PAPER Space-Time Cyclic Delay Transmit Diversity for a Multi-Code DS-CDMA Signal with Frequency-Domain Equalization

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1 IEICE TRANS. COMMUN., VOL.E90 B, NO.3 MARCH PAPER Space-Time Cyclic Delay Transmit Diversity for a Multi-Code DS-CDMA Signal with Frequency-Domain Equalization Ryoko KAWAUCHI a), Kazuaki TAKEDA, Student Members, and Fumiyuki ADACHI, Member SUMMARY Frequency-domain equalization FDE) can take advantage of the frequency-selectivity of the channel to improve the transmission performance in a frequency selective fading channel. To further improve the transmission performance, the transmit diversity technique can be used. Cyclic delay transmit diversity CDTD) can strengthen the frequencyselectivity while space-time transmit diversity STTD) can achieve the antenna diversity gain. In this paper, we propose a 4-antenna space-time cyclic delay transmit diversity STCDTD), which is a combination of 2- antenna STTD and 2-antenna CDTD schemes, for orthogonal multi-code direct sequence code division multiple access DS-CDMA) using FDE. We evaluate the BER performance and the throughput performance by computer simulation and compare them with the original CDTD and STTD schemes. key words: multi-code DS-CDMA, Frequency-domain equalization, Cyclic Delay Transmit Diversity CDTD), Space-Time Transmit Diversity STTD) 1. Introduction High-speed and high-quality data transmissions are demanded in next generation mobile wireless communication systems. However, the wireless channel is composed of many propagation paths with different time delays, producing frequency-selective fading. In a frequency-selective fading channel, the bit error rate BER) performance of single-carrier SC) transmission significantly degrades due to a serve inter-symbol interference ISI) [1]. In direct sequence code division multiple access DS-CDMA), which is adopted in the third generation mobile communication systems, rake combiner is commonly used. However, for a data transmission of higher than a few tens of Mbps, a large inter-path interference is produced, and this deteriorates the BER performance. Recently, it was shown that frequencydomain equalization FDE) based on the minimum mean square error MMSE) criterion can obtain the frequency diversity gain and significantly improve the SC transmission performance [2], [3]. We have shown that MMSE-FDE can also be applied to DS-CDMA [4] [6]. To further improve the BER performance, the use of transmit diversity technique is effective. We have shown that joint use of delay transmit diversity DTD) [7], [8] and MMSE-FDE can improve the BER performance in a weak frequency-selective fading channel [9]. As the number of propagation paths having different time delays increases, Manuscript received March 29, Manuscript revised September 7, The authors are with the Department of Electorical Communication Engineering, Graduate School of Engineering, Tohoku University, Sendai-shi, Japan. a) kawauchi@mobile.ecei.tohoku.ac.jp DOI: /ietcom/e90 b the channel frequency-selectivity gets stronger. This can be achieved by DTD which transmits the same signal from different antennas with different time delays. FDE can be used to exploit the channel frequency-selectivity to improve the transmission performance [9]. However, the use of DTD limits the performance improvement due to inter-block interference IBI) caused by the time delay added at the transmitter. To avoid IBI, cyclic delay transmit diversity CDTD) was proposed for MC-CDMA [10]. With CDTD, the same signal is simultaneously transmitted from different antennas after adding different cyclic delays. CDTD can also be applied to DS-CDMA with FDE [11], [12]. We have shown [11], [12] that CDTD can obtain a larger frequency diversity gain and achieve better BER performance than DTD. Space-time transmit diversity STTD) [13] [16] is another attractive transmit diversity technique that can obtain the antenna diversity gain. With increasing the number of transmit antennas, a larger antenna diversity gain can be obtained. However, 4-antenna STTD reduces the transmission data rate by 3/4 times [17]. In this paper, we propose a 4-antenna space-time cyclic delay transmit diversity STCDTD), which is a combination of 2-antenna STTD and 2-antenna CDTD schemes. 4- antenna STCDTD can improve the BER performance since both the frequency diversity gain and antenna diversity gain are obtained without reducing the transmission rate unlike 4- antenna STTD. We apply 4-antenna STCDTD to multi-code DS-CDMA that can offer flexible variable data-rate transmissions by changing the number of parallel codes [15]. The remainder of this paper is organized as follows. In Sect. 2, we present STCDTD. In Sect. 3, the BER and throughput performances of STCDTD are evaluated by computer simulation, and compared with the original CDTD and STTD schemes. The paper is concluded in Sect Transmission System Model 2.1 Transmit Signal Figure 1 shows the transmitter structure. At the transmitter, a binary data sequence is transformed into a data-modulated symbol sequence and divided into blocks of C /SF) data symbols each. Here, SF is the spreading factor, C is the number of parallel codes, and is the size of fast Fourier transform FFT) operation for FDE at a receiver. The block sequence is serial parallel S/P) converted into C parallel block sequences of /SF symbols each. The Copyright c 2007 The Institute of Electronics, Information and Communication Engineers

2 592 IEICE TRANS. COMMUN., VOL.E90 B, NO.3 MARCH 2007 Fig. 1 Transmitter structure. Fig. 3 Receiver structure. copied to generate four streams. Then, cyclic delay is added to the 1st and 3rd STTD encoded streams to form STCDTD block streams. The even and odd -chip blocks, { s n,e t)} and { s n,o t)}, to be transmitted from the nth transmit antenna, are given as s 0,e t) = s e t) s 1,e t) = s e t ), even s 2,e t) = s o t) s 3,e t) = s o t ) s 0,o t) = s. 2) o t) s 1,o t) = s o t )) s 2,o t) = s, odd e t) s 3,o t) = s e t )) Then the last N g chips in each -chip block are inserted as a cyclic prefix into the guard interval GI). Fig. 2 STCDTD encoding and cyclic delay addition =8, =1). 2.2 Received Signal data symbol sequence {d i m); m=0 /SF 1)} in the ith i=0 C 1) parallel block is spread by an orthogonal spreading code {c i t); SF 1}. The resulting C parallel -chip blocks are added code-multiplexing) and further multiplied with the scrambling code {c scr t); t =..., 1, 0, 1,...}. The scrambling code is used to transform the code-multiplexed chip block into noise-like block. Figure 2 shows the STCDTD encoding for =8, =1 as an example, where is the cyclic time delay. Two consecutive even and odd) code-multiplexed -chip blocks are represented by {s e t)} and {s o t)} with the mth data symbol in the even odd) block being denoted by d eo),i m), m=0 /SF 1). Chip-spaced discrete time representation is used throughout the paper. The even odd) -chip block {s eo) t)} is expressed using the equivalent baseband representation as s eo) t) 1 1 E s C 1 = d eo),i t/sf ) c i t mod SF) c scr t), 2 SF T c i=0 1) where E s represents the transmit signal energy per symbol, T c is the chip length and x denotes the largest integer smaller than or equal to x. Two consecutive -chip blocks, {s e t)} and {s o t)}, are STTD encoded [14] [16] to form two STTD encoded streams as shown in Fig. 2. Two streams are respectively Figure 3 shows the receiver structure. The signals transmitted from each antenna go through a frequency-selective fading channel and are received at the receiver. The received chip block r eo) t) of even odd) time interval is given as { r e t) = h0,l s e t τ l ) + h 1,l s e t ) mod τ l ) } { + h2,l s o t τ l ) + h 3,l s o t ) mod τ l ) } +η e t) { } h0,l s r o t) = o t τ l )) +h 1,l s o t ) mod τ l )) { } h2,l s + e t τ l )) +h 3,l s e t ) mod τ l )) +η o t) where h n,l and τ l respectively represent the complex path gain and delay time of the lth path between the nth transmit antenna and the receiver, and η eo) t) is the noise component characterized by a zero-mean complex Gaussian process with a variance of 2N 0 /T c ; N 0 is the single-sided power spectrum density of additive white Gaussian noise AWGN). After the removal of the GI, the received chip block is decomposed into subcarrier components {R eo) k); k=0 1} by applying -point FFT. The kth subcarrier component R eo) k) ofr eo) t) is given as, 3)

3 KAWAUCHI et al.: SPACE-TIME CYCLIC DELAY TRANSMIT DIVERSITY FOR A MULTI-CODE DS-CDMA 593 R e k) = c 1 r e t)exp j2πk t = H 0 k)s e k) + H 2 k)s o k) +Π e k) c 1 R o k) = r o t)exp j2πk t ) = H 0 k)s ok) + H 2 k)s ek) +Π o k) ), 4) where S eo) k) denotes the kth subcarrier component of s eo) t), H 02) k) is the composite channel gain at the kth subcarrier obtained by CDTD using transmit antennas #0 and #1 antennas #2 and #3), and Π eo) k) isthekth subcarrier component of η eo) t). S eo) k), H 02) k) andπ eo) k) are given by c 1 S eo) k)= s eo) t)exp j2πk t 13) H 02) k)= h n,l exp j2πk n mod 2) +τ ) l n=02) c 1 Π eo) k)= η eo) t)exp ) j2πk t ) 2.3 Joint FDE and STTD Decoding Joint FDE and STTD decoding is carried out as [15], [16] Ŝ e k) = w 0 k)r ek) + w 2 k)r ok) = Ĥk)S e k) + ˆΠ e k) Ŝ o k) = w 2 k)r ek) w 0 k)r, 6) ok) = Ĥk)S o k) + ˆΠ o k) where w 02) k) is the MMSE weight, which minimizes the mean square error MSE) between Ŝ eo) k)ands eo) k), Ĥk) is the channel gain after joint FDE and STTD decoding this is called equivalent channel gain) and ˆΠ eo) k) is the noise. They are given by H 02) k) w 02) k) = ) 1 1 H 0 k) 2 + H 2 k) 2 C E s + 4 SF N 0 Ĥk) = H 0 k) 2 + H 2 k) 2 1 H 0 k) 2 + H 2 k) 2 C + 4 SF ˆΠ e k) = w 0 k)π ek) + w 2 k)π ok) ˆΠ o k) = w 2 k)π ek) w 0 k)π ok) ) 1 E s N 0 5), 7) ˆr eo) t) = 1 c 1 k=0 Ŝ eo) k)exp j2πt k ). 8) Then, despreading is performed on {ˆr eo) t)} to obtain the decision variable ˆd eo),i m), for data demodulation, as ˆd eo),i m) = 1 m+1)sf 1 ˆr eo) t)c i SF t mod SF)c scr t). 9) t=msf 3. Computer Simulation The simulation parameters are given in Table 1. We assume QPSK data-modulation, =256 chips, N g =32 chips. The GI insertion is necessary for performing FDE. Therefore, longer is desirable so as not to significantly reduce the transmission efficiency or throughput. Block fading is assumed FDE requires block fading); the path gains stay unchanged during one block period, but vary block by block. However, if is too long, the assumption of block fading may not hold. According to Ref. [9], the BER performance is almost insensitive to the fading rate if the normalized maximum Doppler frequency f D + N g )T c is smaller than 0.01 this corresponds to a terminal moving speed of 750 km/h for a chip rate 1/T c of 100 Mchip/s and a carrier frequency of 5 GHz for an FFT size of =256 chips and a GI length of N g =32 chips). We have confirmed by computer simulation that, in the case of full codemultiplexing SF=C), the BER performance is always insensitive to SF and therefore, we assume SF=C=256 full code-multiplexing) below. A frequency-selective Rayleigh fading channel having an L=16-path exponential power delay profile Ωτ) with decay factor α db α 1) is assumed. Ωτ) isdefinedas Ωτ) = A α l δτ τ l ), 10) Table 1 Computer simulation parameters. where E s /N 0 is the signal energy per symbol-to-awgn power spectrum density ratio. 2.4 Despreading -point inverse FFT IFFT) is applied to transform {Ŝ eo) k); k = 0 1} into time-domain chip block {ˆr eo) t); t = 0 1}. ˆr eo) t) isgivenby

4 594 IEICE TRANS. COMMUN., VOL.E90 B, NO.3 MARCH 2007 a) N t =1 a) α=0db b) 4-antenna CDTD =32) c) 4-antenna STTD b) α=5db Fig. 4 d) 4-antenna STCDTD =32) Equivalent channel gain L=16, α=5dbande b /N 0 =12 db). where A = 1 α 1) / 1 α L) [ hn,l ] and E 2 = Aα l E[.] denotes the ensemble average operation). We assume that the time delay τ l of the lth l = 0 L 1) path is l chips, and hence the maximum time delay τ L 1 is shorter than the GI length N g i.e., τ L 1 < N g )whenl=16 and N g =32. Ideal sampling timing and ideal channel estimation are assumed. Figure 4 shows the equivalent channel gain after FDE of CDTD, STTD and STCDTD for the case of L=16, α=5db, E b /N 0 =12 db and the number N t =4 of transmit antennas. For CDTD and STCDTD, cyclic delay of =32 chips is used since the use of =32 chips was found by our preliminary computer simulation to minimize the BER. When N t =1, the equivalent channel gain drops over Fig. 5 c) α= db BER performance comparison of STCDTD, CDTD and STTD.

5 KAWAUCHI et al.: SPACE-TIME CYCLIC DELAY TRANSMIT DIVERSITY FOR A MULTI-CODE DS-CDMA 595 an interval of several subcarriers Fig. 4a)). 4-antenna CDTD can strengthen the frequency-selectivity of the channel since the equivalent number of paths increases by 4 times Fig. 4b)). However, sometimes deep drops of the channel gain are seen. These deep drops can be avoided by 4-antenna STCDTD Fig. 4d)). It is interesting to note that 4-antenna STTD can achieve almost a flat channel gain Fig. 4c)). This suggests that 4-antenna STTD provides the best BER performance among the three 4-antenna transmit diversity schemes. Figure 5 compares the average BER performance of 4- antenna CDTD, STTD and STCDTD with decay factor α as a parameter when SF=C=256. The case of α = db is equivalent to the single path case. As α decreases, a larger frequency diversity gain is obtained, and hence the BER performance improves for all schemes. As was anticipated, STTD provides the best BER performance followed by STCDTD. This can be clearly understood from Fig. 4; STTD achieves almost a flat channel gain over the entire frequency range. However, the data rate offered by 4-antenna STTD is reduced to 3/4. On the other hand, there is no data rate reduction in 4-antenna CDTD and STCDTD. Therefore it is interesting to compare the throughputs of STTD and STCDTD. The throughput comparison of STTD and STCDTD is shown in Fig. 6. The throughput S is defined as ) 1 S = Rlog 2 M)1 PER), 11) 1 + N g / where R is the transmit diversity coding rate R=3/4 for STTD and R=1 forstcdtd),m is the modulation level, PER is the packet error rate. The maximum throughput is obtained when PER=0. The maximum throughput of STCDTD R=1) is 1.78 bit/s/hz for M=4 QPSK), 2.67 bit/s/hz for M=8 8PSK),and3.56bit/s/Hz for M=16 16QAM) when =256 and N g =32. The PER was measured by computer simulation of packet transmission with each packet having 1532 symbols. It can be seen from Fig. 6 that STCDTD with 16QAM provides higher throughput than STTD in an E s /N 0 region larger than about 23 db. However, STCDTD does not always provide better throughput performance; STTD with 16QAM gives better throughput in an E s /N 0 region of db. For QPSK data modulation, STCDTD achieves higher throughput in an E s /N 0 region of db while STTD gives higher throughput in an E s /N 0 region lower than 15 db. This suggests that the single use of STCDTD or STTD does not always provide the best throughput performance; either STCDTD or STTD should be selected depending on the E s /N 0 value. 4. Conclusion Fig. 6 Throughput comparison of STCDTD and STTD. In this paper, we proposed a 4-antenna space-time cyclic delay transmit diversity STCDTD) which is a combination of 2-antenna STTD and 2-antenna CDTD, for multi-code DS- CDMA using FDE. We evaluated the BER performance of 4-antenna STCDTD by computer simulation and compared them with those of 4-antenna CDTD and 4-antenna STTD. STTD gives the best BER performance due to 4-branch antenna diversity gain. The throughput performances of STCDTD and STTD were also compared. It was shown that the single use of STCDTD or STTD does not always provide the best throughput performance; either STCDTD or STTD should be selected depending on the E s /N 0 value. In this paper, we considered the uncoded case. The throughput performance of hybrid automatic repeat request HARQ) with STCDTD is an interesting future study. References [1] W.C. Jakes, Jr., ed., Microwave Mobile Communications, Wiley, New York, [2] D. Falconer, S.L. Ariyavisitakul, A. Benyamin-Seeyarand, and B. Eidson, Frequency domain equalization for single-carrier broadband wireless systems, IEEE Commun. Magn., vol.40, pp.58 66, April [3] F. Adachi, M. Sawahashi, and H. Suda, Wideband DS-CDMA for next generation mobile communications systems, IEEE Commun. Mag., vol.36, no.9, pp.56 69, Sept [4] F. Adachi, T. Sao, and T. Itagaki, Performance of multicode DS- CDMA using frequency domain equalization in a frequency selective fading channel, Electron. Lett., vol.39, pp , Jan [5] K. Takeda, T. Itagaki, and F. Adachi, Frequency-domain equalization for antenna diversity reception of DS-CDMA signals, Proc. 8th International Conference on Cellular and Intelligent Communications CIC), p.383, Seoul, Korea, Oct [6] T. Itagaki and F. Adachi, Joint frequency-domain equalization and antenna diversity combining for orthogonal multicode DS-CDMA signal transmissions in a frequency-selective fading channel, IEICE Trans. Commun., vol.e87-b, no.7, pp , July [7] J.H. Winters, Diversity gain of transmit diversity in wireless systems with Rayleigh fading, IEEE Trans. Veh. Technol., vol.47, no.1, pp , Feb [8] C.S. Bontu, D.D. Falconer, and L. Strawczynski, Diversity transmission and adaptive MLSE for digital cellular radio, IEEE Trans. Veh. Technol., vol.48, no.5, pp , [9] K. Takeda, T. Itagaki, and F. Adachi, Joint use of frequency-domain equalization and transmit/receive antenna diversity for single-carrier

6 596 IEICE TRANS. COMMUN., VOL.E90 B, NO.3 MARCH 2007 transmissions, IEICE Trans. Commun., vol.e87-b, no.7, pp , July [10] G. Bauch and J.S. Malik, Parameter optimization, interleaving and multiple access in OFDM with cyclic delay diversity, Proc. 59th IEEE Vehicular Technology Conference VTC), vol.1, pp , Milan, Italia, May [11] R. Kawauchi, K. Takeda, and F. Adachi, Application of cyclic delay transmit diversity to DS-CDMA using frequency-domain equalization, IEICE Technical Report, RCS , March [12] R. Kawauchi, K. Takeda, and F. Adachi, Performance comparison of DS- and MC-CDMA using cyclic delay transmit diversity and frequency-domain equalization, Proc. IEICE Gen. Conf. 2005, B- 5-14, March [13] S.M. Alamouti, A simple transmit diversity technique for wireless communications, IEEE J. Sel. Areas Commun., vol.16, no.8, pp , Oct [14] N. Al-Dhahir, Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels, IEEE Trans. Commun., vol.5, no.7, pp , July [15] T. Itagaki, K. Takeda, and F. Adachi, Performance comparison of delay transmit diversity and frequency-domain space-time coded transmit diversity for orthogonal multicode DS-CDMA signal reception using frequency-domain equalization, IEICE Trans. Commun., vol.e87-b, no.9, pp , Sept [16] K. Takeda, T. Itagaki, and F. Adachi, Application of space-time transmit diversity to single-carrier transmission with frequencydomain equalization and receive antenna diversity in a frequencyselective fading channel, IEE Proc. Communications, vol.151, no.6, pp , Dec [17] V. Tarokh, Space-time block codes from orthogonal designs, IEEE Trans. Inf. Theory, vol.45, no.5, pp , July Fumiyuki Adachi received the B.S. and Dr. Eng. degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1973 and 1984, respectively. In April 1973, he joined the Electrical Communications Laboratories of Nippon Telegraph & Telephone Corporation now NTT) and conducted various types of research related to digital cellular mobile communications. From July 1992 to December 1999, he was with NTT Mobile Communications Network, Inc. now NTT DoCoMo, Inc.), where he led a research group on wideband/broadband CDMA wireless access for IMT-2000 and beyond. Since January 2000, he has been with Tohoku University, Sendai, Japan, where he is a Professor of Electrical and Communication Engineering at the Graduate School of Engineering. His research interests are in CDMA wireless access techniques, equalization, transmit/receive antenna diversity, MIMO, adaptive transmission, and channel coding, with particular application to broadband wireless communications systems. From October 1984 to September 1985, he was a United Kingdom SERC Visiting Research Fellow in the Department of Electrical Engineering and Electronics at Liverpool University. Dr. Adachi served as a Guest Editor of IEEE JSAC on Broadband Wireless Techniques, October 1999, Wideband CDMA I, August 2000, Wideband CDMA II, Jan. 2001, and Next Generation CDMA Technologies, Jan He is an IEEE Fellow and was a co-recipient of the IEEE Vehicular Technology Transactions Best Paper of the Year Award 1980 and again 1990 and also a recipient of Avant Garde award He was a recipient of IEICE Achievement Award 2002 and a co-recipient of the IEICE Transactions Best Paper of the Year Award 1996 and again He was a recipient of Thomson Scientific Research Front Award Ryoko Kawauchi received her B.E. degree in Systems Science and Technology from Akita Prefectural University, Akita, Japan, in 2004, and M.S. degree in communications engineering from Tohoku University, Sendai, Japan, in Her research interests include equalization, transmit diversity, and adaptive antenna array. Kazuaki Takeda received his B.E. and M.S. degrees in communications engineering from Tohoku University, Sendai, Japan, in 2003 and 2004, respectively. Currently he is a PhD student at the Department of Electrical and Communications Engineering, Graduate School of Engineering, Tohoku University. His research interests include equalization, interference cancellation, transmit/receive diversity, and multiple access techniques. He was a recipient of the 2003 IEICE RCS Radio Communication Systems) Active Research Award and 2004 Inose Scientific Encouragement Prize.