BEM-Based Estimation for Time-Varying Channels and Training Design in Two-Way Relay Networks Gongpu Wang † , Feifei Gao ∗ , and Chintha Tellambura † † Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada, Email: {gongpu, chintha}@ece.ualberta.ca ∗ School of Engineering and Science, Jacobs University, Bremen, Germany Email: feifeigao@ieee.org Abstract—In this paper, channel estimation for two-way relay networks (TWRNs) over time-varying channels is investigated. We consider the amplify-and-forward (AF) relaying scheme and adopt the complex-exponential basis expansion model (CE-BEM) that represents the time-varying channel by a finite number of parameters. We develop the estimation methods for both the cascaded channels and the individual channels and also apply the total least square (TLS) algorithm to improve the estimation accuracy. Moreover, the training design is discussed and a heuristic criterion is proposed to minimize the condition number of the estimation matrix. The simulation results verify the goodness of the criterion. I. INTRODUCTION Bidirectional relay networks [1] have attracted much atten- tion recently due to their enhanced spectral efficiency over unidirectional relay networks [2]. Typically, two source termi- nals will simultaneously send data to a relay node, at which a “network coding”-like process is applied [3]. The relay then forwards the resultant data to both source terminals. This system is also named as a two-way relay network (TWRN). In [4] the optimal mapping function at the relay node that minimizes the transmission bit-error rate (BER) was proposed while in [5], the distributed space-time code (STC) was designed for both AF and DF TWRN. Moreover, the optimal beamforming at the multi-antenna relay that maximizes the capacity of AF-based TWRN was developed in [6] and the suboptimal resource allocation in an orthogonal frequency di- vision multiplexing (OFDM) based TWRN was derived in [7]. On the other hand, channel estimation is critically important for those works [4]- [7] that assume perfect channel knowledge at the relay node and/or the source terminals. The first two channel estimation algorithm for TWRN were designed in [8] and [9] for flat and frequency-selective channels, respectively. However, [8] and [9] consider static channels only. In this paper, we address the problem of estimating the time- varying TWRN channels. With the complex-exponential basis expansion model (CE-BEM), the number of the channel pa- rameters to be estimated is substantially reduced. We propose a new channel estimation approach that is to first estimate the cascaded channels from both source terminals to relay The work of F. Gao was supported in part by the German Research Foundation (DFG) under Grant GA 1654/1-1. T 1 T 1 R R T 2 T 2 f [n] g[n] Phase I Phase II Fig. 1. System model for two-way relay network with time varying channel. and then to recover the individual channels. The estimation results are further refined by total least square method (TLS). Due to the complexity of the noise structure, we currently design two training sequences from minimizing the condition number of the estimation matrix. Nonetheless, these training sequences are numerically shown to give superior performance than random training. II. SYSTEM MODEL Consider a TWRN with two source nodes T 1 and T 2 , and one relay node R, as shown in Fig. 1. Each node has only one antenna that can transmit or receive in half-duplex. The baseband channels from T 1 to R, and from T 2 to R are denoted by f [n] and g[n] respectively, where n is the discrete time index. Due to reciprocity, the channels from R to T 1 , and from R to T 2 are f [n] and g[n], too. The channel statistics depend on the movement of the three nodes. For example, if T 1 and T 2 are static but R is moving, then we can assume [11] E{f [n + m]f ∗ [n]} = J 0 (2πf d1 mT s ), (1) E{g[n + m]g ∗ [n]} = J 0 (2πf d2 mT s ), (2) where J 0 is the zero-th order Bessel function of the first kind, f d1 is the maximum Doppler shift associated with f [n], f d2 is the maximum Doppler shift associated with g[n], and T s is the symbol sampling time. If T 1 is static but T 2 and R are moving, then [11] E{f [n + m]f ∗ [n]} = J 0 (2πf d1 mT s ), (3) E{g[n + m]g ∗ [n]} = J 0 (2πf d1 mT s )J 0 (2πf d2 mT s ). (4) 978-1-4244-5637-6/10/$26.00 ©2010 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.