Space Time Block Code for CDMA2000 with Pilot Channel Estimation Bagawan S. Nugroho and Hyuck M. Kwon Wichita State University, Department of Electrical and Computer Engineering, Wichita, KS 67260-0044 Tel: (316) 978-6308, Fax: (316) 978-5408 Email: {bsnugroho, hyuck.kwon}@wichita.edu Abstract--The space time block code (STBC) has recently attracted much attention for its ability to achieve significant diversity gain. And most of the papers related to the STBC have discussed in its applications to the wideband code division multiple access (W-CDMA) system. Only a few papers have studied its application to the CDMA2000 system. The paper in [6] is one of them. Each user in a forward link employs a STBC encoder and the number of the STBC encoders is equal to the number of users, and the channel estimation is not discussed in [6]. However, this paper employs only one STBC encoder for the multiple users at a base station, and provides a practical channel estimation scheme using the STBC and the pilot channel in the CDMA2000 together. For the sake of simplicity, we consider two transmit antennas and one receive antenna. No error correction coding is employed. Also Jakes’ model is employed for the Rayleigh fading channel simulation. Multiple access interference is modeled as an additive white Gaussian noise (AWGN). A RAKE receiver of three fingers is employed for three unequal strength multipath, based on the ITU-R M.1225. The simulation results show that the STBC can improve bit error rate (BER) significantly. For example, the STBC with the channel estimation can make improvement of 4 dB in signal-to-noise ratio at BER=10-2, compared to the one transmit antenna system without STBC. I.

INTRODUCTION

The space time block code (STBC) has recently been introduced [1], and adopted as the transmit diversity scheme in a third generation (3G) wireless communications system standard, i.e., the wideband code division multiple access (WCDMA) [2, pp. 16-17]. The STBC provides more significant diversity gain without expanding the channel bandwidth than the well known RAKE temporal diversity scheme, which has been used in a second generation (2G) system of IS-95 standard [3]. This can briefly be explained as follows: In a RAKE receiver the contribution of the second path (or finger) to the overall diversity gain is much smaller than that of the dominant finger in practice since the gain of the second path is much smaller than that of the dominant path, based on the ITU-R M.1225 standard [4]. The STBC can be cooperated with the temporal diversity, i.e., the RAKE finger. And the STBC can generate multiple independent paths for each multipath with the same average gain by employing multiple antenna elements at the transmitter. In other words, the STBC This material is based upon work supported by the U. S. Army Research Laboratory and the U. S. Army Research Office under grant number DAAD19-01-10537. This paper will be presented at the IEEE VTC Fall 2002, Vancouver, BC, Canada, September 24-28, 2002

can generate multiple dominant paths instead of single dominant path used in the conventional RAKE receiver. Therefore, the overall diversity gain of a STBC can be the number of elements times better than that of a RAKE receiver. Most of the papers related to the STBC have discussed in its applications to the W-CDMA system. Only a few papers have studied its application to the CDMA2000 system [5]. The paper in [6] is one of them. Each user in a forward link employs a STBC encoder and the number of the STBC encoders is equal to the number of users in [6]. Also the channel estimation method is not discussed in [6]. Reducing the complexity and maintaining the same bit error rate (BER) performance is the motivation of this paper. The goal of this paper is to employ only one STBC encoder for the multiple users at a base station, and to provide a practical channel estimation scheme at a mobile receiver by exploiting the benefits of the STBC and the pilot channel in the CDMA2000 together. For the sake of simplicity, we consider two transmit antennas and one receive antenna. No error correction coding is employed. Also Jakes’ model is employed for the Rayleigh fading channel simulation. Multiple access interference is modeled as an additive white Gaussian noise (AWGN). A RAKE receiver of three fingers is employed for three unequal strength multipaths, based on the ITU-R M.1225 model. The BER will be simulated, and compared with that of the one transmit antenna system without the STBC. Section II provides the system model of the STBC for a forward link with pilot channel, e.g., a CDMA2000 system. Section III presents the simulation results. Finally, Section IV concludes the paper. II. SYSTEM MODEL AND ANALYSIS A. Transmitter with STBC We assume two transmit antenna elements at a base station and one receive antenna element at a mobile station for the sake of the simplicity. Figure 1 shows a block diagram of the proposed transmitter with one STBC encoder for the multiple access users in a forward link. The code symbol stream from each user, e.g., dk for the k-th user, is converted into a parallel stream. Then, each parallel stream is mapped into a complex symbol stream using a complex mapping, e.g., a quadrature phase shift keying (QPSK) modulation, and multiplied with Walsh chip stream wn(k) where k and n denote the user and chip index, respectively. The long code can be multiplied right after the Walsh spreading and is omitted in this paper since it does not degrade the performance analysis and conclusions.

The upper and lower branch represent the odd and even numbered complex symbol stream, and are distinguished by the subscription (o) and (e), respectively. In this paper the time first symbol interval (0, Tb) and the second symbol interval (Tb, 2Tb) represent an odd and even numbered symbol interval, respectively, where Tb denotes a complex symbol interval. The odd and even numbered complex symbol streams from all the Ku number of traffic and pilot channels are, respectively, summed and denoted by X(o) and X(e). Then, the STBC encoder forwards X(o) and X(e) to the complex PN spreader in parallel for the transmitter 1 and 2 during the odd numbered interval (0, Tb), respectively. For the even numbered complex symbol interval (Tb, 2Tb), the STBC encoder forwards –X*(e) and X*(o) to the complex PN spreader in parallel for the transmitter 1 and 2, respectively. Superscript * denotes the complex conjugates of the symbol. The outputs of the STBC encoder during two consecutive transmitted symbol intervals (0, 2Tb) can be written as  X ( o ) − X (*e )  (1)   X (*o )   X ( e ) where the first and the second row denote two consecutive transmitted symbols in time at the antenna element 1 and 2, respectively, and the first and the second column represent two transmitted symbols at the antenna element 1 and 2, respectively. The output symbol rate of the STBC encoder is equal to the input symbol rate. This means that there is no bandwidth expansion. Also, the proposed scheme has an advantage to reduce the system complexity since the number of STBC encoders is only one regardless of the number of users. The real and imaginary parts of X(o) and X(e) are denoted by the superscript (I) and (Q), respectively, and X(o) and X(e) are written as (2) X (o ) = X ((oI)) + jX ((oQ)) and (3)

X (e ) = X ((eI)) + jX ((eQ) )

where Ku

X ((oI)) = Ec A0 + ∑ Ec (k ) d n( ,I()o ) (k ) wn (k )

(4)

X ( o ) = Ec A0 + ∑ Ec (k )d n( Q,( o) ) (k )wn (k )

(5)

(Q )

k =1 Ku

k =1

X

(I ) (e)

Ku

= Ec A0 + ∑ Ec (k )d k =1 Ku

(I ) n ,( e )

(k ) wn (k )

X ( e ) = Ec A0 + ∑ Ec (k )d n( Q, ( e) ) (k ) wn (k ) . (Q )

(6) (7)

k =1

In (4)-(7), Ec(k) and A0 are the chip energy and pilot channel amplitude, respectively. The (dn,(o)(I), dn,(o)(Q)) and (dn,(e)(I), dn,(e)(Q)) are the pairs of real and imaginary parts of the complex mapping outputs at the n-th chip time for the transmit antenna element 1 and 2 during the odd numbered symbol interval (0, Tb), respectively. Complex pseudonoise (PN) code spreading is done separately for each transmit antenna. When the input symbols

to the PN spreading are, respectively, X(o) and X(e) for the transmit antenna element 1 and 2 during the odd numbered symbol interval (0, Tb), the PN spreading output can be written as (I ) (Q ) X '(1) ≡ X '(1) + jX ' (1) (8) (I ) (Q ) = X ' ( o ) = X ( I ) + jX ( Q ) a n + ja n

(

(o)

(I )

(o)

X '( 2) ≡ X '( 2 ) + jX '( 2 )

)(

)

(Q )

(

)(

= X '( e ) = X ((eI) ) + jX ((eQ) ) an

(I )

+ jan

(Q )

(9)

)

where an(I) and an(Q) are the PN code sequences for the I and Q channel, respectively at the n-th chip time. When the input symbols to the PN spreading are, respectively, (–)X*(e) and X*(o) for the transmit antenna element 1 and 2 during the even numbered symbol interval (Tb, 2Tb), the PN spreading output can be written as (I ) (Q ) X '(1) ≡ X '(1) + jX '(1) (10) (I ) (Q ) = − X '*( e ) = (− X ((eI)) + jX ((eQ) ) ) a n + ja n

(

(I )

X '( 2 ) ≡ X '( 2) + jX '( 2)

(

)

(Q )

)(

= X '*( o ) = X ((oI )) − jX ((oQ)) an

(I )

+ jan

(Q )

).

(11)

The transmitted signals at the antenna element 1 and 2 can be, respectively, written as (12) Y1 (t ) = Re( X '( o ) e j 2πf c t ) * h(t ) Y2 (t ) = Re( X '( e ) e j 2πf c t ) * h(t ) for the odd numbered symbol interval (0, Tb), and Y3 (t ) = Re[− X '*( e ) e j 2πfct ] * h(t )

Y4 (t ) = Re[ X '*( o ) e j 2πfct ] * h(t )

(13) (14) (15)

for the even numbered symbol interval (Tb, 2Tb) where * denotes the convolution operator, h(t) is the pulse-shaping filter impulse time response, and fc is the carrier frequency. This paper employs a root raised cosine (RRC) filter of rolling off factor 0.22 for the waveform shaping filter. Jakes' Rayleigh fading model is used for a multipath fading channel. Two multipath fading channels from the transmit antenna element 1 and 2 to the receive antenna are, respectively, written as (16) g1 = α1e jφ1 jφ (17) g 2 = α 2e 2

where α1 and α 2 are the fading amplitudes, and φ1 and φ2 are the fading phases. The fading channels are slowly varying, compared to the symbol rate, and g1 and g2 are assumed to be constants during the two consecutive symbols. The received signals under the fading channel can be written in matrix form as  r1 (t )  Y1 (t ) Y2 (t )  g1  υ1  (18) r (t ) = Y (t ) Y (t )  g  + υ  4 2   3  2   2  where R1(t) and R2(t) are the received signal, and υ1 and υ 2 represent the additive white Gaussian thermal noise plus interference from other users for the odd and even number symbol periods, respectively. The AWGN are modeled as the

complex Gaussian random variables with zero mean and variance equal to N0/2. B. Rake Receiver with Pilot Aided Channel Estimator Three fingers are assumed in this paper, based on the ITU multipath channel model. Figure 2 shows a block diagram of one coherent finger RAKE receiver with the STBC decoder. The subscripts 1 and 2 represent the odd and even numbered symbol intervals, respectively. After the frequency down conversion and matched filtering, the baseband signal representation for the I and Q components during the odd numbered (first) symbol interval can be, respectively, written as (I ) (19) I1 (t ) = Re[ r1 (t ) cos 2πf ct ] * h(Tc − t ) + υ1 and (Q ) (20) Q1 (t ) = − Re[ r1 (t ) sin 2πf ct ] * h(Tc − t ) + υ1 where Tc is the chip time interval. Similarly, the baseband signal representation for the I and Q components during the even numbered (second) symbol interval can be, respectively, written as (I ) (21) I 2 (t ) = Re[r2 (t ) cos 2πf ct ] * h(Tc − t ) + υ 2 and (Q) (22) Q2 (t ) = − Re[r2 (t ) sin 2πf ct ] * h(Tc − t ) + υ 2 . Equations (19) through (22) can be rewritten as (I ) (23) I1 (t ) = Re[ X '( o) g1 + X '( e) g 2 ] 12 R(τ ) + υ1 (24)

( Q)

Q1 (t ) = Im[X '( o) g1 + X '(e) g 2 ] 12 R(τ ) + υ1

I 2 (t ) = Re[− X '*( e) g1 + X '*( o ) g 2 ] 12 R(τ ) + υ2

(25)

(I )

Q2 (t ) = Im[− X '*( e) g1 + X '*( o ) g 2 ] 12 R (τ ) + υ 2

(Q )

(26)

where τ is the misalignment time between the received and local PN codes and R(τ ) =

∞

∫ H( f )

2

cos(2πf cτ )df

−∞

which is the inverse Fourier transform of |H(f)|2. The R(τ) is equal to 1 at τ=0 for a filter with normalized coefficients. Samples are taken every chip interval, i.e., t=nTc for integer n. The PN despreading is performed with the locally generated PN codes. The I and Q components of the complex PN despread sample at t=nTc during the first symbol interval are, respectively, written as (I ) (I ) (Q ) (27) y1n (t ) = I1 (t )an + Q1 (t )an and (Q ) (I ) (Q ) (28) y1n (t ) = Q1 (t ) an − I1 (t ) an . The I and Q components of the complex PN despread sample at t=nTc during the second symbol interval are, respectively, written as (I ) (I ) (Q) (29) y2 n (t ) = I 2 (t )an + Q2 (t )an and (Q ) (I ) (Q ) (30) y2 n (t ) = Q2 (t )an − I 2 (t )an .

By substituting (8)-(11) and (23)-(26) into (27)-(30), the samples after the PN despreading can be rewritten as

y1n

(I )

= X ((oI))α 1 cos φ1 − X ((oQ))α1 sin φ1 + X α 2 cos φ 2 − X (I ) (e )

y1n

(Q)

=X

(31)

α 2 sin φ2 + υ1n

(Q) (e )

(I )

α1 cos φ1 + X α1 sin φ1

(Q) (o)

(I ) (o)

+ X ((eQ) )α 2 cos φ 2 + X ((eI))α 2 sin φ 2 + υ1n y2 n

(I )

= − X ((eI))α 1 cos φ1 − X ((eQ) )α 1 sin φ1 + X ((oI))α 2 cos φ 2 + X ((oQ))α 2 sin φ 2 + υ 2 n

y2 n

(Q )

(32)

(Q)

(33)

(I )

= X ((eQ) )α 1 cos φ1 − X ((eI))α 1 sin φ1 − X ((oQ))α 2 cos φ 2 + X ((oI))α 2 sin φ 2 + υ 2 n

(Q )

.

(34)

The desired traffic components can be estimated by taking summation of the products of (31)-(34) with wn(k) over Nc chips interval as Nc

y1( I ) ≡ ∑ y1(nI ) wn (k ) = Re[d ( o ) g1 + d ( e ) g 2 ] + υ '1

(35)

(I )

n =1 Nc

y1( Q ) ≡ ∑ y1(nQ ) wn (k ) = Im[d ( o ) g1 + d ( e ) g 2 ] + υ '1

(36)

(Q )

n =1

Nc

y 2( I ) ≡ ∑ y 2( In) wn (k ) = Re[− d * (e ) g1 + d * (o ) g 2 ] + υ ' 2

(I )

(37)

(Q )

(38)

n =1 Nc

y 2( Q ) ≡ ∑ y 2( Qn ) wn (k ) = Im[−d * ( e) g1 + d * ( o ) g 2 ] + υ ' 2 n =1

where d(o) = d(o)(I)+jd(o)(Q) and d(e) = d(e)(I)+jd(e)(Q) are the desired traffic code symbols. The wn(k) in (35)-(38) represents the product of the Walsh code and the long code used by the desired user. By using (31)-(34) and the orthogonal properties in the Walsh symbol between the pilot and traffic channels, the fading amplitude and phase can be estimated as Nc Nc Nc Nc 1 (Q) (I ) (Q) (I ) αˆ1 cosφˆ1 = [∑ y1n + ∑ y1n − ∑ y2 n + ∑ y2 n ] 4 A0 Ec n=1 n =1 n =1 n =1 (39) Nc Nc Nc Nc 1 (Q ) (I ) (Q ) (I ) αˆ1 sin φˆ1 = [− ∑ y1n + ∑ y1n − ∑ y2 n − ∑ y2 n ] 4 A0 Ec n=1 n=1 n=1 n =1 (40) Nc Nc Nc Nc 1 (I ) (Q) (I ) (Q ) αˆ 2 cosφˆ2 = [∑ y1n + ∑ y1n + ∑ y2 n − ∑ y2n ] 4 A0 Ec n =1 n =1 n =1 n =1 (41)

αˆ 2 sin φˆ2 =

1 4 A0 Ec

Nc

[ −∑ y1n n =1

(I )

Nc

+ ∑ y1n n=1

(Q )

Nc

+ ∑ y2 n

(I )

n =1

Nc

+ ∑ y2 n

(Q )

]

n=1

(42) where Nc is number of chips per code symbol. Thus, the estimated Rayleigh fading channel coefficients during the odd and even numbered symbol intervals can be, respectively, written as ˆ (43) gˆ 1 = αˆ1 (cos φˆ1 + j sin φˆ1 ) = αˆ1 e jφ1 and ˆ (44) gˆ 2 = αˆ 2 (cos φˆ2 + j sin φˆ2 ) = αˆ 2 e jφ . Let S1 and S2 denote the complex signal components consisting of y(I) and y(Q) during the odd and even numbered symbol intervals and be, respectively, written as 2

(I )

S1 = y1

(Q)

+ jy1

(45)

and (I ) (Q ) (46) S 2 = y2 + jy2 . Then, S1 and S2 can be written in a matrix form as g 2  d ( o )   υ '1  .  S1   g 1 (47)  S *  =  g * − g *   d  + υ ' *   2   2  2  1   (e)  The linear combiner in Figure 2 is to find the estimates of the desired traffic code symbols dˆ( o ) and dˆ( e ) as H dˆ( o )   gˆ1 gˆ 2   S1  (48) ˆ = * *  *  d (e )   gˆ 2 − gˆ1   S 2  where the superscript H denotes the Hermitian operation, i.e., conjugate and transpose. If the channel estimation is perfect, i.e., αˆ1 = α1 , αˆ 2 = α 2 ,

φˆ1 = φ1 , and φˆ2 = φ2 , then dˆ( o) and dˆ( e ) can be written as dˆ(o )   g1 + g 2 ˆ = 0  d ( e )   2

2

0 2

g1 + g 2

2

 d ( o )   noise1    +   d   (e )  noise2 

estimation scheme in detail by using the pilot channel for coherent detection with the STBC. This channel estimation scheme can estimate two independent fading channels from two transmit antenna elements to one receive antenna element. Simulation results show significant improvement in signal-tonoise ratio under a Rayleigh fading environment. For example, the STBC with the channel estimation in this paper can make 4 dB improvement in signal-to-noise ratio at BER=10-2, compared to the one transmit antenna system without STBC. REFERENCES [1] [2] [3]

(50)

[4]

where g1 2 + g2 2 = α12 + α 2 2 . The pair of complex demapper

[5]

and parallel to serial converter in Fig. 2 restores the code symbol stream for the traffic channel

[6]

III.

SIMULATION RESULTS

Table I lists the simulation parameters used in this paper. No error correction coding and no power control are considered. The number of the active multiple access users is either 5 or 10. Orthogonal Walsh codes are employed for each user, and the privacy of each message can be protected by a long PN code. For a fair comparison with a system without the STBC, the received power for both schemes must be the same. Thus, each antenna element in the STBC system transmits 50% of the total power. Table II lists a fading channel model from the ITU-R M.1225 standard for a vehicle. The chip time in our simulation is Tc=813.8 ns, which does not match with the delays in Table 2. To simulate a RAKE receiver of three fingers with unequal strength, the delays in Table II are quantized with Tc. Table III lists a multipath power profile used for our simulation and is obtained from Table II by merging the multipaths around an integer times chip time into a path. The first path in Table 3 is the path 1 in Table II. The second path in Table 3 represents the combination of path 3 and 4 in Table II. The third path in Table III does for the combination of path 5 and 6 in Table II. Fig. 3 shows the simulation bit error rate results. We observe about 4 dB improvement in signal-to-noise ratio at BER=10-2, compared to the one transmit antenna system without the STBC. IV. CONCLUSION We presented a CDMA system with one STBC encoder for the multiple access users in a forward link regardless of the number of active users. The system complexity can be reduced, compared to one in [6]. We also provided a channel

[7]

S. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communication,” IEEE J. Select. Areas Comm., vol. 16, pp. 14511458, Oct. 1998. Third Generation Partnership Project, TS25.211, vol.3.6.0, “Physical Channels and Mapping of Transport Channel onto Physical Channel (FDD),” March 2001. TIA/EIA Interim Standard (IS-95) issued for “Mobile Station – Base Station Compatibility Standard for Dual-Mode Wide-band Spectrum Cellular System,” 1993. Rec. ITU-R M.1225 “Guidelines for Evaluation of Radio Transmission Technologies (RTT) for IMT-2000,” 1997. TIA, Interim V&V Text for CDMA2000 Physical Layer (Revision 8.3), March 16, 1999. G. Wu, H. Wang, M. Chen, and S. Cheng, “Performance Comparisson of Space-Time Spreading and Space-Time Transmit Diversity in CDMA2000,” IEEE Vehicular Technology Conference 2001, Atlantic City, NJ, Oct. 7-11, 2001. A. J. Viterbi, CDMA Principle of Spread Spectrum Communication, Addison Wesley, New York, 1995.

TABLE I SIMULATION PARAMETER Number of transmit antennas at BS Number of receive antenna at MS Vehicular speed Carrier frequency Chip rate Walsh code length Number of users Number of Rake fingers

2 1 50 km/h 2 GHz 1.2288 MHz 64 5 or 10 3

TABLE II A FADING CHANNEL MODEL FOR A VEHICULAR FROM ITU-R M 1225 STANDARD Relative Delay (ns) Average Power (dB) 0 0 310 -1 710 -9 1090 -10 1730 -15.5 2510 -20

TABLE III FADING CHANNEL MODEL USED FOR SIMULATION BY MODIFYING TABLE III. Relative Delay (Tc) Average Power (dB) 0 0 1 -9.5 3 -17

cos 2πfct Complex mapper User1 (d1)

. . .

UserKu (dKu)

S/P

wn(1) Complex mapper

wn(0)

S/P

X(o)

Complex PN spreader (an(I);an(Q)) X'(1)(Q)

2Tb Tb 0

X(o)

Σ

H(f)

Y3 H(f)

Space Time Block Code encoder

. . .

A0 Pilot (d0)

-X(e)*

. . .

X'(1)(I)

sin 2πfct cos 2πfct X(o)*

Σ

X'(2)(I)

X(e)

Complex PN spreader (an(I);an(Q)) X'(2)(Q)

2Tb Tb 0

X(e)

Y1

2Tb Tb 0

A0

H(f)

Y4

H(f)

Y2

2Tb Tb 0 sin 2πfct

Fig. 1. STBC multiple access users transmitter.

α^1cos φ^1 r2

Channel estimator

r1

I2

2T b Tb 0

I1

an(I)(k) y2n(I)

cos 2πfct

an(Q)(k)

sin 2πf ct

-an(Q)(k) Q1

Channel estimator

0

10

5 users, STBC 5 users 10 users, STBC 10 users -1

10

B -2 ER 10 E B R

-3

10

-4

4

6

8 EbNo (dB)

y 1(I)

2T b T b 0 y2(Q) y 1(Q)

wn(k) Nc

Σ

10

12

14

16

Fig. 3. BER simulation results for three finger RAKE receiver with STBC and pilot aided coherent channel estimation.

^ sinφ^ α 2 2

Linear Combiner

P/S

to decision

2T b T b 0 j

^ sinφ^ α 1 1

an(I)(k)

Fig. 2. STBC coherent Rake receiver with channel estimations.

2

y2(I)

n=1

t=nTc

0

y1n(Q)

n=1

2Tb T b 0 Q2

10

Σ

y1n(I)

2Tb T b 0 y2n(Q)

H*(f) 2T b Tb 0

Complex Demapper

Nc

2T b Tb 0

H*(f)

^ d(o)(k)

^ cosφ^ α 2 2

j

Complex Demapper ^ d(e)(k)