IEICE TRANS. COMMUN., VOL.E87 B, NO.8 AUGUST 2004 2401 LETTER Adaptive Multi-Stage Parallel Interference Cancellation Receiver for Multi-Rate DS-CDMA Syste Seung Hee HAN a), Student Meber and Jae Hong LEE, Noneber SUMMARY In this letter, adaptive ulti-stage parallel interference cancellation (PIC) receiver is considered for ulti-rate DS-CDMA syste. In each stage of the adaptive ulti-stage PIC receiver, ultiple access interference (MAI) estiates are obtained by the sub-bit estiates fro the previous stage and the adaptive weights for the sub-bit estiates. The adaptive weights are obtained by iniizing the ean squared error between the received signal and its estiate through noralized least ean square (LMS) algorith. It is shown that the adaptive ulti-stage PIC receiver achieves saller BER than the atched filter receiver, ulti-stage PIC receiver, and ulti-stage partial PIC receiver for the ulti-rate DS-CDMA syste in a Rayleigh fading channel. key words: DS-CDMA, ulti-rate, ulti-user detection, PIC 1. Introduction Wireless counication systes are to support various counication services, such as voice, data, iage, and video services that deand ulti-rate transission [1]. Users are to transit their inforation with various data rates and their perforance requireents will vary fro application to application. To accoodate users with various data rates in a direct-sequence code division ultiple-access (DS-CDMA) syste, ultiple processing gain (MPG) schee is used [2]. In the MPG schee, a user with high data rate has saller processing gain and a user with low data rate has larger processing gain while their chip rates are fixed sae. The signal of a high-rate user has larger aplitude than that of a low-rate user so that the forer has sae bit energy as the latter while the forer has shorter bit duration than the latter. The perforance of a ulti-rate DS-CDMA syste is severely degraded by ultiple access interference (MAI), difference of transitted power between users, and nearfar effect. Multi-user detectors are adopted to itigate the perforance degradation due to MAI and near-far effect. Huge potential capacity and perforance iproveent is expected as a result of using ulti-user detector at the expense of increased coplexity [3] [5]. A ulti-stage parallel interference cancellation (PIC) receiver achieves perforance iproveent with oderate coplexity and delay as Manuscript received January 30, 2004. Manuscript revised March 16, 2004. The authors are with the School of Electrical Engineering and Coputer Science, Seoul National University, Seoul 151-742, Korea. a) E-ail: shhan75@snu.ac.kr This work was supported in part by the Brain Korea 21 project and the ITRC progra of the Korean Ministry of Inforation and Counications. a ulti-user detector [6]. In the ulti-stage PIC receiver, however, the perforance is not always iproved as the nuber of stages increases, especially when the nuber of users approaches the processing gain of the DS-CDMA syste. To iprove the perforance of the ulti-stage PIC receiver, it was proposed to cancel MAI partially by introducing a partial cancellation factor in each stage [7]. For a DS-CDMA syste, an adaptive ulti-stage PIC receiver was proposed in which MAI estiates are obtained using bit estiates fro the previous stage and adaptive weights for the bit estiates [8]. The adaptive weights are obtained by iniizing the ean squared error between a received signal and its estiate. It is shown that the adaptive ulti-stage PIC receiver has lower bit error rate (BER) than the atched filter (MF) receiver and ulti-stage partial PIC receiver for the DS-CDMA syste. In this letter, the adaptive ulti-stage PIC receiver is considered for the ulti-rate DS-CDMA syste with the MPG schee and its bit error rate (BER) is obtained for a Rayleigh fading channel by siulation. 2. Syste Model Consider an asynchronous ulti-rate DS-CDMA syste. Suppose that the MPG schee is adopted to accoodate ulti-rate users that are divided into N groups for their data rates. Let the nuber of users and the bit duration of the users in the group n be denoted by K n and T n, n = 1, 2,, N, respectively. Let the transission rate of users in the group n, R n, be an integer ultiple of R 1,i.e. R n = M n R 1, n = 1, 2,, N, with restriction that 1 = M 1 < M 2 < < and M n divides, n = 1, 2,, N. During the bit duration of a group 1 user T 1, a group n user transits M n bits with bit duration T n = T 1 /M n. Assue that the chip duration T c is sae for users in all groups. Then the processing gain of a group n user becoes L n = T n /T c = L 1 /M n, n = 1, 2,, N. The baseband signal transitted by the user k in the group n is given by s (t) = E b b []a (t T n ) (1) where E b is the bit energy, b [] { 1, 1} is the -th source bit, and a (t) is the noralized signature wavefor of the user k in the group n. a (t) isgivenby
2402 IEICE TRANS. COMMUN., VOL.E87 B, NO.8 AUGUST 2004 a (t) = 1 Tn L n 1 a [l]p Tc (t lt c ) (2) l=0 where a [l]isthel-th chip of the signature wavefor of the user k in the group n, l = 0, 1,, L n 1, and p Tc (t) is a rectangular pulse with unit aplitude and duration T c. Assue that transitted signal of the user k in the group n propagates over a channel having fading of α. The received baseband signal fro the user k in the group n is given by x (t) = α s (t τ ) = A b []a (t T n τ ) (3) where τ is the delay of the user k in the group n and A = α Eb. The baseband signal received at the receiver is given by r(t) = = N K n x (t) + n(t) N K n A b []a (t T n τ ) + n(t) (4) where n(t) is an additive white Gaussian noise (AWGN) with the power spectral density of N 0 /2(W/Hz). At the atched filter (MF) output for the user k in the group n, the decision statistic for the -th bit is given by (+1)Tn +τ b [] = r(t)a (t T n τ )dt. (5) T n +τ For the user k in the group n, the-th bit estiate is given by ˆb [] = sgn( b []) (6) where sgn( ) is the signu function defined as { 1, u 0, sgn(u) 1, u < 0. (7) 3. Adaptive Multi-Stage PIC Receiver for Multi-Rate DS-CDMA Syste In the adaptive ulti-stage PIC receiver for the ulti-rate DS-CDMA syste with the MPG schee, a bit of a group n user is divided into T n /T N sub-bits whose bit duration equals the bit duration of the highest-rate user T N. For a highestrate user, a bit corresponds to a sub-bit. Figure 1 shows the block diagra of the s-th stage of the adaptive ultistage PIC receiver for the ulti-rate DS-CDMA syste with the MPG schee. Initial sub-bit estiates for the adaptive ulti-stage PIC receiver are obtained by the MF bank which is referred to as the stage 0. For the user k in the group n in the stage 0, the decision statistic for the i-th sub-bit d (0) [i]is given by d (0) [i] = (i+1)t N+τ it N +τ a (t r(t) i M ) n T n τ dt (8) where x is the greatest integer that does not exceed x. In the stage 0, the i-th sub-bit estiate for the user k in the group n is given by ˆd (0) [i] = sgn( d (0) [i]). (9) Assue that the sub-bit estiates for all users are obtained for the (s 1)th stage. In the s-th stage, s = 1, 2,...,S 1, the estiate for x (t) oftheuserk in the group n, ˆx (s) (t), is obtained using the sub-bit estiates of the previous stage ˆd (s 1) [i], adaptive weights for the sub-bit estiates λ (s 1) [i], the signature wavefor a (t), and the estiate for signal aplitude  for the user k in the group n. The estiates for x (t) inthes-th stage is given by ˆx (s) (t) =  λ (s 1) ˆd (s 1) [i] i a (t i M ) n T n τ p TN (t it N τ ) (10) Fig. 1 Block diagra of the s-th stage of the adaptive ulti-stage PIC receiver for the ulti-rate DS-CDMA syste.
LETTER 2403 where p TN (t) is the rectangular pulse with unit aplitude and duration T N. The adaptive weights are set taking the reliability of each sub-bit estiate into consideration. With λ (s 1) [i] = 1, the adaptive ulti-stage PIC receiver is the sae as the conventional ulti-stage PIC receiver for the ulti-rate DS- CDMA syste [9] [11]. To obtain the adaptive weights, the received signal is sapled at the chip-rate. Suppose that the delay of each user is an integer ultiple of chip duration, i.e. τ = ξ T c, for soe integer ξ, k = 1, 2,, K n, n = 1, 2,, N. The received signal after chip-rate sapling is given by (11) at the botto of the page where n[ j] is the noise saple. In the s-th stage, the estiate for the received signal after chip-rate sapling is given by (12) at the botto of the page. The adaptive weights are obtained by iniizing the ean squared error between the received signal and its estiate, i.e. the adaptive weights ust iniize E( r[ j] ˆr (s) [ j] 2 ). The adaptive weights are adjusted by a noralized least ean square (LMS) algorith and updated every chip duration. Let the initial value of the adaptive weight for the i-th sub-bit of the user k in the group n, λ (s 1) [i], be denoted by λ (s 1) [i][0] = 1 and the adaptive weight after the l-th iteration be denoted by λ (s 1) [i][l]. For the i-th sub-bit of the user k in the group n in the s-th stage, s = 1, 2,, S 1, the adaptive weight after the l- th iteration is given by (13) at the botto of the page where u = il N +l 1 ξ is a teporary index, e (s) [ j] = r[ j] r (s) [ j] is the error between the received signal and its estiate, and µ (s) is the step size of the noralized LMS algorith for the s-th stage. The adaptive weight after L N 1 iterations, λ (s 1) [i][l N 1], is used as the adaptive weight value for the i-th sub-bit of the user k in the group n in the s-th stage. Users with different data rates have different level of adaptive weights since the signature wavefors have different agnitudes according to data rates. Fro (2), we can see that the chip value of the signature wavefor of the users in the group n has agnitude inversely proportional to T n.in general, the longer the sybol duration or equivalently the lower the data rates, the saller the adaptive weight value. For the LMS algorith to converge, µ (s) has to satisfy the condition of 0 <µ (s) < 2. Although larger step size achieves faster convergence in the LMS algorith, it causes larger gradient noise when the adaptive weights are isadjusted. The partial suer sus up the estiates for the received signals of all users but the user k in the group n to obtain MAI estiate for the user k in the group n. For each user the MAI estiate is subtracted fro the received signal and its result is passed on to the MF bank of the s-th stage. After MAI is subtracted in the s-th stage, the received signal of the user k in the group n is given by r (s) (t) = r(t) (l,h) () ˆx (s) l,h (t). (14) In the s-th stage, the i-th sub-bit estiate for the user k in the group n is given by ˆd (s) [i] = sgn( d (s) [i]) = sgn ( (i+1)tn +τ r (s) (t) it N +τ a (t i M n T n τ ) dt ) (15) where d (s) [i] is the decision statistic for the i-th sub-bit. The sub-bit estiates are updated in each stage using the sub-bit estiates fro the previous stage. In the S -th stage of the ulti-stage PIC receiver, the -th bit estiate for the user k in the group n is obtained as (+1)(M N /M n ) 1 ˆb [] = sgn λ (S ) [i] d (S ) [i]. (16) i=( /M n ) 4. Siulation Results and Discussions Consider an asynchronous ulti-rate DS-CDMA syste with the MPG schee for three data rates: high-rate (HR), ediu rate (MR), and low-rate (LR). Suppose that BPSK is used as a odulation schee and the Gold code of length 31 is repeated once, 4, and 16 ties during bit duration of HR, MR, and LR users as a signature sequence for each user, respectively. Assue that the channel for each user has independent identically distributed frequency-flat Rayleigh fading with noralized Doppler frequency f T 1 = 0.01 where T 1 is the bit duration of the low-rate user. Assue that the syste is chip-synchronous and each interfering user s propagation delay is an integer ultiple of chip duration. Also assue that the receiver knows the signature sequences of all users and has perfect power control for slow fading and path-loss. In each stage, the aplitude of the received signal of each user is estiated fro the decision statistic in r[ j] = ˆr (s) [ j] = N N K [ ] [ ] A b ( j ξ )/L n a ( j ξ )odl n + n[ j] (11) K Â λ (s 1) λ (s 1) [i][l] = λ (s 1) [i][l 1] + N [ ] ( j ξ )/L n ˆd (s 1) [ ] [ ] ( j ξ )/L n a ( j ξ )odl n µ (s) (s 1) n=1 K ˆd 2 n (12) [i]a [u od L n ] e (s) [u], l = 1, 2,, L N 1 (13)
2404 IEICE TRANS. COMMUN., VOL.E87 B, NO.8 AUGUST 2004 2- and 3-stage PIC receiver, the 2- and 3-stage partial PIC (PPIC) receiver, and the MF receiver. Figure 2(a) shows the BER of LR users. In Fig. 2(a) it is shown that various ulti-stage PIC receivers achieve uch saller BER than the MF receiver. It is shown that adaptive 2-stage PIC receiver achieves saller BER than the 2-stage PIC receiver and the 2-stage partial PIC receiver. It is also shown that the adaptive 3-stage PIC receiver has saller BER than 3-stage receivers of other types for LR users. Figure 2(b) shows the BER of MR users. In Fig. 2(b) it is shown that adaptive 2- stage PIC receiver achieves saller BER than the 2-stage PIC receiver and the 2-stage partial PIC receiver for MR users. It is shown that the adaptive 3-stage PIC receiver has saller BER than 3-stage receivers of other types for MR users. Figure 2(c) shows the BER of HR users. In Fig. 2(c) it is shown that the adaptive 3-stage PIC receiver has saller BER than other 3-stage receivers for HR users. In Fig. 2(a), Fig. 2(b), and Fig. 2(c), it is also shown that the adaptive 2-stage PIC receiver achieves BER perforance close to the 3-stage partial PIC receiver for all groups. It is also shown in Fig. 2(a), Fig. 2(b), and Fig. 2(c) that the perforance trends are siilar but specific values are different for users with different data rates. It is basically due to that users with different data rates experience different levels of interference. The transitted signal power is generally larger for users with higher data rates, so users with lower data rates experience relatively higher level of interference than users with higher data rates. So, the perforance of MF receiver is better for users with higher data rates. On the other hand, the adaptive ulti-stage PIC receiver achieves perforance iproveent over the MF receiver, ulti-stage PIC receiver, ulti-stage partial PIC receiver for all user groups with different data rates. After applying the adaptive 3-stage PIC receiver, all user groups achieve siilar BER perforance. 5. Conclusions Fig. 2 BER of the adaptive 2- and 3-stage PIC receivers for the ulti-rate DS-CDMA syste with the MPG schee in a Rayleigh fading channel (8 LR,4MR,2HRusers). the previous stage. Figure 2 shows the BER of adaptive 2- and 3-stage PIC (APIC) receiver with µ (1) = 1.0, µ (2) = 0.5, µ (3) = 0.2 in a Rayleigh fading channel for 8 LR, 4 MR, and 2 HR users. It is copared with the BER of the conventional In this letter, the adaptive ulti-stage PIC receiver is extended to the ulti-rate DS-CDMA syste with the MPG schee. A bit of each user is divided into sub-bits and ulti-user detection is applied for sub-bits. In each stage of the adaptive ulti-stage PIC receiver, MAI estiates are obtained using the sub-bit estiates fro the previous stage and the adaptive weights for the sub-bit estiates. The adaptive weights for the sub-bit estiates are obtained by a noralized LMS algorith. In the final stage, the decision statistics for the sub-bits originated fro one bit are cobined to for final bit estiate. It is shown that the adaptive ulti-stage PIC receiver has significant perforance iproveent over the conventional MF receiver for the ultirate DS-CDMA syste. It is also shown that the adaptive ulti-stage PIC receiver achieves saller BER than the ulti-stage PIC receiver and the ulti-stage partial PIC receiver for users with various data rates in a Rayleigh fading channel.
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