caused by the orthogonality distortion of the STBC

Transcription

1 Robust Freuency-omain Eualization Against oubly Selective Fading for Single-Carrier SBC ime-ivision uplex ransmission iroyui MIYAZAKI and Fumiyui AACI ept. of Communications Engineering, Graduate School of Engineering, ohou niversity Aza-Aoba, Aramai, Aoba-u, Sendai, Japan Abstract Single-carrier (SC) space-time bloc coded (SBC) time-division duplex () transmission achieves a good biterror rate (BER) performance while the channel state information (CSI) is not reuired at the mobile terminal (M). owever, in a high mobility environment, the channel changes within a SBC codeword and the BER performance significantly degrades due to the interference caused by the orthogonality distortion of SBC codeword. In this paper, we propose a multi-bloc (MB)-freuency-domain eualization (FE) for SC-SBC- transmission in a high mobility environment. he SBC codeword consists of multiple signal blocs. he proposed MB- FE uses jointly optimized multiple FE weight matrices, each associated with each signal bloc in a SBC codeword. We evaluate, by computer simulation, the BER performance when using the proposed transmit/receive MB-FE and show that the proposed MB-FE achieves a good BER performance in a high mobility environment. Keywords-component; Space-time bloc coding, freuencydomain eualization, single-carrier transmission I. INROCION he bit error rate (BER) performance of broadband singlecarrier (SC) transmissions significantly degrades due to the inter-symbol interference (ISI) caused by the freuencyselective fading [1]. he minimum mean suare error (MMSE) based freuency-domain eualization (FE) can tae advantage of channel freuency-selectivity and obtain large freuency diversity gain [-4]. Space-time bloc coding (SBC) transmit diversity [5-1] is also an effective scheme to improve the BER performance. here are two types of SBC transmit diversity: space-time transmit diversity (S) [6] and space-time bloc coded joint transmit/receive diversity (SBC-JR) [7]. he SBC-JR reuires the channel state information (CSI) at the transmitter while the S reuires it at the receiver. Recently, we proposed SC-SBC time-division duplex () transmission system [8], in which the freuencydomain (F)-S [9] and F-SBC-JR [1] are used for the uplin and downlin transmissions, respectively. Only the base station (BS) reuires the CSI and the complexity problem of mobile terminal (M) can be alleviated. Since the same freuency is used in for the uplin and downlin, the CSI estimate for the uplin F-S reception can be reused for the downlin F-SBC-JR transmission. As a conseuence, no CSI feedbac is reuired between M and BS. In the next generation wireless communications, broadband data services are demanded even in a high mobility environment. When the channel varies within a SBC codeword, the BER performance significantly degrades due to the interference caused by the orthogonality distortion of the SBC codeword [11]. o remedy this performance degradation, the iterative interference cancellation was proposed [13]. owever, the above techniue reuires a high computational complexity and the CSI at the receiver, and hence is not suitable for downlin F-SBC-JR transmission. Recently, we proposed the transmit multi-bloc (MB)-FE for F-SBC-JR [14]. he SBC-JR codeword consists of multiple signal blocs. he transmit MB-FE uses multiple weight matrices, each associated with each signal bloc in a SBC codeword. he transmit MB-FE weight matrices are designed so as to minimize the mean suare error (MSE) between the transmit signal before SBC encoding and the received signal after SBC decoding. owever, the past study for MB-FE [14] assumed a uasi-static fading channel and did not tae into account the channel variation within a SBC codeword. herefore, the BER performance when using the previous MB-FE [14] also degrades due to the interference caused by the orthogonality distortion of the SBC codeword in a high mobility environment. In this paper, we propose a MB-FE for SC-SBC transmission system (uplin F-S and downlin F- SBC-JR) in a high mobility environment. he MB-FE weight matrices (receive MB-FE for uplin F-S and transmit MB-FE for downlin F-SBC-JR), each associated with each signal bloc in a SBC codeword, are jointly optimized based on the MMSE criterion by taing into account the channel variation within a SBC codeword. We evaluate, by computer simulation, the BER performance when using the proposed MB-FE and show that the proposed MB- FE achieves a good BER performance in a high mobility environment. he remainder of this paper is organized as follows. he SC-SBC transmission system is introduced in Sect. II. Sect. III derives the MB-FE weight matrices. Sect. IV discusses the computer simulation results, and Sect. V offers conclusions. II. SC-SBC RANSMISSION SYSEM In this paper, we consider SC-SBC transmission system. We assume that BS euips with N BS antennas and M

2 ata demod. N c -point IFF SBC decoding N c -point FF CP CP+ N c -point IFF ransmit FE SBC encoding N c -point FF ata mod. ata mod. N c -point FF SBC encoding N c -point IFF CP+ CP N c -point FF Receive FE SBC decoding N c -point IFF ata demod. has N M antennas, respectively. Fig. 1 illustrates the frame structure considered in this paper. Fig. and 3 show the transmitter/receiver structures. In SC-SBC transmission system, both channel estimation and FE are performed at BS in order to mae M structure simple and eliminate CSI feedbac. he uplin transmission frame consists of N B SBC encoded data blocs and pilot blocs and the downlin transmission frame consists of N B SBC encoded data blocs, respectively. For uplin transmission, M transmits the uplin transmission frame to BS. After estimating CSI at the uplin transmission frame, BS detects the uplin data signal by applying the receive MB-FE and SBC decoding. hen, BS estimates CSI at the downlin transmission frame. After SBC encoding and the transmit MB-FE, BS transmits the downlin transmission frame to M. Base station Mobile terminal P P Fig.. Fig. 3. Pilot stage plin (a) Mobile terminal (a) Mobile terminal Fig. 1. # ownlin #NM1 #NBS1 P P Frame structure ata stage plin transmitter/receiver structure # ownlin transmitter/receiver structure N B blocs A. plin F-S transmission In the uplin transmission, F-S is performed. At the M transmitter, the J N c data modulated symbols are divided into the a seuence of J bloc of N c symbol each. he J transmit signal blocs are transformed into the freuency-domain signal by the N c -point fast Fourier transform (FF). A seuence of J freuency-domain signals are encoded into N M streams of Q SBC coded freuency-domain single blocs each. enoting the freuency-domain transmit signal bloc as {,j ();=,,N c j=,,j1}, he SBC coded freuency-domain transmit signal bloc {X, (n M,);=,...,N c - n M =,,N M =,,Q1} can be expressed as # #NM1 #NBS1 # (b) Base station (b) Base station X M =, (1a) X X, X M =3, (1b) X,, X,3, X, X, X,, X,3, M =4, (1c) where X ()=[X (,),, X (N M )] is the th SBC coded bloc vector. In F-S, the SBC coding rate J/Q is determined by the number of the transmitter antennas, (i. e. the number of M antennas) [9]. As understood from (1), the conjugate operations is only reuired and no CSI is reuired at the M transmitter. he freuency-domain SBC codeword is transformed bac to the time-domain SBC codeword by applying N c -point inverse FF (IFF). After insertion of cyclic prefix (CP) into the beginning the each bloc, the SBC codeword is transmitted to BS in Q time-slot. At the BS receiver, a super position of N M transmitted signal is received by N BS antennas. After CP removal, the received signal is transformed into the freuency-domain signal by N c -point FF. he freuency-domain received signal, {R, (n BS,); =,,N c - n BS =,,N BS 1} in the th time-slot is expressed as R, X, N, () N J Q,, M where R, () = [R, (,),., R, (N BS )] is the freuency-domain received signal vector in the th time-slot., ()=[, (,),,, (N M )] with, (n M,)=[, (n M,),,, (n M,N BS )] is the N BS N M channel transfer function matrix in the th time-slot. P t denotes the transmit power. N, ()=[N, (,),,N, (N BS )] is the noise vector and N, (n BS,) is the zero mean complex valued additive white Gaussian noise (AWGN) having variance N / s with N and s being the single-sided power spectrum density of AWGN and the symbol duration, respectively. BS performs the receive MB-FE to the received SBC codeword. he th received signal vector, ˆR, =[ R ˆ,,..., N,, M ], after the receive MB-FE is given as W R, (3),,, where W, ()=[ W,,..., W N 1 ] with,, M, W, (n M,)=[W, (,n M,),...,W, (N BS n M,)] is the N M N BS receive MB-FE weight matrix for the th SBC coded bloc vector. After the receive MB-FE, he SBC decoding is performed to obtain the SBC decoded freuency-

3 domain signal. he SBC decoded freuency-domain signal { ˆ ; =,,N c j=,,j1} as, j ˆ, ˆ M =, (4a), ˆ,,, ˆ,,3, ˆ,,,.,3 M =3, (4b) ˆ,,,,3 3, ˆ,, 3,,3, ˆ,, 3,,.,3 M =4. (4c) he SBC decoded freuency-domain signal is transformed bac to the time-domain signal by N c -point IFF, and finally, the data demodulation is carried out. B. ownlin F-SBC-JR transmission In the downlin transmission, F-SBC-JR is performed. At the BS transmitter, the J N c data modulated symbols are divided into the a seuence of J bloc of N c symbol each. he J transmit signal blocs are transformed into the freuency-domain signal by the N c -point FF. A seuence of J freuency-domain signals are encoded into N M streams of Q SBC coded freuency-domain single blocs each. enoting the freuency-domain transmit signal bloc as {,j ();=,,N c j=,,j1}, he SBC coded freuency-domain transmit signal bloc {X, (n M,);=,...,N c - n M =,,N M =,,Q1} can be expressed as X M =, (5a) X X, X M =3,(5b) X,, X,3, X, X, X,, X,3, M =4, (5c) where X, ()=[X, (,),, X, (N M )] is the th SBC coded bloc vector. In F-SBC-JR, the SBC coding rate J/Q is determined by the number of the receiver antennas, (i. e. the number of M antennas) [1]. After SBC encoding, the transmit ˆX MB-FE is performed. he th transmit signal vector,, =[ X ˆ,,..., Xˆ N,, BS ], after the transmit MB-FE is given as Xˆ A W X, (6), N M,, where W, () = [W, (,),, W, (N M )] with W, (n M,) = [W, (,n M,),., W, (N BS n M,)] is the N BS N M transmit MB-FE weight matrix for the th SBC coded bloc vector. A is the power normalization factor to N M eep average transmit power constant given as 1 AN M Q1 N M W n N Q c nm, M,. (7) he freuency-domain SBC codeword after the transmit MB-FE is transformed bac to the time-domain SBC codeword by applying N c -point IFF. After insertion of CP into the beginning the each bloc, the SBC codeword is transmitted to the receiver in Q time-slot. At the M receiver, a super position of N BS transmitted signal is received by N M antennas. After CP removal, the received signal is transformed into the freuency-domain signal by N c -point FF. he freuency-domain received signal, {R, (n M,); =,,N c - n M =,,N M 1} in the th timeslot is expressed as R P Xˆ N, (8), t,,, where R, () = [R, (,),., R, (N M )] is the freuency-domain received signal vector in the th time-slot.,,, N with,,, M, (n M,)=[, (n M,),,, (n M,N BS )] is the N M N BS channel transfer function,matrix in the th time-slot. N, ()=[N, (,),,N, (N M )] is the noise vector and n, (n M,) is the AWGN having variance N / s. he SBC decoding is performed to obtain the SBC decoded freuencydomain signal. he SBC decoded freuency-domain signal { ˆ ; =,,N c j=,,j1} as, j ˆ R, R R R for N ˆ M =, (9a), ˆ R, R R,, ˆ R R, R,3, ˆ R R R,,,.,3 for N M =3, (9b) ˆ R, R R,, R,33, ˆ R R, R,3, R,3, ˆ R R R R,, 3,,.,3 for N M =4. (9c) As understood from (9), addition/subtraction and conjugate operations are only reuired and no CSI is reuired at the M receiver. he SBC decoded freuency-domain signal is transformed bac to the time-domain signal by N c -point IFF, and finally, the data demodulation is carried out. III. MB-FE FOR IG MIBOLIY ENVIRONMEN In this paper, we derive the transmit/receive MB-FE weights for a high mobility environment. he MB-FE weights are jointly optimized based on the MMSE criterion by taing into account the channel variation within a SBC codeword (i.e., and,, Q1

4 ). Since the transmit FE alters the,, Q1 transmitted signal spectrum shape, the signal-to-noise power ratio (SNR) is unproportional to the MSE. herefore, we derive the transmit MB-FE which minimizes the relative downlin MSE and the receive MB-FE which minimizes the uplin MSE, respectively. he downlin and uplin relative MSEs, e and e, are respectively given as J 1 1 ˆ, j AN, j M e E j P t AN E, j M. (1) J 1 1 e ˆ E, j, j j N M J Q Below, we derive the transmit/receive MB-FE weights when N M =. he transmit/receive MB-FE weights when N M =3,4 can be also derived similar to when N M =. owever, it is sipped in this paper due to page limitation. A. erivation of the transmit MB-FE From (5), (6), (7), (8) and (9), e can be rewritten as N 1 c, W, W 1 e W W,, 1 N 1 c, W W, W, W, 1 Q1 N M 1 1 J N M W, nm, Q N nm (11) he first term is the contribution of the residual ISI after MB- FE due to the channel freuency-selectivity and the second term is the contribution of the residual interference after SBC due to the orthogonality distortion in the SBC codeword. he transmit MB-FE weights are jointly optimized so as to minimize the relative downlin MSE given as W,, W arg mine. (1), W,, W By solving e W,,..., e W N, the,, Q 1 M MMSE transmit MB-FE weights are obtained as ~ ~,, W, ~ ~ ~, ~ ~,,3 W ~ ~ ~,3 ~ ~, (13),,3 W, ~ ~ ~,3 ~ ~,, W ~ ~ ~, where. 1 ~ J, N M Q N 1 ~ J, N M, Q N ~,,, ~,3,, (14) and N=N / s is the noise power. he second terms in denominator and numerator in (13) contribute to suppress the interference caused by the orthogonality distortion of the SBC codeword. When the channel variation within a SBC codeword is sufficiently slow (,,...,, Q1 ), (13) corresponds to the MB-FE weights designed based on the assumption of uasi-static fading [14]. B. erivation of the receive MB-FE From (1), (), (3), and (4), e given as (1) can be rewritten as N 1 c W,, W 1 e W, W, 1 N 1 c W,, W W, W, 1 Q1 N M 1 1 J N M W, nm, Q N nm (15) he receive MB-FE weights for uplin are jointly optimized so as to minimize the uplin MSE given as W,, W arg min e. (16), W,, W Similar to the transmit MB-FE, the MMSE receive MB-FE weights are derived as ~ ~,, W, ~ ~ ~, ~ ~,,3 W ~ ~ ~,3 ~ ~, (17),,3 W, ~ ~ ~,3 ~ ~,, W ~ ~ ~, where 1 ~ J, N M Q N 1 ~ J, N. (18) M Q N ~,,, ~,3,,.

5 Average BER Average BER IV. COMPER SIMLAION We evaluate, by the computer simulation, the BER performance when using the proposed transmit/receive MB-FE. We consider QPSK data modulation. FF bloc size N c and CP length N g are set to N c =18 symbols and samples, respectively. he number of BS antennas N BS is set to N BS = as an example. he channel is assumed to be a time and freuency-selective fading channel having symbol spaced L=16 path uniform power delay profile. In this paper, we assume perfect CSI can be obtained at BS. A. BER performance Fig. 4 shows the BER performance when using the proposed transmit/receive MB-FE as a function of transmit signal energy per bit-to-awgn power spectrum density ratio E b /N. he normalized maximum oppler freuency f s is assumed to be f s = For the comparison, the performance when using the MB-FE designed based on the assumption of uasi-static fading [14] (below, we call it as the previously proposed MB-FE) is also plotted in Fig. 4. It is seen from Fig. 4 that the performance when using the previous MB-FE has BER error floor. his is because the previous MB-FE assumes a uasi-static fading channel, and hence, the BER performance degrades due to the interference caused by the orthogonality distortion of the SBC codeword. Furthermore, when N M =3,4, the performance degradation become larger than when N M =. his is because, when N M =3,4, the length of SBC codeword is twice longer than when N M = and the interference caused by the orthogonality distortion of the SBC codeword become larger. It is also seen from Fig. 4 that the proposed MB-FE can significantly improve the BER performance compared to the previous MB-FE. his is because the proposed MB-FE weights are jointly optimized by taing account into the channel variation within a SBC codeword, and as conseuence, it can mitigate the interference caused by the orthogonality distortion of the SBC codeword. When the transmit E b /N =6dB and the number of the M antennas N M =3, the proposed MB-FE can achieve about 1/4 times (1/ times) lower BER than the previous MB-FE for uplin (downlin) transmission. B. Impact of the normalized maximum oppler freuency Fig.5 plots the BER performance when using the proposed MB- FE as a function of the normalized maximum oppler freuency f s. he transmit E b /N is set to 6dB. For comparison, the performance of the previous MB-FE is also plotted in Fig 5. It is seen form Fig. 5 that the proposed MB-FE is more robust to channel time-selectivity than the previous MB- FE. his is because the proposed MB-FE can mitigate the interference caused by the orthogonality distortion of the SBC codeword and obtain high spatial diversity gain. When reuired BER is BER=1 and the number of M antenna N M = (N M =3,4), the proposed MB-FE can tolerate f s =8 1 4 (f s =1 1 3 ) and can tolerate about 3 (8) times higher oppler freuency than the previous MB-FE. Assuming Mz signal bandwidth at the carrier freuency 5Gz, the normalized maximum oppler freuency f s =1 1 3 corresponds to a travelling speed of 43m/h. herefore, SC- SBC transmission system combined with the proposed MB-FE achieves a good BER performance even in a high mobility environment. V. CONCLSION In this paper, we proposed a transmit/receive MB-FE for SC-SBC- transmission in a high mobility environment. It was shown by the computer simulation that the proposed MB-FE suppress the interference caused by the orhtogonality distortion of SBC codeword and tolerates about 8 times higher oppler freuency than the MB-FE designed based on the assumption of uasi-static fading when N M =4. In this paper, we assumed the perfect CSI. he channel estimation for SC-SBC transmission is left as our future wor. Performance comparison of our proposed transmit/receive MB-FE to other techniues, e.g. iterative interference cancellation [13], is also left as our future study. 1.E-1 1.E- 1.E-3 L=16 path niform N c =18 1.E E-1 1.E- Fig. 4. ransmit E b /N (db) (a) plin (b) ownlin N M = 3 4 N M = 3 4 BER performance 1.E-3 L=16 path niform N c =18 1.E ransmit E b /N (db)

6 Average BER Average BER 1.E+ 1.E-1 1.E- 1.E-3 L=16 path niform 1.E-4 N c =18 1.E-5 1.E-5 1.E-4 1.E-3 1.E- 1.E-1 1.E+ 1.E-1 1.E- 1.E-3 N M = 3 4 N M = 3 4 Normalized oppler freuency f s (a) plin [7]. omeba, K. aeda, and F. adachi, Space-time bloc coded joint transmit/receive diversity in a freuency-nonselective Rayleigh fading channel, IEICE rans. Commun., Vol. E89-B, No. 8, pp , Aug. 6. [8] S. Yoshioa, S. Kumagai,. Yamamoto,. Obara, and F. Adachi, Single-carrier SBC diversity using CP-CE and linear inter/extrapolation in a doubly selective fading channel, Proc. the 1th IEEE VS Asia Pacific Wireless Communications Symposium (APWCS13), Seoul, Korea, Aug. 13. [9] K. aeda,. Itagai, and F. Adachi, Application of space-time trasnmit diversity to single carrier transmission with freuency-domain eualization and receive antenna diversity in a freuency-selective fading channel, IEEE Proc. Commun., Vol. 15 No. 6, pp , ec. 4. [1]. omeba, K. aeda, and F. Adachi, Freuency-domain space-time bloc coded joint transmit/receive diversity for direct-seuence spread spectrum signal transmission, IEICE rans. Commun., Vol. E9-B, No. 3, pp , Mar. 7. [11] P.. Chiang,. B. Lin and. J. Li, Performance analysis of twobranch space-time bloc coded S-CMA systems in time-varying multipath rayleigh fading channels, IEEE rans. Vehicular ech., Vol. 56, No., pp , Mar. 7. [1] J. W. Wee, J. W. Seo, K.. Lee, Youn. S. Lee, and W. G. Jeon, Successive interference cancellation of SBC-OFM systems in a fast fading channel, Proc. 61th IEEE Vehicular ech. Conf. (VC 5- spring), Vol., pp , Jun. 5. [13] C. Y. so, J. M. Wu, and P. A. ing, Iterative interference cancellation for SBC-OFM systems in fast fading channel, Proc. IEEE Global elecommunications Conf., pp. 1-5, ec. 9. [14]. Miyazai, and F. Adachi, ransmit FE weight design for singlecarrier space-time bloc coded joint transmit/receive diversity, Proc. the 9th Intern. Conf. on Information and Communication and Signal Processing (ICICS), ainan, aiwan, ec. 13. L=16 path 1.E-4 niform N c =18 1.E-5 1.E-5 1.E-4 1.E-3 1.E- 1.E-1 Normalized oppler freuency f s Fig. 5. (b) ownlin Impact of Normalized oppler freuency REFERENCES [1] J. G. Proais and M. Salehi, igital communications, 5th ed., McGraw- ill, 8. []. Sari, G. Karam, and I. Jeanclaude, ransmission techniue for digital terrestrial V broadcasting, IEEE Commun. Mag., Nol. 33, No., pp. 1-19, Feb [3]. Falconer, S. L. Ariyavistaul, A. Benyamin-Seeyar, and B. Edison, Freuency domain eualization for single-carrier broadband wireless systems, IEEE Commun.. Mag., Vol. 4, No. 4, pp , Apr.. [4] F. Adachi,. omeba, and K. aeda, Introduction of freuencydomain signal processing to broadband single-carrier transmission in a wireless channel, IEICE rans. Commun., Vol. E9-B, pp , Sept. 9. [5] S. M. Alamouti, A simple trasnmit diversity techniue for wireless communication, IEEE J. Sel. Areas. Commun., Vol. 16, No. 8, pp , Oct [6] V. aroh,. Jafarhani, and A. R. Calderban, Space-time bloc coding for wireless communications: performance results, IEEE J. Sel. Areas. Commun., Vol. 17, No. 3, pp , Mar