Design of training sequences and channel estimation for amplifyandforward twopath relaying networks
 JeongMin Choi^{1},
 JaeShin Han^{1},
 Sungho Jeon^{1, 2} and
 JongSoo Seo^{1}Email author
https://doi.org/10.1186/168714992014113
© Choi et al.; licensee Springer. 2014
Received: 10 February 2014
Accepted: 30 June 2014
Published: 10 July 2014
Abstract
This paper proposes a new channel estimation scheme for twopath relaying networks where two amplifyandforward (AF) halfduplex relay nodes alternatively transmit the signals received from a source node. The channel estimation and interference cancellation would be mutually conditional in twopath relaying networks. To overcome such a difficulty, we design new training sequences and propose precoding matrices for use at the source and relays. Deriving the CramerRao lower bound (CRLB), it is shown that the proposed estimator is efficient, i.e., the proposed channel estimation scheme achieves the CRLB. The performance of the proposed channel estimation is evaluated through the computer simulations where the validity of the theoretical analysis is also demonstrated.
Keywords
Introduction
In order to suppress such IRI, many works have been accomplished [4–8]. In [4], a partial interference cancellation (PIC) performed at the destination node was proposed. However, a complete suppression of IRI requires high computational complexity, and a direct link between the source and destination is neglected in the derivation of PIC algorithm. In many practical situations, especially for mobile cooperative communications, the direct link may not be ignored. Furthermore, in [5, 6], cancellation of IRI at one of the relays was proposed. However, such a method requires the knowledge of the channel gain from the source to other relay, and thereby it increases the system overhead and complexity. To resolve such limitations, considering all possible transmission links, [7] developed a full interference cancellation (FIC) technique by which the IRI as well as intersymbol interference (ISI) can be completely eliminated at the destination. The IRI cancellation in the FIC scheme utilizes the fact that the IRI term is essentially a transformation of the signal received in the previous time slot at the destination. As a result, the IRI can be perfectly suppressed at the destination. However, the performance of the FIC scheme is significantly degraded due to a severe error propagation during the ISI cancellation where the ISI is mitigated by performing a forwardandbackward successive interference cancellation (FBSIC). To improve the performance of FIC, a robust SIC algorithm was proposed where the ISI cancellation is performed iteratively by using two consecutive block signals, which ultimately reduces the error propagation of the FBSIC [8]. However, such works assumed that the perfect channel knowledge is available at the destination.
To get all the benefits of the twopath relaying, an accurate channel estimation is required. For the cooperative relaying networks, many works focusing on the channel estimation can be found in [9–12]. Lalos et al. [9] proposed a hybrid channel estimation scheme utilizing both training sequence and channel output correlation information for threenode cooperative relaying networks. Gao et al. [10] presented a CramerRao lower bound (CRLB)based training design and channel estimation for maximizing the signaltonoise ratio (SNR) at the receiver in twoway relaying networks. Under the situation where multiple relays exist, the performance of the best linear unbiased estimation (BLUE) and linear minimum mean square error (LMMSE) estimation was respectively investigated in [11, 12]. Although the various channel estimation schemes have been studied for use in cooperative relaying networks [9–12], a practical channel estimation for the twopath relaying networks has not been extensively studied in the literature. In particular, since the interference cancellation and channel estimation are mutually conditional, the conventional estimation methods in [9–12] cannot be applied to the twopath relaying networks. In [13], a channel estimation for AFbased twopath relaying was proposed. However, it has several practical limitations as follows:

The channel estimation in [13] can be only applied to frequency flat fading channels. In addition, the authors assumed that the channels between nodes remain L consecutive data blocks (each data block consists of data symbols) to preserve the orthogonality between the pilot sequences transmitted by the source and relays. Specifically, in the simulations, it was assumed that L=80. Thus, the reliable channel estimation cannot be achieved in mobile environment which is sometimes modeled by block fading channels [8, 14].

For the channel estimation purpose, authors in [13] slightly modified the relaying mechanism by making the relays forward no information to the destination in some time slots. Therefore, the loss of spectral efficiency is unavoidable.

More importantly, authors in [13] assumed the channel reciprocity between relays, i.e., ${\mathbf{h}}_{r1r2}^{k}={\mathbf{h}}_{r2r1}^{k}$ in Figure 1. The reciprocity principle is based on the property that electromagnetic waves traveling in both directions will undergo the same physical perturbations such as reflection, refraction, and diffraction [15]. However, such a property would not be maintained in most of the realistic cases, and the validity of the estimation algorithm must be guaranteed in every expected situations. In this regard, it is needed to develop a channel estimation that overcomes the limitations of [13].
As a result, such limitations motivate us to develop a practical channel estimation for twopath relaying networks over frequency selective fading channels without any modification of the relaying protocol. Moreover, the unrealistic assumptions such as the channel reciprocity and much too long coherence time are not considered. In twopath relaying networks, the channel estimation and interference cancellation would be mutually conditional. To overcome this difficulty, we design new training sequences and precoding matrices for use at the source and relays. It is shown that our proposed estimator is efficient, i.e., it achieves the CRLB. The accuracy of the theoretical results and the performance with the proposed channel estimation are demonstrated by the simulations.
The remainder of this paper is organized as follows. In ‘Review of twopath relaying network’ section, we briefly review the twopath relaying protocol. The design of training sequences and precoding matrices are described in ‘Design and analysis of trainingbased channel estimation’ section, where the CRLB for the proposed channel estimation is also derived. The numerical results are presented in ‘Numerical results’ section, and finally the paper is concluded in ‘Conclusions’ section.
Notations
Symbols (·)^{∗}, (·)^{T}, and (·)^{ † } denote the conjugate, transpose, and Hermitian transpose operations, respectively. ∥·∥ denotes the Euclidean norm of a vector. ℜ{·} and I{·} represent the real and imaginary parts of its argument, respectively. [A]_{k,l} denotes the (k,l)th entry of a matrix A and [a]_{ k } denotes the k th entry of a vector a. det[·] and tr{·} stand for a determinant and trace of the matrix, respectively. E{·} means a statistical expectation. 0_{M×K} denotes M×K allzero matrix. I_{ M } is an identity matrix of size M×M. The moduloN operation is denoted by (·) mod N.
Review of twopath relaying network
Let us consider a twopath relay network composed of one source ( ), one destination ( ), and two relays (${\mathbb{R}}_{1}$, ${\mathbb{R}}_{2}$) as illustrated in Figure 1. Each node is equipped with a single antenna and relays operate with AF mode [7, 8].
System parameters
We define data blocks transmitted by during odd and even time slots in the k th block time as ${\mathbf{x}}_{\text{s,o}}^{k}={\left[{x}_{\text{s,o}}^{k}\left(0\right),\dots ,{x}_{\text{s,o}}^{k}(N1)\right]}^{\text{T}}$ and ${\mathbf{x}}_{\text{s,e}}^{k}={\left[{x}_{\text{s,e}}^{k}\left(0\right),\dots ,{x}_{\text{s,e}}^{k}(N1)\right]}^{\text{T}}$, respectively. The channel impulse response (CIR) in the k th block time between nodes and is denoted by ${\mathbf{h}}_{\mathit{\text{AB}}}^{k}={\left[{h}_{\mathit{\text{AB}}}^{k}\left(0\right),\dots ,{h}_{\mathit{\text{AB}}}^{k}({L}_{\mathit{\text{AB}}}1)\right]}^{\text{T}}$ where L_{ A B } is the channel length. Let ${\mathbf{H}}_{\mathit{\text{AB}}}^{k}$ be an N×N circulant matrix, whose entries are given by the relation of ${\left[{\mathbf{H}}_{\mathit{\text{AB}}}^{k}\right]}_{m,l}={\mathbf{h}}_{\mathit{\text{AB}}}^{k}\left(\right(ml)\phantom{\rule{0.3em}{0ex}}mod\phantom{\rule{0.3em}{0ex}}N)$. It is assumed that ${\mathbf{H}}_{\mathit{\text{AB}}}^{k}$ is a normalized random vector having a zeromean complex Gaussian distribution. Throughout this paper, we consider a quasistatic fading where the CIRs remain constant within a single block interval, i.e., a single time slot, but vary from block to block [14]. Therefore, to distinguish the CIR generated in the odd time slot between and from that generated in the even time slot, we define them ${\mathbf{h}}_{\text{sd,o}}^{k}$ and ${\mathbf{h}}_{\text{sd,e}}^{k}$, respectively. The transmit powers of and ${\mathbb{R}}_{i}$ (i=1,2) are defined as E_{ s } and ${E}_{{r}_{i}}$, respectively. In addition, the additive white Gaussian noise (AWGN) vector generated at ${\mathbb{R}}_{i}$ in the k th block time is described by ${\mathbf{n}}_{{r}_{i}}^{k}$ with each entry having zeromean and variance ${\sigma}_{{\mathit{\text{nr}}}_{i}}^{2}$. Similarly, the zeromean AWGN vector at during odd (even) time slot in the k th block time is defined as ${\mathbf{n}}_{\text{d,o}}^{k}({\mathbf{n}}_{\text{d,e}}^{k}$) with the covariance matrix ${\sigma}_{\text{nd}}^{2}{\mathbf{I}}_{N}$.
Inputoutput relations
With the notations defined above, we describe inputoutput relations of twopath relaying systems. Specifically, in order to simplify the descriptions, without loss of generality, we equivalently use the cyclicprefix (CP)removed expressions in the rest of this paper. Practically, to eliminate the interblock interference during the first time slot, a CP is appended to the block of data. This CP is discarded at the destination and the relay. The aforementioned operation transforms Toeplitz channel matrix into a circulant one.
During odd time slot in the k th block time
where the effective noise ${\stackrel{~}{\mathbf{n}}}_{\text{d,o}}^{k}$ is defined as ${\stackrel{~}{\mathbf{n}}}_{\text{d,o}}^{k}={\lambda}_{{r}_{2}}{\mathbf{H}}_{{r}_{2}d}^{k}{\mathbf{n}}_{{r}_{2}}^{k1}+{\mathbf{n}}_{\text{d,o}}^{k}$. It is found from (4) that the received signal at is disturbed by the past block received from $\mathbb{S}\to {\mathbb{R}}_{2}\to \mathbb{D}$ link and IRI received from ${\mathbb{R}}_{1}\to {\mathbb{R}}_{2}\to \mathbb{D}$ link.
During even time slot in the k th block time
where ${\lambda}_{{r}_{1}}=\sqrt{{E}_{{r}_{1}}/({E}_{\text{s}}+{E}_{{r}_{2}}+{\sigma}_{{\mathit{\text{nr}}}_{1}}^{2})}$.
where the effective noise ${\stackrel{~}{\mathbf{n}}}_{\text{d,e}}^{k}$ is defined as ${\stackrel{~}{\mathbf{n}}}_{\text{d,e}}^{k}={\lambda}_{{r}_{1}}{\mathbf{H}}_{{r}_{1}d}^{k}{\mathbf{n}}_{{r}_{1}}^{k}+{\mathbf{n}}_{\text{d,e}}^{k}$. It should be noted from (4) and (7) that the interference cancellation and signal combining should be exploited in order to obtain the desired responses.
Interrelay interference cancellation
We can see that the ISI components still remain in (8) and (10). Thus, after the IRI cancellation, the detection procedures such as the interference suppression and signal combining have to be performed [7, 8].
Required channel knowledge
Required channel knowledge at the destination
Symbols  Link (current/previous)  Time slot 

${\lambda}_{\text{s}}{\mathbf{H}}_{\text{sd,o}}^{k}$  $\mathbb{S}\to \mathbb{D}$ (current)  Odd 
${\lambda}_{\text{s}}{\lambda}_{r2}{\mathbf{H}}_{r2d}^{k}{\mathbf{H}}_{\mathit{\text{sr}}2}^{k1}$  $\mathbb{S}\to {\mathbb{R}}_{2}\to \mathbb{D}$ (current)  Odd 
${\lambda}_{r2}{\mathbf{H}}_{r2d}^{k}{\mathbf{H}}_{r1r2}^{k1}$  ${\mathbb{R}}_{1}\to {\mathbb{R}}_{2}\to \mathbb{D}$ (current)  Odd 
${\lambda}_{\text{s}}{\mathbf{H}}_{\text{sd,e}}^{k1}$  $\mathbb{S}\to \mathbb{D}$ (previous)  Odd 
${\mathbf{H}}_{r1d}^{k1}$  ${\mathbb{R}}_{1}\to \mathbb{D}$ (previous)  Odd 
${\lambda}_{\text{s}}{\mathbf{H}}_{\text{sd,e}}^{k}$  $\mathbb{S}\to \mathbb{D}$ (current)  Even 
${\lambda}_{\text{s}}{\lambda}_{r1}{\mathbf{H}}_{r1d}^{k}{\mathbf{H}}_{\mathit{\text{sr}}1}^{k}$  $\mathbb{S}\to {\mathbb{R}}_{1}\to \mathbb{D}$ (current)  Even 
${\lambda}_{r1}{\mathbf{H}}_{r1d}^{k}{\mathbf{H}}_{r2r1}^{k1}$  ${\mathbb{R}}_{2}\to {\mathbb{R}}_{1}\to \mathbb{D}$ (current)  Even 
${\lambda}_{\text{s}}{\mathbf{H}}_{\text{sd,o}}^{k}$  $\mathbb{S}\to \mathbb{D}$ (previous)  Even 
${\mathbf{H}}_{r2d}^{k}$  ${\mathbb{R}}_{2}\to \mathbb{D}$ (previous)  Even 
Design and analysis of trainingbased channel estimation
In this section, we propose a channel estimation in order to estimate the CIRs in Table 1. For that purpose, we design training sequences and precoding matrices for use at the source and relays. Then, we demonstrate that the proposed estimator is efficient by deriving the CRLB [16]. For the ease of notation and without loss of generality, we drop the block indices k and k+1 in the channel matrices.
Problem statement
In symbol recovery aspects, after the channel estimation, interference signals can be handled at [7, 8]. However, in channel estimation aspects, such procedures cannot be achieved since the channel estimation and interference cancellation would be mutually conditional. In other words, in order to properly estimate the CIRs at , the interference cancellation is a prerequisite. On the other hand, the interference cancellation before the channel estimation needs a reliable channel information.
As shown in the previous section, the channel knowledge of $\mathbb{S}\to {\mathbb{R}}_{1}\to {\mathbb{R}}_{2}$ and $\mathbb{S}\to {\mathbb{R}}_{2}\to {\mathbb{R}}_{1}$ links is useless at . Thus, it is not necessary for relays to retransmit the signal received from $\mathbb{S}\to {\mathbb{R}}_{1}\to {\mathbb{R}}_{2}$ or $\mathbb{S}\to {\mathbb{R}}_{2}\to {\mathbb{R}}_{1}$ link. Furthermore, the roundtrip signal, propagated continuously between relays, must be eliminated at the relays prior to retransmission. Otherwise, the transmit power of the relays cannot be efficiently used for amplifying the desired signal since it is divided into interference signals as well as the desired one. As a result, the channel estimation suffers from a strong interference and noise, which makes a reliable channel estimation before the interference cancellation at difficult to be achieved.
To resolve such technical challenges, in what follows, we present an efficient estimator design for use in twopath relay networks. Similar problems of the roundtrip are observed in data transmission as well. However, in this case, it is difficult to treat such problems since it is impossible for the relays to have the knowledge of the transmit signal of . Furthermore, to suppress the interference components, the instantaneous responses of $\mathbb{S}\to {\mathbb{R}}_{i}\to {\mathbb{R}}_{k}$, i,k∈{1,2}, and ${\mathbb{R}}_{i}\to {\mathbb{R}}_{k}$ links must be available at the relays, which significantly increases the system overhead and complexity. On the other hand, in channel estimation, we could overcome such difficulties by using a welldesigned signaling protocol which is predefined.
Design of training sequence and precoder
We construct a repeated structure of training sequences (TSs), which consists of two groups. Each group has four subgroups, and each subgroup is constructed based on a base sequence defined as u=[u(0),…,u(K−1)]^{T}. During the odd time slot, the l th subgroup is generated at by multiplying K×K unitary precoding matrix ${\mathbf{P}}_{\text{s,o}}^{\left(l\right)}$ to u as ${\mathbf{T}}_{\text{sub,o}}^{\left(l\right)}={\left[{\mathbf{u}}^{\text{T}}{\mathbf{P}}_{\text{s,o}}^{\left(l\right)\text{T}},{\mathbf{u}}^{\text{T}}{\mathbf{P}}_{\text{s,o}}^{\left(l\right)\text{T}}\right]}^{\text{T}}$. Note that the i th subgroups in the first and second groups are identical each other. Likewise, during the even time slot, the l th subgroup is defined as ${\mathbf{T}}_{\text{sub,e}}^{\left(l\right)}={\left[{\mathbf{u}}^{\text{T}}{\mathbf{P}}_{\text{s,e}}^{\left(l\right)\text{T}},{\mathbf{u}}^{\text{T}}{\mathbf{P}}_{\text{s,e}}^{\left(l\right)\text{T}}\right]}^{\text{T}}$. The first part in ${\mathbf{T}}_{\text{sub,o}}^{\left(l\right)}({\mathbf{T}}_{\text{sub,e}}^{\left(l\right)}$) prevents interblock interference and second part will be used for the channel estimation, i.e., the first part acts as a CP. Therefore, we explain the proposed channel estimation by only considering the second part without loss of generality.
The basic structures of the training sequences at the relays are similar to that of . However, for the suppression of the unwanted resources, the relays substitute new precoded sequences for one of the received groups, which will be used for the estimation of ${\mathbb{R}}_{i}\to \mathbb{D}$ and ${\mathbb{R}}_{i}\to {\mathbb{R}}_{k}\to \mathbb{D}$ links. The l th subgroup of the newly inserted group at ${\mathbb{R}}_{i}$ is defined as ${\mathbf{T}}_{\text{sub},{r}_{i}}^{\left(l\right)}={\left[{\mathbf{u}}^{\text{T}}{\mathbf{P}}_{{r}_{i}}^{\left(l\right)\text{T}},{\mathbf{u}}^{\text{T}}{\mathbf{P}}_{{r}_{i}}^{\left(l\right)\text{T}}\right]}^{\text{T}}$, where ${\mathbf{P}}_{{r}_{i}}^{\left(l\right)}$ denotes the precoding matrix used for the l th subgroup at ${\mathbb{R}}_{i}$.
During odd time slot
${\mathbb{R}}_{1}$ replaces ${\mathbf{y}}_{{r}_{1}}^{(1,l)}$ with ${\mathbf{r}}_{r1}^{(1,l)}=\sqrt{{E}_{{r}_{1}}}{\mathbf{P}}_{{r}_{1}}^{\left(l\right)}\mathbf{u}$, and scales the second group as ${\mathbf{r}}_{r1}^{(2,l)}={\lambda}_{{r}_{1}}{\mathbf{y}}_{{r}_{1}}^{(2,l)}$ to be transmitted in the next time slot.
During even time slot
where the effective noise vector is defined as ${\stackrel{~}{\mathbf{n}}}_{\text{d,e}}^{(2,l)}={\lambda}_{{r}_{1}}{\mathbf{H}}_{r1d}{\mathbf{n}}_{{r}_{1}}^{(2,l)}+{\mathbf{n}}_{\text{d,e}}^{(2,l)}$.
where ${\stackrel{~}{\mathbf{n}}}_{\text{d,o}}^{(1,l)}={\lambda}_{{r}_{2}}{\mathbf{H}}_{r2d}{\mathbf{n}}_{{r}_{2}}^{(1,l)}+{\mathbf{n}}_{\text{d,o}}^{(1,l)}$.
From Table 1, we can see that the estimates in (19) are the scaled version of the required CIRs used in the detection process. Luckily, the scaling factors do not depend on the statistical quantities such as noise variances at the relays. Therefore, the proposed algorithm would be feasible in practice.
CramerRao lower bound
where we can see that MSE_{1} achieves the CRLB represented by the inverse matrix of (33). Thus, the proposed estimator is efficient. Note that the CRLB for MSE_{2} can be readily formulated by replacing ψ with $2{\sigma}_{\mathit{\text{nd}}}^{2}+{\lambda}_{{r}_{1}}^{2}{P}_{r1d}{\sigma}_{{\mathit{\text{nr}}}_{1}}^{2}$ in the result of (33).
Numerical results
Throughout the simulations, we consider the frequencyselective channels with memory lengths ${L}_{\mathit{\text{SD}}}={L}_{{\mathit{\text{SR}}}_{1}}={L}_{{\mathit{\text{SR}}}_{2}}={L}_{{R}_{1}{R}_{2}}={L}_{{R}_{2}{R}_{1}}={L}_{{R}_{1}D}={L}_{{R}_{2}D}=2$. In particular, we assume that the gain of postecho is 10 dB lower than that of a main path. It is also assumed that a frame consists of 50 data blocks to be constructed by QPSK modulation, and the length of each data block is 64, i.e., N=64. The CP length is 4, which is larger than $max\{{L}_{\mathit{\text{SD}}},{L}_{{\mathit{\text{SR}}}_{1}}+{L}_{{R}_{1}D}1,{L}_{{\mathit{\text{SR}}}_{2}}+{L}_{{R}_{2}D}1,{L}_{{R}_{1}{R}_{2}}+{L}_{{R}_{2}D}1,{L}_{{R}_{2}{R}_{1}}+{L}_{{R}_{1}D}1\}=3$. The root index of the Chu sequence is set to t=1, and its length is equal to that of CP. For the illustration purpose, we introduce new parameters ${\beta}_{\mathit{\text{SD}}}={E}_{s}/{\sigma}_{\mathit{\text{nd}}}^{2}$, ${\beta}_{{\mathit{\text{SR}}}_{i}}={E}_{s}/{\sigma}_{{\mathit{\text{nr}}}_{i}}^{2}$ (i=1,2) and ${\beta}_{{R}_{i}D}={E}_{{r}_{i}}/{\sigma}_{\mathit{\text{nd}}}^{2}$. Assuming that ${E}_{s}={E}_{{r}_{1}}={E}_{{r}_{2}}$ and ${\sigma}_{{\mathit{\text{nr}}}_{1}}^{2}={\sigma}_{{\mathit{\text{nr}}}_{2}}^{2}$, it is further defined that ${\beta}_{\mathit{\text{SD}}}={\beta}_{{R}_{i}D}$ and ${\beta}_{{\mathit{\text{SR}}}_{1}}={\beta}_{{\mathit{\text{SR}}}_{2}}\triangleq {\beta}_{\mathit{\text{SR}}}$. In all experiments, we assume that β_{ S R }=25 dB.
Conclusions
In this paper, we proposed a trainingbased channel estimation for twopath cooperative relaying networks. The problem of the channel estimation in twopath relaying network is that the channel estimation and interference cancellation are mutually conditional. To resolve such a technical limitation, we designed a new sequence structure and proposed precoding matrices for use at the source and relays. The CRLB, a theoretical minimum bound of MSE, for the proposed channel estimation was also derived. Our simulation results demonstrate the accuracy of the theoretical analysis and the performance of the proposed channel estimation.
Declarations
Acknowledgements
This research was funded by the MSIP (Ministry of Science, ICT & Future Planning), Korea in the ICT R&D Program 2014. This research was also supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (NIPA2014H0301141012) supervised by the NIPA (National IT Industry Promotion Agency).
Authors’ Affiliations
References
 Sendonaris A, Erkip E, Aazhang B: User cooperation diversity. Part I. System description. IEEE Trans. Commun 2003, 51(11):19271938. 10.1109/TCOMM.2003.818096View ArticleGoogle Scholar
 Nabar RU, Boelcskei H, Kneubhueler FW: Fading relay channels: performance limits and spacetime signal design. IEEE J. Sel. Areas Commun 2004, 22(6):10991109. 10.1109/JSAC.2004.830922View ArticleGoogle Scholar
 Rankov B, Wittneben A: Spectral efficient signaling for halfduplex relay channels. In Proceedings of Asilomar Conference on Signals, Systems and Computers. Pacific Grove CA, USA, 28 October to 1 November; 2005:10661071.Google Scholar
 Rankov B, Wittneben A: Spectral efficient protocols for halfduplex fading relay channels. IEEE J. Select. Areas Commun 2007, 25(2):379389.View ArticleGoogle Scholar
 Wicaksana H, Ting SH, Ho CK, Chin WH, Guan YL: AF twopath halfduplex relaying with interrelay self interference cancellation: diversity analysis and its improvement. IEEE Trans. Wireless. Commun 2009, 8(9):47204729.View ArticleGoogle Scholar
 Wicaksana H, Ting SH, Motani M, Guan YL: On the diversitymultiplexing tradeoff of amplifyandforward halfduplex relaying. IEEE Trans. Commun 2010, 58(12):36213630.View ArticleGoogle Scholar
 Luo C, Gong Y, Zheng F: Full interference cancellation for twopath relay cooperative networks. IEEE Trans. Veh. Technol 2011, 60(1):343347.View ArticleGoogle Scholar
 Baek JS, Seo JS: Efficient iterative SIC and detection for twopath cooperative block transmission relaying. IEEE Commun. Lett 2012, 16(2):199201.View ArticleGoogle Scholar
 Lalos AS, Rontogiannis AA, Berberidis K: Frequency domain channel estimation for cooperative communication networks. IEEE Trans. Signal Process 2010, 58(6):34003405.MathSciNetView ArticleGoogle Scholar
 Gao F, Zhang R, Liang YC: Optimal channel estimation and training design for twoway relay networks. IEEE Trans. Commun 2009, 57(10):30243033.MathSciNetView ArticleGoogle Scholar
 PremKumar M, SenthilKumaran VN, Thiruvengadam SJ: BLUEbased channel estimation technique for amplifyandforward wireless relay networks. ETRI J 2012, 34(4):511517.View ArticleGoogle Scholar
 Yan K, Ding S, Qiu Y, Wang Y, Liu H: A lowcomplexity LMMSE channel estimation method for OFDMbased cooperative diversity systems with multiple amplifyandforward relays. EURASIP J. Wireless Commun. Netw 2008, 2008: 19.View ArticleGoogle Scholar
 Li B, Lin D, Li S: A channel estimation scheme for AFbased twopath relay cooperative networks. In International Conference on Computational ProblemSolving. Chengdu, China, 21 23 October 2011; 7781.Google Scholar
 McEliece R, Stark W: Channels with block interference. IEEE Trans. Inf. Theory 1984, 30(1):4453.View ArticleGoogle Scholar
 Guillaud M, Slock DTM, Knopp R: A practical method for wireless channel reciprocity exploitation through relative calibration. In Proceedings of the 8th International Symposium on Signal Processing and Its Applications. (Sydney, Australia; 28–31 August 2005:403406.Google Scholar
 Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, New Jersey; 1993.Google Scholar
 Chu DC: Polyphase codes with good periodic correlation properties. IEEE Trans. Inform. Theory 1972, IT18: 531532.View ArticleGoogle Scholar
 Huemer M, Onic A, Hofbauer C: Classical and Bayesian linear data estimators for unique word OFDM. IEEE Trans. Signal Process 2011, 59(12):60736085.MathSciNetView ArticleGoogle Scholar
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