PAPER 2-Dimensional OVSF Spread/Chip-Interleaved CDMA

Transcription

1 IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER PAPER 2-Dimensional OVSF Spread/Chip-Interleaved CDMA Le LIU a), Stdent Member and Fmiyki ADACHI, Member SUMMARY Mltiple-access intererence MAI) limits the bit error rate BER) perormance o CDMA plink transmission. In this paper, we propose a generalized chip-interleaved CDMA with 2-dimensional 2D) spreading sing orthogonal variable spreading actor OVSF) codes to minimize the MAI eects and achieve the maximm available timeand reqency-domain diversity gains. We present the code assignment or 2D spreading to provide sers with lexible mlti-rate data transmission. A compter simlation shows that by the joint se o 2D OVSF spreading and chip-interleaving, MAI-ree transmission is possible or the qasi-synchronos DS- or MC-CDMA plink, and hence the single-ser reqency-domain eqalization based on the MMSE criterion can be applied or signal detection. The BER perormance in a time- and reqencyselective ading mltiser channel is theoretically analyzed and evalated by both nmerical comptation and compter simlation. key words: CDMA, mlti-rate, plink transmission, chip interleaving, 2- dimensional OVSF spreading. Introdction In next generation mobile commnications, a lexible spport o low-to-high bit rate or mlti-rate) mltimedia services is reqired [], [2]. Using code division mltiple access CDMA) techniqe [3], mlti-rate data transmission can be achieved by changing the nmber o parallel orthogonal spreading codes in the mlticode transmission or by simply changing the spreading actor in the single-code transmission [4] [6]. The well-known CDMA techniqes inclde single-carrier direct seqence DS)-CDMA [2], [4] sing time-domain spreading and mlticarrier MC)-CDMA [7] [0] sing reqency-domain spreading. Recently, it was shown [2], [6] that the reqency-domain eqalization FDE) based on the minimm mean sqare error MMSE) criterion can signiicantly improve the BER perormance o DS-CDMA downlink transmission in a severe reqencyselective ading channel, compared to conventional coherent rake combining. The downlink DS-CDMA with MMSE- FDE can achieve almost the same BER perormance as the downlink MC-CDMA. However, in plink transmission, dierent sers signals go throgh dierent channels and are asynchronosly received, which prodces mltiple-access intererence MAI) and limits the plink capacity. The sppression o MAI to increase the link capacity as well as to provide mltirate services is a challenging task or the realization o the Manscript received October 20, Manscript revised Jne 4, The athors are with the Dept. o Electrical and Commnication Engineering,Tohok University, Sendai-shi, Japan. a) lile@mobile.ecei.tohok.ac.jp DOI: 0.093/ietcom/e89 b next generation mobile commnication systems []. Althogh mltiser detection MUD) [2], [3] can be sed to mitigate the detrimental eects o MAI, the MUD algorithms are relatively complex, and their comptational complexity increases exponentially with the nmber o sers. MUD receivers at the base station also reqire the knowledge o all sers channels. In practice, however, the sers channel inormation needs to be estimated rom the received signals and are prone to the MAI and noise. It has been shown by [4] that MUD is sensitive to time delay mismatch, especially in a near-ar environment. Chip repetition in the time-domain was proposed or asynchronos DS-CDMA plink sing coherent rake combing at the base station [5], where the ser-speciic reqency shit is sed to separate simltaneosly accessing sers. Recently, chip-interleaving together with orthogonal spreading codes has been proposed or DS-CDMA to cancel the MAI in a qasi-synchronos mltipath channel [6], [7]. In [6] and [7], it was ond that chipinterleaved DS-CDMA with cyclic preix as a gard interval GI) can provide better perormance by sing simple FDE. Provided that the propagation channel delays and transmit timings o dierent sers are within the GI, MAIree transmission is garanteed by ser-speciic orthogonal codes. More recently, we have introdced 2-dimensional 2D) spreading sing orthogonal variable spreading actor OVSF) codes [8], [9] or the chip-interleaved DS-CDMA plink transmission [20], [2]. A joint se o 2D OVSF spreading and chip-interleaving makes it possible to realize mlti-rate transmission while avoiding high-complexity MUD processing. In this paper, we extend this concept to a generalized chip-interleaved mlti-rate DS- and MC-) CDMA with 2D OVSF spreading or qasi-synchronos plink transmission. This generalized scheme can provide either DSor MC-CDMA with lexible mti-rate/mlti-connection services in both downlink and qasi-synchronos plink. In this paper, we consider mlti-rate, single-code CDMA plink transmission in a mltiser environment and present the optimm code assignment or 2D OVSF spreading with the given overall spreading actor, SF = SF t SF,whereSF is the spreading actor o the st OVSF spreading code or mlti-rate services per ser and SF t is the spreading actor o the 2nd one or orthogonal mltiser mltiplexing. Throgh appropriate code assignment o 2D OVSF spreading, not only the maximm time- and reqency-domain diversity gains can be achieved bt also a lexible spport or Copyright c 2006 The Institte o Electronics, Inormation and Commnication Engineers

2 3364 IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER 2006 the low-to-high bit rate o mltimedia services is possible. Most o the previos works aiming at MAI sppression ocsed on the ncoded case. However, analyses o dierent schemes withot coding do not always properly predict the perormances o those with coding [22], [23]. In this paper, the trbo-coded BER perormance o or proposed 2D OVSF spread/chip-interleaved CDMA is evalated and compared with that o conventional mltiser CDMA with MUD reception. The remainder o this paper is organized as ollows. Section 2 presents the plink transmission model o 2D OVSF spread/chip-interleaved DS- and MC-CDMA. Then, the code assignment or the 2D OVSF spreading is discssed in Sect. 3. In Sect. 4, an exact theoretical analysis o the conditional BER perormance is presented taking the ading Doppler spread into accont. Using the derived conditional BER expression, the average BER is evalated by the Monte-Carlo nmerical comptation method in Sect. 5, which is conirmed by compter simlation. The trbocoded BER perormance obtained by compter simlation is also presented in Sect. 5 and the impact o the ading Doppler reqency on the BER perormance is discssed. Finally, Sect. 6 oers conclding remarks and tre work. 2. Transmission System Model We assme the mlti-rate, single-code CDMA plink transmission with U active sers this scheme can also be applied to the CDMA downlink transmission). The transmission model is illstrated in Fig., where only the th ser, = 0 U, is considered this scheme can also be applied to downlink transmission). Here, we assme the sqareroot Nyqist chip shaping ilter at the transmitter and the same ilter at the receiver as the chip-matched ilter. Ideal chip sampling timing is assmed at the receiver. Thereore, the chip-spaced discrete-time signal representation is sed throghot the paper. In this paper, a denotes the amplitde o complex-valed a, a is the largest integer smaller than or eqal to the real-valed variable a and a is the smallest integer larger than or eqal to a. E[ ] denotes the ensemble average operation and x mod y is the modls operation to get the remainder ater division x/y. 2. Transmitted Signal We consider the block data transmission o / symbols, where is the spreading actor o the th ser s st OVSF spreading code c SF t); t = 0 } with c SF t) = and is the FFT/IFFT block size or FDE sed at the base-station receiver. The th ser s data symbol seqence d n); n = 0 / )} with E[ d n) 2 ] = is spread by c SF t); t = 0 } and is rther mltiplied by a binary scramble seqence c scr t); t = 0 } to prodce the DS-CDMA signal s DS t). s DS t) can be expressed as ) s DS t) = c scr t)d t/sf SF c t mod ). ) I -point IFFT is applied to s DS t), an MC-CDMA Fig. Uplink transmitter/receiver strctre.

3 LIU and ADACHI: 2-DIMENSIONAL OVSF SPREAD/CHIP-INTERLEAVED CDMA 3365 signal s MC t) is generated. In order to make better se o the channel reqency-selectivity, / )-chip interleaving is perormed beore IFFT. Then, the data chips are distribted, with an eqal distance o / ) sbcarriers, over sbcarriers. s MC t) can be expressed as s MC t) = Nc / n=0 exp j2π t sds n + i) n + i. 2) Next, the -chip CDMA signal s t) is spread by the 2nd OVSF spreading code c SF t t); t = 0 SF t } with spreading actor SF t. Then, the chip-interleaving, as shown in Fig. 2, is perormed with colmn-wise inpt and row-wise otpt. As illstrated in Fig. 3, the 2D OVSF spreading or DS-CDMA is done in the time-domain only; while, in the case o MC-CDMA, data is spread in both the time- and reqency-domain. The interleaver otpt chip seqence is divided into -chip blocks. Beore transmission, an N g - chip GI is inserted every -chip block to avoid inter-block intererence IBI). The transmitted signal can be expressed sing eqivalent lowpass representation as s t) = 2E c / s t mod )c SF t t/ ) 3) or t = N g SF t +N g ) N g, where E c is the average chip energy and is the chip dration. 2.2 Channel The GI-inserted signal is transmitted over a reqency- and time-selective ading channel. Assming that the channel has L independent propagation paths, the discrete-time implse response h τ, t) otheth ser at time t is expressed as [24] L h τ, t) = h,l t/t )δτ τ,l ), 4) l=0 where h,l t/t ) and τ,l are respectively the complexvaled path gain and time delay o the lth path with L l=0 E[ h,l t) 2 ] =, and δx) is the delta nction. We assme a block ading, where the path gains h,l t/t ) remain constant over one block interval T = + N g ), bt vary block-by-block. τ,l is assmed to be -spaced time delays and eqal to τ,l = τ + l, l = 0 L, where τ is the th ser s transmit timing oset. The maximm time delay o τ,l } is assmed to be shorter than the GI we assme some transmit timing control). 2.3 Received Signal The sm o U sers aded signals is received by a basestation receiver. The received signal is sampled at the chip rate and the GI is removed irst. The GI-removed received signal can be written as U L rt) = h,l t/t ) s t τ,l ) + nt), 5) =0 l=0 where nt) is the zero-mean additive white Gassian noise AWGN) with the variance o 2N 0 / N 0 is the one-sided power spectrm density). 2.4 Chip-Deinterleaving/st Despreading Chip-deinterleaving is illstrated in Fig. 4. As shown in Fig. 4, rt)issf t -chip deinterleaved and then the st despreading is perormed sing the 2nd OVSF spreading code c SF t t); t = 0 SF t } as ŝ t) = SF t SF t rt + i ) [ c SF t i) ] or t = 0, where ) denotes the conjgate operation. Since c SF t t); = 0 U } are orthogonal, the MAI can be cancelled i the ading is very slow so that the path gains stay almost constant over at least SF t consective blocks. 6) Fig. 2 Chip-interleaving. 2.5 MMSE-FDE Ater despreading, -point FFT is applied to decompose a) DS-CDMA b) MC-CDMA Fig. 3 2D OVSF spreading and chip-interleaving Fig. 4 Chip-deinterleaving.

4 3366 IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER 2006 the despread signal ŝ t); t = 0 )} into reqency components ˆR k); k = 0 )} as ˆR k) = Nc t=0 ŝ t)exp j2πk t ). 7) I U =0 SF t ) andu sers are assigned dierent 2nd OVSF spreading codes, the MAI can be perectly eliminated and hence, single-ser one-tap MMSE-FDE can be carried ot on each reqency component as Y k) = w k) ˆR k), 8) where w k) is the MMSE-FDE weight given by [2], [6] H w k) = k) H k) 2 + SF ) t E c /N 9) 0 with H k) beingthekth reqency component o the th ser s channel gain. On the other hand, i U =0 SF t ) >, the same 2nd OVSF spreading code is assigned to more than one sers. Users with the same OVSF spreading code belong to the same grop and they are intererence-ree rom other grops with dierent 2nd OVSF spreading codes. I there are morethan-one sers in some grops, the MAI is prodced in those grops and the MMSE-MUD is necessary to minimize the residal MAI. However, since the nmber o sers in those grops is still mch smaller than U, MMSE-MUD is mch less complex than that considered in [2], which needs to combat the MAI rom all U sers. For DS-CDMA, an -point IFFT is applied to Y k); k = 0 } to get the time-domain chip seqence: y DS t) = Nc Y k)exp j2πt k ) 0) or t = 0. On the other hand, as shown in Fig., the MC-CDMA signal y MC t) is obtained directly rom the reqency-domain deinterleaver as y MC t) = Y t mod SF ) / ) + ) t/ ) or t = nd Despreading The 2nd despreading sing the st OVSF spreading code c SF t) is perormed to get the decision variable ˆd n) associated with d n) as ˆd n) = n+)sf t=n [ y t) c SF t)c scr t)], 2) based on which the log-likelihood ratio LLR) [22], [23] is compted or trbo decoding. 2.7 LLR Comptation A seqence o sot vales or trbo decoding can be generated sing LLR [22]. The LLR vale shold be compted taking into accont the eqivalent channel gain and residal MAI ater FDE [25]. When the channel is time-selective de to the ading Doppler spread, even i all sers are assigned dierent 2nd OVSF spreading codes, the MAI cannot be cancelled completely. According to the central limit theorem, the residal intererence-pls-noise can be treated as a Gassian process [3], [25]. We can show that Eq. 2) can be expressed as ˆd n) = µ n)d n) + ξ SI n) + ξ MAI n) + ξ noise n), 3) where µ n) is the eqivalent channel gain or the th ser s signal and ξ SI n), ξ MAI n)andξ noise n) respectively represent the sel intererence SI), MAI and noise components. ˆd n) is a random variable with mean µ n)d n) and variance 2σ 2 n) µ n) and2σ 2 n) are derived in Sect. 4). Assming qaternary phase shit keying QPSK) data-modlation, the LLRs or the st bit and 2nd bit o the nth QPSK symbol are given by [2], [3] Re µ n) ˆd n) } /2σ 2 n) or the st bit LLR = Im µ n) ˆd n) } /2σ 2 n) or the 2nd bit. 4) 3. Code Assignment or 2D OVSF Spreading The overall spreading actor o the th ser s 2D OVSF codes is SF = SF t. The total data rate normalized by the chip or sample) rate or the mlti-rate and mltiser case is deined as [5] U R total = =0 SF t ) <. 5) The st OVSF spreading code o spreading actor is or mlti-rate services per ser and can be arbitrarily set according to the reqested data rate, independently o the FFT block size,bt. The 2nd OVSF spreading code is or orthogonal mltiser mltiplexing. The MAI is cancelled de to the orthogonality property o the 2nd OVSF spreading codes. However, the code orthogonality may be distorted in a time-selective ading channel. I the path gain stays almost constant over SF t consective blocks, the MAI reslting rom the orthogonality distortion may not be severe. Hence, SF t shold be smaller than the maximm permitted vale SF t, which is determined by the ading Doppler reqency. For the assignment o 2D OVSF spreading actor SF t, ), SF t is determined by the nmber o sers and then is set at SF /SF t, where the total spreading actor SF is inverse-proportionate to the data rate. Thereore, the assignment o SF t, ) is independent o the channel reqencyselectivity. As discssed in [26], the reqency-selectivity or

5 LIU and ADACHI: 2-DIMENSIONAL OVSF SPREAD/CHIP-INTERLEAVED CDMA 3367 the delay spread only aects the perormance o 2D OVSF spread CDMA. In general, as the delay spread decreases, the reqency-selectivity becomes weaker, reslting in less reqency-diversity eect. In 2D OVSF spread DS-CDMA, the data symbol is always spread over the entire signal bandwidth, yielding the same reqency diversity gain irrespective o. On the other hand, in the case o 2D OVSF spread MC-CDMA, the data symbol is spread over only sbcarriers. Thereore, the achievable reqency-diversity gain decreases as decreases. 3. Mlti-Rate/Single-Connection Case 3.. SF t -Code Assignment Fig. 5 OVSF code tree. I U < SF t and U = 2 k k = 0,, ), all sers can be assigned SF t = 2 k. An MAI-ree channel is constrcted ater the chip-deinterleaving/st despreading as described in Sect The MUD problem is converted into a set o eqivalent single-ser detection problems and the se o complicated MUD receivers can be avoided. I U < SF t bt 2 k < U < 2 k,2 k U) sers among U sers can be assigned SF t = 2 k and then the other 2U 2 k ) sers can se SF t = 2 k. By doing so, all U sers are orthogonal i Eq. 5) holds. I U > SF t, sers are partitioned into SF t grops irst. Each grop ses a dierent OVSF spreading code with the spreading actor SF t. Users with the same 2nd OVSF spreading code belong to the same grop. Users in the same grop are intererence-ree rom other grops. We then apply MUD per grop, which is practically easible since the nmber o sers per grop is at most U/SF t, mch smaller than U. In contrast, the MUD or the conventional DS- or MC-CDMA needs to sppress the MAI rom all U ) interering sers, and ths has prohibitive complexity Code Assignment Ater setting the vale o SF t or each ser, can be set eqal to SF /SF t, where the overall spreading actor SF = SF t ) is determined by the th ser s data rate. Thereore, or proposed code assignment achieving MAIree plink transmission is very lexible or mlti-rate services Example One example or the spreading code assignment is shown in Fig. 5, which illstrates the OVSF code tree [8]. We assme the maximm permitted spreading actor is SF t = 6. There are U = 5 active sers and among them, 2 sers with rate R L, 2 sers with rate 2R L and ser with rate 4R L, where the lowest data rate R L corresponds to SF t ) = /6. According to Sect. 3.., two sers may be assigned SF t = 8 and the other three sers SF t = 4. We assme ser = 0 with R L = 8 2),ser = with R L = 4 4),ser = 2 with 2R L = 8 ),ser = 3 Fig. 6 Mti-rate/mlti-connection or the th ser. with 2R L = 4 2), and ser = 4 with 4R L = 4 ). Then, OVSF codes c 8, and c 8,2, are selected as the spreading codes, c SF0 t =0 t) andcsf2 t =2 t) with SF0 t = SF 2 t = 8, to maintain the orthogonality between each other. As shown in Fig. 5, they have the same mother code c 4, and thereore, OVSF codes c 4,2, c 4,3,andc 4,4 shold be assigned to sers =, 3, 4, respectively. 3.2 Mlti-Rate/Mlti-Connection Case Until now, we have discssed mlti-rate, single-connection transmission. Or proposed scheme can be extended allow mltiple connections per ser. Data seqences o mltiple connections are channel-coded, data-modlated and spread sing dierent st OVSF spreading codes. Mltiple connections are independent each other and depend on their own reqested commnication qalities and types o data traic i.e., continos traic or packet traic) [5]. As shown in Fig. 6, there are V parallel connections or the th ser. The vth data-modlated symbol seqence d,v n)} o the th ser is spread sing the st OVSF spreading code c SF,v t); t = 0 SF,v } with spreading actor SF,v. The resltant V parallel chip seqences are smmed p and rther mltiplied by a binary scramble seqence c scr t); t = 0 } to prodce the -chip DS-CDMA signal, which can be expressed as s DS t) = c scr V t) v=0 d,v t/sf,v ) c SF,v t mod SF,v ). 6) In the case o single connection V = ), Eq. 6) redces to

6 3368 IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER 2006 Eq. ). For the sake o convenience, the eqivalent spreading actor,eq is deined as /,eq = V v=0 SF,v ). 7) The same 2nd spreading with the spreading actor SF t is applied to s DS t) as in the single-connection case. Thereore, the normalized total data rate or mlti-rate/mlticonnection/mltiser transmission becomes U [ ) R total = SF =0 t SF ],eq. 8) At the receiver side shown in Fig. 6, the 2nd despreading sing the st OVSF spreading code c SF t) is perormed to get the decision variable ˆd,v n) or the detection o d,v n) as ˆd,v n) = n+)sf,v SF,v t=nsf,v y t) c SF,v t)c scr t)}, 9) based on which data symbol demodlation and trbo decoding are carried ot or the vth connection. y t) in Eq. 9) is given by Eq. 0). For MC-CDMA, we apply,eq /,eq )-chip interleaving to s DS t)andthen,an -point IFFT is sed to get s MC t) = Nc V v=0 /,eq ) n=0 d,v n)c SF,v,q ) m=0 m) exp cscr j2πt nsf,eq + m ) n + m,eq. 20) The same 2nd spreading is also sed as in the singleconnection case. The decision variable ˆd,v n) is obtained sing Eq. 9), where y t) is given by Eq. ) or MC- CDMA. 3.3 Special Cases I we set V = and =, or proposed 2D OVSF spread DS-CDMA becomes chip-interleaved block spread DS-CDMA [6], [7] and or 2D OVSF spread MC-CDMA becomes MC/DS-CDMA [8], where dierent narrowband DS-CDMA signal is transmitted on each sbcarrier. In this paper, OVSF spreading codes are sed to separate sers in the time-domain. I we se the orthogonal phase-rotating seqences or the reqency-shiting seqences), given by c SF t t) = exp j2π t } or = 0 SF t, 2) t instead o OVSF spreading codes, 2D OVSF DS-CDMA becomes the variable spreading and chip repetition actor VSCRF) based CDMA [5]. The se o the orthogonal phase-rotating seqences reslts in non-overlappping combshaped reqency spectra o dierent sers and hence no MAI is prodced. 4. BER Analysis For theoretical analysis, we assme V parallel connections or each ser and each connection ses the same SF,v = bt every ser has a dierent SF t, )pair. -chip CDMA signal s t), given by Eq. 6) or DS-CDMA and Eq. 20) or MC-CDMA, is transmitted ater the insertion o GI over a reqency-selective ading channel. Dierent ser s ading channels are independent each other. Withot loss o generality, we assme the ideal slow transmit power control or all sers. 4. Decision Variable and Eqivalent Channel Gain Sbstitting Eqs. 3) 6) into Eq. 7) gives ˆR k) = 2E c / S k)h k) + U 2E c / S k)z k) +Πk) 22) =0 or k = 0, where denotes the interering ser and the st, 2nd and 3rd terms represent the desired signal, MAI and AWGomponents, respectively, with S k) = s t)exp j2πk t ) Nc t=0 SF t L t=0 h,l i)exp j2πk τ,l H k) = SF t l=0 Z k) = SF t c SF t i) c SF t i) } L SF t h,li)exp l=0 Πk) = N c ηt)exp j2πk t ) Nc ) j2πk τ,l. ) 23) As shown in Eqs. 8) and 9), MMSE-FDE is applied to ˆR k) to obtain Y k), ollowed by IFFT to get the timedomain signal y t) given as Eq. 0). The decision variable ˆd,v n) is obtained by sbstitting Eq. 0) into Eq. 9). For DS-CDMA, we sbstitte Eq. 6) into Eq. 23) and then se Eqs. 22), 8), and 0) to obtain the vth connection o the th ser ˆd,v n). On the other hand, or MC- CDMA, we sbstitte Eq. 20) into Eq. 23) and then sing Eqs. 22), 8), and ) to get ˆd,v n). ˆd,v n) can be expressed as ˆd,v n) = µ,v n)d,v n) + ξ SI n) + ξ MAI n) + ξ noise n), 24) where µ,v n), ξ SI n), ξ MAI n), and ξ noise n) are respectively the eqivalent channel gain, sel-intererence, MAI, and noise components, which are given by

7 LIU and ADACHI: 2-DIMENSIONAL OVSF SPREAD/CHIP-INTERLEAVED CDMA 3369 µ,v n) = 2Ec ξ SI n) = ξ MAI n) = 2Ec N c n+) V v =0 v v n+) t=n t=n w k)h k) w n + i c SF 2Ec c SF or DS-CDMA } N t)c scr c t) N c τ=0 t s DS τ)exp H n + i SF or MC-CDMA 25) w k)h k) j2πk t τ or DS-CDMA } SF i) c,v i)d,v n) 2Ec w T n + i c SF H n + i SF or MC-CDMA 26) c SF 2Ec c SF } N t)c scr c t) U =0, U 2Ec ξ noise n) = S k)z k) exp w k) or DS-CDMA j2πt k ) } i)c scr n + i) w n + i =0 S n+) t=n n + i or MC-CDMA c SF ) Z n + i } t)c scr t) 27) N c w k)π k)exp j2πt k ) c SF w n + i or DS-CDMA i)c scr n SF + i ) } Π n + i SF or MC-CDMA 28) 4.2 Variance Since ξ SI n)andξ MAI n) are approximated as complex Gassian variables, the sm o ξ SI n), ξ MAI n)andξ noise n) can be treated as a new zero-mean Gassian variable ξ,v n). Its variance 2σ 2,vn) isgivenby 2σ 2,vn) = 2σ 2 SI + 2σ2 MAI + 2σ2 noise, 29) where σ 2 SI, σ2 MAI and σ 2 noise are the variances o ξ SIn), ξ MAI n), and ξ noise n), respectively. Following [26], they can be derived as 2σ 2 SI = V 2E c V ) 2E c 2σ 2 MAI = 2σ 2 noise = N c σ 2 Z σ 2 Z N w k)h k) 2 c 2 w k)h k) or DS-CDMA w 2E c 2E c SF t SF t n + i w n + i 2N 0 2N 0 N c 2 H n + i SF 2 H n + i SF or MC-CDMA 30) w k) 2 or DS-CDMA 2 w n + i SF or MC-CDMA 3) N c w k) 2 or DS-CDMA 2 w n+i SF or MC-CDMA 32) In Eq. 3), 2σ 2 Z is the variance o Z k) deinedin Eq. 23). Since h,l t/t ) andh,l t/t ) are zero-mean compelx Gassian processes, H k)andz k) are also zeromean complex Gassian variables. Thereore, the second term in Eq. 22) can be approximated as a zero-mean complex Gassian variable with variance 2E c / )σ 2 Z,whereσ2 Z is deined as

8 3370 U σ 2 Z = E S k)z k). 33) =0 2 S k) is the reqency component o the th ser s signal s t) and is a zero-mean variable with the variance o E[ S k) 2 ] = this can be derived rom Eq. 23) since a binary scramble seqence is assmed). Since S k) is independent o Z k), we have U σ 2 Z = E[ Z k) 2 ]. 34) =0 We assme the Jake s model [27] and each path consists o many nresolvable paths with the same time delay arriving rom all directions niormly. From Eq. 23), Eq. 34) becomes U σ 2 Z = =0 SF t SF t ) 2 SF t i =0 [c SF t i)c SF t i ) U =0 SF t i= SF t SF t c SF t J 0 2π i i ) D T) } ]} i )c SF t i) J 0 2π i ) D T), 35) where ) D is the th ser s maximm Doppler reqency and J 0 ) is the zero-th order Bessel nction o the irst kind. It is nderstood that σ 2 Z is the sm o the weighted crosscorrelations o the OVSF spreading codes c SF t t); = 0 U }. I ) D = 0, σ2 Z beomes zero de to the orthogonality property o the OVSF spreading codes. Thereore, the MAI between dierent grops can be eliminated completely. In the case o single connection V = ), it can be nderstood rom Eq. 30) that there is no SI or MC-CDMA bt SI still exists or DS-CDMA. In the case o DS-CDMA, even with MMSE-FDE, variations in the eqivalent channel gain, deined as w k)h k), still remain. This residal variation prodces the SI, which is not negligible when V is large. However, note that the BER perormance dierence between DS- and MC-CDMA diminishes as approaches. IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER 2006 )) Ec P b γ, H k)} N 0 = ) 2 erc 4 γ Ec, H k)}. N 0 37) The theoretical average BER o ncoded CDMA can be nmerically evalated by averaging Eq. 4) over H k); k = 0 } as P b Ec N 0 ) = E 5. Simlation Reslts ))] Ec [P b γ, H k)}. 38) N 0 The nmerical and compter simlation conditions are shownintable. AnL = 6-path reqency-selective block Rayleigh ading channel having the niorm power delay proile is assmed. The transmit timing osets τ ; = 0 U } are niormly distribted over [ /2, /2] with < N g L so that the maximm time delay dierence is less than the GI. A rate-/3 trbo encoder consists o two 3, 5) recrsive systematic convoltional RSC) encoders [23] connected in parallel with an S-random S = I)interleaver [29] between them. The inpt to the second RSC encoder is the interleaved version o the inormation seqence inpt to the irst RSC encoder. The ollowing pnctring matrix P is sed to get a rate-/2 trbo code: P = 0, 39) 0 where the irst row corresponds to the systematic or inormation) bit seqence, and the second and third rows correspond to the two parity bit seqences. The trbo decoder is an iterative decoder. The log-map decoding with eight iterations is carried ot at the trbo decoder. The nmerical evalation o the theoretical average BER is done by Monte-Carlo nmerical comptation method as ollows. The set o path gains h,l t/t ); l = 0 L } or dierent sers are generated to obtain H k); k = 0 } sing Eq. 23) and then w k); k = 0 } sing Eq. 9). The conditional BER is Table Nmerical and simlation conditions. 4.3 Conditional BER The conditional signal-to-intererence pls noise ratio SINR) γ E c /N 0, H k)}) or the given set o H k); k = 0 } is deined as ) Ec µ,v n) 2 γ, H k)} = N 0 σ 2,vn). 36) Assming QPSK data-modlation, the conditional BER is then given by [28]

9 LIU and ADACHI: 2-DIMENSIONAL OVSF SPREAD/CHIP-INTERLEAVED CDMA 337 Fig. 7 Uncoded BER comparison between 2D OVSF spread CDMA and conventional CDMA sing MUD. Fig. 8 Uncoded BER perormance o 2D OVSF spread CDMA or varios pairs o SF t, SF ) with SF t = 6. compted sing Eqs. 4) and 42). This is repeated a sicient nmber o times to obtain the theoretical average BER according to Eq. 38). 5. Uncoded Case We irst consider the V = case. Fig. 7 plots the ncoded BER perormance o both DS- and MC-CDMA as a nction o the average received bit energy-to-the AWGN power spectrm density ratio E b /N 0,deinedbyE b /N 0 = 0.5E c /N 0 )SF t ) + N g/ ) with D T = 0 4 or all sers. For comparison, the BER perormance o conventional CDMA sing MMSE-MUD [2] is also plotted or U =, 8 and 6 R total = /6, /2 and ). We assme the spreading actor o SF = SF t = 6 or 2D OVSF spread CDMA, where SF t, ) = U, 6/U), and the same spreading actor o SF = 6 or conventional CDMA sing MUD. The good agreement between the theoretical and simlation reslts conirms or BER analysis. Or proposed 2D OVSF spread CDMA is an MAI-ree system de to σ 2 Z = 0 see Eqs. 3) and 36)) since all the sers with SF t = U are orthogonal and the channel is almost constant when the ading is very slow D T = 0 4 ). The MUD problem is converted into a set o eqivalent singleser detection problems and only single-ser MMSE-FDE is applied here. On the other hand, or conventional CDMA, MUD is necessary to combat the MAI. When the system is lightly loaded i.e., U = 8), conventional DS-CDMA sing MUD exhibits better perormance since the MAI is less severe. However, when the system is heavily loaded i.e., U SF ), large MAI reslts in severe BER degradation or conventional DS-CDMA with MUD. When U = 6, or proposed 2D OVSF spread DS-CDMA otperorms conven- tional DS-CDMA with MUD. In 2D OVSF spread DS-CDMA, the data symbol is always spread over all sbcarriers, yielding large reqency diversity gain irrespective o. However, DS-CDMA sers rom SI, the variance o which is in inverse proportion o. On the other hand, in the case o MC-CDMA, the data symbol is spread over smaller nmber eqal to ) o sbcarriers than in DS-CDMA, the reqency diversity gain is in linear proportion o.btmc-cdma can achieve a large reqency-domain interleaving gain and there is no SI present when V =. When U = = 6), 2D OVSF spread MC-CDMA perorms slightly better than DS-CDMA. As U increases, decreases, reslting in less reqency-diversity gain in MC-CDMA and increasing SI in DS-CDMA. It can be seen that the BER perormances o both 2D OVSF spread DS- and MC-CDMA degrade as U increases. When U = 6 = ), 2D OVSF spread DS-CDMA provides mch better BER perormance than MC-CDMA. This is becase that there is neither reqencydiversity gain nor interleaving gain in 2D OVSF spread MC- CDMA withot coding; while, althogh there is SI in 2D OVSF spread DS-CDMA, larger reqency-diversity gain can be obtained in DS- than that in MC-CDMA. Figre 8 plots the ncoded BER perormance o both DS- and MC-CDMA assming that all sers have the same spreading actor pair, i.e., SF t, ) = SF t, SF ). We assme a ll-loaded case i.e., U = SF t SF = 6) with the same data rate or all sers. As explained in Sect. 3, i SF t < U, sers are partitioned into SF t grops. Users in each grop are intererence-ree rom other grops; bt the MAI is present in each grop and MUD is applied per grop. As the nmber o sers per grop, U/SF t, increases,

10 3372 IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER 2006 Fig. 9 Impact o D T on ncoded 2D OVSF spread CDMA. Fig. 0 Coded perormance comparison between 2D OVSF spread CDMA and conventional CDMA sing MUD. the residal MAI per grop increases, reslting in the degradation o the BER perormance. It is necessary to apply MMSE-MUD per grop to combat with this residal MAI and its implementation complexity increases exponentially with U/SF t. When SF t, SF ) = 6, ), the MAI can be eliminated completely and single-ser MMSE-FDE is applied instead o complicated MMSE-MUD. It is seen orm Fig. 8 that DS-CDMA with SF t, SF ) = 6, ) perorms better than that o SF t, SF ) 6, ). Thereore, the se o SF t, ) = U, SF /U) can achieve the best BER perormance with the lowest receiver complexity. However, MC-CDMA with SF t, SF ) = 6, ) does not give a good BER perormance similar to DS-CDMA. This is becase MC-CDMA with SF t, SF ) = 6, ) cannot obtain the reqency-diversity gain i error-control coding is not sed. How the ading Doppler reqency inlences the BER perormance is shown or SF t = 6 and SF t, ) = U, 6/U) in Fig. 9. Both the theoretical and simlated BER perormances are plotted or the ncoded CDMA with single connection V = and mltiple sers. We assme the same ading Doppler spread D T = 0 4 and 0 2 or all sers corresponding to the mobile terminal speed o abot 7km/h and 700 km/h, respectively, or the carrier reqency 5 GHz and the chip data rate 00 Mcps). It can be seen that the theoretical reslts agree well with those o compter simlation. For small nmber o sers i.e., U = or 8), there is only a slight perormance dierence between D T = 0 4 and D T = 0 2. However, when D T = 0 2, since the orthogonality among dierent sers cannot be maintained de to the time-selective ading, the perormances o both ncoded DS- and MC-CDMA degrade or the heavy-loaded case i.e., U = 6). 5.2 Trbo-Coded Case Trbo-coded BER perormance comparison between conventinal CDMA sing MUD with SF = 6 and 2D OVSF spread CDMA with SF t, ) = U, 6/U) orsf t = 6 is shown in Fig. 0. In contrast to the ncoded case shown in Fig. 7, de to the coding gain together with reqency-diversity and interleaving gain, 2D OVSF spread/chip-interleaved MC-CDMA can achieve almost the same BER perormance as the DS-CDMA even or small i.e., U = 8 and 6). Also 2D OVSF spread CDMA provides better perormance than conventional CDMA with MUD. Moreover, althogh the comptational complexity o MUD grows exponentially with the nmber o sers U, the receiver complexity o 2D OVSF spread CDMA is linear de to the se o single-ser FDE. Figre plots the trbo-coded BER perormance o ll-loaded CDMA U = 6) with dierent spreading actor pair SF t, ) = SF t, SF ) or all sers. Similar to the case o Fig. 8, U sers are partitioned into SF t grops i SF t < U. Each grop is intererence-ree rom other grops. However, since SF t < U, some grops have more-than-one sers; the MAI is present in those grops and MUD is necessary to combat the residal MAI. Compared with the ncoded case in Fig. 8, trbo-coded MC-CDMA can achieve a similar perormance to DS-CDMA or dierent SF t, SF ) pair and 2D OVSF spread CDMA with trbo coding provides dierent BER perormance or varios SF t, SF ). 2D OVSF spread CDMA with SF t, SF ) = 6, ) perorms the best by sing only single-ser MMSE-FDE. As SF t decreases, the BER perormance degrades de to the increasing residal MAI rom U/SF t sers. When SF t, SF ) =, 6), 2D OVSF

11 LIU and ADACHI: 2-DIMENSIONAL OVSF SPREAD/CHIP-INTERLEAVED CDMA 3373 Fig. Trbo-coded BER perormance o 2D OVSF spread CDMA or varios pairs o SF t, SF ). Fig. 3 Trbo-coded BER perormance o mlti-rate/single-connection 2D OVSF spread CDMA. spread. The chip-interleaving perorms like a channel interleaving or trbo-coded CDMA [30]. Chip interleaving scrambles the chips and transorms the transmission channel into a highly time-selective or highly memoryless channel. There is a tradeo between the residal MAI and the interleaving gain or the trbo decoding. Thereore, or 2D OVSF spread/chip-interleaved CDMA with trbo coding is insensitive o the Doppler spread compared with ncoded case. 5.3 Mtli-Rate/Mlti-Connection Case Fig. 2 Impact o D T on trbo-coded 2D OVSF spread CDMA. spread CDMA redces to conventional CDMA, which ses the most complicated MMSE-MUD bt perorms worse than 2D OVSF spread CDMA with SF t, SF ) 6, ). The impact o the ading Doppler reqency on the BER perormance was shown in Fig. 9 or the ncoded case. Assming the same conditions, we show in Fig. 2 the trbo-coded BER perormance or D T = 0 4 and D T = 0 2. It can be seen that or proposed 2D OVSF CDMA with trbo coding is very robst against large Doppler Figre 3 plots the trbo-coded BER perormance o the mtli-rate case with U = 5, R total = and the lowest data rate R L = /6. As described in Sect. 3..3, the data rates o sers = 0 4areR L, R L,2R L,2R L and 4R L, respectively. User = 2 with SF 2 t, SF 2 ) = 8, ) and ser = 4 with SF 4 t, SF 4 ) = 4, ) have dierent data rates bt show the same BER perormance, which is worse than that o sers = 0 and 3. User = 0 with SF 0 t, SF 0 ) = 8, 2) and ser = 3 with SF 3 t, SF 3 ) = 4, 2) with dierent data rates also perorms the same, bt their BER perormances are still worse then ser = with SF t, SF ) = 4, 4). It can be seen that i is the same, the BER perormance is the same irrespective o data rate. However, as decreases, the BER perormances o both 2D OVSF spread DS- and MC-CDMA degrade. The reason or this has been discssed in Sect. 5.. The BER perormance o trbo-coded CDMA with mlti-rate/mlti-connection is shown or = U = 6 in Fig. 4. We assme dierent eqivalent spreading actors,,eq =, 2 and 6 R total =, /2, and /6). In

12 3374 IEICE TRANS. COMMUN., VOL.E89 B, NO.2 DECEMBER 2006 In this paper, we proposed a 2-dimensional 2D) OVSF spread/chip-interleaved CDMA in a reqency-selective ading channel or mlti-rate plink transmission. Code assignment or 2D OVSF spreading was presented. Relying on the joint se o 2D OVSF spreading and chipinterleaving, a mltiser detection MUD) problem is converted into a set o eqivalent single-ser eqalization problems. The sppression o mlti-access intererence MAI) not only increases the plink capacity withot applying the sophisticated MUD techniqe, bt also allows lexible mlti-rate transmission sing or proposed 2D OVSF spreading code assignment. We also presented the theoretical analysis or the ncoded BER perormance based on the Gassian approximation o the MAI. The theoretical ncoded BER perormance in a time- and reqencyselective Rayleigh ading channel was evalated by Monte- Carlo nmerical comptation and conirmed by compter simlation. It was also shown by simlation reslts that when trbo coding is applied, or proposed 2D OVSF spread/chip-interleaved DS- and MC-CDMA can achieve similar BER perormance and are very robst against large Doppler spread. Reerences Fig. 4 Trbo-coded BER perormance o mlti-rate/mlti-connection 2D OVSF spread CDMA. the case o,eq =, we consider SF, V) =, ) and 256, 256). Both, V) = 64, 32) and 256, 28) correspond to the case o,eq = 2; while, SF, V) = 64, 4) and 256, 6) correspond to the case o,eq = 6. MC- CDMA with trbo coding can achieve almost the same BER perormance as DS-CDMA or dierent, V). The mlti-connection CDMA with, V) = 256, 256) shows the identical BER perormance to that o single-connection CDMA with, V) =, ) since they have the same,eq = ). According to the BER analysis in Sect. 4, we can see by sbstitting Eqs. 25), 29) 32) into Eq. 36) that i,eq is the same, the conditional SINR or the mlti-connection CDMA are the same as that o the singleconnection CDMA. Mlti-connection CDMA with the same,eq presents the same BER perormance; however, 2D OVSF spread CDMA with dierent,eq has dierent R total and exhibits dierent BER perormance. 6. Conclsions [] F. Adachi, Wireless past and tre-evolving mobile commnications systems, IEICE Trans. Fndamentals, vol.e84-a, no., pp.55 60, Jan [2] F. Adachi, D. Garg, S. Takaoka, and K. Takeda, Broadband CDMA techniqes, IEEE Wireless Commn., vol.2, no.2, pp.8 8, April [3] A.J. Viterbi, CDMA: Principles o spread spectrm commnications, Addison Wesley, 995. [4] T. Ottosson and A. Svensson, On schemes or mltirate spport in DS/CDMA, J. Wireless Personal Commn., vol.6, no.3, pp , March 998. [5] F. Adachi, Reverse link capacity o orthogonal mlti-code DS- CDMA with mltiple connections, IEICE Trans. Commn., vol.e85-b, no., pp , Nov [6] F. Adachi, T. Sao, and T. Itagaki, Perormance o mlticode DS- CDMA sing reqency domain eqalization in a reqency selective ading channel, Electron. Lett., vol.39, no.2, pp , Jan [7] S. Hara and R. Prasad, Overview o mticarrier CDMA, IEEE Commn. Mag., vol.35, no.2, pp.26 44, Dec [8] L.-L. Yang and L. Hanzo, Mlticarrier DS-CDMA: A mltiple access scheme or biqitos broadband wireless commnications, IEEE Commn. Mag., vol.4, no.0, pp.6 24, Oct [9] S. Hara and R. Prasad, Design and perormance o mlticarrier CDMA system in reqency-selective Rayleigh ading channels, IEEE Trans. Veh. Technol., vol.48, no.5, pp , Sept [0] M. Helard, R. Le Goable, J.-F. Helard, and J.-Y. Badais, Mlticarrier CDMA techniqes or tre wideband wireless networks, Ann. Telecommn., vol.56, pp , 200. [] Z. Wang and G.B. Giannakis, Block precoding or MUI/ISIresilient generalized mlticarrier CDMA with mltirate capabilities, IEEE Trans. Commn., vol.49, no., pp , Nov [2] S. Tsmra, S. Hara, and Y. Hara, Perormance comparison o MC- CDMA and cyclically preixed DS-CDMA in an plink channel, Proc. IEEE VTC 04 Fall, pp.44 48, Los Angeles, USA, Sept [3] X.D. Wang and H.V. Poor, Iterative trbo) sot intererence cancellation and decoding or coded CDMA, IEEE Trans. Commn., vol. 47, no.7, pp , Jly 999. [4] S. Parkvall, E. Strom, and B. Ottersten, The impact o timing errors on the perormance o linear DS-CDMA receivers, IEEE J. Sel. Areas Commn., vol.4, no.8, pp , Oct [5] H. Atarashi, N. Maeda, Y. Kishiyama, and M. Sawahashi, Broadband wireless access based on VSF-OFCDM and VSCRF-CDMA and its experiments, Eropean Trans. Telecommn., vol.5, pp.59 72, Jan [6] S. Zho, G.B. Giannakis, and C.L. Martret, Chip-interleaved block-spread code division mltiple access, IEEE Trans. Commn., vol.50, no.2, pp , Feb [7] X. Peng, F. Chin, T.T. Tjhng, and A.S. Madhkmar, A simpliied transceiver strctre or cyclic extended CDMA system with re-

13 LIU and ADACHI: 2-DIMENSIONAL OVSF SPREAD/CHIP-INTERLEAVED CDMA 3375 qency domain eqalization, Proc. IEEE VTC 05 Spring, pp , Sweden, May [8] F. Adachi, M. Sawahashi, and K. Okawa, Tree-strctred generation o orthogonal spreading code with dierent lengths or oward link o DS-CDMA mobile radio, Electron. Lett., vol.33, no., pp.27 28, Jan [9] K. Okawa and F. Adachi, Orthogonal orward link sing orthogonal mlti-spreading actor codes or coherent DS-CDMA mobile radio, IEICE Trans. Commn., vol.e8-b, no.4, pp , April 998. [20] L. Li and F. Adachi, Chip-interleaved DS-CDMA with 2- dimansional OVSF spreading codes, IEICE Technical Report, RCS , pp.33 38, March [2] L. Li and F. Adachi, 2-dimensional OVSF spreading or chipinterleaved DS-CDMA plink transmission, Proc. WPMC05, pp , Alborg, Denmark, Sept [22] A. Steanov and T. Dman, Trbo coded modlation or wireless commnications with antenna diversity, Proc. IEEE VTC 99 Fall, pp , Netherlands, Sept [23] J.P. Woodard and L. Hanzo, Comparative stdy o trbo decoding techniqes: An overview, IEEE Trans. Veh. Technol., vol.49, no.6, pp , Nov [24] T.S. Rappaport, Wireless Commnications, Prentice Hall, 996. [25] D. Garg and F. Adachi, Throghpt comparison o trbo-coded HARQ in OFDM, MC-CDMA and DS-CDMA with reqencydomain eqalization, IEICE Trans. Commn., vol.e88-b, no.2, pp , Feb [26] F. Adachi and K. Takeda, Bit error rate analysis o DS-CDMA with joint reqency-domain eqalization and antenna diversity combining, IEICE Trans. Commn., vol.e87-b, no.0, pp , Oct [27] W.C. Jakes, Microwave Mobile Commnications, Wiley, New York, 974. [28] J.G. Proakis, Digital Commnications, 3rd ed., McGraw-Hill, New York, 995. [29] O.F. Acikel and W.E. Ryan, Pnctred trbo codes or BPSK/QPSK channels, IEEE Trans. Commn., vol.47, no.9, pp , Sept [30] D. Garg and F. Adachi, Chip interleaved trbo codes or DS- CDMA mobile radio in a ading channel, Electron. Lett., vol.38, no.3, pp , Jne Fmiyki Adachi received the B.S. and Dr. Eng. degrees in electrical engineering rom Tohok University, Sendai, Japan, in 973 and 984, respectively. In April 973, he joined the Electrical Commnications Laboratories o Nippon Telegraph & Telephone Corporation now NTT) and condcted varios types o research related to digital celllar mobile commnications. From Jly 992 to December 999, he was with NTT Mobile Commnications Network, Inc. now NTT DoCoMo, Inc.), where he led a research grop on wideband/broadband CDMA wireless access or IMT-2000 and beyond. Since Janary 2000, he has been with Tohok University, Sendai, Japan, where he is a Proessor o Electrical and Commnication Engineering at the Gradate School o Engineering. His research interests are in CDMA wireless access techniqes, eqalization, transmit/receive antenna diversity, MIMO, adaptive transmission, and channel coding, with particlar application to broadband wireless commnications systems. From October 984 to September 985, he was a United Kingdom SERC Visiting Research Fellow in the Department o Electrical Engineering and Electronics at Liverpool University. Dr. Adachi served as a Gest Editor o IEEE JSAC or special isse on Broadband Wireless Techniqes, October 999 and or special isse on Wideband CDMA I, Agst 2000, and Wideband CDMA II, Jan He is an IEEE Fellow and was a co-recipient o the IEEE Vehiclar Technology Transactions Best Paper o the Year Award 980 and again 990 and also a recipient o Avant Garde award He was a recipient o IEICE Achievement Award 2002 and a co-recipient o the IEICE Transactions Best Paper o the Year Award 996 and again 998. He was a recipient o Thomson Scientiic Research Front Award Le Li received B.S. and M.S. degrees in electrical engineering rom Beijing University o Posts and Telecommnications BUPT), Beijing, China, in 2000 and 2003, respectively. From April 2003 to September 2004, she took part in the collaboration between the National Institte o Inormation and Commnications Technology NICT), Japan, and BUPT on the 4G Wireless Telecommnications Project. Crrently, she is a Ph.D. candidate at the Dept. o Electrical and Commnication Engineering, Gradate School o Engineering, Tohok University with a scholarship rom the Japanese government. Her research interests inclde digital signal transmission techniqes or direct seqence CDMA and mlticarrier CDMA.