Cyclic delay transmission for unique word OFDM systems

Transcription

1 . RESEARCH PAPER. SCIENCE CHINA Information Sciences August 2014, Vol : :9 doi: /s Cyclic delay transmission for unique word OFDM systems LIAO Mang 1, XIA XiangGen 2 & ZHANG YouGuang 1 1 School of Electronic Information Engineering, Beihang University, Beijing , China; 2 Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, 19711, USA Received September 6, 2013; accepted December 3, 2013; published online April 15, 2014 Abstract In this article, we propose a cyclic delay diversity (CDD) transmission scheme for unique word (UW) OFDM system, which is denoted as CDD-UW-OFDM. In our proposed CDD-UW-OFDM system, the first transmit antenna transmits a UW-OFDM and then, for every UW-OFDM block, the i-th transmit antenna transmits a cyclically delayed version of the symbols transmitted at the first transmit antenna. With this proposed CDD-OFDM system, each antenna transmission is a UW-OFDM. Also, at the receiver under a certain condition on the cyclic delay amounts, the received signal is equivalent to that of a single transmit antenna UW-OFDM transmission with a longer multipath channel. We design the lengths of UW and cyclic delays to achieve the full multipath and spatial diversities for the CDD-UW-OFDM system when the linear MMSE receiver is used. We then present some simulation results to illustrate the claimed performance of the proposed system. Keywords MIMO-OFDM systems, frequency-selective fading channels, cyclic delay diversity (CDD), unique word (UW), transmit diversity Citation Liao M, Xia X G, Zhang Y G. Cyclic delay transmission for unique word OFDM systems. Sci China Inf Sci, 2014, 57: (9), doi: /s Introduction For frequency-selective fading channels with multiple transmit antennas, there are spatial and multipath diversities. To collect the spatial and multipath diversities, space-frequency coding (SFC) has been proposed in the past decades 1. However, its decoding complexity at the receiver is high 1 3, or its transmission rate is low and multiple OFDM blocks are involved together 4. Cyclic delay diversity (CDD), on the other hand, is a low complexity scheme for MIMO-OFDM systems to collect the spatial and multipath diversities with only one OFDM block 5,6. It uses multiple transmit antennas to transmit cyclically delayed versions of the same signal. Compared with SFC, CDD not only has a lower decoding complexity but also is applicable to any number of transmit antennas without the need of any modification of the receiver 7. The direct estimation of the equivalent single-input channel for CDD-OFDM systems is analyzed in 8. The maximum diversity for a CDD MIMO-OFDM system can be achieved with either the linear MMSE receiver 9 or the combined error correction coding 10. Because of these advantages, CDD OFDM transmissions have been adopted in current WiFi standards A mixed CDD and Corresponding author ( xianggen@gmail.com) c Science China Press and Springer-Verlag Berlin Heidelberg 2014 info.scichina.com link.springer.com

2 Liao M, et al. Sci China Inf Sci August 2014 Vol :2 space-time/frequency coding has also been considered in Ref. 14. It should be emphasized that the OFDMs in these systems are cyclic prefix (CP) based. As an alternative ofthe CP based OFDM system, in 15, unique word (UW) basedofdm is proposed, whereauw isaknown(and fixed) sequenceinsertedin anofdm blockinstead ofacpinthe traditional OFDM.ThemostsignificantdifferencebetweenCP-andUW-OFDMsisthattheCPisarandomsequence that depends on the data to transmit in the OFDM block, whereas the UW is deterministic and fixed. Hence, the UW can be used for synchronization and channel estimation purposes 16. There have been many studies on the performance of UW-OFDM systems In 17, one general structure of the UWs in OFDM symbols is provided. In 18, one-step and two-step approaches of UW generation are proposed and it proves that the two-step approach performs better. The performance of combined coding and UW prefix is analyzed in 19,20.. The positions of redundant symbols and the power allocation are studied in 21. With this UW-OFDM, a natural question rises: what do we do if there are multiple transmit antennas? In this article, we propose a CDD transmission scheme for a UW-OFDM system, which is denoted as CDD-UW-OFDM. There exist two challenges to combine CDD transmission into the UW-OFDM system: 1) Owing to the structure of UW-OFDM, how to shift the samples as well as satisfy the UW-OFDM structure in each OFDM block? 2) How to design the relationship among the cyclic delay parameter δ, the number of the transmit antennas, the channel length L, and the UW length N u? In our proposed CDD-UW-OFDM system, the first transmit antenna transmits a UW-OFDM with UW length N u and then, for every UW-OFDM block, the i-th transmit antenna transmits the cyclically delayed version of the same signal as the first transmit antenna with a cyclic delay amount δ i. With this proposed CDD-OFDM system, interestingly, all the antenna transmissions are UW-OFDMs. Also, at the receiver under a certain condition on the cyclic delay amounts δ i, the received signal is equivalent to that of a single transmit antenna UW-OFDM transmission with a longer multipath channel, and therefore all the techniques for the conventional UW-OFDM can be applied. By choosing the proper N u and δ i, the proposed CDD-UW-OFDM system can achieve the full multipath and spatial diversities when the linear MMSE receiver is used. We then present some simulation results to illustrate the claimed performance of the proposed system. The remainder of this article is organized as follows. In Section 2, we present our CDD-UW-OFDM transmission system. In Section 3, we describe the linear MMSE receiver for our proposed system. In Section 4, we provide some simulation results for the proposed system. Finally, in Section 5, we conclude this article. Some notations: lower-case bold face variables (a, b,...) indicate vectors; capital bold face variables (A,B,...) indicate matrices; I N denotes the N N identity matrix; 0 N M is the all-zero N M matrix; ( ) T and ( ) H represent transpose and conjugate transpose, respectively; x and x denote the symbols in time domain and frequency domain, respectively; and (m) mod N denotes the m mod N operation. 2 CDD-UW-OFDM In this section, we propose CDD-UW-OFDM systems. To do so, let us briefly review a UW-OFDM system 15, A brief review of UW-OFDM In a UW-OFDM system, we assume that a signal in the time domain is decomposed into blocks and each block has N samples. These N samples are composed of two parts: the data part corresponds to the sequential N N u samples and the unique word part corresponds to the other N u samples. Notice that the position of unique word could be in the first or the last of the N samples to guarantee the data part samples are sequential. For the analysis of the positions of redundant symbols, the works mentioned assume the unique word part that corresponds to the last N u samples. Considering the two-step approach of generating the

3 Liao M, et al. Sci China Inf Sci August 2014 Vol :3 transmit signals for the UW-OFDM system 18, first we transmit N d data symbols and N r, N r N u, redundant symbols in the frequency domain with N d +N r = N. The N r redundant symbols are used to obtain that the last N u samples of the IFFT output are zeros. The signal samples after the IFFT are expressed as x = F 1 N P x d x r = x p 0 Nu 1, (1) where the N d 1 vector x d and the N r 1 vector x r present the data and the redundant symbols in the frequency domain, respectively. x p = x p (0),..., x p (N N u 1) T represents the transmit signals in the time domain. F 1 N is the N N IFFT matrix and P is an N N permutation matrix, which defines the positions of the data and the redundant symbols. In the second step, we add UW into the transmit signals, i.e., x = x + 0(N Nu) 1 where the N u 1 vector x u = x u (0),..., x u (N u 1) T denotes the UW. We define x u M = F 1 N P = M11 M 12 M 21 M 22, (2) where M ij are appropriately sized sub-matrices. From (1), it can be obtained that M 21 x d +M 22 x r = 0, and thus the redundant signals can be expressed as, x r = M 22 1 M 21 x d = T x d. (3) Therefore, before adding the UW, the relationship between the transmitted symbols and the data symbols can be given by x = P 2.2 CDD-UW-OFDM system x d x r = P INd T x d = G x d. (4) We now propose a CDD-UW-OFDM system. For simplification, we only consider one receive antenna. For multiple receive antennas, the signal model is similar by just stacking all the received signals from the receive antennas together. Consider a MISO system of N t transmit antennas with frequency-selective fading and assume that the number of subcarriers is N. The channel impulse response from the i-th transmit antenna to the receive antenna is given by T h i = h i (0), h i (1),..., h i (N 1) T, = h i (0), h i (1),..., h i (L 1), 0,..., 0 (5) where L denotes the channel multipath (or memory) length. Our proposed CDD-UW-OFDM system is shown in Figure 1. Because UW is a known sequence, we assume all the elements in the UW are the same for simplification. In an OFDM block, we assume that the first transmit antenna transmits the first N N u data symbols and the last N u unique words, i.e., x 0 = x 0 (0),..., x 0 (N 1) T = T. x p (0),..., x p (N N u 1), x u,..., x u (6) N u

4 Liao M, et al. Sci China Inf Sci August 2014 Vol :4 x d (k) S/P x d (0) x d (N d 1) Add redundant symbols x d (0) x d (N d 1) x r (0) x r (N r 1) Permutation matrix P N-point IFFT x p (0) x p (N N u 1) 0 Add UW x p (0) x p (N N u 1) x u =x (0) 0 0 x u (N u 1) P/S δ 1 x 0 (n) x 1 (n) δ Nt 1 x Nt 1(n) y (n) S/P y(0) y(n 1) N-point FFT y(0) y(n 1) Remove UW Figure 1 CDD-UW-OFDM system T IDFT T IDFT T x 0 Data UW UW Data UW UW δ 1 N u δ 1 δ 1 N u δ 1 T x 1 UW Data UW UW Data UW T IDFT T IDFT Figure 2 Transmit data structure with two transmit antennas for CDD-UW-OFDM system The signal x i for the i-th transmit antenna to transmit is obtained by cyclically delaying the signal x 0 with an amount δ i, 1 i N t 1. For simplification, we let δ i = iδ in this article and a general case of δ i can be similarly studied. In this case, the maximum cyclic delay for all the antennas is (N t 1)δ. Because of the sequence N N u data symbols in each transmit antenna, it is not hard to see that each transmit antenna still transmits a UW-OFDM signal. However, across all the transmit antennas, their UW parts are not aligned in the same time slots. To avoid the intersymbol interference (ISI) from all the transmit antennas at the receiver, we require N u (N t 1)δ +L 1. (7) Figure 2 shows the transmit signals from two antennas for the CDD-UW-OFDM system. From Figure 2, one can see that the symbols with cyclic delay of δ 1 (δ 1 = δ) symbols at the second transmit antenna still have a UW-OFDM structure, i.e., x 1 = x u,...,x u,x p (0),...,x p (N N u 1),x u,...,x u. (8) δ 1 N u δ 1 Also, we next show that, under the condition (7) on the cyclic delay parameter δ, the number N t of the transmit antennas, the channel length L, and the UW length N u, the received signal at the receiver is equivalent to that of a single transmit antenna UW-OFDM transmission. As a remark for the condition (7), when the channel length L is large, the UW length N u in (7) will be large too, which may reduce the spectral efficiency. In the traditional UW-OFDM system, the length of UW is not less than L 1 to avoid the inter-block interference (IBI) and thus the linear convoluted expression of received signals can be changed to the circular convolution in one OFDM block 15. In the CDD-UW-OFDM system, the circular convoluted

5 Liao M, et al. Sci China Inf Sci August 2014 Vol :5 expression of the received signals from all the transmit antennas can be achieved, only if after the cyclic shift amount δ i of the UW, the remaining UW length is still not less than L 1 for the i-th transmit antenna for all i. Because the maximum cyclic delay from all the transmit antennas is (N t 1)δ and the condition (7), i.e., N u (N t 1)δ + L 1, the linear convolution becomes the circular convolution at the receiver in one OFDM block. Thus, we have the following received signal expression. For 0 n N 1, the received signals can be written as y(n) = = N t 1 i=0 N t 1 i=0 N 1 l=0 N 1 l=0 h i (l)x i ((n l) mod N)+z(n) h i (l)x 0 ((n l iδ) mod N)+z(n), (9) where z(n) is zero mean additive white Gaussian noise (AWGN) with variance σ 2 n. Similar to the expression of the traditional CDD-OFDM in 10, the received signals in (9) can be represented as where y(n) = N 1 l=0 h eqv (l) = h eqv (l)x 0 ((n l) mod N)+z(n), (10) N t 1 i=0 h i ((l iδ) mod N). (11) From (10), one can see that the transmissions from all the N t transmit antennas are equivalent to a single transmit antenna UW-OFDM system with the equivalent channel h eqv (l) expressed in (11). Thus, in the matrix form, the model in (10) can be rewritten as y = H eqv x 0 +z, (12) where H eqv is the N N circular channel matrix from the equivalent channel h eqv (l) in (11): h eqv (0) h eqv (N 1) h eqv (N 2)... h eqv (1) h eqv (1) h eqv (0) h eqv (N 1)... h eqv (2) H eqv = (13)... h eqv (N 1) h eqv (N 2)... h eqv (1) h eqv (0) According to condition (7) and N N u, we obtain N (N t 1)δ+L 1. Now we discuss the effect of the relationship between the cyclic delay parameter δ and the number of multipaths L on the structure of the equivalent channel. We list some special representative cases for illustration purposes below, while a general case can be similarly but tediously done. Case 1: δ L and N (N t 1)δ +L. From (5) and (11), the equivalent channel can be expressed as h eqv = h 0 (0),...,h 0 (L 1),0,...,0,h 1 (0),...,h 1 (L 1),0,...,0, δ L δ L...,h Nt 1(0),...,h Nt 1(L 1), 0,...,0 N (N t 1)δ L T. (14)

6 Liao M, et al. Sci China Inf Sci August 2014 Vol :6 When δ = L and N = (N t 1)δ +L, the equivalent channel of (14) becomes h eqv = h 0 (0),h 0 (1),...,h 0 (L 1),h 1 (0),h 1 (1),...,h 1 (L 1),...,h Nt 1(0),h Nt 1(1),...,h Nt 1(L 1) T. (15) From (14) and (15), it illustrates when δ L, there is no channel overlap in the equivalent channel, which allows to achieve the maximal spatial and multipath diversities. Also, the condition of δ = L and N = (N t 1)δ +L is the lower bound to achieve no channel overlaps for the CDD-UW-OFDM system. In particular, when N t = 2, δ L, i.e., the cyclic delay amount δ for the second transmit antenna is no less than the channel length, N u δ+l 1 and N u N δ+l, the equivalent channel in this case can be represented as h eqv = h 0 (0),h 0 (1),...,h 0 (L 1),0,...,0,h 1 (0),h 1 (1),...,h 1 (L 1),0,...,0 δ L N δ L Case 2: δ = L 1 and N (N t 1)δ +L. In this case, the equivalent channel can be written as h eqv = h 0 (0),h 0 (1),...,h 0 (L 1)+h 1 (0),h 1 (1),...,h 1 (L 1)+h 2 (0), T. (16)...,h Nt 2(L 1)+h Nt 1(0),h Nt 1(1),...,h Nt 1(L 1), 0,...,0 N (N t 1)δ L T. (17) From (17), because the cyclic delay parameter δ is not long enough, the equivalent channel contains channel overlaps between the last and the first channel coefficients of the i-th and the (i+1)-th transmit antennas, respectively. In particular, when N t = 2, N δ+l, N u δ+l 1, and δ = L 1, the equivalent channel becomes h eqv = h 0 (0),h 0 (1),...,h 0 (L 1)+h 1 (0),h 1 (1),...,h 1 (L 1),0,...,0 N δ L Case 3: 2δ = L 1 and N (N t 1)δ +L. The equivalent channel can be represented as ( ) ( ) L 1 L 1 h eqv = h 0 (0),h 0 (1),...,h 0 +h 1 (0),...,h 0 (L 1)+h 1 +h 2 (0), 2 2 ( ) L 1...,h Nt 1(L 1)+h Nt,...,h Nt (L 1), 0,...,0 2 N (N t 1)δ L T. (18) T. (19) In this case, the channel overlaps are quite severe and there exist overlaps between three channels from three transmit antennas. According to these cases, to avoid any channel overlap to achieve the maximal spatial and multipath diversities, the lengths of the cyclic delay amounts {δ i = iδ}, the OFDM block length N and the UW length N u must be designed to satisfy the following conditions δ L, N (N t 1)δ +L, (20) N u (N t 1)δ +L 1.

7 Liao M, et al. Sci China Inf Sci August 2014 Vol :7 Hence, the minimum values of the cyclic delay amounts {δ i } and the UW length N u are δ i = il and N u = LN t 1, respectively. Also, the minimum of the bandwidth-reduction of the CDD-UW-OFDM is LN t 1 N, which can be close to 0, when the numbers, N t and L, of transmit antennas and multipaths are small compared to the number, N, of subcarriers. Next, we see two specific examples about the equivalent channels with two transmit antennas to explain the effect of cyclic delay parameter δ on the channel overlaps. Example 1: L = 3, N t = 2, N = 6, δ 1 = δ = 3, 6 N u δ +L 1 = 5. In this example, the equivalent channel is T. h eqv = h 0 (0), h 0 (1), h 0 (2), h 1 (0), h 1 (1), h 1 (2) (21) Example 2: L = 3, N t = 2, N = 6, δ 1 = δ = 2, 6 N u δ +L 1 = 4. The equivalent channel in this example is h eqv = h 0 (0), h 0 (1), h 0 (2)+h 1 (0), h 1 (1), h 1 (2), 0 T. (22) Notice that the length of CP is independent of the cyclic delay amount δ in a CDD-CP-OFDM system and in contrast, in a CDD-UW-OFDM, the length of UW is correlated to the maximum cyclic delay size (N t 1)δ. This is because even though every transmit antenna transmits a UW-OFDM signal after a cyclic delay, its UW is also cyclically delayed and the UWs from all the transmit antennas may not be aligned in the same time slots after their different cyclic delays. In this case, the received signal from all the transmit antennas may not be equivalent to a single antenna UW-OFDM signal, if the channel length L is large, and thus the ISI can not be eliminated. 3 LMMSE UW-OFDM receiver From (12), the receiver is the same as a UW-OFDM receiver with the same structure of transmitted codes in 15,17 21, but for the equivalent channel H eqv. In this article, we follow the receiver in 15. After the DFT operation, the received OFDM frequency domain symbols can be written as where x = F N x p 0 Nu 1 ỹ = F N H eqv F 1 N x 0 +F N z = F N H eqv F 1 N ( x + x u )+F N z, (23) and x u = F 0(N Nu) 1 N x are the data symbols and the UW in the frequency u domain, respectively. We definethe matrix H = F N H eqv F 1 N which isdiagonalandcontainsthe sampled channel frequency response on its main diagonal. Hence, the received symbols can be given by ỹ = H x + H x u +F N z. (24) Note that x u denotes a known sequence. To determine the Bayesian LMMSE estimator, we define ỹ = ỹ H x u. By applying the Bayesian Gauss-Markov theorem 22, the LMMSE estimator can be expressed as ˆ x = C x x H H( HC x x H H +Nσ 2 ni) 1ỹ, (25) with C x x = E x x H = σd 2GGH (here, we assume uncorrelated and zero-mean data symbols with variance σd 2). Because the data symbols can be calculated as ˆ x d = I Nd 0 Nd N r P 1ˆ x, the LMMSE equalizer in (25) can be rewritten as ( 1 E LMMSE = G H H H HG+ Nσ2 n I) σd 2 G H H H. (26)

8 Liao M, et al. Sci China Inf Sci August 2014 Vol : UW OFDM CDD UW OFDM CDD CP OFDM 1 6 SIMO flat fading δ = 1 δ = 2 δ = 3 BER BER E b /N 0 (db) Figure 3 BER comparisons among the UW-OFDM with one transmit antenna, CDD-CP-OFDM, CDD- UW-OFDM with two antennas, and SIMO flat-fading channels with one transmit and six receive antennas E b /N 0 (db) Figure 4 BER performance with two transmit antennas and different cyclic delay parameter for CDD-UW-OFDM system 4 Simulation results We now want to show some simple simulations for the BER performance of the CDD-UW-OFDM system. In the simulations, the IFFT size N is 64, the length of the data symbols N d is 48, the number of multipaths L is 3, and the modulation scheme is QPSK. UW corresponds to the last 16 samples of transmitted symbols at the first transmit antenna, i.e., the length of UW N u = 16. After a cyclic delay of δ 1 = δ, one part of the UW becomes the first δ 1 samples and the remaining part of the UW is the last (N u δ 1 ) samples at the second transmit antenna. In the simulation, the UW is zero for simplification, i.e., x u = 0. Figure 3 depicts the BER performance of the CDD-UW-OFDM system with the number of transmit antennas N t = 2, the cyclic delay parameter, which is equal to the number of multipaths, i.e., δ 1 = δ = L = 3. In this case, the diversity order is 6. The BER performance of the UW-OFDM with one transmit antenna and CDD-CP-OFDM with two transmit antennas are depicted in Figure 3 for comparison. The diversity order for this single transmit antenna case is 3. From Figure 3, the performance of the CDD- UW-OFDM system is much better than the one of UW-OFDM system, because it can achieve the spatial and multipath diversities in the CDD-UW-OFDM system. From Figure 3, the BER performance of CDD- UW-OFDM system is the same with the one of CDD-CP-OFDM system with the same parameters. The reason is that the equivalent channel in Eq. (10) is calculated similarly to the one in CDD-CP-OFDM system 10. To show that our proposed CDD-UW-OFDM system achieves diversity order 6, we compare it with the 1 6 SIMO system with flat fading and ML receiver. Figure 4 depicts the effect of the cyclic delay parameter δ on the BER performance of the CDD-UW- OFDM system with the number of transmit antennas N t = 2. From Figure 4, with the cyclic delay parameter δ 1 = δ decreasing, the performance of the CDD-UW-OFDM becomes worse. When the cyclic delay parameter δ 1 = δ = 3 is same as the number of multipaths L, the diversity orderis 6 and this case is the same as the two transmit antenna CDD-UW-OFDM case in Figure 3, where there is no overlap in the equivalent channel and the full spatial and multipath diversities are achieved. When δ 1 = δ = 2 = L 1, because there is an overlap in the equivalent channel, the equivalent channel length is 5 and thus the achievable diversity order for this CDD-UW-OFDM is 5. When δ 1 = δ = 1, because there are two channel coefficients overlapped in the equivalent channel, the equivalent channel length is 4 and thus the achievable diversity order for this CDD-UW-OFDM is 4. 5 Conclusion In this article, we proposed a CDD transmission for a UW-OFDM system with multiple transmit antennas.

9 Liao M, et al. Sci China Inf Sci August 2014 Vol :9 In our proposed CDD-UW-OFDM system, every transmit antenna transmits a UW-OFDM signal and under a certain condition on the UW length and cyclic delay amounts, the received signal from all the transmit antennas is also equivalent to a single antenna UW-OFDM signal, even though every antenna transmits a cyclically delayed version of what another antenna transmits. The proposed CDD-UW- OFDM system may be able to collect the spatial and multipath diversities within one OFDM block and with a simple receiver, such as the MMSE receiver. Acknowledgements This work was supported in part by the National Science Foundation (NSF) (Grant No ), National Basic Research Program of China (Grant No. 2010CB731803), and National Science Foundation for Innovative Research Groups of China (Grant No ). References 1 Bölcskei H, Paulraj A. Space-frequency coded broadband OFDM systems. In: Proc IEEE WCNC, Chicago, Su W, Safar Z, Olfat M, et al. Obtaining full-diversity space-frequency codes from space-time codes via mapping. IEEE Trans Signal Proc, 2003, 51: Zhang W, Xia X G, Letaief K B. Space-time/frequency coding for MIMO-OFDM in next generation broadband wireless system. IEEE Trans Wirel Commun, 2007, 14: Zhang W, Xia X G, Ching P C. Full-diversity and fast ML decoding properties of general orthogonal space-time block codes for MIMO-OFDM system. IEEE Trans Wirel Commun, 2007, 6: Dammann A, Kaiser S. Standard conformable antenna diversity techniques for OFDM and its application to the DVB-T system. In: Proc IEEE Global Telecommun Conf, San Antonio, Gore D, Sandhu S, Paulraj A. Delay diversity codes for frequency selective channels. In: Proc IEEE ICC, New York, Lodhi A, Said F, Doher M, et al. Performance comparison of space-time block coded and cyclic delay diversity MC-CDMA systems. IEEE Trans Wirel Commun, 2005, 12: Fan J, Yin Q, Wang W. Pilot-aided channel estimation for CDD-OFDM systems. Sci China Inf Sci, 2010, 53: Mehana A H, Nosratinia A. Cyclic delay transmission achieves full diversity without (pre)coding. In: Proc IEEE ICC, Ottawa, Bossert M, Hüebner A, Schüehlein F, et al. On cyclic delay diversity in OFDM based transmission schemes. In: Proc the 7th International OFDM-Workshop (InOWO 02), Hamburg, Mujtaba S A. TGn sync proposal technical specification. Doc.: IEEE /0889r7. Draft proposal, Yan W, Sun S, Li Y, et al. Transmit diversity schemes for MIMO-OFDM based wireless LAN systems. In: Proc IEEE Personal, Indoor and Mobile Radio Commun, Helsinki, Femenias G, Riera-Palou F. Enhancing IEEE n WLANs using group-orthogonal code-division multiplex. Intern Federat Inform Proc, 2007, 245: Feng A, Yin Q, Wang H. Cyclic-delay time-reversal space-time block codes for single-carrier transmission with frequency-domain decision-feedback equalization. Sci China Inf Sci, 2011, 54: Hofbauer C, Huemer M, Huber J B. Coded OFDM by unique word prefix. In: Proc ICCS, Singapor, Huemer M, Witschnig H, Hausner J. Unique word based phase tracking algorithms for SC/FDE-systems. In: Proc IEEE GLOBECOM, San Francisco, Huemer M, Hofbauer C, Huver J B. The potential of unique words in OFDM. In: Proc Intern OFDM-Workshop, Hamburg, Onic A, Huemer M. Direct vs. two-step approach for unique word generation in UW-OFDM. In: Proc Intern OFDM Workshop, Hamburg, Huemer M, Hofbauer C, Huber J B. Non-systematic complex number RS coded OFDM by unique word prefix. IEEE Trans Signal Proc, 2012, 60: Huemer M, Onic A, Hofbauer C. Classical and Bayesian linear data estimators for unique word OFDM. IEEE Trans Signal Proc, 2011, 59: Steendam H. The quasi-uniform redundant carrier placement for UW-OFDM. In: Proc IEEE VTC, Quebec City, QC, Kay S M. Fundamentals of Statistical Signal Processing: Estimation Theory. Rhode Island: Prentice Hall, 1993