Order-4 Quasi-Orthogonal Cooperative Communication in STFC MB-OFDM UWB

Transcription

1 Unversty of Wollongong Research Onlne aculty of Engneerng and Informaton Scences - Papers: Part aculty of Engneerng and Informaton Scences 202 Order-4 Quas-Orthogonal Cooperatve Communcaton n STC MB-ODM UWB Zxuan Ln Unversty of Wollongong, zl75@uowmal.edu.au Le Chung Tran Unversty of Wollongong, lctran@uow.edu.au arzad Safae Unversty of Wollongong, farzad@uow.edu.au Tadeusz. Wysock Unversty of ebraska-lncoln, wysock@uow.edu.au Publcaton Detals Ln, Z., Tran, L. Chung., Safae,. & Wysock, T.. (202). Order-4 Quas-Orthogonal Cooperatve Communcaton n STC MB- ODM UWB. 6th Internatonal Conference on Sgnal Processng and Communcaton Systems (ICSPCS 202) (pp ). ustrala: IEEE. Research Onlne s the open access nsttutonal repostory for the Unversty of Wollongong. or further nformaton contact the UOW Lbrary: research-pubs@uow.edu.au

2 Order-4 Quas-Orthogonal Cooperatve Communcaton n STC MB- ODM UWB bstract Recently, cooperatve communcaton and Space-Tme-requency-Codes (STCs) have been ntroduced nto the Multband ODM Ultra-Wdeband (MB-ODM UWB) to mprove the relablty, data rate and system capacty. Ths paper proposes a cooperatve communcaton scheme for a four source node MB-ODM UWB system usng Quas-Orthogonal STCs, whch s referred to as order-4 Quas-Orthogonal Cooperatve Communcaton Scheme (4-QOCCS). Smulaton results show that the proposed 4-QOCCS provdes sgnfcantly better error performance over the conventonal MB-ODM UWB and our order-2 Orthogonal Cooperatve Communcaton Scheme (2-OCCS) usng the lamout STCs, and even better than the order-4 Orthogonal Cooperatve Communcaton Scheme (4-OCCS), whch we have been recently proposed, n the hgh spectral effcency cases. Keywords era205, 4, quas, orthogonal, cooperatve, communcaton, stfc, mb, ofdm, order, uwb Dscplnes Engneerng Scence and Technology Studes Publcaton Detals Ln, Z., Tran, L. Chung., Safae,. & Wysock, T.. (202). Order-4 Quas-Orthogonal Cooperatve Communcaton n STC MB-ODM UWB. 6th Internatonal Conference on Sgnal Processng and Communcaton Systems (ICSPCS 202) (pp ). ustrala: IEEE. Ths conference paper s avalable at Research Onlne:

3 Order-4 Quas-Orthogonal Cooperatve Communcaton n STC MB-ODM UWB Zxuan Ln, Le Chung Tran and arzad Safae aculty of Informatcs Unversty of Wollongong, ustrala {zl75,lctran,farzad}@uow.edu.au Tadeusz. Wysock Peter Kewt Insttute Unversty of ebraska - Lncoln, US twysock@mal.unomaha.edu bstract Recently, cooperatve communcaton and Space-Tme- requency-codes (STCs) have been ntroduced nto the Multband ODM Ultra-Wdeband (MB-ODM UWB) to mprove the relablty, data rate and system capacty. Ths paper proposes a cooperatve communcaton scheme for a four source node MB- ODM UWB system usng Quas-Orthogonal STCs, whch s referred to as order-4 Quas-Orthogonal Cooperatve Communcaton Scheme (4-QOCCS). Smulaton results show that the proposed 4-QOCCS provdes sgnfcantly better error performance over the conventonal MB-ODM UWB and our order-2 Orthogonal Cooperatve Communcaton Scheme (2-OCCS) usng the lamout STCs, and even better than the order-4 Orthogonal Cooperatve Communcaton Scheme (4-OCCS), whch we have been recently proposed, n the hgh spectral effcency cases. I. ITRODUCTIO Recently, the combnaton of the emergng technologes ncludng Multband Orthogonal requency Dvson Multplexng Ultra-Wdeband (MB-ODM UWB) [], Multple Input Multple Output (MIMO), and Space-Tme requency Codes (STCs), whch s referred to as STC MB-ODM UWB, has receved great attenton researchers. The lterature shows that the STC MB-ODM UWB system s able to mprove sgnfcantly the relablty (bt error performance), data rate, system capacty and achevable wreless communcaton range compared to the conventonal MB-ODM UWB system [2], [3], [4]. The STC MB-ODM UWB systems proposed n [2], [3], [5] must have multple antennas at the transmtter. However, the source nodes (.e. the transmtters, such as portable devces) may only be equpped wth a sngle antenna due to ther tny physcal sze, whch does not facltate the space of at least a half wavelength to nstall two uncorrelated transmt (Tx) antennas. Cooperatve communcaton has been ntroduced to the source nodes to create a vrtual MIMO system, so that the concepts of MIMO and STCs can stll be mplemented n the MB-ODM UWB system n order to acheve large dversty. Whle cooperatve communcaton has been ntensvely researched for the conventonal wreless network, such as n [6] [7] [8], t s almost unexplored for MB-ODM UWB. In [9], we proposed an order-2 orthogonal cooperatve communcaton scheme (2-OCCS) for STC MB-ODM UWB systems usng the lamout STC, whch s the modfed verson of the orgnal lamout space-tme block code [4], for two source nodes. The framework of STCs for MB- ODM UWB systems has been derved for the frst tme n our prevous publcaton [2]. Readers may refer to [2] for more detal about how a STC s constructed the correspondng Space-Tme Block Code (STBC). The results n [9] show that the combnaton of cooperatve communcaton, STCs and MB-ODM UWB s able to gan the benefts of the MIMO system and mprove sgnfcantly the performance, compared to the conventonal MB-ODM. The lmtaton of the 2-OCCS n [9] that s the aforementoned lamout STC cannot be used for more than two source nodes. Thus, n [0], we proposed an order-4 orthogonal cooperatve communcaton scheme (4-OCCS) for four source nodes through the applcaton of an order-4 orthogonal Space-Tme-requency Code (OSTC). Ths hgher order STC s the modfed verson of the conventonal order-4, rate-3/4 STBC proposed n []. The order-4 rate-3/4 STBC offers a greater dversty wth the cost of havng a smaller code rate, compared to the conventonal lamout STBC [4]. The results n [0] show that the 4-OCCS performs sgnfcantly better, compared to the 2-OCCS, at the same data rate and wth the same transmsson power. In ths paper, we proposes another cooperatve scheme, namely order-4 quas-orthogonal cooperatve communcaton scheme (4-QOCCS), for four source nodes by applyng an order-4 quas-orthogonal Space-Tme-requency Code (QOSTC), whch s the modfed verson of the conventonal order-4, full-rate quas-orthogonal STBC proposed n [2]. Ths QOSTC provdes full-rate transmsson for four source nodes wth the cost of smaller dversty than the order-4, rate- 3/4 STC mentoned n [0]. ddtonally, a new subband allocaton technque for the 4-QOCCS s also ntroduced n ths paper. We wll then show that the performance of the 4- QOCCS s sgnfcantly better than that of the 2-OCCS we proposed prevously, and even better than the 4-OCCS n some cases. Ths paper s organzed as follows. Secton II brefly revews our 4-OCCS proposed n [0]. Secton III presents the proposed 4-QOCCS. Smulaton results are shown n Secton IV and Secton V concludes the paper. otatons: The followng notatons wll be used throughout the paper. The superscrpts. and. T denote the complex conjugaton and transposton operaton, respectvely. We denote a b to be the element-wse (or Hadamard) product of the two vectors a and b. and are the number of data subcarrers and the T/IT sze, respectvely (for MB- ODM UWB communcatons [], = 00 and = 28) /2/$ IEEE

4 g.. Cooperatve communcaton for a four source node MB-ODM UWB system urther, a.^2 denotes the element-wse power-2 operaton of a. The complex space C of a symbol s denotes all potental possbltes that the symbol s can take, whle the D dmensonal complex space C of a -length vector denotes all D potental possbltes that the vector can take. We defne as a column vector of length, whose elements are all ones. We denote. to be the robenus norm. nally, we refer the tme requred to transmt a MB-ODM symbol to as a MB-ODM symbol tme slot, whch s 32.5 ns, ncludng the T/IT perod of ns and the zero padded suffx duraton of ns []. II. ORDER-4 ORTHOGOL COOPERTIVE COMMUICTIO SCHEME (4-OCCS) Ths secton brefly revews the 4-OCCS that we proposed n [0]. The proposed system model s llustrated n g.. Due to the lmted space, the STC constructon method for MB- ODM UWB system wll not be revewed n ths paper. Interested reader may refer to our prevous publcaton [2, Secton III] for more detal. In ths scheme, we consder the applcaton of the followng rate-3/4 orthogonal STC, whch s a modfed verson of the rate-3/4 STBC n [], to enable four sngle-antenna source nodes to cooperate s sb sc 0 sb s 0 sc S = sc 0 s s B 0 sc s B s where the STC symbols, and are correspondng to the -th MB-ODM symbols transmtted the nodes, B and C, respectvely, n the frst tme slot. These MB-ODM symbols are the column vectors that consst of the orgnal transmtted data (.e. before the IT operaton). It s assumed that the nodes n the proposed system are perfectly synchronzed. The channels between nodes are modeled as ndependent log-normally dstrbuted random varables (RVs) [3]. Denote,,,,, to be the channel vector () g.2. Subband allocaton n the 4-OCCS n four tme slots between two nodes j and k, at the m-th antenna of the destnaton node, where j {,B,C,D}, k {,B,C,D,d}, m {,2...,}, and represents the number of multpath n ths lnk. We assume the channel vectors reman constant durng every four MB-ODM symbol tme slots, and are known at the destnaton node. Each of the source nodes, B, C and D s equpped wth only one antenna for transmttng and recevng sgnals, whle the destnaton node d mght be equpped wth antennas. One may have a queston: Does the four source nodes need to occupy four subbands n the cooperatve MB-ODM UWB system to work properly? rom Eq. (), t s clear that, n the proposed system, one source node always remans dle when three other nodes transmt three MB-ODM symbols over ther three antennas n every tme slot. Thus, n the 4-OCCS, we proposed a new subband allocaton method that allows the system to work properly by occupyng just three subbands n the frst band group of MB-ODM UWB [0]. It s noted that MB-ODM UWB devces are standardzed to support for the frst band group ( MHz) [, Table 7-], and that the TC (Tme-requency Code) numbers 5, 6 and 7 for the frst band group are non-overlapped wth each other [, Table 7-2]. In order for the system to work properly by just takng three subbands, the source nodes, B and C n the proposed system must be able to transmt data n one certan subband and receve data n other two subbands. In the 4-OCCS, ode transmts sgnals usng TC 7 (R s n the range MHz correspondng to the subband 3) and receves sgnals usng TC 6 (R n the range MHz, subband 2) and TC 5 ( MHz, subband ). ode B transmts sgnals usng TC 6 and receves sgnals usng TC 5 and TC 7. ode C transmts sgnals usng TC 5 and receves va TC 6 and TC 7. ode D transmts sgnals n the subband, 2 and 3 sequentally,.e. ths node uses TC when transmttng, and receves data all the subbands. The destnaton node must be able to receve sgnals all subbands n the frst band group. s shown n g.2, n the frst tme slot, odes, B and C broadcast the MB-ODM symbols,, and, to all the nodes n the system n the subbands 3, 2 and respectvely, whle ode D does not transmt, but just receves the data these three nodes n three dfferent subbands. fter frst tme slot, every node has receved at least two MB-ODM symbols ther partners. The receved data can be

5 TBLE I DECODIG METRICS OR THE 4-OCCS I THE CSE O PSK OR QM MODULTO Symbol Decodng Metrc r = h s + h s + h s + n m dm Bdm B Cdm C m 2m = dm ŚB + Bdm Ś + ŚC + 2m r h h h n 3m = dm ŚC + Cdm Ś ŚB + 3m r h h h n 4m = Bdm ŚC + Cdm ŚB + Ś + 4m r h h h n (2) s s B { ( arg mn 2 D h dm r m + hbdm r m hcdm r3m h r4m ) s.^2 [ ( hdm.^2 + hbdm.^2 + hcdm.^ h ( s ) )] }.^2.^2 { ( ( s ) 2 arg mn D h Bdm r m hdm r2m h r3m h Cdm r4m ) s.^2 [ ( hdm.^2 + hbdm.^2 + hcdm.^ h )] }.^2.^2 2 where h jkm = T ( h jkm ), n tm = T( ntm ),whle n tm ( t =,2,3,4) denotes the column vector of complex Gaussan nose affectng the m-th Rx antenna at the destnaton node durng the t-th MB-ODM symbol tme slot. Denote T T hjkm = [ jkm,, jkm,2,,..., jkm, ] and rtm = [ r fft tm,, rtm,2,..., r tm, ]. ssume that the nformaton transmtted the source nodes fft can be error-freely decoded by ther partners,.e., and. The ML decodng wll be appled to decode the symbols. In the proposed system, each of the MB- ODM symbols, and can be decoded separately, rather than jontly, thanks to the orthogonalty of the code matrx () as shown n Table I. Moreover, each among data wthn each MB-ODM symbol can also be separately decoded, rather than decodng the whole data smultaneously. Thus the decodng complexty s relatvely smple. or n =,...,, the decodng metrcs for the n-th data subcarrer n MB-ODM symbols, and are s C { ( arg mn D h dm rm + hbdm r2m hcdm r3m h r4m ) s.^2 [ ( hdm.^2 + hbdm.^2 + hcdm.^ h ( s ) )] }.^2.^2 dstngushed by dfferent subbands. We denote the decoded symbols at each nodes to be, and. In the second tme slot, odes, B and D transmt the decoded MB-ODM symbol -, and to the destnaton n the subbands 3, 2 and respectvely. ode D occupes the subband because ode C s slent n the second tme slot. In the thrd tme slot, ode B keeps slent whle ode, C and D transmt the data -, and - to the destnaton node d n the subbands 3, and 2 respectvely. ode D occupes the subband 2 snce ode B s slent. In the fourth tme slot, odes B, C and D transmt the data -, and to the destnaton n the subbands 2, and 3 respectvely. ode D occupes the subband 3 snce ode s slent. The destnaton s able to decode the MB-ODM symbol, and after four tme slots. The decodng procedure s presented as follows. fter the overlap-and-add operaton (OO) [], [2] and T have been performed, the sgnals receved at the m-th receve (Rx) antenna at the destnaton node durng the four tme slots can be represented as 2 s s {, = arg mn ( n r mn, ) s + [ + ( Cdm, n, n )] s } { B, = arg mn ( n r mn, ) s + [ + ( + + )] s } (3) { C, = arg mn ( n r mn, ) s + [ + ( )] s } s It has been shown that the 4-OCCS n [0] acheves a sgnfcantly better performance than the 2-OCCS n [9] that we proposed prevously. However, the 4-OCCS provdes better dversty to the system wth the cost of havng a smaller bt rate. The smaller bt rate may cause the performance degradaton n the hgh spectral effcency cases. Thus, n ths paper, we propose a full-rate order-4 quas-orthogonal cooperatve communcaton STC scheme, referred to as 4-QOCCS.

6 g.3. Transmsson protocol n the 4-QOCCS III. ORDER-4 QUSI-ORTHOGOL COOPERTIVE COMMUICTIO SCHEME (4-QOCCS) In ths scheme, we consder the applcaton of the followng full-rate quas-orthogonal STC (QOSTC), whch s n turn the STC verson of the full-rate QOSTBC n [2], s sb sc sd s B s sd sc S = sc sd s sb s D s C s B s where the STC symbols,, and are column vectors that consst of the orgnal transmtted data and correspond to the -th MB-ODM symbol transmtted by the nodes, B, C and D respectvely n the frst tme slot. Symbols transmtted n the subsequent tme slots are depcted n g.3. The four symbols can be decoded after four MB-ODM symbol tme slots. It s well-known that the orthogonalty (and thus the dversty) of QOSTBCs s partally released,.e. not all columns (and rows) are orthogonal wth each others, to ncrease the code rate, and that these rate-mproved codes mght stll provde better error performance than the counterpart STBCs at a certan SR range [2]. Denote,,,,, to be the channel vector between two nodes j and k, at the m-th Rx antenna of the destnaton node, where j {,B,C,D}, k {,B,C,D,d}, m {,2...,}, and represents the number of multpath n ths lnk. The channels between nodes are modeled as ndependently log-normally dstrbuted RVs [3] and we assumed the channel vectors reman constant durng every four MB-ODM symbol tme slots, and are known at the destnaton node. Each of the source nodes, B, C and D s equpped wth only one antenna, whle the destnaton node d mght be equpped wth antennas. It s also assumed that the nodes n the proposed system are perfectly synchronzed.. Subband llocaton The transmsson protocol n the proposed 4-QOCCS s presented n g. 3. rom Eq. (4), t s clear that, n the proposed system, all the nodes are transmttng sgnals over four tme slots. Thus, n the 4-QOCCS, we have to use at least four subbands to allow all the source nodes to receve and transmt the sgnals smultaneously. In ths paper, we propose a new (4) g 4. Subband allocaton n the 4-QOCCS n four tme slots subband allocaton method for the 4-QOCCS that allows every source node n the system to work wth mnmum number of subbands n each tme slot to reduce the complexty of the system. The MB-ODM UWB devces n the 4-QOCCS must support the three subbands n the frst band group ( MHz) and the frst subband n the second band group ( MHz) [, Table 7-]. In order for the system to work properly, the source nodes, B, C and D n the proposed system must be able to transmt data n one certan subband and receve data two other subbands. The destnaton node d must able to receve the data usng these four subbands. The subband allocaton for the 4-QOCCS s shown n g.4. ode transmts sgnals usng TC 5 n band group (R s n the range MHz correspondng to the subband ) and receves sgnals usng TC 6 n band group (R n the range MHz, subband 2) and TC 5 n second band group ( MHz, subband 4). ode B transmts sgnals usng TC 6 n band group and receves sgnals usng TC 5 and TC 7 (R n the range MHz, subband 3) n band group. ode C transmts sgnals usng TC 7 and receves va TC 5 n band group and TC 5 n band group 2. ode D transmts sgnals usng TC 5 n band group 2 and receves sgnals usng TC 7 and TC5 n frst band group. Detal of how the nodes transmt sgnals n the proposed 4- QOCCS system s explaned as follows. our nodes cooperate n sendng the quas-orthogonal matrx n (4) to the destnaton. The ssue of how ths node quadruple s selected among the nodes n the network s out of the scope of ths paper. Instead, ths paper addresses the full-duplex cooperatve communcatons scheme for ths quadruple and the decodng method. s shown n g.4 and g.5, each source node n the proposed system transmts sgnals n one subband and receves sgnals one partner n other subband n ever tme slot. In the frst tme slot, odes, B, C and D broadcast the MB- ODM symbols,,, and, to all the nodes n the system n the subbands, 2 and 3 n band group and subband 4 n the band group 2 respectvely. ode receves ode B n subband 2. ode B receves ode n subband. Smlarly, ode C receves the data ode D n subband 4 and ode D receves the symbol

7 TBLE II DECODIG METRICS OR THE 4-QOCCS WITH PSK OR QM MODULTO where h jkm = T ( h jkm ), n tm = T( ntm ),whle n tm ( t =,2,3,4) denotes the column vector of complex Gaussan nose affectng the m-th Rx antenna of the destnaton node at the t-th MB- T ODM symbol tme slot. Denote h = [,,,2,,...,, ] Symbols Decodng Metrc g.5. Subband allocaton at dfferent tme slots n the 4-QOCCS ode C n subband 3. t ths pont, every source nodes has the nformaton to construct the transmsson for the second tme slot of the QOSTC n (4). We denote the decoded symbols at each nodes to be,, and. In the second tme slot, odes, B, C and D transmt the decoded symbol -,,- and to the destnaton n the subbands, 2, 3 and 4 respectvely. In ths tme slot, ode receves the sgnal ode D and ode B receves - ode C. ode C receves ode B and ode D receves - ode. In the thrd tme slot, odes, B, C and D transmt the sgnal -, -, and to the destnaton node d n the subband to 4 respectvely. In ths tme slot, ode and ode B exchange the sgnals, thus ode receves - ode B and ode B receves - ode. ode C and ode D exchange the sgnals, thus ode C receves ode D and ode D receves ode C. In the fourth tme slot, odes, B, C and D transmt the symbol,-,- and to the destnaton n the subband to 4 respectvely. The destnaton s able to decode the MB- ODM symbol,, and after four tme slots (cf. g.3). The decodng procedure for 4-QOCCS s presented as follows. B. Decodng Metrcs fter the overlap-and-add operaton (OO) [4], [6] and T have been performed n the destnaton node, the sgnals receved at the m-th Rx antenna at the destnaton node durng the four tme slots can be represented as r = h s + h s + h s + h s + n m dm Bdm B Cdm C Cdm D m 2m = dm ŚB + Bdm Ś Cdm ŚD + ŚC + 2m 3m = dm ŚC Bdm ŚD + Cdm Ś + ŚB + 3m r h h h h n r h h h h n r = h Ś h Ś h Ś + h Ś + n 4m dm D Bdm C Cdm B 4m jkm jkm jkm jkm fft (5) ( s, arg mn D ( h (.^2) ( s.^2 + sd.^2) jdm D s D ) s, sd C j= + 2Re {( h dm rm hbdm r2m hcdm r3m h r4m ) s + ( h r m + h Cdm r2m + h Bdm r3m hdm r4m ) sd + ( hdm h h Bdm hcdm hbdm h Cdm + h dm h ) s ( D sd}) 2 ( s B, arg mn ( h jdm.^2) ( sb.^2 + sc.^2) D s C ) sb, sc C j= + 2Re {( hbdm r m + h dm r2m h r3m h r4m ) sb + ( hcdm r m h r2m + h r + h r ) s + ( h h dm 3m Bdm 4m C Bdm Cdm dm dm Bdm Cdm ) h h h h + h h s and tm = tm, tm,2 tm, fft B sc}) 2 T r [ r, r,..., r ].We also assume that the nformaton transmtted the source nodes can be error-freely decoded by ther partners as mentoned n Secton II. The ML decodng wll be appled to decode the symbols. Unlke the 4- OCCS, n the 4-QOCCS, the MB-ODM symbols cannot be decoded separately owng to the partal (rather than complete) orthogonalty characterstcs of the QOSTC n (4), n the smlar manner of the QOSTBC n [2]. Specfcally, the MB- ODM symbols and, and can be decoded n par, rather than jontly, as mentoned n Table II. More mportantly, each among data wthn each MB-ODM symbol can also be decoded n par, rather than decodng the whole 2 data smultaneously. or n =,...,, the decodng metrcs for the n-th data subcarrer n MB-ODM symbols,, and are as follows (the subscrpt s omtted for smplcty) ( D ( s, s D) = arg mn ( jdm, n )( s + sd ) s, sd C j= + 2Re {( r mn, ) s+ ( r mn, Bdm, nr3 m, n dm, nr 4 m, n ) sd + ( dm, n, n Bdm, n ) ss D})

8 ( D ( sb, s C) = arg mn ( jdm, n )( sb + sc ) sb, sc C j= + 2Re {( r mn, ) sb+ ( r mn, r 4 mn, ) sc + ( dm, n ) ss B C}) C. Comments on Transcever Desgn Complexty and Power Consumpton The nherent desgn of MB-ODM UWB devces provdes an mportant feature that t mght have already allowed the devces to work wth dfferent TCs (.e. dfferent subbands) n dfferent band groups. s a result, n order to mplement the proposed cooperatve system, we only need to make all the source nodes to be able to transmt sgnals n one subband, and receve sgnals n two other subbands (one subband at a tme), whle the destnaton node to be able to receve sgnals all four subbands n the frst and second band groups at the same tme. These are not very dffcult tasks thanks to the mplementaton of precse flters. Therefore, desgn of the transcevers at nodes can be created by modfyng ther current desgn wthout heavy addtonal complexty. s mentoned n detal n Secton IV, the total transmtted power the four source nodes, whch s the man porton of the consumed power at these nodes, s kept to be the same when comparng to our prevous 2-OCCS and 4-OCCS schemes, for the far comparson. Wth ths power constrant, the proposed 4-QOCCS can stll provde sgnfcantly better error performance, compared to the 2-OCCS, and even the 4- OCCS (n hgh spectral effcency cases). IV. SIMULTIO RESULTS To examne the performance advantage of cooperatve communcaton, we ran several Monte-Carlo smulatons for the 2-OCCS, 4-OCCS, and 4-QOCCS. Each run of smulatons was carred out wth 200 MB-ODM symbols. One hundred channel realzatons of each channel model (CM to CM4) were consdered for the transmsson of each MB- ODM symbol. In smulatons, SR s defned to be the sgnal-to-nose rato (db) per sample n a MB-ODM symbol at each Rx antenna. In order to farly compare the error performance of noncooperatve and our two prevous cooperatve communcaton schemes, namely 2-OCCS and 4-OCCS, the followng constrant s appled to all smulatons. Power constrant: The total receved power at each Rx antenna at the destnaton durng each tme slot need to be the same n all systems. Therefore, the sgnal constellaton ponts n the 2-OCCS are scaled down by a factor of / 2. The sgnal constellaton ponts n the 4-OCCS (cf. Eq.()) are scaled down by a factor of / 3, whle the factor s /2 for the case of 4- QOCCS (cf. Eq.(4)) (6) g.6. 4-QOCCS vs. 2-OCCS and conventonal MB-ODM UWB wth 3bts/s/Hz spectral effcency g.7. 4-QOCCS vs. 4-OCCS wth 3bts/s/Hz spectral effcency and oneantenna destnaton node g.8. 4-QOCCS vs. 4-OCCS wth 5bts/s/Hz and 4.5bts/s/Hz spectral effcency, respectvely, and two-antenna destnaton node

9 g.6 compares the error performances of the three systems, namely conventonal MB-ODM, 2-OCCS and 4- QOCCS, n the case where all nodes are equpped wth one antenna. rom g.6, t s clear that the 4-QOCCS provdes sgnfcantly better error performance than the conventonal system and the 2-OCCS scheme n the channel models CM and CM2. The performances of the two cooperatve systems become closer n CM3 and CM4 due to the fact the channels are extremely dspersve, causng a serous nter-symbol nterference problem that neutralzes the dversty advantage of the order-4 cooperatve communcaton. g.7 presents the error performances of the 4-OCCS and 4-QOCCS n the case where all nodes are equpped wth one antenna. In ths smulaton, the rate-3/4 4-OCCS uses 6- QM whle the full rate 4-QOCCS uses 8PSK, thus they all have 3bts/s/Hz spectral effcency. g. 7 shows that the 4- OCCS scheme provdes better error performance than the 4- QOCCS scheme. The reason s the order-4 orthogonal STC provdes more dversty than the order-4 quas-orthogonal STC (as mentoned prevously n Secton III, QOSTCs possess partal, rather than full, dversty snce not all columns (and rows) are orthogonal). In ths case, although the 4-OCCS uses hgher densty modulaton to have the same spectral effcency as the 4-QOCCS, havng hgher dversty thanks to the orthogonal STC stll allows the 4-OCCS to have better error performance than the 4-QOCCS. g.8 demonstrates the error performance of the two order-4 systems n the case where the destnaton node s equpped wth 2 Rx antennas. In ths smulaton, the rate-3/4 4-OCCS uses 64- QM to acheve 4.5bts/s/Hz spectral effcency. The full rate 4-QOCCS uses 32-QM and t has 5bts/s/Hz spectral effcency, whch s even greater than that n the 4-OCCS. rom g.8, one can observe that the 4-QOCCS s sgnfcantly better than the 4-OCCS. The reason s the 4-OCCS only has the code rate of ¾, unlke the 4-QOCCS whch has the code rate of one. To acheve the 4.5bts/s/Hz spectral effcency, a hgher densty modulaton scheme has to be used n the 4-OCCS. The hgh densty modulaton neutralzes the beneft of the hgher dversty possessed by the orthogonal STC. In other words, the 4- QOCCS has full-rate transmsson and t has more advantages when the systems are compared at hgh spectral effcency values. V. COCLUSIOS Ths paper has proposed an order-4 quas-orthogonal STC cooperatve communcaton scheme (4-QOCCS) for MB- ODM UWB communcaton. novel subband allocaton scheme has also been proposed for ths QOCCS n the paper. In addton, the paper has compared the performance of the proposed 4-QOCCS wth the 4-OCCS, whch we have proposed prevously, at dfferent spectral effcency values. rom the smulaton results, an mportant observaton can be drawn that, at lower spectral effcency, the performance of the 4-OCCS s better than the 4-QOCCS,.e. the full dversty brngs more beneft than the full rate. However, at hgher spectral effcency, the 4-QOCCS can acheve better performance than the 4- OCCS,.e. the full rate mght be more preferred n ths case. Our future work would be the examnaton of the proposed schemes n the scenaro where nodes mght be erroneously decoded by ther partners. Together wth our exstng analyses, ths work shall provde a more comprehensve evaluaton of the proposed cooperatve communcaton schemes. REERECES [] WMeda, Multband ODM physcal layer specfcaton, WMeda llance, Release., July [2] L.C.Tran and. Mertns, Space-Tme-requency Code mplementaton n MB-ODM UWB communcatons: Desgn crtera and performance, IEEE Transactons on Wreless Communcatons, vol. 8, no. 2, pp , eb [3] L. C. Tran,. Mertns, E. Dutkewcz, and X. Huang, Space-tmefrequency codes n MB-ODM UWB communcatons: dvanced order-8 STC and ts performance, Proc. 7th IEEE Internatonal Symposum on Communcatons and Informaton Technologes ISCIT 2007, Oct [4] T.-H. Tan and K.-C. 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