Iterative detection for frequency-asynchronous distributed Alamouti-coded (FADAC) OFDM

Transcription

1 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 DOI /s RESEARCH Open Access Iterative detection for frequency-asynchronous distriuted Aamouti-coded (FADAC) OFDM Bong-seok Kim 1 and Kwonhue Choi 2* Astract We propose a near intercarrier interference (ICI)-free and very ow compexity iterative detector for frequency-asynchronous distriuted Aamouti-coded (FADAC) orthogona frequency division mutipexing (OFDM). In the previous canceation schemes, the entire sucarrier signas from one transmit (TX) antenna are estimated and canceed in the received signa from the other TX antenna and vice versa. However, the reiaiity of the estimated symos are reveaed to significanty vary across the sucarriers and thus, the poory estimated symos ead to the incorrect canceation. Motivated from this, we first propose a scheme which does not cance the interfering sucarrier(s) at the haf and edges which undergo very high interference in FADAC-OFDM. For further improvement, we propose a so-caed seective scheme which instanty measures the reiaiity of the detected symos at each iteration and then excude the unreiae symos in the estimated interference generation. Moreover, the proposed scheme has a drasticay reduced compexity y converting the canceation process from the sucarrier domain to the time domain. In accordance with the anaysis on the considered reiaiity measures, the numerica resuts show that the proposed scheme achieves the near ICI-free eve ony within three or four iterations for wide ranges of SR, frequency offset, and deay spread. Keywords: Iterative MIMO, Aamouti, ICI canceation, OFDM, Distriuted antennas, Frequency offset 1 Introduction Recenty, severa studies on Aamouti-coded OFDM (orthogona frequency division mutipexing) for cooperative systems have een reported. One of the main chaenging issues in this area is to mitigate sef-interference due to the carrier frequency offset (CFO) etween the distriuted transmit antennas 1 8]. Very recenty in 4], the so-caed FADAC-OFDM (frequency-asynchronous distriuted Aamouti-coded OFDM) has een proposed and shown to outperform the other existing approaches in 3 5]. In contrast to the conventiona distriuted Aamouti-coded OFDM, FADAC-OFDM is free from ICI (intercarrier interference) terms from the near sucarriers due to its ICI sef-canceation property ony y simpe Aamouti-decoding process. Especiay, 4] tried to expoit this ICI sef-canceation property even in the seective *Correspondence: gonew@ynu.ac.kr 2 Department of ICE in Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeonguk, 38541, Repuic of Korea Fu ist of author information is avaiae at the end of the artice fading channe y dividing the entire sucarriers into mutipe suocks. However, in the severey frequencyseective fading channes, FADAC-OFDM gets worse due to non-negigie inter-ock ICI terms. Meanwhie, in 5 7], typica types of iterative ICI canceation schemes for the conventiona Aamouti-coded OFDM with the distriuted antennas have een proposed. Since the conventiona Aamouti-coded OFDM 9] has no ICI sef-canceation property for frequency and timing asynchronous distriuted antennas, the accuracy of the initia detection is poor. Thus, a considerae numer of iterations of canceation has to e performed unti the performance converges. Moreover, the converged performances are not so impressive. Athough in 5] they derived the performance resut cose to no-cfo case, they assumed the perfect ICI canceation which has not een justified. The schemes in 6, 7] rapidy reak down as the CFO gets arger than 0.5. Moreover, they have high computation overheads ecause at each iteration, the required numer of compex mutipications for the interference The Author(s) Open Access This artice is distriuted under the terms of the Creative Commons Attriution 4.0 Internationa License ( which permits unrestricted use, distriution, and reproduction in any medium, provided you give appropriate credit to the origina author(s) and the source, provide a ink to the Creative Commons icense, and indicate if changes were made.

2 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 2 of 14 reconstruction is 4 2 where denotes the tota numer of OFDM sucarriers. Recenty, in 10] and 14], the decision-directed iterative ICI canceation schemes to distriuted mutipe input mutipe output (MIMO) have een proposed. In 14], the authors considered spatia moduation MIMO as the appication system mode and they showed the performance resuts ony for the sma vaues of CFO. In 10], we, the authors of this paper, comined a typica decision-directed iterative ICI canceation scheme to FADAC-OFDM. We achieved etter performance compared with 5] even with ow compexity due to etter initia detection performance of FADAC-OFDM compared to the conventiona Aamouti-coded OFDM. This scheme uses a the detected symos in the interference reconstruction step without any consideration of reiaiity of detection symos. However, even in FADAC- OFDM, some of the detection symos may eventuay have reativey high possiiity of errors due to severe ICI terms such as inter-ock ICI as mentioned efore. It is shown that after the first iteration, the performance fairy improves, ut from the second iteration, the performance is stuck in the same vaue. This is ecause the reconstructed interference term for canceation is not updated anymore due to the erroneous portion of the constructed interference. Consequenty, the performance gap etween this scheme 10] and the case of no ICI is sti considerae. In order to sove drawacks of the previous canceation scheme 10], it is important to carefuy decide whether or not to use each of the detected symos in the interference reconstruction step at each iteration. In other words, wehavetouseordeviseacertainmeasuretoassessthe reiaiity of the detected symos at each iteration, ased on which we have to excude the unreiae symos in the interference reconstruction. To this end, we first propose a deterministic scheme where the fixed numer of data symos at the haf and edges are not used in the interference reconstruction ecause they themseves undergo very high interference in FADAC-OFDM, and thus, they are ess reiae. In order to further improve the canceation performance, we propose a method which instantaneousy measures the reiaiity of the soft detected symos 12] at each iteration and then excude the unreiae symos in the estimated interference generation. We jointy empoy two reiaiity check measures: (1) square error of the decision variae from the corresponding consteation point and (2) the detection consistency for two consecutive iterations. Apart from the ICI canceation performance itsef, the computationa compexity of the scheme shoud e feasie from the impementation viewpoint. In the proposed scheme, we empoy a drasticay ow compexity structure which attains the compexity reduction in terms of poynomia order. The remainder of this paper is structured as foows: First, we review FADAC-OFDM in Section 2. In Section 3, we first review our previous iterative canceation scheme and its proem and then we propose two types of iterative canceation schemes. In Section 4, we propose a compexity-reduced ICI canceation structure. In Section 5, we provide the various performance resuts which support the improved ICI canceation capaiity of the proposed schemes. 2 Review on FADAC-OFDM In this paper, we are considering the iterative ICI canceation schemes for FADAC-OFDM. In this section, we descrie the motivation of FADAC-OFDM and give a sefcontained review on the TX and receive (RX) structures of FADAC-OFDM. In addition, we revisit its residua ICI terms for the susequent sections. FADAC-OFDM has een proposed for FO-toerant Aamouti-coded OFDM for frequency-asynchronous distriuted antenna systems 4]. FADAC-OFDM empoys a frequency reversa structure at the TX side. Then, FADAC-OFDM detects the symos y performing simpe inear comining after two separate DFT operations with oca carriers synchronized to each TX antenna. By doing so, FADAC-OFDM cances the major parts of intraock ICI terms from neighoring sucarriers, and thus, FADAC-OFDM significanty improves the performance for the distriuted antenna systems. However, despite the ICI sef-canceation property of FADAC-OFDM, two kinds of ICI terms, i.e., intra-ock ICI and inter-ock ICI, sti remain non-negigie. This eads us to consider a further canceation of the remaining ICI terms y using an iterative canceation scheme which wi e introduced in Section The system mode and the OFDM symo structure of FADAC-OFDM In this section, we introduce the system mode and the OFDM symo structure of FADAC-OFDM. We consider the distriuted antenna system that is composed of two TX antennas and one RX antenna. In each TX antenna, OFDM-moduated signas are transmitted with tota sucarriers, as in 1 6]. Let the variae x, denote the th data symo of the th suock and the variaes X (A) and X(B) denote the Aamouti-coded symos at the kth sucarrier of th suock of TX antennas A and B, respectivey. Figures 1 and 2 show the OFDM symo structures of the conventiona distriuted Aamouticoded (CDAC) OFDM 5, 6] and FADAC-OFDM 4], respectivey. In CDAC-OFDM, Aamouti code pairs are mapped to the neighoring sucarriers just ike the typica

3 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 3 of 14 Fig. 1 OFDM symo structure of CDAC-OFDM space-frequency Aamouti code structure 15], i.e., X (A) and X (B) are set to X (A) = { x,1 if k = 1, x,2 if k = 2, (1) X (B) = { x,2 if k = 1, x,1 if k = 2, (2) where x,1 and x,2 denote the two data symos for the th suock. Meanwhie, in FADAC-OFDM, the suock size (the numer of sucarriers per suock) is arger than 2, and then, Aamouti-coded symo pairs are packed into the mirror images in each suock as shown in Fig. 2. Specificay, -tota sucarriers are partitioned into suocks, and thus, the ock size n c is equa to /. Thus, in FADAC-OFDM, X (A) and X(B) for 1 are set as foows: { X (A) = x,2k 1 for 1 k n c /2, x,2(n c k+1) for n (3) c/2 + 1 k n c, { X (B) = x,2k for 1 k n c /2, x,2(n c k)+1 for n (4) c/2 + 1 k n c. We assume that the fading is ocay fat over the Aamouti-coded ock. To justify this assumption, the ock size n c is set smaer than the coherent andwidth. From Figs. 1 and 2, it is straightforward that as an extreme case, the FADAC-OFDM with n c = 2 is equivaent to CDAC-OFDM. 2.2 RX structure of FADAC-OFDM Figure 3 shows the overa structures for the previous and the proposed ICI canceation schemes, which wi e expained ater. The parts inside the od oxes which are common to oth structures correspond to the RX structure of FADAC-OFDM. We assume that there exists an inevitae carrier frequency offset (CFO) etween f c (A) and f c (B) which denote the received carrier frequencies from distriuted TX antennas A and B, respectivey.two FFTs (fast Fourier transforms) are performed on the RX signa y separatey synchronizing to two asynchronous TX antennas carrier frequencies and arriva timings. Let the variaes r (A) and r (B) denote two FFT input vectors synchronized to TX antennas A and B, respectivey, as shown in Fig. 3, then the FFT outputs corresponding to the kth eements of the thsuockoftwotxantennas are expressed as 10] R (A) = H(A) X(A) + I(A) + w(a) (5) R (B) = H(B) X(B) + I(B) + w(b) (6) where w (A) and w(b) are AWG terms and H(A) and H(B) are channe fading coefficients at the kth sucarrier of the th suock from TX antennas A and B, respectivey, and they are each independent and foow zero mean, unit variance compex Gaussian distriution. The variaes I (A) and I(B) denote ICI terms due to CFO and they are expressed as foows: I (A) = n c β=1 m=1 Q ((β ) n c + m ε k) H (B) β,m X(B) β,m, (7) Fig. 2 OFDM symo structure of FADAC-OFDM

4 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 4 of 14 a Fig. 3 Receiver structures for the previous scheme in 10] (a) and the proposed scheme () I (B) = n c β=1 m=1 Q ((β ) n c + m + ε k) H (A) β,m X(A) β,m where ε is the normaized CFO etween two transmit antennas, i.e., ε = (f c (B) f c (A) )/f where f is the sucarrier spacing and Q(x) is the ICI coefficient given as 16] Q(x) = (8) sin(πx) sin((π/)x) exp jπ(1 1/)x ]. (9) With a typica Aamouti decoding, the normaized decision variaes (DVs) x,2k 1 and x,2k corresponding to x,2k 1 and x,2k, respectivey, are otained as foows: x,2k 1 = H (A) x,2k = H (B) R(A) + H(B),n c k+1 R (B),n c k+1 H (A) 2 + H (B),n c k+1 R(B) H(A),n c k+1 R (A),n c k+1 H (B) 2 + H (A),n c k+1 2, (10) 2. (11) Sustituting (5) and (6) into (10), with X (A) and X(B) repaced y (3) and (4), resuts in x,2k 1 as the summation of the data symo x,2k 1 and degrading effect terms, i.e., interference term i,2k 1 and noise term w,2k 1,respectivey, as foows 4]: x,2k 1 = x,2k 1 + H (A) I(A) + H(B),n c k+1 I (B),n c k+1 H (A) 2 + H (B),n c k+1 2 }{{} interference term, i,2k 1 + H (A) w(a) + H(B),n c k+1 w (B),n c k+1 H (A) 2 + H (B),n c k+1 2. } {{ } noise term, w,2k 1 (12) In (12), w,2k 1 sti foows Gaussian distriution ecause w,2k 1 is the inear comination of two i.i.d noise sampes with the same weighting factors. Therefore, w,2k 1 has the identica static to that of w (A) and

5 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 5 of 14 w (B),n c k+1. Meanwhie, sustituting (7) and (8) into i,2k 1 in (12), i,2k 1 is expressed as the summation of the intra-ock ICI and inter-ock ICI terms, as foows: H (A) n c Q (m + ε k) H (B),m X(B),m i,2k 1 = m=1 +H (B) n c,n c k+1 Q (m ε (n c k + 1)) H (A),m X (A),m m=1 }{{} i intra,2k 1,intra-ock ICI H (A) n c Q ((β ) n c + m + ε k) H (B) β,m X(B) β,m β = m=1 + +H (B),n c k+1. n c Q ((β ) n c + m ε (n c k + 1)) H (A) β,m X (A) β,m β = m=1 }{{} i inter,2k 1,inter ock ICI (13) Measured ICI power db] intra,(1) intra,(4) i,2k 1,1, i,2k 1,1 intra,(2) i, intra,(3) i,2k 1,1,2k 1,1 ε=0.2 ε= sucarrier index, k Fig. 4 The variances of the four terms in intra-ock ICI with n c = 32 for ε = 0.2 and ε = 0.5 We assume that the ock size n c is set smaer than coherent andwidth, that is, the fading is ocay fat over the Aamouti-coded ock. By our assumption, H (A) and H (B) are repaced y H(A) and H (B), respectivey. Therefore, i intra,2k 1 is expressed as the summation of the four interference terms i intra,(1),2k 1, iintra,(2),2k 1, iintra,(3),2k 1,andiintra,(4),2k 1,as foows 4]: n i intra,2k 1 = H (A) H (B) c/2 m=1 Q (m + ε k) X (B),m } {{ } i intra,(1),2k 1 + H (A) H (B) n c m=n c/2+1 Q (m + ε k)x (B),m } {{ } i intra,(2),2k 1 + H (A) n H (B) c/2 m=1 Q (m ε (n c k + 1)) X (A),m } {{ } i intra,(3),2k 1 + H (A) H (B) n c m=n c/2+1 Q (m ε (n c k + 1)) X (A),m } {{ } i intra,(4),2k 1. (14) Figure 4 shows the variances of the four interference terms mentioned aove for ε = 0.2 and ε = 0.5. Intuitivey, the variances of i intra,(1),2k 1 and iintra,(4),2k 1 are identica and the variances of i intra,(2),2k 1 and i intra,(3),2k 1 are identica. ote that the variances of i intra,(1),2k 1 and iintra,(4),2k 1 are significanty dominant over those of i intra,(2),2k 1 and iintra,(3),2k 1.This is ecause i intra,(1),2k 1 and iintra,(4),2k 1 are the ICI from the sucarriers of the haf suock where the desired sucarrier eongs to, whereas i intra,(2),2k 1 and iintra,(3),2k 1 aretheicifrom the other haf suock 4]. Let us focus on one of the dominant intra-ock ICI terms i intra,(4),2k 1. From (9), Q(x) = Q ( x), and thus, Q ( (m ε k)) = Q(m + ε k), and from (3) and (4), X (A),n c m+1 = X (B),m. Using these properties and introducing a new indexing variae, i.e., m = n c m + 1to rearrange n c /2 + 1 m n c in reverse order, i intra,(4),2k 1 in (14) can e rewritten as i intra,(4),2k 1 = H (A) n H (B) c /2 m =1 Q (n c m + 1 ε (n c k + 1))X (A),n c m +1 = H (A) = H (A) H (B) /2 m=1 H (B) /2 m=1 ( Q ( m ε + k) Q (m + ε k) X (B),m X (B),m = i intra,(1) 2k 1 (15) which concudes that i intra,(1),2k 1 and i intra,(4),2k 1 in (14) cance each other. By canceing i intra,(1),2k 1 and i intra,(4),2k 1 which are dominant terms in intra-ock ICI, the performance degradation due to ICI can e sustantiay ameiorated. On the other hand, we can show that i intra,(2) 2k 1 = i intra,(3) 2k 1 without difficuty, and thus, the overa intra-ock ICI term i intra,2k 1 can e expressed as the reativey weak ICI term i intra,(2),2k 1 as foows: i intra,2k 1 = 2H (A) H (B) n c m=n c /2+1 Q (m ε k) X (B),m = 2i intra,(2),2k 1. (16) )

6 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 6 of 14 Therefore, (12) is rewritten as the summation of the data symo, the minor part of the intra-ock ICI term, interock ICI term, and additive noise term, as foows: x,2k 1 = x,2k 1 + 2i intra,(2),2k 1 + iinter,2k 1 + w,2k 1 (17) Using a simiar cacuation and notation, x,2k is represented without difficuty and oss of generaity as x,2k = x,2k + 2i intra,(2),2k + i inter,2k + w,2k. (18) Figure 5a shows the normaized average ICI powers in the decision variaes according to the pair of suock numer and sucarrier index, i.e., (, k) with = 256 and n c = 32. The term i in the egend denotes the numer of the iterative canceations whose detaied agorithm wi e proposed in the susequent susection. In Fig. 5a, it is shown that even without the iterative canceation (i = 0), the ICI power of FADAC-OFDM is maintained ower than 15 db in the midde of haf suocks even for a arge ε, i.e., 0.5. This is due to the intrinsic property of FADAC-OFDM, i.e., the major ICI terms from the neighoring sucarriers in the considered suock are competey sef-canceed. Meanwhie, despite intra-ock ICI sef-canceation, the ICI power sharpy increases at the haf and edges (k = n c /2ork = n c ). This is ecause in the vicinity of the haf suock edges, the frequency distances etween the considered sucarrier and the sucarriers eonging to the counterpart (the other side) haf suock or the consecutive suocks decrease and the interferences from these sucarriers are not canceed y FADAC-OFDM as shown in (17) and (18). Motivated from this, y using an iterative canceation step which wi e introduced in the next section, we try to cance further the remaining ICI terms. In Fig. 5a, y empoying iterative canceation, it is shown that ICI powers at haf and edge and and edge significanty decrease compared to the case efore iterative canceation. However, the ICI powers at haf suock edges are sti reativey arge compared to the midde and. This is ecause the iterative ICI canceation is not perfect, and thus, the reason for high interferences at the haf suock edges mentioned aove sti hods. For a reference, Fig. 5 shows the normaized ICI power of FADAC-OFDM with n c = 2 which is equivaent to CDAC-OFDM. With n c = 2, the feature of FADAC- OFDM, i.e., sef-canceation of the intra-ock ICI term, is meaningess ecause there exists ony one sucarrier in each haf suock. Thus, the ICI powers over a sucarriers are very high as shown in Fig. 5, and the iterative canceation is not so effective either. This impies that CDAC-OFDM is not suitae for the frequencyasynchronous distriuted antenna systems. Figure 6 shows the it error rate (BER) resuts of FADAC-OFDM according to the suock size n c with ε = 0.5 for the severa cases of T max which denotes the maximum deay spread of muti-path, and T denotes the OFDM symo duration. It is shown that the optima n c is arger than 2 and is getting arger as the deay spread decreases, which accords with our expectation. In addition, as the deay spread decreases, the suoptima zone where the performance is rather insensitive to n c is getting wider. However, if n c is set excessivey arge, the performance is getting worse. ICI power db] ICI power db] (1,16) (1,32) (2,16) (2,32) (3,16) (3,32) (4,16) (4,32) n =32 c (8,2) (16,2) (24,2) (32,2) (40,2) (48,2) (56,2) (64,2) n =2 (CDAC OFDM) c a Fig. 5 ormaized average ICI power in decision variaes of FADAC-OFDM with n c = 32 (a)andnc = 2 (CDAC-OFDM) (), according to the pair of suock numer and sucarrier index and the numer of iterations for canceation i, ε = 0.5 and = 256 i=0 i=2 i=4 i=0 i=2 i=4

7 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 7 of 14 BER T max =T/10 T max =T/50 T max =T/ suock size, n c Fig. 6 The BER resuts according to n c for the severa T max s, ε = 0.5 for BPSK with E / 0 = 20 db 3 Comining iterative ICI canceation schemes to FADAC-OFDM 3.1 The previous iterative ICI canceation scheme for FADAC-OFDM The procedure of the previous iterative ICI canceation scheme to FADAC-OFDM in 10] is shown in Fig. 3a. First, FADAC-OFDM is performed for initia detection. Then, the estimated ICI terms are generated y using initia detection symos and channe information to sutract ICI terms from RX signa. This is iterativey performed y updating the detection symos at each iteration. Denote ˆx (i),2k 1 and ˆx(i),2k as the detection symos otained y sicing x,2k 1 and x,2k in (17) and (18), respectivey, at the ith iteration. By sustituting ˆx (i),2k 1 and ˆx(i),2k into (3) and (4) and then into (7) and (8), we reconstruct the estimated versions of I (A) and I(B),respectivey,attheith iteration. Denote Î (A) (i) and Î(B) (i) as the estimated versions of I(A) and I (B) at the ith iteration, respectivey. We update the FFT outputs R (A) and R(B) at the ith iteration as foows: R (A,i) R (B,i) R (A) Î(A,i), (19) R (B) Î(B,i), (20) where R (A,i) and R (B,i) denote the updated versions of R (A) and R (B),respectivey,attheith iteration. Finay, at each iteration, we perform the Aamouti comining in (10) and (11) using R (A,i) and R (B,i) to otain the updated detection symos ˆx (i+1),2k 1 and ˆx(i+1),2k, respectivey, for the next ((i + 1)th) iteration. In 10], it is shown that due to the good performance of FADAC-OFDM y intra-suock ICI sef-canceation, this asic iterative scheme for FADAC-OFDM achieves etter performance with ower compexity compared with 5]. However, this scheme sti has room to e improved. Due to high ICI power at the suand edges shown in Fig.5, the detection symos at those edges are more ikey to e erroneousy detected compared to the other detection symos. The incorrect detection symos resut in the incorrect ICI term reconstruction and thus the incorrect ICI canceation. As a resut, even with increasing iterations, the improvement of performance is imited and the error proaiity is stuck in a certain point where the non-negigie incorrect contriution to the reconstructed ICI term is not sef-corrected y the iterations any more. This wi e checked out again in the simuation resuts. 3.2 The proposed iterative ICI canceation schemes In the previous section, we addressed the issue of the previous iterative ICI canceation in 10], i.e., the drawack of using the entire detection symos for ICI reconstruction and canceation. To tacke this issue, we propose two types of seective ICI canceation schemes Scheme I. DS scheme As the first scheme to avoid the proem of using the unreiae symo detection at the suand edges, we simpy do not use the fixed numer of symos at the suand edges for ICI term reconstruction. In other words, if we denote ˆx (i,used),2k 1 and ˆx(i,used),2k as the symo estimates which wi e finay used to reconstruct the ICI terms for canceation at the ith iteration, they are set as foows: ˆx (i,used),2k 1 = ˆx (i,used),2k = { 0 if k E ˆx (i) (21),2k 1,esewhere, { 0 if k E ˆx (i) (22),2k,esewhere, where E is a set of indices of edge sucarriers, i.e., E = {1, 2,..., M, n c 2 M + 1, n c 2 M + 2,..., n c 2 },andm is the numer of data symos (sucarriers) at each edge to e excuded in the ICI term reconstruction. For exampe, if M is set to 2 with n c = 16, then set E is equa to {1, 2, 7, 8}. Consequenty, 2M(=M pairs of Aamouti code) data symos are not used, and they are repaced y nu data symos in the ICI term reconstruction. Simpy y excuding 2M detection symos at the edge in each suock which are severey interfered y inter-ock ICIs, we can avoid the performance degradation due to wrong ICI term canceation. Another merit of this scheme is that it does not need any additiona hardware or computations compared to 10]. This scheme excudes the data symos in the deterministic carrier positions, i.e., predetermined positions ased on the average ICI power distriution across the sucarriers as shown in Fig. 5. However, we know from (7) and (8) that the ICI term at each sucarrier contains ots of random variaes such as the data symos in the other sucarriers and their fading coefficients and thus the

8 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 8 of 14 ICI power at each sucarrier instantaneousy varies. This impies that some of the edge sucarriers can eventuay undergo rather sma instantaneous ICI despite the high average ICI power. As we need the instantaneous reiaiity of the detection symos to decide whether or not to use each detection symo, the proposed DS (deterministicay seective) scheme which simpy excudes the fixed numer of and edge sucarriers sti has room to e improved if we can accommodate the instantaneous reiaiity of the detection symos Scheme II. AS scheme To aeviate the proem of the proposed DS scheme mentioned in the previous paragraph, we propose another socaed adaptivey seective (AS) scheme. In the proposed AS scheme, we use two measures for the instantaneous reiaiity of the detection symos. As one of the reiaiity measures, we use the square error etween the soft decision variae x and its nearest consteation point ˆx as the tentative decision vaue 11]. Let us denote this reiaiity measure for a certain detection symo ˆx y γ,then it is cacuated as γ = x ˆx 2. (23) In order to check whether or not this measure we refects the reiaiity of the detection symo, we simuated the cumuative distriution function (CDF) of γ for the correct detection case and the incorrect detection case.figure 7 shows CDFs of γ for two (correct and incorrect) cases when = 256 and n c = 16. It is cear in Fig. 7 that γ for the correct case is distriuted in the quite ow range whereas γ for the incorrect case is distriuted in the quite high range. For exampe, in the initia (i = 0) detection, for the correct detection case, 96% of γ s is smaer than 0.5 whereas for the incorrect detection case, 95% of γ s is arger than 0.5. This feature ecomes even more remarkae as the iteration goes on. This impies that y simpy comparing γ with a threshod, we can propery measure the reiaiity of the corresponding detection symo. We use the foowing criterion to decide whether or not to use the detection symo in the ICI reconstruction. { ˆx (used) ˆx, ifγ ρ = (24) 0, ese where ˆx (used) denotes the actua vaue which wi e used in the ICI reconstruction and ρ is a threshod vaue which determines whether or not the detection is sufficienty reiae or not. ote in Fig. 7 that this criterion possiy misses the correct symos or possiy uses the incorrect symos in the ICI reconstruction step. The threshod ρ shoud e set y considering oth of these two possiiities. The optimum vaue wi vary according to the channe parameters, the system parameters, or even the iteration ayer. However, in the practica system, it is ikey to use, rather, a constant threshod, i.e., goa suoptima setting, and thus, we cannot avoid the performance oss compared to the optimized case. To compement this, we use another measure to assess the reiaiity of the detection symos, i.e., detection consistency etween two consecutive iterations. If a certain detection symo is sufficienty reiae at the ith iteration, the detection resut woud not change in the (i + 1)th iteration. Hence, we treat a detection symo as the reiae one if its detection resut is maintained etween two consecutive iterations. This measure we compromises the proaiity that the first criterion in (24) uses the incorrect symo(s) in the ICI reconstruction step. For exampe, when a certain incorrect detection symo has a sma γ, correct case incorrect case correct case incorrect case correct case incorrect case correct case incorrect case PrX<γ ] X numer of iterations i= X a c numer of iterations i=2 d Fig. 7 a d CDF of γ at each iteration numer of iterations i= X X numer of iterations i=3

9 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 9 of 14 we concude that it eventuay has the sma γ and it is unreiae if the detection resut in the previous iteration is not equa to the detection resut in the current iteration. Summing up, the proposed AS scheme uses the foowing criterion for seecting the detection symos in the ICI reconstruction step. ˆx (i) (i),2k 1,ifγ,2k 1 ρ, for i < 2 ˆx (i,used),2k 1 = 0, ese ˆx (i),2k 1,ifˆx(i),2k 1 = ˆx(i 1) (i),2k 1and γ,2k 1 ρ, fori 2, 0, ese ˆx (i,used),2k = ˆx (i) (i),2k,ifγ 0, ese ˆx (i),2k 0, ese,2k,if ˆx(i),2k = ˆx(i 1),2k (25) ρ, for i < 2 (i) and γ,2k ρ, fori 2. (26) In order to check whether or not the two conditions in (25) and (26) we discriminate the correct or incorrectdetections,wehavetoseethetwokindsofconditiona proaiities: (1) p condition fase denoting the proaiity of incorrect symo detection despite the condition eing satisfied ( fase rate in short) and (2) p condition miss denoting the proaiity of correct symo detection despite the condition eing unsatisfied ( miss rate in short). First, p condition fase for two conditions are written as foows: ] p C1 fase = Pr ˆx (i),2k 1 = x,2k 1 γ (i),2k 1 ρ (27) ] p C2 fase = Pr ˆx (i),2k 1 = x,2k 1 ˆx (i),2k 1 = ˆx(i 1),2k 1 (28) and p condition miss for two conditions are written as foows: ] p C1 miss = Pr ˆx (i),2k 1 = x,2k 1 γ (i),2k 1 >ρ p C2 miss = Pr ˆx (i),2k 1 = x,2k 1 ˆx (i),2k 1 = ˆx(i 1),2k 1 (29) ] (30) where C1 denotes the condition γ (i),2k 1 ρ and C2 denotes the condition ˆx (i),2k 1 = ˆx(i 1),2k 1.Asthesimiar expressions hod for x,2k, we excude the expressions for x,2k 1 without oss of generaity. To avoid the wrong canceation, we have to ower p condition fase, and to avoid missing thecorrectdetectionsymos,wehavetoowerp condition miss. Figure 8 shows the four conditiona proaiities in (27) (30) with ρ = 0.4 and ε = 0.5. Due to symmetry, x,2k shoud have the same resuts. The condition C1 has smaer fase rate ut much arger miss rate compared to the condition C2. We can expect the performance improvement y jointy using the two conditions. To confirm this, the resuts for the joint condition { C1 C2 } fase and miss rates 10 0 C1 p fase (18) C2 p (19) fase C1 C2 p fase C1 p (20) miss C2 p (21) miss C1 C2 p miss E / db] 0 Fig. 8 Fase and miss rates, ρ = 0.4, ε = 0.5 which is adopted in the proposed AS scheme are aso potted in Fig. 8. ote that this joint condition achieves much ower miss rate than that of using the condition C1 aone whie achieving the fase rate as ow as that of using the condition C1 aone. Compared to the condition C2, the joint condition has the simiar eve of miss rate in the practicay high (signa-to-noise ratio) SR region whie achieving quite smaer fase rate. 4 Compexity reduction The hardware structures of the iterative canceations in 5 7, 10] are asicay the same. They a incude the cacuations for reconstructing the interference term at each FFT outputs expressed in (7) and (8) at each iteration. The interference term in (7) and (8) have2 compex mutipications. Asthere are twofftswith outputs, the overa required numer of compex cacuations for interference term reconstruction per iteration is equa to 4 2. Meanwhie in the proposed scheme, we modify this compexity-expensive structure into a mathematicay equivaent ut ow compexity structure. Figure 3 shows the receiver structures for the previous iterative canceation scheme in 10] and the proposed scheme. Instead of performing canceation at the FFT output stage (sucarrier domain), we can equivaenty cance the interference at the FFT input stage (time domain). Hence, the reconstructed interference corresponds to the time domain version. The reduced computation is intuitive due to the fact that the time domain interference takes the form of just a singe samped vector ut it contains the parae interfering sucarriers. Reca that r (A) and r (B) denote the origina input vectors to -point FFTs which are synchronized to TX A and TX B frequencies, respectivey. Then, at the ith iteration of the proposed scheme, they are repaced y r (A,i) and

10 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 10 of 14 r (B,i), respectivey, which are the updated versions given as foows: ] r (A,i) = r (A) IFFT H (B) (B,i) 1,1 ˆX 1,1, H(B) (B,i) 1,2 ˆX 1,3,, H(B),n c,n c e j2πε j2π2ε, e e j2πε] (31) r (B,i) = r (B) IFFT H (A) 1,1 (A,i) ˆX 1,1, H(A) 1,2 e j2πε j2π2ε, e e j2πε]. In (31) and (32), ˆX (A,i) β,m and β,m estimated versions of X (A) and X(B) β,m e j2πε, e j2π2ε ] (A,i) ˆX 1,3,, H(A),n c ˆX (A,i),n c β,m, (32) denote the respectivey, at the ith iteration, e j2πε] and e j2πε, e j2π2ε e j2πε] denote the samped versions of the residua compex exponentias y CFO, and denotes the eement-wise mutipication. ote that the term IFFT H (B) (B,i) 1,1 ˆX 1,1, H(B) 1,2 e j2πε, e j2π2ε e j2πε] in (31) corresponds to the reconstructed time domain-samped signa from TX antenna B to the received signa synchronized to TX antenna A. The simiar remark hods for (32). In order to prove that the time domain ICI canceation of the proposed scheme is identica to the frequency (sucarrier) domain canceation, et us expand (31) first. We denote the nth output of IFFT, IFFT ] (B,i) ˆX 1,3,, H(B),n c,n c i.e., H (B) (B,i) 1,1 ˆX 1,1, H (B) (B,i) 1,2 ˆX 1,2,, H(B),n c,n c ], y η (A,i) (n), thenη (A,i) (n) for 1 n is cacuated as foows: η (A,i) (n) = 1 n c β=1 m=1 H (B) (B,i) β,m ˆX β,m e j2π((β 1)nc+m)n/.(33) For simpicity, we set = (β 1)n c + m, and then, (33) is expressed as η (A,i) (n) = 1 =1 H (B) e j2πn/. (34) Then, to reconstruct the received signa from the other TX antenna (antenna B here) in the time domain, the samped versions of the residua compex exponentia term are mutipied to η (A,i) (n).thenth sampe of the received signa from the other TX antenna in the time domain is denoted y i (A,i) (n), andthen,i (A,i) (n) is expressed as foows: i (A,i) (n) = η (A,i) (n) e j2πnε/ = 1 H (B) e j2πn( ε)/. (35) =1 Denote the kth output of FFT i (A,i) (1), i (A,i) (2),..., i (A,i) () ] y F (A) k,thenf (A) k for 1 k is expressed as F (A) 1 k = H (B) e j2πn( ε)/ e j2πnk/ n=1 = 1 =1 =1 H (B) e j2πn( k ε)/. (36) n=1 By using the summation formua for the geometric series, (36) is rewritten as F (A) k = 1 H (B) e jπn( k ε) ( e jπn( k ε) e jπn( k ε)) e jπn( k ε)/ ( e jπn( k ε)/ e jπn( k ε)/ ) =1 sin (π ( k ε)) = sin (π ( k ε) /) H(B) =1 = Q ( k ε) H (B). =1 (37) By reusing the reation = (β 1)n c + m and setting k = ( 1)n c + k, (37) is expressed as F (A) k = n c β=1 m=1 Q ( (β )n c + m k ε ) H (B) (B,i) β,m ˆX β,m. (38) From (38), we know that F (A) k is finay equa to (7), and thus, it is proved that the proposed time domain canceation is equivaent to the previous sucarrier domain canceation. ote that in each of (31) and (32),, /2og 2,and mutipications are required for IFFT input vector generation, -point IFFT operation, and -point compex sinusoid mutipication, respectivey. In addition, we have to incude the computations for two FFT ocks for the origina OFDM demoduation which are now inside the canceation oop (see Fig. 3a) unike the previous sucarrier domain canceation schemes (see Fig. 3). Consequenty, og 2 mutipications are required in tota at each iteration to reconstruct the interference in the time domain canceation as shown in Tae 1. Tae 1 The numer of mutipications required in the operations for the interference term reconstruction at each ranch per iteration of the proposed scheme Operation umer of mutipications IFFT input vector generation IFFT for time domain conversion -point compex sinusoid mutipication FFT for the origina OFDM demoduation Tota 2 og 2 2 og og 2

11 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 11 of 14 ote that as increases to the practica range, the computationa compexity of the proposed structure is proportiona to og 2 whereas that of the previous scheme is proportiona to 2. Figure 9 and Tae 2 compare the compexity etween the previous sucarrier domain canceation schemes and the proposed time domain canceation scheme. It is remarkae that the proposed structure drasticay reduces the compexity compared to the previous sucarrier domain canceation schemes whie maintaining the mathematica equivaence to the sucarrier domain canceation schemes. 5 Simuation resuts In this section, we provide the simuation resuts to evauate the performance of the proposed scheme. Commony, we set = 256. Regarding muti-path profie for generating H (A) and H(B), the numer of muti-paths is 8 and their deays are distriuted uniformy in 0 T max ]wheret max is the maximum deay spread. The guard interva is set to e arger than T max. The sucarrier spacing (=1/T where T = OFDM symo duration prior to the guard time insertion) is set to 15 khz y referring to the Long-Term Evoution (LTE) standard. For the proposed AS (adaptive seective) scheme, the threshod vaue ρ is set to 0.4 regardess of the iteration numer and the other parameters. Figure 10 shows BERs of iterative ICI canceation schemes according to the numer of iterations i for ε = 0.5 with inary phase shift keying (BPSK) and T max = T/100, T/50, and T/10.ThesuocksizeofFADAC- OFDM frame n c is set to 8 irrespective of T max. We excude the extremey frequency-seective fading channes where the optima n c of FADAC-OFDM is equa to 2, and then, the transmitter structure of FADAC-OFDM is triviay the same as that of CDAC-OFDM. umer of compex mutipicatons 10 x previous (sucarrier domain canceation) proposed (time domain canceation) umer of sucarriers Fig. 9 umer of compex mutipications per iteration Tae 2 Comparison of the numer of mutipications etween the previous and the proposed schemes according to Previous (frequency domain) Proposed (time domain) , , ,144 11, ,048,576 24, Proposed/previous As a aseine for the performance comparison, CDAC- OFDM with the iterative ICI canceation using the entire detection symos in the OFDM frame is incuded. ote that the iterative ICI canceation resuts in amost no improvement to CDAC-OFDM. This is ecause the initia detection performance of CDAC-OFDM under frequency-asynchronous environment is poor, and thus, the ICI canceation ased on unreiae initia detection does not work propery. On the other hand, the iterative ICI canceation works etter for the case when it is appied to FADAC-OFDM which has a super initia detection performance. However, the performance gain of ICI canceation scheme in 10] is sti not so significant. This scheme uses a the detected symos in the interference reconstruction step without any consideration of the reiaiity of the detection symos. Even in FADAC- OFDM, some of the detection symos may eventuay have reativey high possiiity of errors due to severe ICI terms such as inter-ock ICI as mentioned efore. It is shown that after the first iteration, the performance fairy improves ut from the second iteration, the performance is stuck in the same vaue. This is ecause the reconstructed interference term for canceation is not updated anymore due to the erroneous portion of the constructed interference. Consequenty, the performance gap etween the scheme in 10] and the case of no ICI is sti significant. ote that two proposed schemes in this paper achieve significanty improved performance compared to the scheme in 10]. In the first iteration, the proposed DS scheme with M = 1 achieves a sustantiay decreased BER compared to the scheme in 10]. This impies that simpy excuding the and edge sucarriers can efficienty avoid the erroneous ICI reconstruction. This resuts in the significant improvement y the canceing ICI from the rest of the sucarriers in the first iteration. However, the and edge sucarriers wi not e canceed in the remaining iterations as we, and the BER converges to a sti significanty higher eve than that of the ICI-free case. Meanwhie, the proposed AS scheme has significanty improved performance compared to the proposed DS scheme. Ony within three or four iterations, the proposed AS scheme approaches neary ICI-free eve. This means

12 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 12 of 14 BER CDAC OFDM +canceation FADAC OFDM+canceation 10] CDAC OFDM +canceation FADAC OFDM+canceation 10] CDAC OFDM +canceation FADAC OFDM+canceation 10] numer of iterations, i numer of iterations, i a T =T/100 max T =T/50 max c Fig. 10 a c BER according to the numer of iterations for ε = 0.5 and the severa T max s with n c = numer of iterations, i T max =T/10 that adaptivey seecting the detection symos for ICI reconstruction works propery, and as the iteration goes on, even the and edge sucarriers having high ICI power are graduay canceed. Despite the inferior performance of the proposed DS scheme to the proposed AS scheme, the proposed DS scheme has a merit that it is easy to impement and needs neary no compexity overhead. We can further improve the performances of the proposed schemes y more carefuy optimizing or adaptivey changing the system parameters such as the suock size of FADAC-OFDM n c, M for the proposed DS scheme, or ρ for the proposed AS scheme. However, we do not cover this case ecause the main point of this paper is to make sure of the improved performance of the proposed schemes even with suoptima parameters. In addition, adaptivey changing the system parameters is practicay a urden in terms of system impementation. Figure 11 shows BERs according to E / 0 with i = 4 and ε = 0.5. From Fig. 10, i issetto4sincetheperformances of a cases roughy converge at i = 4. The resuts for the schemes without ICI canceation are aso incuded to see the improvement y adding the iterative BER CDAC OFDM CDAC OFDM + canceation FADAC OFDM 4] FADAC OFDM + canceation 10] E / 0 db] CDAC OFDM CDAC OFDM + canceation FADAC OFDM 4] FADAC OFDM + canceation 10] E / 0 db] a T max =T/100 T max =T/50 c Fig. 11 a c BER according to E / 0 and i = 4 for severa T max sandε = 0.5 with n c = 8 CDAC OFDM CDAC OFDM + canceation FADAC OFDM 4] FADAC OFDM + canceation 10] E / db] 0 T max =T/10

13 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 13 of 14 BER CDAC OFDM + canceation FADAC OFDM 4] FADAC OFDM + canceation 10] frequency offset, ε frequency offset, ε a T =T/100 max T max =T/50 c Fig. 12 a c BER according to ε and i = 4 for severa T max s with n c = 8 CDAC OFDM + canceation FADAC OFDM 4] FADAC OFDM + canceation 10] CDAC OFDM + canceation FADAC OFDM 4] FADAC OFDM + canceation 10] frequency offset, ε T max =T/10 ICI canceation. Athough there exist sight deviations in the high SR region, the proposed AS scheme achieves neary ICI-free performance with the fixed system parameters over the wide SR range and the considered deay spread range. In Fig. 12, the BER resuts are potted for the arge CFO (>0.5) cases. Athough the performance graduay degrades and gets off from the ICI-free eve as the CFO increases, the proposed schemes sti attain the significant ICI reduction. Especiay, the proposed AS scheme maintains the BER sti in the meaningfu eve even forcfo>0.5.thisisecausethefadac-ofdmasicay hods its intrinsic feature, i.e., intra-ock ICI sefcanceation irrespective of CFO athough the inter-ock ICI eve increases as CFO increases. On the other hand, the ICI canceation schemes to CDAC-OFDM arupty reak down as CFO gets arger than 0.5. For reference, see Fig. 5 in 6] and Fig. 5 in 7] which we cannot overay on Fig. 12 in this paper as the system parameters and the channe parameters are not the same. To investigate the performance under the practica situation, we aso consider the case when there exists a channe estimation error. Figure 13 shows the BER resuts of each canceation scheme according to the variance of the channe estimation error with ε = 0.5, i = 4, E / 0 = 20 db, T max = T/250, and n c = 32. The mode of the imperfect channe estimation in 13] is empoyed, and the channe estimation error refers to the normaized one y the mean channe gain. The resuts show that performance degradation of the proposed scheme increases and the performance gaps among the schemes accordingy decrease as the variance of the error exceeds 0.2. ote however that in the practica range of the channe estimation error, say, ower than 0.2, a the schemes performances are amost insensitive to the channe estimation error and thus the significant performance gap etween the proposed AS scheme and the other schemes sti remains the same. 6 Concusions We proposed an enhanced iterative ICI canceation scheme distriuted Aamouti-coded OFDM oth in terms of the performance and the compexity. By avoiding the incorrect canceation due to incorrect symos, the proposed scheme achieves etter performance than other ICI canceation schemes. Ony within three or four iterations, BER 10 0 CDAC OFDM + canceation FADAC OFDM + canceation 10] Variance of the channe estimation error Fig. 13 BER according to the variance of the channe estimation error with ε = 0.5, i = 4, E / 0 = 20 db, T max = T/250, and n c = 32

14 Kim and Choi EURASIP Journa on Wireess Communications and etworking (2017) 2017:39 Page 14 of 14 the proposed scheme achieves near ICI-free performance y instantaneousy refecting the reiaiity of detection symos at each iteration. As for compexity, y converting the ICI canceation with functiona equivaence, the proposed scheme has a drasticay reduced computationa compexity. The performance resuts shown in this paper sufficienty appea as a promising soution for the current and future cooperative transmit antenna systems using OFDM waveform and Aamouti code. The proposed scheme wi e further improved y comining with some sophisticated schemes, such as the adaptivey seective canceation ased on the soft decision feedack 12]. We eave this as one of our future works. 12. SH Muer, WH Gerstacker, JB Huer, in Proc. GLOBECOM 96. Reduced-state soft-output treis-equaization incorporating soft feedack, (1996), pp Y Chen, C Teamura, Performance anaysis of maximum ratio transmission with imperfect channe estimation. IEEE Commun. Lett. 4(9), (2005) 14. B Zhou, Y Xiao, P Yang, S Li, in Proc. WiCOM, An iterative CFO compensation agorithm for distriuted spatia moduation OFDM systems, (2011) 15. SM Aamouti, A simpe transmitter diversity scheme for wireess communications. IEEE J. Seect. Areas Commun. 16(8), (1998) 16. P Dharmawansa, Rajatheva, H Minn, An exact error proaiity anaysis of OFDM systems with frequency offset. IEEE Trans.Commun. 57(1),26 31 (2009) Acknowedgements This work was supported in part y the DGIST R&D Program of the Ministry of Science, ICT and Future Panning, Korea (17-IT-01), Basic Science Research Program through the ationa Research Foundation (2015R1D1A3A ) funded y the Ministry of Education, and the Information Technoogy Research Center support program (IITP-2016-R ) supervised y the Institute for Information & Communications Technoogy Promotion funded y the Ministry of Science, ICT and Future Panning, Korea. Competing interests The authors decare that they have no competing interests. Author detais 1 Advanced Radar Technoogy Laoratory in DGIST, 333 Techno Jungang-daero, Hyeonpung-myeon, Daseong-gun, Daegu, 42988, Repuic of Korea. 2 Department of ICE in Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeonguk, 38541, Repuic of Korea. Received: 7 June 2016 Accepted: 1 Feruary 2017 References 1. H Wang, XG Xia, Distriuted space-frequency codes for cooperative communication systems with mutipe carrier frequency offsets. IEEE Trans. Wire. Commun. 8(2), (2009) 2. Z Li, XG Xia, An Aamouti coded OFDM transmission for cooperative systems roust to oth timing errors and frequency offsets. IEEE Trans. Wire. Commun. 7(5), (2008) 3. K Choi, Inter-carrier interference-free Aamouti-coded OFDM for cooperative systems with frequency offsets in non-seective fading environments. IET Commun. 5(15), (2011) 4. B Kim, K Choi, FADAC-OFDM: frequency asynchronous distriuted Aamouti-coded OFDM. IEEE Trans. Vehi. Tech. 64(2), (2015) 5. Y Zhang, J Zhang, in Proc. IEEE WCC Mutipe CFOs compensation and BER anaysis for cooperative communication systems, (2009), pp T Lu, H Lin, T Sang, in Proc. IEEE ISPMRC An SFBC-OFDM receiver to comat mutipe carrier frequency offsets in cooperative communications, (2010) 7. J Lee,H Lin,T Sang,in Proc. IEEE ISCAS An SFBC-OFDM receiver with MLSE equaizer to comat mutipe carrier frequency offsets, (2012) 8. Y Yao, X Dong, Mutipe CFO mitigation in ampify-and-forward cooperative OFDM transmission. IEEE Trans. on Commun. 12(60), (2012) 9. K Lee, D Wiiams, in Proc. IEEE GLOBECOM 00. A space-frequency transmitter diversity technique for OFDM systems, (2000), pp B Kim, J Lee, D Jeong, K Choi, in Proc. ITG Comining successive ICI canceation to ICI suppressed Aamouti coded OFDM for frequency asynchronous distriuted antenna systems, (2014) 11. OE Agazzi, Seshardsi, On the use of tentative decisions to cance intersymo interference and noninear distortion (with appication to magnetic recording channes). IEEE Trans. Inf. Theory. 2(43), (1997) Sumit your manuscript to a journa and enefit from: 7 Convenient onine sumission 7 Rigorous peer review 7 Immediate puication on acceptance 7 Open access: artices freey avaiae onine 7 High visiiity within the fied 7 Retaining the copyright to your artice Sumit your next manuscript at 7 springeropen.com