. ote at, e value of proposed technque. We rewrte () as follows: k r z v gurantees e full transmtter dversty gan of e k k k k, k,,..., K () where e nose vector v can be calculated from v usng k v k v k : k for k,,..., K, and ts samples are..d. zero-mean Gaussan random varables w auto-corelaton matr equal to C k n. v k. Therefore, e frequency-doman MMSE equalzer k for block r, denoted by w, can now be epressed as: k w k n,, n,..., k nn, SR (4) Fnally, e equalzer output s converted to tme-doman usng IFFT block and e output s appled to a slcer for block detecton. As an eample, our proposed technque s appled to /4 rate OSTBC presented n (A.) n Append. ote at for s code, such a desgn s not possble by Al-Dhahr technque. The desgn detals are presented n Append and e smulaton results for s eample are presented n net secton. IV. SIMULATIO RESULTS In s secton, we present our smulaton results for dfferent ndoor and outdoor OPERA channels and dfferent nose scenaros usng SC transmsson, OSTBC and FDE. Snce for ndoor and outdoor low voltage PLC systems up to ree ndependent feedng ports are avalable, we present e smulaton results for OSTBCs w two and ree transmt antennas n s secton. We use e MIMO-PLC model based on e procedure proposed by Canova, Benvenuto and Bsagla [7]. Actually, s model s an etenson of OPERA reference channels to MIMO case. For realzaton of each subchannel, e taps of SISO-OPERA channel are multpled by a dfferent random j phase e where s unformly dstrbuted between e nterval0. The nose n each MIMO subchannel s also generated based on e models presented n (5) and (6). In ese smulatons 8-PSK modulaton s employed and for a far comparson, equal radated powers for MIMO, MISO and SISO confguratons are assumed. A. Smulaton Results for Indoor PLC Smulaton results for ndoor PLC usng OPERA ndoor reference channels are presented. The results are for a -wres ndoor PLC structure usng Alamout code. In Fgs. and e smulaton results are presented for OPERA channel and respectvely. Bernoull-Gaussan nose w p 0and. PR 0 for Fg. and Mddleton class A noses w

10 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. 0 mpulsve nde A 0and. PR 0 for Fg. s consdered. Each Fg. presents e results for SISO, MISO, and MIMO confguratons. The superorty of MIMO over MISO, and MISO over SISO are apparent from ese results for ndoor PLC channels when dversty technques are combned w SC-FDE under dfferent nose and channel condtons. For eample, as can be seen from Fg., at e BER of 0, about 5dB SR gan s acheved for MIMO as compared w SISO and s gan s about 0dB n Fg.. ote at e superorty of MISO over SISO s due to full transmtter dversty gan of MISO scheme and e superorty of MIMO over MISO s due to e fact at bo transmtter and recever dverstes are employed n MIMO. To verfy our smulatons, e performances of OPERA channels and 4 are compared n Fg. 4 for dentcal nose condtons. The performance of OPERA channel under Bernoull-Gaussan nose for dfferent Bernoull parameters ( p ) and dfferent mpulsve to background power ratos ( PR ) are also compared n Fgs. 5 and 6 respectvely. The results n Fgs. 5 and 6 are also compared w e stuaton where e channel s only affected by AWG nose. Smulaton results for SISO and MIMO are shown n Fgs As epected e system performance mproves for a better channel and nose crcumstances. In addton, e advantages of dversty n ndoor PLC channels are apparent from fgs 4 to 6. For eample, Fg. 4 shows about 0dB SR gan at e BER of 0 for channel 4. The performance degradaton of mpulsve nose s also apparent from Fgs. 5 and 6 when e mpulsve nose curves are compared w e AWG nose curves. Space-tme and space-frequency block codes have been proposed for MIMO-OFDM systems by many research works lke [8]-[0]. Here, to compare our block-level STBC SC-FDE technque w OFDM, we use e block-level STBC-OFDM technque for Alamout code presented by Lu el al. [8]. It s wor sayng at n s paper, a proper desgn for combnaton of Alamout code w OFDM for frequency-selectve wreless channels s presented. The comparson of our technque w e OFDM are presented n Fg. 7 for OPERA channel 4 under Mddleton class A nose w A 05. and PR 40. Ths smulaton s performed for SISO and MIMO confguratons. As can be seen, e two systems behave smlar at low and medum SRs, whle at hgh SRs SC-FDE performs better an OFDM. It s wor sayng at whle e complety of SC-FDE s not more an OFDM; t does not suffer from e OFDM drawbacks lke hgh peak to average power rato and carrer frequency offset senstvty.

11 Journal of Communcaton Engneerng, Vol., o., Autumn 0 Fg.. BER performance of OPERA ndoor reference channel under Bernoull- Gaussan nose w p = 0. and PR = 0. Fg.. BER performance of OPERA ndoor reference channel under Mddleton class A nose w A = 0. and PR = 0. Fg. 4. BER performance of OPERA ndoor reference channel and 4 under Bernoull-Gaussan nose for SISO and MIMO confguratons.

12 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. Fg. 5. BER performance of OPERA ndoor reference channel under Bernoull-Gaussan nose w dfferent p. Fg. 6. BER performance of OPERA ndoor reference channel under Bernoull- Gaussan nose w dfferent PR. Fg. 7. BER performances of OFDM and SC-FDE systems usng Alamout code and OPERA reference channel 4. B. Smulaton Results for Outdoor PLC Snce usually 4 wres are avalable n outdoor low voltage power networks, we can use up to transmttng channels for PLC purposes. For outdoor, OSTBCs presented n (A.) and (A.) for two dfferent code rates (/ and /4) togeer w SC-FDE technque are employed. Smlar to ndoor,

13 Journal of Communcaton Engneerng, Vol., o., Autumn 0 Fg. 8. BER performance of OPERA outdoor channel usng half rate code under Bernoull- Gaussan nose w p = 0.5 and PR = 40. Fg. 9. BER performance of OPERA outdoor channel usng half rate code under Bernoull- Gaussan nose w p = 0.5 and PR = 40. we use OPERA reference channels presented for outdoor wres [5]. Our smulatons results are presented for SISO, MISO and MIMO confguratons. Fgs. 8 and 9 present e smulaton results for outdoor OPERA channel models and respectvely usng half rate OSTBC gven n e Append. The nose samples for bo cases are generated by Bernoull-Gaussan model w p 05and. PR 40. As can be seen from ese results, a sgnfcant mprovement s acheved when OSTBC combned w SC-FDE n outdoor PLC channels. For eample, n Fg. 9 at e BER of as compared w SISO. 0 about 5dB SR gan s acheved n MIMO Fgs. 0 and show e smulaton results for OPERA outdoor reference channels 5 and 6 usng /4 rate OSTBC gven n (A.) under Mddleton class A nose. The Mddleton class A nose parameters for bo channels are A 0and. PR 40. Smlar to half rate code, e advantage of dversty technques combned w SC-FDE s apparent from ese Fgs for s case.for eample, n Fg. 0 at e BER of 0 about 0dB SR gan s acheved n MIMO as compared w SISO.

14 Sngle-Carrer Frequency-Doman Equalzaton for Orogonal STBC.. 4 Fg. 0. BER performance of OPERA outdoor reference channel 5 usng /4 rate code under Mddleton class A nose w A = 0. and PR = 40. Fg.. BER performance of OPERA outdoor reference channel 6 usng /4 rate code under Mddleton class A nose w A = 0. and PR = 40. V. COCLUSIO In s paper a new approach for broadband MIMO-PLC transmsson over bo ndoor and outdoor low voltage power lnes usng SC-FDE technque combned w OSTBC was presented. A new technque for combnaton of SC-FDE w orogonal STBCs applcable to all dspersve multpa channels mpared by mpulsve nose s presented. The proposed technque s en appled to space dversty frequency-selectve PLC channels. Smulaton results were presented for dfferent ndoor and outdoor channels under dfferent nose scenaros. Smulaton results show at usng e proposed dversty technque results n a sgnfcant mprovement n BER performance as compared w SISO under all channel and nose scenaros. The superorty of our proposed technque over OFDM, especally at hgh SRs, was also demonstrated. APPEDIX Here we frst ntroduce OSTBCs requred n s paper and en present e desgn meod for

15 Journal of Communcaton Engneerng, Vol., o., Autumn 0 5 combnng SC-FDE w /4 rate code. The / and /4 rate orogonal codes for 4 antennas gven n [] and [] are respectvely: C C,..., 4,..., (A.) (A.) The OSTB codes for transmt antennas can be obtaned by removng e codes. 4 column of e above To combne e SC-FDE w /4 rate code presented n (A.), we etend e code to block level based on e proposed prouder gven n secton III. Ths leads to: C,, (A.) CP s prepended to s etended code before transmsson. The receved blocks after removng CP and passng rough e FFT block are rearrange as: r a r v r 0 0 v 4 r v z 0 0 z v 4 4 r 4 v z r v * * z r 0 v * * r 0 v * * 4 4 r 0 v * where a s a 8 comple orogonal matr. Multplyng bo sde of (A.4) by a yelds: a (A.4)

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