Evaluation of Chip Space-Time Block Coding for DS-WCDMA in Time-Varying Channels Ivan R. S. Casella1, Paul Jean E. Jeszensky1 and Elvino S. Sousa2 1
Laboratório de Comunicações e Sinais - Universidade de São Paulo –
[email protected],
[email protected] 2 Department of Electrical and Computer Engineering – University of Toronto –
[email protected]
Abstract–In this paper, we investigate the performance of the downlink of a wideband code division multiple access system employing space-time block coding in a time-varying multipath channel. Space-time block coding is applied at the chip level to improve the robustness of the system to fading envelope variations. Simulation results show that the presented scheme offers considerable diversity gain even for high mobility users transmitting low data rate, outperforming a system employing symbol level space-time block coding in time-variant channels.
envelope is not totally fulfilled. In order to improve the robustness of the system to fading envelope variations, we propose to apply STBC at the chip level (CSTBC). The paper is organized as follows: the system model is introduced in section II; application of chip space-time block coding is given in III; simulation results are shown in section IV and finally, concluding remarks are presented in section V. II.
I.
INTRODUCTION
The next generation of wireless systems is expected to provide multimedia services such as high-speed Internet access and mobile computing. However, the system performance is degraded in wireless communications due to the destructive effects of multipath fading. Spatial diversity is a very efficient technique in combating multipath fading channels. Using multiple transmit and/or multiple receive antennas to achieve spatial diversity increases throughput without necessarily sacrificing precious bandwidth and power resources. In the downlink, the use of spatial transmit diversity is a very attractive approach, since it can transfer most of the system complexity to the base station. Although a variety of spatial transmit diversity schemes have been presented within the last decade [1], space-time block codes (STBC) emerged as a promising spatial transmit diversity scheme due to its simple decoding complexity at the receiver, and not requiring channel state information (CSI) at the transmitter. Initially, Alamouti introduced a remarkable transmit diversity scheme in [2] that established the basis for STBC. The proposed scheme provides similar diversity gain to that obtained by using maximum ratio combining (MRC) at the receiver. Later, Tarokh, Jafarkhani and Calderbank generalized Alamouti’s work to an arbitrary number of transmit antennas [3], [4]. These generalized schemes were named STBC. The orthogonal structure of STBC provides decoupling of the signals from different antennas and allows a decoding complexity dependent only on constellation size [5]. In spite of all the advantages, STBC requires that the complex fading envelope is constant across two consecutive time slots to perfectly recover the transmitted information. In this paper, we investigate the performance behavior of the downlink of a direct sequence wideband code division multiple access (DSWCDMA) system employing STBC in a time-varying multipath channel, where the requirement of constant fading
SYSTEM MODEL
In this work, we consider the downlink of a synchronous DSWCDMA system employing complex spreading and QPSK data modulation in accordance with the UTRA FDD standard [6]. There are Nw downlink dedicated physical channels (DPCH) and each channel is composed of packets of Nb data symbols. The complex data stream of each channel is first spread by an orthogonal channelization code and then scrambled by a base station specific complex scrambling code [6]. The resulting chip sequence is first filtered before being modulated and transmitted. Assuming that the discrete-time baseband transmitted signal of the mth cell/sector at time n is given by: b(n)=
N w −1
w= 0
γw
N b −1
d w (k )⋅Ww (n − kG )⋅cm (n − kG ) ,
k =0
n = 0, , GN b −1 (1) Where γ m is the transmitted signal power of the wth channel;
d w (k )= d wI (k )+ jd wQ (k ) is the kth information symbol of the
wth code channel with d wI (n ), d wQ (n ) ∈ {+1, −1} ; Ww (n ) is the wth channelization code at time n (nth element of the wth row of the Hadamard matrix of order G) with Ww (n ) ∈ {+1, −1} ; cm (n )=υ mI ,n + jυ mQ,n is the complex scrambling code of the mth
cell/sector at time n with υ mI ,n ,υ mQ, n ∈{+1, −1} and G is the processing gain. We can represent the received signal without employing STBC at time n by: r (n )=b(n )⋅h(n)+ν (n)
(2)
Where ν (n ) is a complex white Gaussian noise with variance
σ 2 and h(n) is the flat fading multipath channel coefficient at time n.
III.
CHIP SPACE-TIME BLOCK CODING
We consider that the base station employs two transmit antennas placed far enough apart so that their signals undergo independent fading. At a given chip interval, two signals are simultaneously transmitted from the two antennas. The signal transmitted from antenna 1 is denoted by b1 and the signal transmitted from antenna 2 is denoted by b2 . During the next chip interval − b2∗ is transmitted from antenna 1 and b1∗ is transmitted from antenna 2, where * is the complex conjugate operation. Modeling the channel by the time-variant flat fading channel presented in [7], we can represent the received signal at the jth receive antenna and chip interval chip_slot by: r jchip _ slot (n )=
2
_ slot hi , j (n )⋅ s ichip _ slot (n )+ v chip (n ) j
(3)
i =1
Where hi , j (n ) is the channel coefficient from transmit
antenna i to receive antenna j at time n; sichip_ slot (n ) is the transmitted signal from transmit antenna i at time n; and _ slot v chip (n) is the complex white Gaussian noise at time n. j Considering first the case of a receiver employing just one receive antenna (j=1) and assuming that the STBC codification matrix is given by [2]: s(n ) =
s (n ) s (n ) 1 1
1 2
s12 (n ) s 22 (n )
=
b1 (n ) * − b2 (n )
b2 (n ) * b1 (n )
(4)
Where b j (n ) is the chip transmitted from antenna j at time n. The received signal at the receive antenna in the chip intervals 1 and 2 in a vector notation can be represented by: r11 (n)
r12 (n)
=
b1 (n) * − b2 (n )
b2 (n ) h1,1 (n ) v11 (n ) ⋅ + * h2 ,1 (n ) b1 (n ) v12 (n )
(5)
We can recover the transmit chips by extracting signals b1 and b2 from the received signal at the chip intervals 1 and 2 using the scheme presented in [2]. Combining r11 and r12 by providing perfect estimation of the diversity channels, it’s possible to extract signals b1 and b2 using simple signal processing. Specifically, in order to extract the signal b1 , we can combine the received signals at the chip intervals 1 and 2, r11 and r12 , as follows: ∗ ∗ bˆ1 (n )= h1,1 (n ) ⋅ r11 (n )+ h2,1 (n )⋅ r12 (n )
(6)
Similarly, we can obtain the signal b2 by: ∗ ∗ bˆ2 (n )= h2 ,1 (n ) ⋅ r11 (n )− h1,1 (n )⋅ r12 (n )
(7)
The method proposed by Alamouti [2] can be extended to an arbitrary number of received antennas. The encoding and transmission will be identical to the case of one single receive antenna and the received signals in the chip intervals 1 and 2 for the two receive antennas are given by: r11 (n) r12 (n) r21 (n)
r22 (n)
b1 (n )
b2 (n )
−b2 (n )
*
=
0
b1 (n )
0
*
b1 (n ) * −b2 (n )
b2 (n ) * b1 (n )
⋅
h1,1 (n ) h2 ,1 (n )
h1, 2 (n ) h2 , 2 (n )
+
v11 (n ) v12 (n ) v 12 (n )
v 22 (n ) (8)
For the two receive antennas (j=2) case, we can extract the signal b1 by: ∗ ∗ ∗ ∗ bˆ1 (n ) = h1,1 (n ) ⋅r11 (n )+ h2 ,1 (n )⋅r12 (n ) + h1, 2 (n) ⋅r21 (n)+ h2 , 2 (n )⋅r22 (n) (9)
And we can obtain the signal b2 by: ∗ ∗ ∗ ∗ bˆ1 (n ) = h2 ,1 (n) ⋅r11 (n)− h1,1 (n)⋅ r12 (n ) + h2 , 2 (n ) ⋅r21 (n )− h1, 2 (n )⋅ r22 (n )
(10) Using these procedures, we can obtain a transmit scheme that presents the same diversity order as performing MRC at the receiver. After space-time decoding, the chip streams at chip interval 1 and 2 are merged and despread as in a conventional CDMA system. IV.
SIMULATION RESULTS
In this section, we evaluate the performance of a DSWCDMA system operating at 2GHz and employing the CSTBC scheme in a flat fading time-variant channel. The base station employs two transmit antennas whose signals present independent fading and the mobile station may use one or two receive antennas. We consider that there are 4 orthogonal channels (Nw=4) per cell, each one transmitting frames with 200 symbols (Nb=200). The chip rate is 3.84 Mcps and the channelization codes are obtained by the rows of the Hadamard matrix. The complex scrambling code is based on Gold (G=63 and G=255) or Gold-like (G=15) codes, depending on the data rate. One chip is added at the end of the scrambling code for perfect timing matching to the channelization code. Spreading sequences are normalized to unit energy. Simulations are performed for three different data rates: low data rate (LDR=15ksps / G=256), medium data rate (MDR=60ksps / G=64) and high data rate (HDR=240ksps / G=16). Multipath fading channel coefficients are obtained by the channel model presented in [7], considering 15 oscillators (Nosc=15). The results are obtained by computing 2500 frames (Nfr=2500).
We compare the performance of the CSTBC using one and two receive antennas against the performance of a system without diversity in Fig.1 to Fig.3. The curves are obtained for different data rates and for different Doppler spreads (∆dopp=100, 200, 300 and 400 Hz).
outperforms SSTBC, but the performance improvement appears at higher SNR and lower BER when compared against LDR systems. Again the performance improvements are more pronounced for the case of one receive antenna system.
In Fig.1, we analyze the performance of CSTBC for LDR transmission in each DPCH. Due to the low data rate, the effect of fading is more pronounced and the CSTBC brings significant advantage when compared against the case of no diversity for all Doppler spreads. The use of two receive antennas also provides additional improvements.
In Fig.6, comparison between CSTBC and SSTBC for HDR is presented. For the evaluated SNR the two schemes are equivalent.
In Fig.2, the performance of CSTBC when transmitting at the MDR is presented. The use of CSTBC also provides significant improvements for all analyzed Doppler spreads. In Fig.3, we present the performance of CSTBC when transmitting HDR. As the data rate increases, the timevarying effect of the multipath channel decreases and the performance improvement of transmit diversity starts to decrease. In this situation, a system without diversity starts to present reasonable performance figures at low Doppler spread. Even so, for the analyzed Doppler spreads, CSTBC still presents significant improvements. In Fig.4 to Fig.6, we compare the performance of CSTBC against the one obtained by symbol-level STBC (SSTBC) for a system using one and two receive antennas. We consider different data rates and ∆dopp=400 Hz. The results presented in Fig.4 show that CSTBC outperforms SSTBC for LDR in a wide SNR range. The performance improvements are more pronounced in the case of one receive antenna system, although the same performance improvement should be obtained by the case of two receive antennas at lower bit error rates (BER). In Fig.5, we compare the performance of CSTBC and SSTBC for MDR transmission. The results show that CSTBC also
Finally, samples of a time-variant multipath fading channel for one and two antennas are shown in Fig.7 and Fig.8, respectively. It is considered that ∆dopp= 400 Hz and the transmission of LDR. CONCLUSIONS
V.
In this paper, we investigated the performance of the downlink of a WCDMA system employing STBC in a timevarying flat fading multipath channel for different data rates. As originally proposed in [2], STBC requires constant complex fading envelope across two consecutive time slots to perfectly recover the transmitted information, however this requirement is not completely fulfilled in time varying channels. In order to improve the robustness of the system to fading envelope variations, we propose to apply STBC at the chip level. Simulations were performed to STBC at the chip level and STBC at the bit level for a time varying channel with different Doppler spreads. Simulation results show that chip level STBC scheme offers considerable diversity gain and performance improvements compared against a system not employing transmit diversity. Also, the proposed chip-level STBC offers considerable robustness even for high mobility users (216 km/h - ∆dopp=400 Hz at 2GHz) and outperforms symbol-level STBC when users transmit at low and medium data rate.
Error Probability - CSTBC - CDMA
0
10
Error Probability - CSTBC - WCDMA
0
10
No Diversity CSTBC - Antrx =1
No Diversity CSTBC - Antrx =1
CSTBC - Antrx =2
CSTBC - Antrx =2
-1
-1
10
10
-2
-2
-3
10
10
BER
BER
10
Nfr=2500
-3
10
Nb=200
-4
-5
10
G=256 Chip Rate=3840000 Simb Rate=15000 Patzold Channel Model Nosc=15 ∆ Dopp =100, 200, 300, 400 0
Nb =200 Nw=4
Nw=4 10
Nfr=2500
5
-4
10
-5
10
15
20
25
SNR (dB)
Fig.1. Comparison between a system employing CSTBC (one and two receive antennas) and a system without diversity for LDR channels and different Doppler spreads (∆dopp=100, 200, 300 and 400 Hz)
10
G=64 Chip Rate=3840000 Simb Rate=60000 Patzold Channel Model Nosc=15 ∆ dopp r=100, 200, 300, 400 0
5
10
15
20
25
SNR (dB)
Fig.2. Comparison between a system employing CSTBC (one and two receive antennas) and a system without diversity for MDR channels and different Doppler spreads (∆dopp=100, 200, 300 and 400 Hz)
Error Probability - CSTBC - WCDMA
0
10
Error Probability - STBC - WCDMA
0
10
No Diversity CSTBC - Antrx =1
STBC-Chip Level-Antrx =1 STBC-Bit Level-Antrx=1 STBC-Chip Level-Antrx =2
CSTBC - Antrx =2 -1
-1
10
STBC-Bit Level-Antrx=2
10
-2
10
-2
BER
BER
10 Nfr=2500
-3
10
Nb=200 G=16 Chip Rate=3840000 Simb Rate=240000 Patzold Channel Model Nosc=15 ∆ Dopp =100, 200, 300, 400
-4
-5
10
Nb =200 -3
Nw=4
-4
G=256 Chip Rate=3840000 Simb Rate=15000 Patzold Channel Model Nosc=15 Max Doppler= 400 Max Doppler Norm=0.0267
10
Nw=4 10
Nfr=2500
0
10
5
10
15
20
25
0
5
10
SNR (dB)
Fig.3. Comparison between a system employing CSTBC (one and two receive antennas) and a system without diversity for HDR channels and different Doppler spreads (∆dopp=100, 200, 300 and 400 Hz)
10
25
30
STBC-Bit Level-Antrx=1 STBC-Chip Level-Antrx =2
-1
Error Probability - STBC - WCDMA
0
10
STBC-Chip Level-Antrx =1
10
STBC-Chip Level-Antrx =1 STBC-Bit Level-Antrx=1 STBC-Chip Level-Antrx =2
-1
10
STBC-Bit Level-Antrx=2
-2
10
STBC-Bit Level-Antrx=2
-2
10
BER
BER
20
Fig.4. Comparison between Chip-Level STBC and Bit-Level STBC (one and two receive antennas) for LDR channels and ∆dopp= 400 Hz
Error Probability - STBC - WCDMA
0
15
SNR (dB)
Nfr=2500
-3
10
Nb =200 Nw=4 G=64 Chip Rate=3840000 Simb Rate=60000 Patzold Channel Model Nosc=15 Max Doppler=400 Max Doppler Norm=0.0067
-4
10
-5
10
0
Nfr=2500 -3
10
5
Nw=4
-4
10
-5
10
15
20
25
30
Nb=200
10
G=16 Chip Rate=3840000 Simb Rate=240000 Patzold Channel Model Nosc=15 Max Doppler=400 Max Doppler Norm.=0.00167 0
2
4
6
8
SNR (dB)
Fig.5. Comparison between Chip-Level STBC and Bit-Level STBC (one and two receive antennas) for MDR channels and ∆dopp= 400 Hz
12
14
16
18
20
Fig.6. Comparison between Chip-Level STBC and Bit-Level STBC (one and two receive antennas) for HDR channels and ∆dopp= 400 Hz
Time-Variant Multipath Channel (Antrx=1)
4
10
SNR (dB)
Time-Variant Multipath Channel (Antrx=2)
4 2
2
0
0
-2
Envelope (dB)
Envelope (dB)
-2 -4 -6 -8
-4 -6 -8 -10 -12
-10
-14 -12 h1,1
-14
h -16
0
10
20
30
40
50
60
70
80
90
2,1
100
Data Symbol
Fig.7. Multipath channels for one receive antenna, LDR transmission and ∆dopp= 400 Hz
h1,1
-16
h2,1
-18
h1,2
-20
h 0
10
20
30
40
50
60
70
80
90
2,2
100
Data Symbol
Fig.8. Multipath channels for two receive antennas, LDR transmission and ∆dopp= 400 Hz
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