Submitted to IEEE ICC 2011 Sparse Channel Estimation for Amplify-and-Forward Two-way Relay Network with Compressed Sensing Guan Gui 1,2 , Qun Wan 1 , Wei Peng 2 , and Fumiyuki Adachi 2 1 Department of Electrical Engineering, University of Electrical and Science Technology of China, Xiyuan Road 2006, Chengdu 611731, China, 2 Department of Electrical and Communication Engineering, Tohoku University, 6-6-05 Aza-Aoba, Aramaki, Aoba-ku, Sendai, 980-8579, Japan. Email: gui @ mobile.ecei.tohoku.ac.jp Abstract—Amplify-and-forward two-way relay network (AF- TWRN) was introduced to realize high-data rate transmission over the wireless frequency-selective channel. However, AF- TWRC requires the knowledge of channel state information (CSI) not only for coherent data detection but also for the self- data removal. This is partial accomplished by training sequence-based linear channel estimation. However, conventional linear estimation techniques neglect anticipated sparsity of multipath channel and thus lead to low spectral efficiency which is scarce in the field of wireless communication. Unlike the previous methods, we propose a sparse channel estimation method which can exploit the sparse structure and hence provide significant improvements in MSE performance when compared with traditional LS-based linear channel probing strategies in AF-TWRN. Simulation results confirm the proposed methods. Keywords- compressed sensing (CS), Amplify-to-forward two- way relay network (Af-TWRN), sparse recontruction, Restricted Isometry Property (RIP) I. INTRODUCTION Relay communications have drawn great attentions in recent. In this paper, amplify-to-forward two-way relay network (AF-TWRN) is investigated, where two terminals, 1  and 2  , exchange information based on the assistance of a relay R . AF-TWRN have been intensively studied due to their capability of enhancing the transmission capacity and providing the spatial diversity for single-antenna wireless transceivers by employing the relay nodes as “virtual” antennas [1]. A major difficulty is how to effectively recover the data transmitted over an unknown frequency- selective fading channel. Because of demodulation and coherence detection of each terminal, not only needs to know the channel state information (CSI) from relay to itself but also the CSI from the other terminal to RN. Training-based linear channel estimation methods have been proposed in [1-3] for AF-TWRN, the authors considered optimal training sequence design and linear probing methods based on the implicit assumption of a rich underlying multipath environment. On other words, training-based methods proposed in these works are mainly composed of linear reconstruction techniques such as least square (LS) and minimum mean square error (MMSE), thus reducing the problem of channel estimation to that of designing optimal training sequences for AF-TWRN [1-3]. In recent years, numerous channel measurements have shown the multipath channels tend to exhibit cluster or sparse structures which majority of the channel taps end up being either zero or below the noise floor [4]. However, traditional training-based linear methods that rely on linear reconstruction strategies at the receiver seem incapable of exploiting the potential sparse multipath channels, thereby leading to the overutilization of the key communication resources such as energy and bandwidth. In other words, exploiting this channel sparsity will improve spectral efficiency and energy with some effective channel estimation techniques. As the development of compressed sensing, a number of researches have presented sparse channel schemes on point-to-point (P2P) communication systems including single-antenna [5] or multiple-antenna [6]. These studies classify numerical methods and theoretical analysis. The former studies mainly have been directed towards establishing the feasibility of the proposed schemes but have not theoretic analysis. While the latter focus on quantitative theoretical analysis of the their performance in terms of the reconstruction error while neglect the acceptable computational complexity [6] in practical applications. All of the above sparse channel estimation schemes are limited in P2P communication systems. In this paper, the contribution is that we first introduce a sparse channel estimation technique with CoSaMP [7] for AF-TWRN which differ from previous P2P communication system. The presented method can capture channel sparsity effectively especially when two-way relay channel (TWRC) becomes very sparse, such as the length of delay spread is 16 while the dominant coefficients (namely, nonzero taps) are 2. And we given theoretical analysis on sparse TWRC channel estimation method and verify it with computer simulations. This work is supported in part by the NSF of China under grant 60772146, and the 863 Program under grant 2008AA12Z306. It is also supported in part by China Scholarship of China Scholarship Council ˄CSC˅ under grant No. 2009607029 as well as the Outstanding Doctor Candidate Training Fund of UESTC. This work is also supported in part by the Global COE program of Tohoku University.