Vector Channel Estimation and Multiuser Detection for Multicarrier DS ...

Wireless Personal Communications (2007) 43:481–494 DOI 10.1007/s11277-006-9245-0

c Springer 2007


Vector Channel Estimation and Multiuser Detection for Multicarrier DS CDMA in Time and Frequency Selective Fading Channels SHU-MING TSENG Department of Electronic Engineering, National Taipei University of Technology, Taipei 106, Taiwan E-mail: [email protected]

Abstract. In a multicarrier direct-sequence code-division multiple access (MC DS CDMA) system, different fading channels for different users and/or different carriers are correlated in general; thus a vector channel model is more appropriate than disjoint scalar channel models. For multiuser MC DS CDMA systems, we propose (1) a generalized vector autoregressive model which accounts for correlation between different user/carrier fading channels, (2) the use of a two-phased algorithm to obtain the proposed model’s parameters, and (3) a receiver structure that consists of a generalized decorrelator followed by maximal-ratio combining (MRC) of uncorrelated carrier channel outputs of each user. The estimated fading coefficients provide the necessary quantities to MRC. The computer simulation results show that the proposed scheme has performance close to the case in which the channel is perfectly known, and outperforms separate scalar channel estimation case. Keywords: Multiuser detection, diversity combining, multicarrier DS CDMA, vector fading channel model

1. Introduction In CDMA systems, multiuser detection [1] is proposed to suppress multiple access interference (MAI) and improve performance. In the literature, it is usually assumed that the multiuser detector has perfect knowledge of the fading channel coefficients for different users. Thus, good channel estimators are required. Recently, the scalar channel estimation and multiuser detection for single-carrier direct-sequence code clinision multiple access (DS CDMA) has been investigated in [2] where disjoint Kalman channel estimators are used. We propose a vector channel model for multiuser detection of the multi carrier directsequence code clinision multiple access (MC DS CDMA) systems described in [3] because of the following reason. Due to frequency-selective fading, spectral overlapping of carriers, Doppler shift causing loss of orthogonality among carriers, nonzero spectral sidelobes of waveforms, cross correlation of different spreading sequences, etc., fading channels of different (carriers, user) pairs are indeed correlated. The related references can be found in [4] (p. 488, references 28 and 29 on p. 494). Thus, it is more appropriate to use a vector channel model, which allows arbitrary correlation between multiple fading channels where the fading process for a specific user and a specific carrier is defined as a fading channel. Note that the fading channel defined here is the composite channel of filtering (spreading/dispreading) and physical channel plus the effect of inter-carrier/inter-user interference.

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Expectation maximization (EM) algorithm [5] is popular in estimating parameters of statistical models in various fields. EM algorithm may be viewed as an iterative maximum likelihood (ML) method. Most recent applications are [6–9]. In particular, Gao et al. [8, 9] use EM algorithm to obtain a vector channel model’s parameters for the single-user single-carrier DS CDMA systems. [8] is a training-based algorithm, and [9] is an approximation of [8] and is a blind adaptive algorithm. In this paper, we generalize the vector channel estimation algorithm for the single-user single-carrier DS CDMA systems in [8] and [9] for multiuser multicarrier DS CDMA systems. First of all, we propose a generalized first-order vector autoregressive (FVAR) model [10] to account for the fading channels for different users and different carriers in MC DS CDMA systems. We propose the Kalman filtering/smoothing/EM (KFS/EM) algorithm for channel estimation of multiuser MC DS CDMA systems. Second, we propose a two-phased blind approach to estimate these parameters. The cyclic prefix used in multicarrier modulation (MCM) and the corresponding bits in the data part of MCM symbols can be treated as training data pairs [11]. Thus, we use the KFS/EM algorithm similar to the one in [8] during the cyclic prefix period of MCM symbols (Phase I) and the blind adaptive EM algorithm similar to the one in [9] during data transmission period of MCM symbols (Phase II). This two-phased method is similar to a periodic dual-mode approach of semi-blind algorithm [12]. The FVAR channel model parameters obtained from the KFS/EM algorithm are used in decorrelation and diversity combining. We finally propose the generalization of diversity combining in [1], where diversity branches are assumed independent. We should decorrelate all fading channels consisting of all users and all carriers (diversity branches). This paper is organized as follows: In Section 2, we describe the transmitter, multiuser receiver and vector channel models. In Section 3, we state the proposed two-phased blind vector channel estimation algorithm. In Section 4, we describe the proposed multiuser detection algorithm including the generalized decorrelator. We give simulation results in Section 5 and Section 6 is the conclusion.

2. Transmitter, Multiuser Receiver and Vector Channel Models We consider the K -user, M-carrier MC DS CDMA communication system over time-selective Rayleigh correlated fading channels. The block diagrams of MC DS CDMA transmitter and multiuser detector are shown in Figures 1 and 2, respectively.

2.1. T h e T r a n s mitter Model The transmitter has M branches in parallel. During l-th symbol interval [lT (l + 1) T ], the information source generates a binary symbol with equal probability. Then it is modulated into a differentially encoded BPSK symbol dl . In each of the M carriers, the same symbol  isspread
J −1 1 √ by the same spreading waveform vl (t) = j=0 J c j ψ (t − lT − j TC ), where c j is the quadri-phase short spreading code and ψ(t) is the chip waveform with time duration [0, Tc ). The spreading waveform is of unity energy. Hence, the transmitted signal in each carrier is of

Vector Channel Estimation and Multiuser Detection

vl(t)

. . . .

dl

MultiCarrier Modulation

. . . .

483

Parallel to Serial

vl(t) Figure 1. The transmitter of the multicarrier DS CDMA system. User 1 rl(1)

(1)

MRC rl

…...

rl

Decorrelator

User 1 detection

…... …...

MF bank

…...

…...

Multi-Carrier Demodulation

MRC

(S )

User K detection

User K

The MF bank output is given in (1) is S-by-S matrix and

(S fading channels),

(noise) are all S-by-1

vectors. The fading channels are assumed FVOR model in (2)

+

Figure 2. The multiuser detector of the multicarrier DS CDMA system (K users, M carriers, S = KM fading channels). M.F.: matched filter. MRC: maximal ratio combining.

the form  (t) =

∞ 

dl vl (t).

l=−∞

2.2. T h e M u ltius er and Vector Channel Model The multiuser receiver has S = K M branches in parallel. For the l-th symbol, the s-th branch for the k-th user and m-th subcarrier performs matched filtering (MF) matched to the spreading waveform and samples the output at time instant (l + 1) T , 1 ≤ k ≤ K , 1 ≤ m ≤ M,

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1 ≤ s = (k − 1)M + m ≤ K M to form the S = K M matched filters’ sampled outputs   (1) (2) (S) T rl = rl rl • • • r l , where rl = Dl gl + nl ,

(1)

where Dl is a diagonal matrix whose diagonal components are the l-th data bit for the k-th (s) user and m-th subcarrier (the s-th channel), and nl is the measurement noise, including the filtered AWGN. The superscript T denotes the transpose. We define the channel vector   (1) (2) (S) T as gl = gl gl • • • gl . A FVAR model is used to model the vector fading channel process. gl =
gl−1 + wl (FVAR channel model, the state equation) and rl = Dl gl + nl , (the measurement equation)

(2)

where
and wl are the S-by-S autoregressive matrix and the S-by-1 FVAR model noise vector, respectively. In addition, the model noise vector wl and the measurement noise vector   (1) (2) (S) T nl = nl nl • • • nl are assumed to be zero-mean, and complex white Gaussian     process with the covariance matrix Q = E wl wlH and Ul = E nl nlH , respectively. The superscript H denotes the complex conjugate transpose. Ul is approximated by averaging the outer products of the off-peak samples of the matched filter bank outputs. Thus, unknown parameters in the system model are the set θ = {
, Q}.

3. The Proposed Two-Phased Blind Vector Channel Estimation 3.1. A B r i e f D e s c r i ption Our proposed vector channel estimation is a modified version of that in Gao et al. [8, 9] and different in the following aspects – In Gao et al. vector channels mean multiple resolvable paths. In this paper, the vector channel includes different users and different carriers. For example, there are six channels when there are two users and the MC DS CDMA systems have three carriers. – Since our model includes multiple users, our data is represented by a diagonal matrix Dl instead of a scalar dl in Gao et al. – A decorrelator multiuser detector is used to eliminate the correlation between channels, thus optimal maximum ratio combining is allowed. On the contrary, due to correlation between fading channels, maximum ratio combining is not optimal in Gao et al. We divided the physical layer transmission into two phases that occur periodically: – Phase I: cyclic prefix is transmitted. The cyclic prefix is a cyclic extension of the last few symbols of the real data block of an MCM symbol. It can be viewed as a training sequence via the scheme in [11]. Thus, the Phase I vector channel estimation algorithm is similar to

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a training-based algorithm proposed in [8]. That is, the diagonal matrix Dl is estimated and is assumed known in the algorithm. – Phase II: real data is transmitting in this phase, thus a training-based algorithm is not applicable here. Therefore, we use a blind algorithm similar to the one in [9]. In addition, since the changing rate of channels (Doppler shift) may vary from symbol to symbol, a forgetting factor is introduced. We also propose to adapt the forgetting factor by fuzzy IF-THEN rules. In the following, we give summaries of channel estimation algorithms for Phases I and II. For details, please see [8] and [9]. Note that
is a FVAR channel model parameter for fading channels in (2), and Q is the covariance matrix of the FVAR model noise in (2). P is the fading channel estimation error covariance matrix. 3.2. P h a s e I V e ctor Channel Es timation Algorithm Summary ∧(0)

∧ (0)

∧

∧(i)

∧ (i)

Initially, we set
(0) = (1 − δ) I, Q(0) = δI, g0 = 0, P0 = I, g 0|0 = g0 , and P0|0 = P0 . We also assume the cyclic prefix is of fixed size N symbols. In this phase, training pairs from cyclic prefix by using the method proposed in [11] is used. At the i-th iteration, we process the whole block of length N by doing the following: 1. Kalman filtering Forward direction: For l = 1, 2, • • • , N Pl|l−1 =
Pl−1|l−1
H + Q(i) (get predicted fading channel estimation error covariance matrix Pl|l−1 from estimated fading channel estimation error covariance matrix Pl−1|l−1 ) ∧ gl|l−1

∧

=
(i) gl−1|l−1 (get predicted fading channel coefficient from estimated fading channel coefficient) ∧ ∧ r l|l−1 = Dl gl|l−1 (get predicted received signal)  −1 E inv = Dl Pl|l−1 DlH + Ul KGl = DlH Pl|l−1 E inv , which is the Kalman filtering gain,   ∧ ∧ ∧ gl|l = gl|l−1 + KGl rl − r l|l−1 (apply Kalman filtering) Pl|l = (I − KGl Dl ) Pl|l−1 . ∧

∧ , Quantities stored for backward smoothing: gl|l , Pl|l , for l = 0, 1, • • • , N , and gl|l−1 Pl|l−1 , for l = 1, 2, • • • , N . 2. Smoothing (we use future measurement to improve current estimation, p. 304 of [13]) Backward direction: For l = N , N − 1, • • • , 1, −1 Al−1 = Pl−1|l−1
H Pl|l−1

∧ ∧ ∧ ∧ gl−1|N = gl−1|l−1 + Al−1 gl|N − gl|l−1 (smoothing gain, similar to p. 308 of [13])  H Pl−1|N = Pl−1|l−1 + Al−1 Pl|N − Pl|l−1 Al−1 . (i)

(i) H

(i)

Pl,l−1|N = Pl|N Al−1 .

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3. Compute M1 , M2 , and M12 , and then


∧ (i+1)

and Q

H N N   ∧(i) ∧(i) (i) g g M12 = Pl,l−1|N , l|N l−1|N +

l=1

where

l=1

(i) Pl,l−1|N E (i)



 H (i) (i) (i) and channel coefficient estimation gl|N gl−1|N |r, θ

(i)

∧

error gl|N gl − gl|N



H N N     ∧(i) ∧(i) (i) (i) (i) (i) H gl|N gl|N + Pl|N where Pl|N E gl|N gl|N |r, θ (i)

M1 =

l=1

M2 = ∧ (i+1)




∧ (i+1)

Q

l=1

H N  ∧(i) ∧(i) gl−1|N gl−1|N l=1

+

N 

(i)

Pl−1|N

l=1

= M12 M2−1  1  H = M1 − M12 M2−1 M12 N

4. Set initial condition for the (i + 1)-th iteration: ∧(i+1) g0

∧

(i+1)

∧ (i+1)

∧ (i+1)

= g0|N , P0 = P0|N and
=
,Q=Q . 5. Repeat steps 2, 3, and 4 (i+1 iteration) until
and Q do not change significantly.

3.3. P h a s e I I V e ctor Channel Es timation Algorithm Summary The major modifications of [9] from [8] are as follows: – One symbol, not one block of N symbols, is processed at a time. Thus, all variables conditioned on N are now conditioned on l. – No iterations at each processing. Thus, all superscripts (i) are replaced by (l). – To adapt to the slowly varying Doppler shift, we introduce a forgetting factor λ, which is fuzzy adaptive. ∧

(0) (0) Initialization: set
(0) = (1 − δ) I , Q(0) = δI , g0|0 = 0, P0|0 = I , M12 = M1 = (0) M2 = 0 , and scalar (0) = 0.

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1. Kalman filtering  (l)  H (l) Pl|l−1 =
Pl−1|l−1
+ Q(l) ∧ gl|l−1

∧

=
(l) gl−1|l−1 ∧

∧ r l|l−1

= Dl gl|l−1  −1 E_inv = Dl Pl|l−1 DlH + Ul

KGl = DlH Pl|l−1 E_inv   ∧ ∧ ∧ gl|l = gl|l−1 + KGl rl − r l|l−1 Pl|l = (I − KGl Dl ) Pl|l−1 . 2. One-lag smoothing  (l)  H −1 Pl|l−1 Al−1 = Pl−1|l−1


∧ ∧ ∧ ∧ gl−1|l = gl−1|l−1 + Al−1 gl|l − gl|l−1  H . Pl−1|l = Pl−1|l−1 + Al−1 Pl|l − Pl|l−1 Al−1 (i)

H Pl,l−1|l = Pl|l Al−1 . ∧ (l+1)

3. Compute M1 , M2 , and M12 , and then
(l+1) M12 (l+1) M1 (l+1) M2

=

(l) λM12

=

(l) λM1

=

(l) λM2

+ (1 − λ) + (1 − λ) + (1 − λ)

∧ ∧H gl|l gl−1|l ∧ ∧H gl|l gl|l

∧ (l+1)

and Q

+ Pl,l−1|l

+ Pl|l

∧H ∧ gl−1|l gl−1|l

+ Pl−1|l

scalar (l+1) = λ · scalar (l) + 1 − λ   ∧ (l+1) (l+1) (l+1) −1
= M12 M2    

∧ (l+1) 1 (l+1) (l+1) (l+1) −1 (l+1) H M1 Q = − M12 M2 M12 scalar (l+1) In the proposed method, I is an M-by-M identity matrix and δ is a small number. The ∧(i)

(i)

quantities gl|N and Pl|N of the fixed-interval (of length N ) smoothing of the i-th iteration are ∧

replaced by gl|l and Pl|l of the one-lag smoothing, respectively.

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S

M

L

Membership grade

1

0

0

1.5

(b) S

M

L

Membership grade

1

0 0.9

1

Figure 3. The fuzzy sets used for forgetting factor adaptation. (a) The fuzzy sets of
l (b) The fuzzy sets of λl . The membership grade represents the fuzziness of the fuzzy set with values between [0,1]. The membership grade for traditional (non-fuzzy) set is either 0 (not in the set) or 1(in the set). S: small, M: medium, L: large.

3.4. T h e A d a ptation of Forgetting Factor To account for the slow variation in the Doppler spread, we use a weighted sum with a forget(l+1) (l+1) (l+1) ting factor λ to compute M12 , M1 , and M2 . The selection of λ is a trade-off between good tracking ability (λ small) and noise insensitivity (λ = 1). Fuzzy logic  has solved similar tradeoff in communication problems [14, 15]. Let
l= gˆ l|l − gˆ l−1|l−1 . We thus apply the following fuzzy IF-THEN rules to the adaptation of the forgetting factor: If
l is large, then λl is small. If
l is medium, then λl is medium. If
l is small, then λl is large. The fuzzy sets of
l and λl are shown in Figure 3. This set of fuzzy IF-THEN rules is based on the following intuition: if the channel estimate is varying significantly, the channel estimation algorithm seems to have not “lock” the true channel coefficients, thus the forgetting factor should be small to “forget” the past channel estimate, and vice versa. 3.5. D i s c u s s i o n s This two-phased vector channel estimation algorithm (periodic dual-mode approach) is more attractive than pure training-based or blind approaches, especially in multicarrier DS CDMA systems where a source of training data, i.e., cyclic prefix, is appended to every multicarrier modulated symbol to combat frequency-selective fading. Although Phase I is a training-based

Vector Channel Estimation and Multiuser Detection

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algorithm, it does not require additional training sequence transmission periods. Phase II is conducted jointly with multiuser detection (described in the next section), symbol by symbol. Usually cyclic prefix is not long, thus the training-based Phase I algorithm does not achieve adequate performance. Blind algorithms alone such as Phase II usually require longer data records than training-based algorithms to demonstrate comparable performance. When combined with the training-based Phase I algorithm (although not a long period), blind Phase II algorithm will deliver a better performance.

4. Multiuser Detection: Decorrelating, Maximal Ratio Combing and Detection During Phase I (cyclic prefix period), the proposed Phase I vector channel estimation algorithm is carried out but not multiuser detection. During Phase II (information symbols part of multicarrier modulated symbols), the proposed Phase II vector channel estimation algorithm and multiuser detection are jointly conducted symbol by symbol. In the following, we describe the proposed multiuser detection scheme. Because we allow correlation between carriers, our decorrelator is more general than that described in [1] (Section 5.7). For simplicity, we drop the subscript l of all variables in this section. For decorrelating (Figure 2), we pass the matched filter bank output r into decorrelator R−1 , and get r˜ = R−1 r, where R = gg H is the cross correlation matrix of S = KM fading channels. For maximal ratio combining and detection, we take user 1 as an example. User 1 has M fading channels (carriers) and combines its M components in r˜ (first M components) and performs data detection as follows: 
∗ r j |α j } V ar {˜r j |α j } to maximize signal-todˆ = sign(Re{ M j=1 g j r˜ j }), where g j = E{˜ noise ratio (thus minimize error probability) [3], α j is the magnitude of fading coefficients of user 1 and carrier j (the first M components of g), and Re{} takes the real part. Note that conditional expectation E{˜r j |α j } = α j and conditional variance V ar {˜r j |α j } = (R−1 ) j j , where (R−1 ) j j is the j-th row, j-th column of the matrix R−1 , the inverse of R. This is because the noise component’s variance has changed due to multiplication of the decorrelator R−1 .

5. Computer Simulation Results We consider a three-carrier (M = 3) MC DS CDMA system in a time-selective Rayleigh fading channel with normalized Doppler rate [16] is 0.02. Correlated fading coefficients are generated in the following way. Assume there are  ∼

∼(1) ∼(2) ∼(3) ∼(4)

K = 2 users. We generate S = K M = 6 independent fading processes g l = g l g l g l g l  ∼(5) ∼(6) T gl gl , for l ≥ 1. If the correlation matrix of channel vector gl at the zero-time shift is ρ, then we generate the multiple correlated fading coefficients gl by the following expression 1∼

gl = ρ 2 g l . According to some references in [4], high correlation may be observed in carriers’ fading in some fading environments. Thus, we set the autocorrelation matrix of the channel vector at a

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250 s y m bol

Figure 4. The magnitude of true (the upper one) and estimated (the lower one) Rayleigh fading channel coefficients over Phase I (cyclic prefix period, training period) of 500 symbols after 13 iterations. SNR = 0 dB.

zero-time shift ⎡ 1 ⎢ 0.9 ⎢ ⎢ 0.81 ρ=⎢ ⎢ 0.9 ⎢ ⎣ 0.81 0.729

0.9 1 0.9 0.81 0.9 0.81

0.81 0.9 1 0.729 0.81 0.9

0.9 0.81 0.729 1 0.9 0.81

0.81 0.9 0.81 0.9 1 0.9

0.729 0.81 0.9 0.81 0.9 1

⎤ ⎥ ⎥ ⎥ ⎥. ⎥ ⎥ ⎦

The differentially encoded BPSK data symbol is spread by a periodic random signature sequence with processing gain 128. The time-varying statistics of the channel vector is modeled as a FVAR process. In Phase I of 500 symbols (cyclic prefix), the parameters of the FVAR process are obtained by iterating the KFS/EM procedure until the estimated channel coefficient are almost unchanged. In Figure 4, we plot the true and estimated magnitude of a Rayleigh fading process versus symbol time. The SNR is 0 dB. The Doppler rate is assumed to be 0.02 and constant over Phase I. In Phase II, a real data block of 5000 symbols is transmitting, and we assume the Doppler rate is changing at a uniform rate from 0.02 to 0.03. To show the benefit of vector channel estimation using a FVAR model over separate scalar channel estimation, we also consider a scalar version of the proposed two-phased vector channel estimation algorithm: We assume the fading channels for carriers are independent although they are actually correlated. Thus a scalar AR process is used to model each fading channel, (s) (s) (s) (s) (s) given by gl = φs gl−1 + nl , where s = 1, . . . , K M. Define ql E{|nl |2 }. During Phase (s)

I, the parameter set {φ(s) , ql } for each fading channel is estimated separately by the scalar version of the proposed Phase I vector channel estimation algorithm. The estimated parameters

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A B C D

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Figure 5. Performance comparison: A. single user only and perfect channel knowledge. B. multiuser detection and perfect channel knowledge. C. the proposed two-phased vector channel estimation and multiuser detection. D. two-phased separate scalar channel estimation and multiuser detection (scalar version of C).

are combined to get  ∧

∧ (1) ∧ (2) ∧(3) ∧(4) ∧(5) ∧ (6)


= diag φ

φ

φ

φ

φ

φ



 (1) (2) (3) (4) (5) (6)  ∧ ∧ ∧ ∧ ∧ ∧ . , Ql = diag q l q l q l q l q l q l ∧

Similarly, in Phase II, we use the scalar version of the proposed Phase II vector channel ∧

∧

estimation algorithm and
and Ql are combined the same way. In Figure 5, the bit error probability of the following cases is simulated. A. B. C. D.

Single user only and perfect channel knowledge Multiuser detection and perfect channel knowledge The proposed two-phase vector channel estimation and multiuser detection Two-phased scalar channel estimation and multiuser detection

For each simulation point of each curve, we conduct simulation until there are at least 100 error bits. In Figure 6, we simulate the bit error probability when the normalized Doppler rate is high (0.01 more than the previous figure). That is, the Doppler rate is assumed to be 0.03 and constant over Phase I. In Phase II, a real data block of 5000 symbols is transmitting, and we assume the Doppler rate is changing at a uniform rate from 0.03 to 0.04. We note that curve C is close to curve B, thus the proposed algorithm has a performance near that of the case of a perfect knowledge of fading channels. We also note the significant difference between curves C and D, which demonstrates the advantage of the vector channel model over the scalar channel model.

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Figure 6. The performance comparison when normalized Doppler rate is high (0.01 more than the previous figure): A. single user only and perfect channel knowledge. B. multiuser detection and perfect channel knowledge. C. the proposed two-phased vector channel estimation and multiuser detection. D. two-phased separate scalar channel estimation and multiuser detection (scalar version of C).

6. Conclusion In this paper, we propose a vector autoregressive model which accounts for correlation between different user/carrier fading channels. It is the multiuser generalization of that in [8]. The simulation results show the proposed algorithm performs better than the case where separate scalar channels are estimated. We also propose the use of a two-phased and blind algorithm to obtain the proposed model parameters. The proposed Phase I and II vector channel estimation algorithms are trainingbased and blind approaches, respectively. The proposed two-phased algorithms allows for a short training period (cyclic prefix length in MC DS CDMA systems) in Phase I and a blindly adaptive vector channel estimation algorithm in Phase II; thus they are better than exclusive training or a blind one. Note that we also incorporate simple fuzzy IF-THEN rules to adjust the forgetting factor (determine how fast it adapts to Doppler shift changes) in the blind adaptive Phase II algorithm. Finally, we propose a receiver structure consisting of a generalized decorrelator followed by maximal-ratio combining (MRC) of uncorrelated carrier channel outputs of each user. This is a generalized version of that in [1] to allow correlations between diversity branches. Acknowledgments This paper was presented in part at the IEEE Wireless Communications and Networking Conference (WCNC 2004), Atlanta, GA, USA, March 21–25, 2004 [10]. This paper was supported in part by the National Science Council under Grant NSC94–2213-E-027–013.

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References 1. S. Verdu, Multiuser Detection, Cambridge: Cambridge University Press, 1998. 2. P. Wu and A. Duel-Hallen, “Multiuser detectors with disjoint Kalman channel estimators for synchronous CDMA mobile radio channels”, IEEE Trans. Commun., Vol. 48, No. 5, pp. 752–756, May 2000. 3. S. Kondo and L.B. Milstein, “Performance of multicarrier DS CDMA systems”, IEEE Trans. Commun., Vol. 44, No. 2, pp. 238–246, Feb. 1996. 4. M.K. Simon and M.-S. Alouini, Digital Communication over Fading Channels: a unified approach to performance analysis, New York: Wiley, 2000. 5. T.K. Moon, “The expectation-maximization algorithm”, IEEE Signal Process Mag., Vol. 13, No. 6, pp. 47–60, Nov. 1996. 6. K.Y. Lee and S. Jung, “Time-domain approach using multiple Kalman filters and EM algorithm to speech enhancement with non-stationary noise”, IEEE Trans. Speech Audio Process., Vol. 8, No. 3, pp. 282–291, May 2000. 7. W. Turin, “MAP decoding in channels with memory”, IEEE Trans. Commun., Vol. 48, No. 5, pp. 757–763, May 2000. 8. W. Gao, S. Tsai, and J.S. Lehnert, “Diversity combining of a fast-varying, correlated multipath fading channel for direct-sequence spread-spectrum systems”, Proc. IEEE Veh. Technol. Conf. (VTC’00), Vol. 3, pp. 1445–1451, 24–28 Sept. 2000. 9. W. Gao, S. Tsai, and J.S. Lehnert, “Blind adaptive estimation and diversity combining of a fast varying, correlated multipath channel for DS/SS systems,” Proc. IEEE Mil. Commun. Conf. (MILCOM’ 00), Vol. 2, pp. 759–763 22–25, October, 2000. 10. S.-M. Tseng and H.-C. Yu, “Vector Channel Estimation and Multiuser Detection for Multicarrier DS CDMA in Time and Frequency Selective Fading Channels”, IEEE Wireless Commun. Networking Conf. (WCNC 2004), Atlanta, GA, USA, vol. 1, pp. 18–23, Mar. 2004. 11. X. Wang and R.J. Ray Liu, “Adaptive channel estimation using cyclic prefix in multicarrier modulation system”, IEEE Commun. Lett., Vol. 3, No. 10, pp. 291–293, Oct. 1999. 12. A.M. Kuzminskiy, “Finite amount of data effects in spatio-temporal filtering for equalization and interference rejection in short burst wireless communications”, Signal Process, Vol. 80, pp. 1987–1997, 2000. 13. J.M. Mendel, Lessons in Estimation Theory for Signal Processing, Communications, and Control, Englewood Cliffs, New Jersey, Prentice-Hall, 2nd Edition, 1995. 14. S.-M. Tseng and Y. Zheng, “Fuzzy two-stage carrier synchronization”, Fuzzy Sets and Systems, Vol. 102, No. 2, pp. 211–219, Mar. 1999. 15. S.-M. Tseng and Y. Zheng, “Adaptive fuzzy frequency estimator with applications in fading communication channels”, Fuzzy Sets Syst., Vol. 114, No. 2, pp. 255–259, Sep. 2000. 16. P. Dent, G.E. Bottomley, and T. Croft, “Jakes fading model revisited”, Electro. Lett., Vol. 29, No. 13, pp. 1162–1163, June 1993.

Shu-Ming Tseng was born in Taipei, Taiwan in 1972. He received the B.S. degree with highest honors from National Tsing Hua University, Taiwan, and the M.S. and Ph.D. degrees from

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Purdue University, IN, USA, all in electrical engineering, in 1994, 1995, and 1999, respectively. From 1999 to 2003, he was an Assistant Professor with the Department of Electrical Engineering, Chang Gang University, Taiwan, and the Department of Electronic Engineering, National Taipei University of Technology, Taiwan. Since August 2003, he has been an Associate Professor with the Department of Electronic Engineering, National Taipei University of Technology, Taiwan. His research interests are PHY and MAC layers of communication systems. Since 1999, he has 15 published/accepted SCI journal papers and 10 National Science Council research grants. Prof. Tseng served as a Technical Program Committee member for two symposia of the IEEE Vehicular Technology Conference, Orlando, Florida, Fall, 2003, one symposium of the IEEE WirelessCom, Maui, Hawaii, 2005, and general symposia of the International Wireless Communications and Mobile Computing Conference (IWCMC2006). He is listed in 2006 Edition (23rd) Marquis Who’s Who in World. He was a member of Patents Reviewing Panel, Optical Society of America from 2000 to 2004.